Hydrogen in Engineering Metallic Materials: From Atomic-Level Interactions to Mechanical Properties 3030985490, 9783030985493

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V. G. Gavriljuk V. M. Shyvaniuk S. M. Teus

Hydrogen in Engineering Metallic Materials From Atomic-Level Interactions to Mechanical Properties

Hydrogen in Engineering Metallic Materials

V. G. Gavriljuk · V. M. Shyvaniuk · S. M. Teus

Hydrogen in Engineering Metallic Materials From Atomic-Level Interactions to Mechanical Properties

V. G. Gavriljuk G. V. Kurdyumov Institute for Metal Physics National Academy of Sciences of Ukraine Kiev, Ukraine

V. M. Shyvaniuk G. V. Kurdyumov Institute for Metal Physics National Academy of Sciences of Ukraine Kiev, Ukraine

S. M. Teus G. V. Kurdyumov Institute for Metal Physics National Academy of Sciences of Ukraine Kiev, Ukraine

ISBN 978-3-030-98549-3 ISBN 978-3-030-98550-9 (eBook) https://doi.org/10.1007/978-3-030-98550-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

In remembrance of Professor Vitaliy Gridnev, brilliant scientist and teacher

Preface

A potential reader of this book is certainly aware that, be the most widespread chemical element in the solar system and generally in the universe, hydrogen represents itself as the cheapest and ecologically pure source of energy. Just with this element, the hope to remove the so-called carbon trace in the planet’s atmosphere averting thereby the coming menacing changes in the climate is related. As the hydrogen storage and transport are necessary to realize this aspiration, the usage of metals is unavoidable. Possibly, a smaller part of the audience suspects that there are no metals in the nature which could be fully resistant to a destructive hydrogen effect on their properties. The hydrogen-caused degradation of mechanical properties was the first time demonstrated by Johnson in 1874 for iron. Since then, different fatal hydrogen effects have been found in a number of metals including even the noble metals of group 1B in the periodical table. Hydrogen-caused effects in three most important classes of engineering materials based on the iron, nickel and titanium constitute the subject of this book. Its feature is that all entities including the location of hydrogen atoms in solid solutions, hydrogen solubility, interaction with crystal lattice defects, diffusivity, phase transformations and, finally, mechanical properties are analyzed in terms of hydrogen effect on the electron structure. In contrast, available studies of hydrogen-caused phenomena in metals are still predominantly studied within the frames of continuum mechanics. The launched electron concept originates from the hydrogen-caused increase in the concentration of free electrons discovered by the authors on austenitic steels in 1990s and confirmed in their further theoretical and experimental studies of the Fe-, Ni- and Ti-based alloys. The main point is that hydrogen-induced enhancement of the metallic character of interatomic bonds is expected to be accompanied by improvement of metal ductility, which all the more makes intriguing and enigmatic the opposite phenomenon of hydrogen-caused brittleness. The book structure follows the abovementioned succession of described phenomena. The consistent understanding of rather complicated mechanism for hydrogen embrittlement makes possible to clarify a physical reason for positive hydrogen effects in metals, e.g., its usage as interim alloying element, a unique grain vii

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Preface

refinement of metal microstructure, etc., which constitutes the final chapter of this book. Engineers and researchers dealing with hydrogen industry and science, as well as students of last semesters at the universities, can be the target audience. Kiev, Ukraine

V. G. Gavriljuk V. M. Shyvaniuk S. M. Teus

Contents

1 Atomic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Hydrogen Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Hydrogen Location in Crystal Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Atomic Complexes and Snoek-Like Relaxation . . . . . . . . . . . . . . . . . 1.4 H–H Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Hydrogen Effect on the Electron Structure: Electron Exchange . . . . 1.5.1 Hydrogen in Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Hydrogen in Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.3 Hydrogen in Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 4 10 13 18 23 23 29 29 31 38

2 Crystal Lattice Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Hydrogen-Induced Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Hydrogen-Vacancy Interaction in Metals . . . . . . . . . . . . . . . . 2.1.2 Hydrogen-Induced Vacancies in Austenitic Steels . . . . . . . . . 2.2 Interaction Between Hydrogen Atoms and Dislocations . . . . . . . . . . 2.2.1 Stacking Fault Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Hydrogen Softening-Hardening . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Hydrogen Effect on Mobility of Grain Boundaries . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 46 48 51 52 58 78 82

3 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Migration Paths and Enthalpies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 H in Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 H in Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 H in Titanium and Its Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Hydrogen Trapping by Crystal Lattice Defects . . . . . . . . . . . . . . . . . . 3.2.1 H in bcc Iron and Plain Carbon Steels . . . . . . . . . . . . . . . . . . . 3.2.2 H in Austenitic Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 H in Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 H in Titanium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91 91 92 97 99 103 106 111 115 117 ix

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3.3 Hydrogen Transport by Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Hydrogen Migration Along Grain Boundaries . . . . . . . . . . . . . . . . . . 3.4.1 Grain Boundary Diffusion of Interstitial and Substitution Solutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Thermodynamic Simulation of Hydrogen Atom Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 A Mechanism for Enhanced Hydrogen Flux Along Grain Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Hydrogen Effect on Metallic Atom Diffusion in the Crystal Lattice and Short-Range Atomic Order . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Phase Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Hydrogen-Induced Phases in Iron-Based Alloys . . . . . . . . . . . . . . . . . 4.1.1 Atomic Interactions in Hydrogen-Charged γ and ε Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Hydrogen-Caused Stresses and Plastic Deformation as a Reason for γ → ε Transformation . . . . . . . . . . . . . . . . . . 4.1.3 Hydrogen-Induced γ*-Phase and Short-Range Decomposition of the Solid Solution . . . . . . . . . . . . . . . . . . . . 4.2 Nickel Hydride or Miscibility Gap?! . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Atomic Interactions in the Ni–H System . . . . . . . . . . . . . . . . . 4.2.2 Thermodynamics of Ni–H Solid Solution . . . . . . . . . . . . . . . . 4.3 H-Induced Transformations in Ti Alloys . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Titanium Hydrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Metal Pseudo-Hydrides and Thermodynamics . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Hydrogen Embrittlement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Available Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Hydrogen Pressure Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Hydrogen Surface Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Hydrogen-Induced Lattice Embrittlement . . . . . . . . . . . . . . . . 5.1.4 Hydrogen-Enhanced Decohesion, HEDE . . . . . . . . . . . . . . . . 5.1.5 Adsorption-Induced Dislocation Emission, AIDE . . . . . . . . . 5.1.6 Hydrogen-Enhanced Strain-Induced Vacancies, HESIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.7 Nanoscale Hydrogen Embrittlement . . . . . . . . . . . . . . . . . . . . 5.1.8 Hydrogen-Enhanced Localized Plasticity, HELP . . . . . . . . . . 5.2 Hydrogen Embrittlement of Fe-, Ni- and Ti-Based Alloys . . . . . . . . 5.2.1 Austenitic Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Nickel-Based Superalloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Ti Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

121 125 127 130 135 139 143 153 153 157 164 168 174 176 178 184 190 193 194 201 203 203 205 206 208 219 221 223 224 242 242 251 255 261

Contents

6 Hydrogen as Alloying Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Temporary Alloying of Titanium Alloys with Hydrogen for Improving their Technological Plasticity . . . . . . . . . . . . . . . . . . . . 6.2 Hydrogen-Induced Grain Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Austenitic Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Titanium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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275 275 281 281 285 288

Chapter 1

Atomic Interactions

Interactions between the atoms constructing a crystal lattice in metals represent a first step in formation of their structure. Traditionally, metal scientists and engineers relate the term “structure” with a type of crystal lattice, its imperfections and grain size. In the case of solid solutions, the type of solute atoms, their distribution and precipitates should be also included. In reality, however, structure starts with localized and free valence electrons. An applied mechanical force shifts the atoms from their sites, and any response from the crystal lattice, either plastic deformation or brittle fracture, is controlled by interatomic bonds. The relaxation time of valence electrons is shorter by several orders of magnitude in comparison with that of atomic nuclei. The closed ion shell does not take part in any reactions and is merely slightly polarized under strain. Only valence electrons forming interatomic bonds are responsible for the character of deformation behavior. Their prevailing localization at the atomic sites creates covalent bonds resulting in brittleness, as in the case of group V and VI metals in the periodic table (V, Nb, Ta, Cr, Mo, W). In contrast, in metals where the so-called bonding states of the d-electron band are only starting to be filled, e.g. Ti in group IV, or in the metals from Fe to Cu in groups VIII to XI with essentially filled anti-bonding electron states, the prevailingly free electrons promote ductility. Free electrons assist the so-called metallic character of interatomic bonds, and therefore the ductility of metals and their alloys is the higher, the larger the fraction of free electrons. In the case of phase transformations, as well as in diffusion processes, valence electrons determine the height of the energy barrier for atom hopping. Moreover, they control important properties of dislocations, e.g. their splitting and specific energy denoted as line tension. The high fraction of free electrons is a necessary condition in the design of contemporary engineering metallic materials. Iron and nickel are preferable for this purpose, whereas titanium is also important because of its small specific weight and thermal resistance. As will be shown in this Chapter, hydrogen dramatically changes atomic interactions in these metals and the corresponding alloys.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. G. Gavriljuk et al., Hydrogen in Engineering Metallic Materials, https://doi.org/10.1007/978-3-030-98550-9_1

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1 Atomic Interactions

The first ab initio calculations of metal electron structure were carried out by Wigner and Seitz (1933) using the Schrödinger equation. They obtained the values of the lattice parameter (the Wigner–Seitz radius), cohesion energy and the bulk modulus in metallic sodium with the accuracy of about 10%. It took 50 years to achieve the same accuracy in polyvalent metals. The point is that a single valence electron in metallic sodium feels only the potential created by the ion core, i.e. the closed electron shell. In contrast, the interdependence between the ion core and the valence electrons, as well as the repulsive interaction between the valence electrons themselves, need to be taken into account if their number increases. In line with these conditions, the following two problems need to be solved: (i) the self-consistent computation of a change in the core potential and, consequently, in the wave functions of the valence electrons which in turn are changed under the effect of the modified core potential, (ii) the so-called statistical correlations between the electrons having parallel spins (the Hartree–Fock correction) and the dynamic correlations between the electrons with anti-parallel spins. In time, based on the density functional theory developed by Hohenberg and Kohn (1964) and Kohn and Sham (1965), considerable success was achieved with the addition of a small local exchange correlation potential to the Coulomb potential in the Schrödinger equation. The main idea of the Hohenberg–Kohn-Sham theory of the local density functional can be formulated by the following statement: instead of the electron wave functions, knowing the spatial distribution of electron density and the potential acting on these electrons is sufficient for obtaining the physical properties of solids. In other words, the Hamilton operator in the Schrödinger equation is replaced by that of the total energy, whereas the electron wave functions are substituted by the local electron densities:   σ · χσ,i,k (r ) = εσ,i,k (r ) · χσ,i,k (r ), −∇ 2 + VNe + Vee + Vxc

(1.1)

where potentials V Ne , V ee and V σ xc correspond to the attraction between the electrons and the nuclei, the electron–electron repulsion and the exchange–correlation interaction, respectively, ε is the electron energy, χ is the electron density, σ is the electron spin, i is the energy electron level number, k is the electron wave vector. Since then, the Kohn–Sham equations have been successfully used in the calculations of free energy, heat capacity, cohesive properties etc. in crystal solids and

1 Atomic Interactions

3

molecules. One of the first attempts in this respect was undertaken by Morucci et al. (1978) who succeeded in calculating the lattice parameter, cohesive energy and bulk modulus in the 3d and 4d metal series with the same accuracy of about 10%, as was done before by Wigner and Seitz. In line with this progress, the studies of the hydrogen effect on atomic interactions in metals can be roughly divided into two main stages which partially overlap in time. In the first one, the calculations were based on the electron band theory, predominantly using the method of the linear combination of atomic orbitals, LCAO. The experimental studies included mainly measurements of the electron heat capacity and magnetic susceptibility. Mössbauer spectroscopy was also actively involved in relation to the rare-earth metals. The Pd-H system was predominantly chosen as the object of these studies because of its practical use in diffusion membranes for hydrogen cleaning and due to the easily obtained equilibrium hydrogen concentrations at gas pressures smaller than 1 bar. The main results of this stage can be summarized as the identification of the electron bonds between H and Pd atoms below the bottom of the electron d-band, the filling of the energy levels above the d-band and a decrease in the Pd states density just below the Fermi energy (see, e.g. Eastman et al. 1971 and Switendick 1972). Along with the Pd–H system, the Ti–H, V–H and Ti–V–H ones were also thoroughly analyzed (see, e.g., review articles edited by Alefeld and Fölkl 1978). Some early naive beliefs were abandoned in these studies, among them the idea that hydrogen electrons fill the states of the host metal (the proton model). Some of the studies were also devoted to the hydrogen effect on the electron structure of iron, with the main focus on the atomic bonds in the vicinity of crystal lattice imperfections. For example, Juan and Hoffman (1999) compared the H adsorption on the (110) surface and near the vacancies in the iron with the body centred cubic lattice, bcc Fe. A diminution in the Fe–Fe bond strength and the formation of new Fe–H bonds was obtained and attributed to the occupation of more Fe antibonding states. It was also shown that the Fe–H bonding gets stronger if the H atom is close to a vacancy. As a consequence, the conclusion was derived that hydrogen embrittlement of bcc iron is caused by the decohesion of Fe–Fe-bonds. The Fe–C–H interaction at the edge dislocations in bcc iron was analyzed by Simonetti et al. (2003). The presence of a carbon atom in the dislocation core was found not to benefit its occupation by the H atom, and therefore no bonding was formed between the H and C interstitial atoms. This result seems to be particularly interesting because of some discrepancy in the available experimental results about the harmful role of carbon in the hydrogen embrittlement of steels in the aqueous environment and the positive effect of carbon in the case of high-pressure gaseous hydrogen charging (see, e.g., Bernstein and Thompson 1976). As will be discussed in Chap. 3, in contrast to gaseous hydrogenation, cathodic charging is accompanied by plastic deformation, which increases dislocation density. The bonding of hydrogen atoms near the stacking faults in face-centred cubic iron, fcc Fe, was simulated by Moro et al. (2000). As in the case of hydrogen atoms near the vacancies in bcc iron, the Fe–Fe bonds were found to be remarkably destabilized near the stacking fault to about 27% of its original value. Again, the conclusion that

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hydrogen-caused decohesion is the reason for hydrogen brittleness was drawn from these calculations. A distinctive feature of the second-stage studies, particularly in the new millennium, was the increased interest in construction metals like Fe, Ni, Ti and their alloys with a view to the development of new methods for calculating atomic interactions in real-life metal systems and a deeper understanding of the mechanisms for hydrogen-caused brittleness. Based on the density functional theory, the embedded-atom method was developed earlier by Daw and Baskes (1984). Its essence is that an impurity atom is assumed to change the local environment thereby creating a quasi-atom. The energy of this quasi-atom is presented as Equas = Ez (ρh (R)),

(1.2)

where ρh (R) is the electron density of the host atom at the R site without impurities, Ez is the quasi-atom energy of an impurity atom with atomic number Z in this site. Using this concept, the authors calculated the surface energy and the energy of H adsorption at different atomic planes, as well as the migration of hydrogen atoms and their binding to vacancies in Pd and Ni. Moreover, hydrogen-eased fracture on the planes {111} in Ni was demonstrated. A modified interatomic potential for the embedded atom method was proposed by Lee and Jang (2007) for studies of the Fe–H system including both its fcc and bcc lattices. Using the density functional theory, the ab initio calculations of hydrogen trapping by vacancies in iron were carried out by Counts et al. (2010) for bcc iron and by Nazarov et al. (2010) for fcc iron. Along with the hydrogen effect on vacancy mobility, these data will be discussed further on, see Chaps. 2 and 3. The aim of this Chapter is to analyze the hydrogen effect on atomic interactions in iron, titanium and nickel using the density functional theory for ab initio calculations of the electron structure. First, some available data on hydrogen solubility and the location of hydrogen atoms in the crystal lattices of these metals will be considered.

1.1 Hydrogen Solubility H solubility in iron. As in the retreating Silicon Age, so in the nascent Carbon age, iron and its compounds dominate our civilization. On the other hand, hydrogen is the most widespread element in the Universe. This may be the reason the Fe–H system remains the predominant object in numerous studies. The solubility SH of hydrogen in iron is controlled by Sieverts’ equation SH = K



PH2

(1.3)

1.1 Hydrogen Solubility

5

Fig. 1.1 Hydrogen solubility in α-, γ- and δ-iron. Modified from Geller and Sun (1950). This was the first time the deviation of solubility in δ-iron from the Arrhenius equation was noted. John Wiley and Sons

where PH2 is the hydrogen partial pressure and K is the constant controlling the temperature dependence of SH . Geller and Sun (1950) were probably the first to systematize available experimental data on hydrogen solubility in different iron phases (Fig. 1.1). Fitting the Arrhenius equation to collected experimental data, they obtained the enthalpies H of hydrogen solubility S as ~0.28 eV in α-iron and ~0.23 eV in γ-iron describing the relation between them as log

(Hγ − Hα ) Sα , =− Sγ 4.55764T

(1.4)

where (Hγ − Hα ) is a change in the enthalpy at transition of 0.5 Mol H2 from the α-Fe to γ-Fe without a change in the H concentration. Further experiments on hydrogen solubility confirmed its consistency with the Arrhenius temperature dependence within the range between 400 and 700 °C, whereas a remarkable deviation occurred at higher and lower temperatures, particularly below 300 ºC (see e.g., Silva et al. 1976; Kiuchi and McLellan 1983). At temperatures from the γ → α transformation down to ~300 °C, the scattering was found to be of one order of magnitude, reaching four orders of magnitude when the temperature approaches RT, see Fig. 1.2. Scattering below 300 °C has been attributed mainly to the trapping of hydrogen atoms by crystal lattice imperfections, see Silva et al. (1976) and also Yutaka and Masayoshi (1975) in relation to the mechanisms of hydrogen-caused relaxation phenomena.

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1 Atomic Interactions

Fig. 1.2 Hydrogen solubility in α-iron θi = NH /NFe as a function of temperature. Modified from Kiuchi and McLellan (1983). Elsevier

Reviewing an array of experimental results on hydrogen solubility in bcc iron, Kiuchi and McLellan (1983) described the data below 300 °C along with those above 600 °C as a “Fe + H + defects” system and proposed a “correct model concept” for bcc Fe–H solid solutions. A plot of these data as a function of ln(θi ·T7/4 ) versus T−1 is given in Fig. 1.3. Fig. 1.3 Hydrogen solubility in bcc iron at temperatures below 300 °C and above 600 °C. Modified from Kiuchi and McLellan (1983). Elsevier

1.1 Hydrogen Solubility

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The non-linear character of the curve describing both temperature ranges is attributed to the oscillation of hydrogen atoms in their interstitial sites. The occupation of tetrahedral sites is stable below 300 °C. Change in the entropy with a rise in temperature enables increasingly mixed occupation of tetra- and octahedral sites. The hydrogen location in the t- and o-sites will be analysed in detail in Sect. 1.2. Using α-iron of different purity, as well as single crystals, cold work and annealing, the abovementioned researchers came to the conclusion that hydrogen solubility at temperatures above ~300 °C and up to the α → γ transformation does not depend on either the purity grade of α-iron or the presence of grain boundaries in it. H solubility in nickel. In contrast to hydrogen in iron, numerous measurements revealed a significantly smaller scattering of the experimental data on hydrogen dissolved in nickel. Nevertheless, a clear curvature of the θi = θi (T−1 ) curve occurs, see Fig. 1.4. A possible reason for this curvature was discussed in terms of interaction between the H atoms themselves in the nickel solid solution or between isolated solute H atoms and the Ni lattice (McLellan and Sutter 1984). Taking into account the unreasonably large trapping sites needed for realization of the former and the absence of expected discontinuities in the temperature dependence of H diffusivity in nickel in the latter case, both possibilities were rejected. Instead, the authors ascribed the nonlinearity of the Arrhenius plot in Fig. 1.4 to thermal activation of energy levels for dissolved H atoms acting as harmonic oscillators, as was supposed in the case of hydrogen in iron. When reviewing these calculations, it should be noted that McLellan and his coworkers studied the thermodynamics of binary interstitial solid solutions by taking into account only interactions between the first neighbors, see e.g. Alex and McLellan (1971) for carbon and McLellan and Alex (1970) for nitrogen in fcc iron. In contrast,

Fig. 1.4 Temperature dependence of hydrogen solubility in nickel, θi = NH /NNi , at atmospheric pressure. Modified from McLellan and Sutter (1984). Elsevier

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1 Atomic Interactions

Fig. 1.5 Phase diagram NiH at 1 bar of gaseous pressure (a) and the same at 100 bar of gaseous pressure (b). Calculated compared with the experimental data of θH = NH /NNi . Redrawn from Zeng et al. (1999). Elsevier

Mössbauer studies along with thermodynamic activity calculations have shown the important role of interaction between the interstitial atoms in the first two coordination spheres (e.g., Sozinov et al. 1997 for carbon and Sozinov et al. 1999 for nitrogen in fcc iron). Hydrogen solution enthalpy in nickel was calculated by Zeng et al. (1999) using the CALPHAD and experimental data on hydrogen solubility at different temperatures, see Fig. 1.5. A good consistency with different experimental data was obtained. In particular, one could mention that the temperature of the three-phase solid + gas ↔ liquid equilibrium coincides with that measured by Shapovalov and Serdyuk (1979). A feature of the calculated heat for hydrogen solution is its increase with increasing temperature along with a sharp peak at the Curie temperature. Both branches of the hydrogen solution heat temperature dependence in nickel in its ferromagnetic and paramagnetic states are consistent with the experimental measurements carried out by Shapovalov and Boyko (1983) and Vyatkin et al. (1983), respectively. This analysis did not include the miscibility gap in the Ni–H system at high gaseous hydrogen pressures, which is traditionally interpreted as the formation of a nickel hydride and will be analyzed in detail in Chap. 4, Sect. 4.2. H solubility in titanium did not attract much attention because of hydride formation at rather small H concentrations in the low temperature hcp α-Ti phase, whereas the high temperature bcc β-Ti can be stabilized at ambient temperatures only due to its significant complex alloying. Quite small amounts of hydrogen are dissolved in α-titanium at around room temperature (see, e.g., Lenning et al. 1954). Below 125 °C, the hydrogen content in the α solid solution remains negligible and is detected only in the presence of dislocations and impurities. It grows with increasing temperature and reaches its maximum atomic ratio of H/Ti ≈ 0.08 above 300 °C.

1.1 Hydrogen Solubility

9

Fig. 1.6 Phase diagram TiH at hydrogen pressure ≤1 MPa. Manchester and San-Martin (2000). ASM International

A number of Ti–H phase diagrams were proposed later, and one of the versions is presented in Fig. 1.6 for hydrogen gas pressures ≤1 MPa. More detailed information about hydrogen solubility in α-titanium at low temperatures was obtained by Vitt and Ono (1971) in their measurements of the change in electrical resistivity with increasing ageing temperature. The authors reported an increase in the content of dissolved hydrogen from 20 wt ppm at 300 K to 1000 wt ppm at 560 K. According to high resolution in-situ observations performed by Bourret et al. (1986), hydride precipitation starts at temperatures of 40–60 °C if the H solubility limit of ~130 wt ppm is exceeded. The precipitation process is partly reversible, and the hydride platelets disappear at 75–80 °C. This phenomenon proceeds via a ledge mechanism, and the rearrangement of metallic atoms is accomplished by shear stresses in addition to the normal dilatation caused by the increase in volume. The same is also true for zirconium hydride precipitation, see Carpenter (1978). In order to take into account the deviation of hydrogen gas from ideality, hydrogen activity in titanium was calculated as a function of H concentration by Arita et al. (1982) using hydrogen fugacity instead of pressure. Presented in Fig. 1.7 is hydrogen solubility in Ti at different temperatures starting from the α-phase through the β-phase up to TiH2 hydride (compare with Fig. 1.6). The plateau in the presented curves is caused by the α → β transition. Its appearance is usually interpreted in terms of the lattice-gas model with the H–H interaction depending on hydrogen distribution over interstitial sites in the conjugated phases. Such a plateau has been described in detail for the Pd–H system (see, e.g., Wicke and Brodowsky 1978). However, the application of the lattice-gas model was straightforward for H in Pd because α-Pd and β-Pd have the same crystal lattice and, correspondingly, the same interstitial sites. This is not the case for H in Ti with the hcp α-phase and bcc β-phase lattices. Therefore, a more sophisticated analysis would be desirable.

10

1 Atomic Interactions

Fig. 1.7 Fugacity of hydrogen used for its dissolution in titanium versus the obtained hydrogen concentration. Modified from Arita et al. (1982). Springer

1.2 Hydrogen Location in Crystal Lattice The occupation of interstitial sites by hydrogen atoms in the crystal lattice of Fe, Ni, Ti alloys, as well as the interaction between hydrogen atoms themselves, so far remains debatable. H in iron. Based on thermodynamic calculations, the dual site occupancy of octahedral and tetrahedral sites in α-, γ- and δ-iron was proposed by Silva et al. (1976). They claimed the percentage of H-occupied octahedral sites to be of 50% at 1450 °C (δ-iron), 23% at 1023 °C (γ-iron) and only 2% at 300 °C (α-iron). The preferential location of hydrogen atoms in the tetrahedral sites of the α-iron crystal lattice follows from the ab initio calculations of electron structure, see e.g. Teus and Gavriljuk (2020). Using the functional density theory, the cohesion energy in hydrogen-containing α-iron with hydrogen atoms in the octahedral and tetrahedral interstitial sites at its atomic ratio of NH /NFe = 1/54 has been calculated as a difference between total energy per elementary cell and the sum of energies for isolated atoms constructing this cell,  Ei . (1.5) E cohesion = E total − i

Accounting for the relaxation of stresses induced by hydrogen in the α-Fe crystal lattice, hydrogen in the tetrahedral sites provides the larger cohesive energy and, correspondingly, the higher thermodynamic stability of the Fe-H solid solution in comparison with the hydrogen occupation of octahedral sites, see Fig. 1.8.

1.2 Hydrogen Location in Crystal Lattice

11

Fig. 1.8 Cohesion energy per elementary cell as a function of unit cell volume in the solid solution α-Fe54 H with hydrogen in octahedral and tetrahedral interstitial sites

This result is consistent with calculations performed by Erlässer et al. (1998), Miwa and Fukumoto (2002) and Jiang and Carter (2004). If the H atom is placed in the octahedral site, the cell shape and the atomic construction in the first coordination sphere around it are subjected to tetragonal distortion. Some distortion occurs even in the second and third coordination spheres. In contrast, if the H atom is present in the tetrahedral site, the cell retains the same shape and only 4 Fe atoms in the first coordination sphere move homogeneously outward. This difference in the induced lattice distortions determines a preferential hydrogen location in tetrahedral sites. As follows from Table 1.1, the location of hydrogen atoms in the tetrahedral sites of the relaxed α-Fe-H solid solution is stable at hydrogen concentrations up to 6 at.%. In contrast, theoretical and experimental results obtained for hydrogen in fcc γiron provide unambiguous evidence of hydrogen location in the octahedral sites, see Teus et al. (2007). In this case, the cohesion energy in the FeH solid solution increases in comparison with hydrogen in the tetrahedral sites, as presented in Fig. 1.9. This location of hydrogen atoms in fcc iron is supported by theoretical Table 1.1 The energy difference (δE = Eo − Et ) between H in the o- and t-sites of bcc Fe for relaxed structures (after Jiang and Carter 2004)

Supercell

E, relaxed (eV)

Fe2 H

0.01

Fe16 H

0.13

Fe54 H

0.13

Fe128 H

0.13

12

1 Atomic Interactions

Fig. 1.9 Cohesion energy per elementary cell as a function of the interatomic distance in the solid solution γ-FeH with hydrogen in octahedral and tetrahedral interstitial sites

calculations (Erlässer et al. 1998; Saravia et al. 2009; Ismer et al. 2010) and neutron spectroscopy measurements (Danilkin et al. 2003). It also follows from the data in Fig. 1.9 that the equilibrium volume of the fcc γiron elementary cell becomes much smaller after hydrogen atoms enter the octahedral sites, in comparison with tetrahedral ones. A possible reason for that is the different size ratio of octahedral and tetrahedral sites in the fcc and bcc lattices. H in nickel. Hydrogen atoms in the Ni–H system are located in the octahedral sites, which is established by neutron diffraction measurements in the high hydrogen Ni phase, as well as in the low hydrogen one (e.g., Wollan et al. 1963; Cable et al. 1964). Both phases have the fcc crystal lattice of pure nickel. The high hydrogen Ni phase is usually defined as a nickel hydride. The validity and rationale for this definition will be analyzed in detail in Chap. 4. H in titanium. Quite a different situation occurs in Ti–H solid solutions. Using inelastic neutron scattering, Pinto et al. (1979) have shown that, at room temperature, hydrogen atoms occupy tetrahedral sites in α-Ti with θH = 0.04. This result is consistent with the earlier data of nuclear magnetic resonance obtained by Korn and Zamir (1970) at temperatures above 125 °C. From measurements at 320 °C, where θH in the α-phase reaches the value of 0.08, these authors concluded that hydrogen is partially located in the octahedral sites. This octahedral site occupation was also reported by Eichenauer (1968). However, later on, Khoda-Bakhsh and Ross (1982) measured inelastic neutron scattering in α-Ti with θH of 0.05 at 315 °C and in β-Ti with θH = 0.14 at 715 °C and observed hydrogen location only in the tetrahedral sites of both phases. Meanwhile, these experimental data are clearly contradicted by the results of subsequent ab initio calculations performed by Kuksin et al. (2013) and Lu and Zhang (2013). Both groups of authors reported that octahedral positions are preferential in the hcp lattice of α-Ti due to a small energy gain in the H solution energy of 0.06 eV, according to Kuksin et al., and 0.08 eV, according to Lu and Zhang. Kuksin et al. attributed the inconsistency between theoretical calculations and experimental measurements of inelastic neutron scattering to the closeness of studied

1.2 Hydrogen Location in Crystal Lattice

13

Fig. 1.10 Cohesion energy per elementary cell as a function of interatomic distance in the bcc Ti54 H (a) and Ti2 H (b) solid solutions with hydrogen in octahedral and tetrahedral interstitial sites, respectively

Ti–H compositions to the two-phase α + β region, which can lead to a significant release of hydrogen in the β-phase having higher hydrogen solubility, see also data of Hempelmann et al. (1982) for TiH0.07 . As regards β-titanium, the location of hydrogen atoms has been ab initio calculated depending on the hydrogen content, see Teus (2018). At small hydrogen contents, the local atomic relaxation in the case of the hydrogen atom entry is possible for both octahedral and tetrahedral sites. In this case, hydrogen atoms prefer to occupy tetrahedral sites, see Fig. 1.10a for the calculated bcc Ti54 H system. For sufficiently high hydrogen content, the local atomic relaxation is impossible for the octahedral sites and this is an additional factor along with their smaller free volume to make preferential the occupation of tetrahedral sites, see Fig. 1.10b for the bcc Ti2 H system.

1.3 Atomic Complexes and Snoek-Like Relaxation A simple experimental test for calculations of hydrogen distribution over interstitial sites is provided by mechanical spectroscopy which is sensitive to local lattice distortions caused by interstitial atoms. It is based on the inelastic response of a solid solution to periodical stresses applied to crystal solids characterized by the occurrence of local deviations from the cubic symmetry. According to Novick and Berry (1972), the inverse modulus defect δG−1 caused by the non-cubic elastic dipoles in a cubic crystal is described by the following equation:   1 δG −1 = δS44 + 4 δ(S11 − S12 ) − δS44 · , 2

(1.6)

14

1 Atomic Interactions

where S ij are components of the tensor of elastic compliances, = γ 1 2 γ 2 2 + γ 2 2 γ 3 2 + γ 3 2 γ 1 2 is an orientation factor, γ i are directing cosines of the angles between the crystal axes and the main axis of a non-cubic defect. The corresponding relaxation strength depends on the symmetry of three possible non-cubic defects and their orientations in relation to directions of the applied stress. In turn, the symmetry of the defects is determined by the principal values λ1 , λ2 and λ3 of a strain tensor λij . For a tetragonal symmetry defect, λ1 = λ2 = λ3 , the principal axes are of directions, the number of independent components of the λ tensor nt = 3, and the relaxation strength is equal to zero in the case of applied stress (δG−1 = 0) and is the largest for applied stress. For a trigonal defect, λ1 = λ2 = λ3 , one of the directions is the axis of 3rd order, nt = 4, δG−1 = 0. For an orthorhombic defect, λ1 = λ2 = λ3 , two principal axes are of and one axis is of directions, nt = 6. Neither of the relaxation strengths is zero: δG−1 = 23 δ(S11 − S12 ) = 0 and δG−1 = 13 δS44 = 0. Caused by the diffusive hops of hydrogen atoms in the bcc lattice, the so-called Snoek relaxation occurs if hydrogen occupies the octahedral sites. In the case of tetrahedral site occupation, this relaxation is impossible because there are no local deviations from the cubic symmetry. The absence of Snoek relaxation for hydrogen in α-iron was reported by Dufresne et al. (1976). They proved that the damping peak at ~30 K, observed earlier by Heller (1961) in hydrogen-charged α-iron of high purity, is not related to the diffusion hops of hydrogen atoms. It exists without hydrogen and is caused by the formation of paired kinks at non-screw dislocations (the so-called α-relaxation). Therefore, it was confirmed that hydrogen in the bcc iron lattice does not occupy the octahedral sites. Interstitial atoms in the octahedral sites of the fcc lattice of pure metals cannot cause deviations from the cubic symmetry. Therefore, Snoek-like relaxation can occur only in two cases: (i) the existence of paired interstitial atoms changing their crystallographic orientation in the crystal lattice due to hops under applied periodical mechanical loading and (ii) the formation of i-s complexes between single interstitials and the substitutional atoms of alloying elements, which locally distorts the cubic symmetry of the lattice. As example, tetragonal and orthorhombic defects in the fcc solid solution containing substitutional and interstitial atoms are shown in Fig. 1.11. The crystallographic orientation is acquired by the i-s tetragonal defect, whereas a more complicated atomic configuration i-s1 s2 creates the orthorhombic defect . Studies of internal friction in single crystals make it possible to determine the type of each non-cubic defect responsible for relaxation. The orientation dependence of the relaxation strength in hydrogen-charged austenitic steel Cr23Ni21 close in its

1.3 Atomic Complexes and Snoek-Like Relaxation

15

Fig. 1.11 A tetragonal i-s defect (a) and an orthorhombic i-s1 s2 defect (b) in the fcc crystal lattice of a substitution-interstitial solid solution

chemical composition to steel AISI 310 is presented in Fig. 1.12 (Gavriljuk et al. 1996). The relaxation peaks are located in the temperature range of 200–250 K. Peaks at higher temperatures are transient. Caused by hydrogen degassing, they appear only at certain heating rates and do not depend on the frequency. The linear dependence of the relaxation strength on the orientation factor consistent with that predicted by the Eq. (1.6) confirms its Snoek nature. For all orientations, the relaxation strength is not zero, which suggests the absence of tetragonal defects. Activation enthalpy is an important criterion when discussing the mechanism of relaxation. The internal friction spectra of the hydrogen-charged polycrystalline

Fig. 1.12 The orientation dependence of internal friction in single crystals of hydrogen-charged steel Cr23Ni21 cut on the {110} plane in different directions. Shown in the upper left corner is the area under the relaxation peaks as a function of the orientation factor

16

1 Atomic Interactions

Fig. 1.13 Internal friction in hydrogen-charged Cr18Ni16Mn10 steel measured at two frequencies: 1 f300 K = 0.472 Hz and 2 f300 K = 1.697 Hz. The frequency shift of peak temperatures measured for 5 frequencies to determine the activation enthalpy is presented in the Arrhenius co-ordinates in the upper left corner

austenitic steel Cr18Ni16Mn10 obtained at different frequencies are shown in Fig. 1.13, for detail see Gavriljuk et al. (1995). A feature of the IF spectrum in the polycrystalline samples is the occurrence of two clearly resolved relaxation subpeaks H1 and H2 characterized by the same activation enthalpy of ~0.46 eV and quite different relaxation times. The values obtained are ) × 10−12 s for H2 . τ0 = (0.8 ± 0.81) × 10−12 s for H1 and τ0 = (0.15 +0.203 −0.087 The occurrence of these two peaks follows from the above analysis of the modulus defect δG−1 and is a sign of “frozen splitting” in the internal friction spectra of the solid solution with a sufficiently high concentration of substitutional impurity atoms. This is just the case in austenitic steels. More than one substitutional atom can neighbour an interstitial one leading to the replacement of “i-s” non-cubic defects with “i-s1 s2 ” ones which have a lower symmetry. Therefore, the orthorhombic atomic configurations exist along tetragonal axis, and two relaxation peaks appear with the relaxation times τ−1 (S44 ) = 2ν12 + 4ν13 and τ−1 (S11 − S12 ) = 6ν13 , where ν12 and ν13 are the frequencies of atomic hops in corresponding directions (see Novick and Berry 1972 for detail). Following from Figs. 1.12 and 1.13, “frozen splitting” can be observed only in the internal friction spectra of polycrystals or in the single crystals with some arbitrary orientation of the crystal lattice. It is a common feature of interstitial-substitutional solid solutions. For example, similar IF spectra have been obtained in austenitic steels where hydrogen was substituted for nitrogen (see Gavriljuk et al. 1997b). It follows from the above that Snoek-like relaxation depends on the type of atomic complexes created by interstitial atoms in metallic solid solutions. For this reason, it

1.3 Atomic Complexes and Snoek-Like Relaxation

17

has been used for discussing the hydrogen location and its binding with other solutes in Fe, Ni and Ti alloys. The Snoek-like relaxation was first observed by Asano and his colleagues in austenitic steels, see Asano et al. (1975), Asano et al. (1980), Asano and Kazaoka (1985), Asano and Seki (1984), and Asano (1985), and Nishino et al. (1987) in Fe–Ni alloys with a high Ni content. Using cathodic hydrogen charging and measurements at frequencies of about 0.7 kHz, these authors registered a relaxation peak at 300 K in steels of the 310S, 316 and 304 type and attributed it to hydrogen atomic pairs. They obtained the activation enthalpy for this relaxation as ~0.51 eV, which matches that for hydrogen diffusion in austenitic steels. This interpretation was disputed by Zielinski (1985), see also Zielinski and Lunarska (1985) and Zielinski (1986), who performed a similar measurement, but interpreted the obtained IF peak in terms of interaction between hydrogen atoms and dislocations and denoted it as Snoek-Köster relaxation. However, their interpretation was at variance with the activation enthalpy measurements, HS-K , which considerably exceeds that for hydrogen diffusion, Hd . Depending on the available hypotheses of S-K relaxation, it should include either the sumd Hd +Hb (Schoeck 1963), where Hb is the enthalpy of binding between dislocations and hydrogen atoms, or the sum Hd +2Hk (Seeger 1979) with Hk as the enthalpy of kink formation on the dislocations. It is also worth noting that the S-K relaxation is never observed in solid solutions with a low stacking fault energy because of split dislocations and, correspondingly, excessively wide dislocation kinks, which is the case in austenitic steels. In addition, one can also remark that, in contrast to the data presented in Fig. 1.12 for Snoek relaxation, Snoek-Köster relaxation has no orientation dependence since it is caused by the movement of dislocations dragged by interstitial atoms. The interpretation of the hydrogen-caused Asano peak in terms of Snoek relaxation has been confirmed by Gavriljuk et al. (1993, 1995, 1997a) who measured internal friction in hydrogen-charged austenitic steels within the low-frequency range. For this reason, they obtained a higher resolution of the IF spectra in comparison with measurements in the kHz frequency range and could resolve the frozen splitting of Snoek-like relaxation, as shown in Fig. 1.13. In fact, the hydrogen IF relaxation peak discovered by Asano and his colleagues in austenitic steels is a particular case of relaxation caused by the diffusion hops of interstitial atoms in substitutional solid solutions with an fcc crystal lattice. For this reason, first we will analyze the available experimental data on Snoek-like relaxation caused by other interstitial elements in fcc iron-based alloys in order to estimate the application of this method for studies of hydrogen diffusion. The carbon-caused IF peak at ~300 °C was discovered by Rozin and Finkelstein (1953) in their studies of steel Cr25Ni20 doped with carbon. The authors attributed the detected peak to carbon atom diffusion as is the case with carbon in bcc iron at ~40 °C. However, no specific relaxation mechanism was proposed. Later, Ke and Tsien (1956) found this effect in Fe–Mn–C and Fe–Mn–Cr–C fcc alloys, whereas Werner et al. (1961) and Werner (1965) reported it for nitrogen in austenitic steels.

18

1 Atomic Interactions

Accordingly, a number of models were proposed for the operative relaxation mechanism. Ke and Tsien suggested that a single interstitial atom creates complexes with substitutional atoms or with single vacancies thereby inducing a local deviation from the cubic symmetry. Their idea was based on fitting the relaxation strength concentration dependence by a straight line. The fact that this line does not pass through the co-ordinate origin and intersects the concentration axis was explained by the authors as resulting from the preferential absorption of carbon atoms by vacancies before they occupy interstitial sites. However, the critical carbon concentration at which Ke and Tsien observed this Snoek-like peak was about 1.5 at.%, which is several orders of magnitude higher than any reasonable vacancy concentration in metals. Quite a different model was proposed by Cheng and Chang (1958) who analyzed the data obtained by Ke and Tsien, as well as those of Wu and Wang (1958) in Fe–Ni–C alloys. These authors attributed Snoek-like relaxation to the stress-induced reorientation of carbon atom pairs one half of which is located in the vacancy. The same mechanism was later discussed by Ulitchny and Gibala (1973) while studying the effect of solution treatment temperature, quenching rate, electron irradiation and cold work on Snoek-like relaxation in fcc Fe–Ni–C alloys. Both groups of authors reported the square concentration dependence of relaxation strength, which was interpreted as evidence of the carbon pair mechanism. Similarly, while studying nitrogen-caused Snoek-like relaxation in fcc iron-based alloys containing Ni, Cr, Mn and Co, Werner et al. (1961) and Werner (1965) concluded that neither substitution atoms nor vacancies affect peak intensity, and relaxation is caused by the nitrogen atom pairs located in the third to fifth coordination spheres. The applied stress induces pair reorientation resulting in the transfer of nitrogen atoms from one coordination sphere to the other. Asano and his colleagues have also interpreted hydrogen-induced relaxation in austenitic steels in terms of hydrogen atom pairs and, for substantiation, demonstrated the square dependence of relaxation strength (see Asano et al. 1998). Based on this feature of hydrogen-caused Snoek relaxation and taking into account the formation of hydrogen segregation at grain boundaries, we are going to discuss interaction between hydrogen atoms dissolved in iron, nickel and its alloys.

1.4 H–H Interaction Iron. Statements about hydrogen clustering and even the formation of “nanohydrides” are encountered often in scientific periodicals. Such studies focus on the theoretical analysis of hydrogen segregations in the vicinity of dislocations, see e.g. Hickel et al. (2014), or at the grain boundaries, e.g. Du et al. (2011). In relation to hydrogen distribution in the bulk, the discussion is mainly limited to features of the nearest neighbourhood of hydrogen atoms in the crystal lattice. According to ab initio calculations performed by Movchan et al. (2010), H–H interaction between hydrogen atoms entering fcc iron lattices is characterized by a positive

1.4 H–H Interaction

19

Fig. 1.14 Internal friction spectra of single crystal austenitic steel Cr18Mn10Ni8 charged with hydrogen at different current densities. For illustration, experimental data fitting is shown in the upper right corner for a sample charged at current density of 5 mA/cm2

binding energy EH-H (Fe) of 0.36 eV, which suggests their strong repulsive interaction and rules out the formation of H–H pairs. As mentioned in the previous Section, paired hydrogen atoms in the nearest interstitial sites of the fcc iron lattice were claimed by Asano et al. based on measurements of the concentration dependence of Snoek-like relaxation strength. Similar measurements were performed by Teus et al. (2006) using hydrogencharged single crystals of austenitic steel Cr18Mn10Ni8, see Fig. 1.14. A number of single crystal samples were cut on the {110} plane in an arbitrary but identical crystallographic orientation and hydrogen-charged at varied current densities to study the concentration dependence of hydrogen Snoek-like relaxation. Two relaxation subpeaks of Snoek-like relaxation at temperatures of 200–250 °C, H1 and H2 , were revealed, along with a third transient peak H3 caused by hydrogen degassing at higher temperatures. Their linear behaviour with varying hydrogen content clearly testifies against paired hydrogen atoms contributing to relaxation, see Fig. 1.15. Another feature is the extrapolation of experimental data to the coordinate origin, which is at variance with the results obtained by Asano et al. for polycrystalline austenitic steels, see inset in the upper left corner of this Figure. The linear hydrogen concentration dependence of Snoek relaxation strength proves that hydrogen is distributed as single atoms in the Fe-based solid solution. The discrepancy with the data obtained by Asano et al. (1998) obviously originates from the occurrence of hydrogen grain boundary segregation in polycrystals, which is absent in the case of single crystals.

20

1 Atomic Interactions

Fig. 1.15 Amplitudes of Snoek subpeaks H1 and H2 (see Fig. 1.14) versus hydrogen concentration in the single crystals of Cr18Mn10Ni8 austenitic steel. Shown in the upper left corner are the data obtained by Asano et al. (1998), Elsevier

The importance of the segregation factor can be illustrated by the available findings on Snoek relaxation caused by carbon and nitrogen in austenitic steels. These elements are characterized by a different affinity with the grain boundaries in iron-based solid solutions. Carbon is known to form strong segregation at grain boundaries. For example, using the energy dispersive X-ray analysis, the carbon content of 2.65 mass % was found within the grain boundary region in steel containing 22% of manganese and 0.69% of carbon, see Petrov (1993). In contrast, using the electron energy loss spectroscopy, no significant difference in the nitrogen content between the bulk and grain boundaries was found in austenitic steel Cr22Mn9Ni6 containing 1.05% N (Petrov et al. 1999). It is also worth noting that, using Auger spectroscopy, Briant (1987) observed some enrichment of the grain boundaries by nitrogen after the intergranular fracture of steel Cr18Ni9 aged at 600–700 °C for 5–100 h. However, a number of experimental data provides clear evidence that, compared to carbon, nitrogen has a smaller tendency to form grain boundary segregation in steel. For example, Rudy and Huggins (1966) carried out a comparative study of nitrogen and carbon grain boundary segregation in ferritic steel and observed no significant nitrogen segregation in contrast to the high enrichment of the grain boundaries with carbon. Lagerberg and Josefsson (1955) also reported quite a different carbon and nitrogen affinity with the grain boundaries. And, moreover, they also showed that carbon assists the creation of veins in the ferrite sub-boundaries produced in the course of hot deformation, whereas nitrogen does not cause this effect. This is obviously related to the difference in the segregation effects of carbon and nitrogen.

1.4 H–H Interaction

21

Fig. 1.16 Effect of carbon content (mass %) on the amplitude of the Snoek-like peak in iron-based solid solutions Fe–24.7Ni (Teus et al. 2006), Fe–35Ni (Wu and Wang 1958) and Fe–18.5Mn (Ke and Tsien 1956)

The concentration dependences of Snoek-like relaxation strength caused by carbon and nitrogen in austenitic steels are presented in Figs. 1.16 and 1.17, respectively. It is seen that the extrapolation of experimental data in Fig. 1.16 to a zero Snoek-like peak cuts a segment on the concentration axis, which is evidence of carbon atom segregation at the grain boundaries. Remarkably, the increase in nickel content increases relaxation strength due to the increased volume caused by the invar effect and, more significantly, decreases the segment cut on the concentration axis. The latter is due to competitive grain-boundary nickel-carbon segregation, which decreases the grain-boundary carbon content because of repulsive Ni–C interaction. In contrast, the extrapolation of experimental data to a zero nitrogen Snoek-like peak in Fig. 1.17 demonstrates the prevailing occurrence of single nitrogen atoms in the iron-based solid solution. This evidence of repulsive interaction between nitrogen atoms is obtained because of the negligible grain-boundary nitrogen segregation in the polycrystals. Thus, the measurements of hydrogen Snoek-like relaxation in single crystals unambiguously confirm repulsive H–H interaction in iron-based solid solutions. Nickel. The absence of hydrogen atomic pairs in nickel follows from the positive H–H interaction energy, 0.27 eV, obtained in the ab initio calculations by Movchan et al. (2010). It is also evidenced by internal friction studies, see Fig. 1.18. The only relaxation phenomenon caused by hydrogen in pure nickel is the SnoekKöster relaxation related to dislocation vibrations accompanied by hydrogen atom diffusion. Remarkably, this is the only example of S-K relaxation in fcc crystals. The reason for that is the high stacking fault energy in nickel, ~120–130 mJ/m2 (Carter

22

1 Atomic Interactions

Fig. 1.17 Effect of nitrogen content (mass %) on the amplitude of the Snoek-like peak in austenitic steels Cr18Ni16Mn10 (Teus et al. 2006) and Cr18MNn14 (Banov et al. 1978)

Fig. 1.18 Snoek-Köster relaxation in cold worked hydrogen-charged polycrystalline nickel. The arrow marks the expected temperature position of the Snoek-like peak with the existence of H–H pairs

1.4 H–H Interaction

23

and Holmes 1977), which is not typical of fcc metals. This is why dislocation kinks in nickel are narrow and can be easily formed. The temperature position of the hydrogen-caused Snoek-Köster peak in Fig. 1.14 is the same as observed by Zielinski et al. (1996) in their studies of hydrogen-charged nickel single crystals. The activation enthalpy for this relaxation was found to be 0.59 ± 0.06 eV, which includes the hydrogen diffusion enthalpy in nickel of about 0.4 eV and that for the formation of paired dislocation kinks, 0.19 ± 0.03 eV, if one is to interpret S-K relaxation in terms of Seeger’s theory (Seeger 1979). According to other possible interpretation, see Schoeck (1963), the enthalpy of S-K relaxation is equal to the sum of H diffusion enthalpy and that of binding between dislocations and hydrogen atoms. It is also worth noting that, in fact, like the data presented by Zielinski et al. for Ni single crystals, the S-K peak in Fig. 1.14 consists of two subpeaks. One can suppose following to Seeger (1979) that pre-existing single kinks on dislocations of arbitrary orientation also contribute to S-K relaxation because they are expected to move along screw dislocations under applied stress prior to the formation of kink pairs. Titanium. According to Naito et al. (1996), the maximum of one H atom can be the nearest neighbour of each Ti atom in the hcp α-phase, whereas in the bcc β-phase two sites in the nearest neighbourhood of a Ti atom are available for occupation by H atoms. The alloying of titanium by substitutional elements decreases the population of Ti– H neighbourhoods. For example, aluminium atoms in titanium block a part of the sites available for hydrogen atoms because of the more stable Al–H bonds, which results in the reduced fraction of Ti–H bonds. Such a conclusion is supported by the smaller solution heat of hydrogen in aluminium (e.g., Eichenauer 1968) in comparison with that for hydrogen in titanium (e.g., Nagasaka and Yamaschina 1976) and by the weaker bonding states formed by hydrogen with metallic atoms in aluminium hydride (Gupa and Burger 1980) than in titanium hydride (Fujimori and Tsuda 1982).

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange We shall analyze the role of hydrogen in the electron structure of Fe, Ni, Ti and their alloys, focusing on the electron exchange between the atoms and the corresponding spatial distribution of valence electrons.

1.5.1 Hydrogen in Iron The structure of the electron band in bcc hydrogen-free α-iron and that with hydrogen at the atomic ratio H/Fe = 1/54 is presented in Fig. 1.19a. The calculations were

24

1 Atomic Interactions

Fig. 1.19 a Density of electron states in α-iron without (dashed line) and with (solid line) hydrogen at H/Fe = 1/54. The insets on the left show state density at the Fermi level for the spin up and spin down electrons. b Partial densities of electron states: Fe-d (solid line), H–s (dotted line) and Fe-s (dashed line), in α-iron with H/Fe = 1/54

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange

25

Table 1.2 The density of electron states, DOS, states/cell × eV, at the Fermi level in hydrogen-free and hydrogen-containing bcc iron at the ratio H/Fe = 1/54 States

DOS spin up

DOS spin down

Total DOS

H-free

36.88

12.81

49.69

H-containing

37.18

13.67

50.85

performed taking into account the magnetism of iron atoms, i.e. the electron spin states along and against the internal magnetic field, respectively, see Teus and Gavriljuk (2020) for detail. It is seen that hydrogen atoms cause bound electron states with iron atoms below the d-band. Following from the calculation of partial state density in Fig. 1.19b, these bonds are formed by the s-electrons of hydrogen with the d-electrons of iron. For better resolution, the hydrogen-caused change in the density of electron states at the Fermi level is presented in the left section of Fig. 1.19a on a larger scale. Hydrogen in α-iron increases the density of electron states at the Fermi level in both cases, spin-up and spin-down, see Table 1.2. This result suggests an increase in the concentration of free electrons, which should enhance the metallic character of interatomic bonds with corresponding consequences for the properties of dislocations and the mechanical behavior of hydrogen-charged iron. The spatial distribution of external electrons throughout the crystal lattice is important because hydrogen atoms are not homogeneously distributed in solid solutions and prefer to be localized at crystal lattice imperfections such as vacancies, dislocations or grain boundaries. For example, any change in the concentration of free electrons within the hydrogen atmosphere around dislocations is expected to affect their properties and, particularly, dislocation mobility.

Fig. 1.20 Spatial distribution of valence electrons in the 3D format on the plane (002) in bcc α-iron containing hydrogen in the tetrahedral site. The electrons of the ion core are cut

26

1 Atomic Interactions

Fig. 1.21 Hydrogen effect on the spatial distribution of external electrons on the atomic plane (002) throughout the crystal lattice of bcc α-iron in the 2D format. Hydrogen atoms are located in the tetrahedral sites

The density of external electrons at the atomic plane (002) is presented in Figs. 1.20 and 1.21 in the 3D and 2D formats, respectively. It follows from Fig. 1.20 that a hydrogen atom in the tetrahedral site of bcc iron is surrounded by a cloud of external electrons. Moreover, it is clear from Fig. 1.21 that hydrogen increases electron density in the interstitial space between iron atoms. A similar effect on the electron structure has been found for hydrogen in fcc γ -iron (Teus et al. 2007; Gavriljuk et al. 2017). The density of electron states for external electrons in fcc iron with the H/Fe ratio of 1/32 is shown in Fig. 1.22.

Fig. 1.22 Density of electron states in fcc iron without (solid line) and with (dashed line) hydrogen at the atomic ratio H/Fe of 1/32. The inset on the left shows the density of states at the Fermi level for spin up and spin down electrons

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange Table 1.3 Density of electron states, DOS, states/cell × eV, at the Fermi level in hydrogen-free and hydrogen-containing fcc γ -iron at the atomic ratio H/Fe = 1/32

States

DOS spin up

DOS spin down

27 Total DOS

H-free

5.40

28.71

34.11

H-containing

5.68

30.52

36.20

Fig. 1.23 Spatial distribution of valence electrons on the atomic plane (002) throughout the fcc γ -iron lattice at the H/Fe ratio of 1/32. Hydrogen atoms are located in the octahedral sites

The computational data are presented in Table 1.3. As in the case of the bcc iron lattice, hydrogen increases the density of electron states in the fcc lattice. The distribution of external electron density on the plane (002) throughout the fcc iron crystal lattice is presented in Fig. 1.23 in the 2D format. FCC iron with a higher hydrogen content was chosen to present the spatial distribution of external electrons in the 3D format, see Fig. 1.24. It is remarkable that, at high hydrogen contents, the density of electron clouds around hydrogen atoms exceeds that for iron atoms. Moreover, one can see that localized electrons at iron atoms form directional electron bonds, whereas the spatial electron distribution in the vicinity of hydrogen atoms is symmetrical and uniform. In other words, confirming the calculated data of electron state density at the Fermi level, this suggests that the electron clouds around hydrogen atoms prevailingly consist of free electrons. The concentration of free electrons has been directly measured using electron spin resonance (Shanina et al. 1999). These measurements required the samples to be paramagnetic, which is possible only in fcc γ -iron or in γ -iron based solid solutions, see Fig. 1.25.

28

1 Atomic Interactions

Fig. 1.24 Spatial distribution of external electrons in fcc γ -iron containing hydrogen with H/Fe = 1/4

Fig. 1.25 Electron spin resonance in hydrogen-free (dashed line) and hydrogen-charged (solid line) steel Cr18Mn20N0.88. Measurements were performed at 77 K. Signal A0 belongs to the reference sample (borate glass) containing 1015 electron spins and is seen on the left side of the main signal

As pure γ-iron is thermodynamically stable only at temperatures above 910 °C, the iron needs to be alloyed in order to get a paramagnetic fcc crystal lattice for measurements. The appropriately alloyed austenitic steel Cr19Mn20N0.88 was chosen for this experiment, see Shanina et al. (1999) for detail. This steel remains paramagnetic at temperatures below −196 °C. Moreover, alloying with manganese instead of nickel ensured the absence of superparamagnetic clusters which would cause a weak ferromagnetism.

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange

29

The ESR signal in this Figure represents a derivative of the energy spent on the transfer of free electrons between their ground and excited states under an applied magnetic field. The absorbed microwave energy, i.e. the area A under the signal, is proportional to the concentration of free electrons in the sample. It is seen that hydrogen significantly increases free electron concentration in austenitic steel. The obtained data will be used in Chaps. 2 and 5 to discuss dislocation properties and operative mechanisms for the hydrogen brittleness phenomenon.

1.5.2 Hydrogen in Nickel Not much is currently known about the electron structure of Ni–H solid solutions. One can mention the calculations performed by Feng et al. (2001) who, using the discrete variational method, obtained the preferential localization of hydrogen atoms in the octahedral lattice sites along with a reduction in the interaction between neighboring nickel atoms. The essential role of H–H interaction in the formation of the ordered structure in the Ni–H solid solution was reported by Muscat (1981). The predominant H–H interaction through a neighboring nickel atom, i.e. the existence of dumb-bell like H-Ni–H configurations, is similar to the N–Fe–N atomic constructions in binary Fe– N solid solutions, which was observed by Gavriljuk et al. (2000) using Mössbauer spectroscopy. It is worth noting in this regard that both hydrogen and nitrogen increase the concentration of free electrons in transition metals. The structure of electron state density in the 3d-band of nickel is presented in Fig. 1.26 according to Teus and Gavriljuk (2018). The computational data are given in Table 1.4. As in the case of hydrogen in iron, bound Ni–H states are formed at the bottom of the 3d-band, and hydrogen increases the density of electron states at the Fermi level. Another similarity is the spatial distribution of external electrons throughout the nickel crystal lattice, see the data in Figs. 1.27 and 1.28 presented in the 3D and 2D formats, respectively. Hydrogen atoms in the octahedral sites of the nickel lattice are encased in electron clouds, as in H-containing iron.

1.5.3 Hydrogen in Titanium Titanium is placed at the beginning of the 4th period in the periodic table of chemical elements, and the external electron shell 3d 2 4s2 of a titanium atom contains only two d-electrons, which causes the practical absence of paramagnetism. The spinpolarized calculation of the electron structure in bcc Ti produces a negligibly small magnetic moment at Ti atom, equal to −0.00011 μB , i.e. the spin polarization does not provide any remarkable correction to the total energy. Therefore, in the course of

30

1 Atomic Interactions

Fig. 1.26 Electron d-band of the fcc Ni without (dashed line) and with (solid line) hydrogen at the H/Ni atomic ratio of 1/32. The insets on the left show the density of electron states in the vicinity of the Fermi level Table 1.4 Density of electron states, DOS, states/cell × eV, at the Fermi level in hydrogen-free and hydrogen-containing nickel at the ratio H/Ni = 1/32 H/Ni ratio

DOS spin up

DOS spin down

Total DOS

H-free Ni

5.52

49.66

55.18

1/32

5.66

50.77

56.42

calculations, bcc β-Ti can be treated as a non-magnetic structure consistently with the experiment. The effect of hydrogen on the electron structure of bcc titanium is demonstrated in Fig. 1.29 for different hydrogen contents. In contrast to the case of iron and nickel, a feature of DOS at the Fermi level in titanium is its non-monotonous behavior with increasing hydrogen content. It decreases in TiH and TiH2 compositions, which reflects the formation of Ti hydride. At smaller hydrogen contents, H/Ti = 0.5, hydrogen increases the DOS and, correspondingly, an increase in the concentration of free electrons is expected. The calculated data are presented in Table 1.5. As shown in Fig. 1.30, and just as in bcc iron, hydrogen atoms in bcc titanium occupy tetrahedral interstitial sites and are surrounded by free electron clouds. The concentration of free electrons is increased within the interstitial sites, which enhances the metallic character of atomic interactions.

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange

31

Fig. 1.27 Spatial distribution of external electrons at the plane (002) in the 3D-format throughout the nickel crystal lattice at H/Ni = 1/32. Hydrogen atoms are located in the octahedral sites

Fig. 1.28 Hydrogen effect on the spatial distribution of external electrons on the atomic plane (002) throughout the crystal lattice of fcc nickel in the 2D format. Hydrogen atoms are located in the octahedral sites

1.5.4 Concluding Remarks Electron charge at the hydrogen atoms As follows from the spatial distribution of electron density in hydrogen-containing Fe, Ni and Ti, see Figs. 1.20, 1.21, 1.23, 1.24, 1.27, 1.28 and 1.30, hydrogen atoms are surrounded by clouds of electrons. The same is true for hydrogen atoms in the strong hydride formers Nb and V, see Fig. 1.31. A deeper insight into the topology of electron density distribution can be obtained while carrying out charge integration inside the spheres surrounding selected atoms.

32

1 Atomic Interactions

Fig. 1.29 Density of electron states in bcc β-Ti and β-Ti–H solid solutions at different hydrogen contents Table 1.5 Density of electron states, DOS, states/cell × eV, at the Fermi level in hydrogen-free and hydrogen-containing titanium at different H/Ti ratios

H/Ti ratio

Total DOS

H-free

4.278

1/2

4.699

1/1

3.348

2/1

1.677

Fig. 1.30 Spatial distribution of valence electrons in 2d format in the bcc titanium for Ti2 H composition

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange

33

Fig. 1.31 Spatial distribution of valence electrons in 2D format in the bcc Nb (a) and V (b)

As an example, this analysis is performed for bcc Fe–H and bcc Nb–H systems based on a theory proposed by Bader (1995, 1998). In both cases, the charge around a hydrogen atom located in a tetrahedral site exceeds one electron: 1.39 e− and 1.65 e− , respectively. Two conclusions can be derived from this: (i) the electron density around a hydrogen atom dissolved in both metals is increased in comparison with a neutral H atom, i.e., hydrogen atoms in metals are electron acceptors; (ii) as the value of the integrated charge around a hydrogen atom dissolved in hydride-forming niobium is higher than in the case of H in Fe, the interatomic bonding between hydrogen and hydride-forming elements is stronger. Density of electron states, DOS Let us compare the hydrogen concentration dependence of the DOS in titanium, γ-iron and nickel, see Figs. 1.29, 1.32 and 1.33, respectively. The calculated data for DOS in nickel at increased hydrogen contents are given in Table 1.6. Three distinctions are clearly seen.

34

1 Atomic Interactions

Fig. 1.32 Density of electron states in fcc γ -Fe and γ -FeH solid solutions at different hydrogen contents

First, with increasing hydrogen content, the bound metal-hydrogen states approach the bottom of the electron d-band in all the studied M-H systems. This tendency shows an increase in hydrogen-metal bonding. Second, in contrast to iron, the hydrogen concentration dependence of DOS at the Fermi level is non-monotonous in the case of titanium and nickel, which is a sign of instabilities in their crystal lattices and consequent phase transformations. The formation of titanium hydride with a crystal lattice quite different from that in the matrix phase has been well-substantiated. It is also widely accepted that a nickel hydride is formed at hydrogen contents approaching the ratio H/Ni > 0.6, which was first declared by Baranowski et al. (1958, 1959). However, it is unusual that this “hydride” acquires the same fcc crystal lattice as matrix fcc nickel. This ambiguity will be discussed in detail in Chap. 4 for the interpretation of experimental data on hydrogen induced phase transformations in iron, nickel, titanium and their alloys. Third, hydrogen increases the density of electron states at the Fermi level throughout its concentration in the Fe–H solution and, at its moderate contents, in the Ni–H and Ti–H systems. Consequently, hydrogen increases the concentration of free electrons, thereby enhancing the metallic character of interatomic bonds, which was confirmed using measurements of electron spin resonance for hydrogen in austenitic steel, see Fig. 1.25. The opposite effect on the density of electron states at the Fermi level occurs in the hydride-forming metals in the group V of periodic table, see e.g. Figure 1.34 for hydrogen in niobium and vanadium, which correlates with a higher electron charge at hydrogen atoms, as it is shown above for H inNb.

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange

35

Fig. 1.33 Concentration dependence of the density of electron states in fcc Ni and Ni–H solid solutions at different hydrogen contents for spin up (a) and spin down states (b) Table 1.6 Density of electron states, DOS, states/cell × eV, at the Fermi level in hydrogen-free and hydrogen-containing nickel at different H/Ni ratios above 1/32

H/Ni ratio

DOS spin up

DOS spin down

Total DOS

H-free Ni

5.52

49.66

55.18

3/32

6.16

55.9

62.10

6/32

7.01

57.84

64.85

16/32

10.40

45.14

55.54

32/32

12.59

12.63

25.22

36

1 Atomic Interactions

Fig. 1.34 Density of electron states in the hydrogen-free and hydrogen-doped Nb (a) and V (b) at the atomic ratio H/M = 1/54. DOS in the vicinity of Fermi level is presented in the inset

Along with the decreasing DOS in titanium at high H concentrations, this result suggests the enhancement of covalent interatomic bonds by hydrogen in the hydrideforming elements. Consequently, a remarkable difference should occur in the hydrogen effect on the elasticity moduli controlling properties of dislocations in the above mentioned metals. Elastic constants For example, let us compare the ab initio calculated shear moduli in iron and niobium. Due to the cubic symmetry of the crystal lattice in the both metals, only three independent elastic constants, namely c11 , c12 and c44 need to be calculated in order to obtain the full elastic tensor. This allows to apply the strain of only three types to the crystal lattice, namely bulk tension–compression, tetragonal and rhombohedral distortions, in order to obtain a system of three equations containing three elastic moduli. By fitting the Murnaghan solid state equation, Murnaghan (1944), to the dE(V)/dV curve with the total energy E and volume V, respectively, the (c11 + c12 + c44 ) combination is obtained. The values of (c11 -c12 ) and (c11 + 2c12 + 2c44 ) were calculated from two other sets of curves for the total energy as a function of strain in the rhombohedral or tetrahedral distortions. The obtained shear modulus c44 for hydrogen in fcc iron, as earlier obtained by Teus (2007), and those for hydrogen in the bcc niobium, are presented in Table 1.7 along with the densities of electron states at the Fermi level. Significantly higher values of total DOS for niobium are obtained because of the increased number of metallic atoms in the calculated cell. It is seen that, along with increasing DOS at the Fermi level in iron, modulus c44 decreases. Be calculated for the temperature of 0 K, the data for hydrogen in fcc iron cannot be directly compared with the experiment because, having the fcc structure, the γ iron phase is thermodynamically stable only at temperatures above 910 °C. It is also worth noting that the electron structure of fcc iron is rather complicated because of disordered spin orientations. For example, as shown by Tsunoda (1989),

1.5 Hydrogen Effect on the Electron Structure: Electron Exchange

37

Table 1.7 Calculated data for the DOS at Fermi level per atomic cell and the elasticity moduli of fcc iron and bcc niobium System and M/H ratio DOS at Fermi level, states/(eV × cell) Shear modulus Moduli c44 , GPa C 11 (c12 ), GPa Fe

6.90

279

–

FeH (4/1)

7.06

229

–

FeH (1/1)

8.2

186

–

Nb

83.76

26

250(129)

NbH (54/1)

81.3

29

257(129)

the ground state of γ-Fe is located at a crossing point of the ferromagnetic (FM) and antiferromagnetic (AFM) magnetic states, which substantially depends on the atomic volume. It is also obtained in that research using the neutron diffraction measurements that magnetic moments in the γ-Fe form the spin density waves. For this reason, the nonmagnetic state of γ-Fe is considered in the current simulation for simplicity. It is one of the several approaches to describe the magnetic configuration of fcc iron in its ground state. Thus, the obtained data demonstrate a clear trend: hydrogen in the fcc iron-based lattice decreases the shear modulus. The hydrogen effect in niobium is opposite: elastic constants c44 , c11 and c12 are increased by hydrogen. Moreover, the constant c = (c11 − c12 )/2 controlling the shear stress along the slip planes {110} is increased from 60.5 to 64 GPa by hydrogen in niobium. These data for H in Nb are consistent with the experiments performed using the ultrasonic technique. The shear constants c44 , c11 and c12 for niobium doped with hydrogen were measured by Magerl et al. (1976). In the H-free niobium, the authors obtained 28, 246, 133 GPa for c44 , c11 , c12 , respectively. Alloying with hydrogen increased c44 by 18.4 × 10−3 per 1% of H, but, unexpectedly, decreased c by −4.7 × 10−3 . The reason is that a small plastic deformation accompanies the ultrasonic measurements, which causes the modulus defect due to diffusion hops of hydrogen atoms identified as Snoek relaxation. Similar experimental results were reported earlier by Fisher et al. (1975). Thus, in contrast to strong hydride forming metals, the hydrogen-enhanced metallic character of interatomic bonds in iron, nickel and in the bcc titanium, for the latter at H concentrations far below the hydride formation, results in the decrease of the shear modulus, which is expected to change properties of dislocations in the following way: (i)

(ii)

a decrease in the critical stress for the start of dislocation sources, e.g., σ ≈ 2μb/L for the Frank-Reed dislocation source, where L is the distance between the pinning points, which decreases the yield stress for plastic deformation; a decrease in the specific energy of dislocations, namely their line tension Γ ≈ (μb2 /4π )/log( /5b), where is the dislocation curvature radius, which enhances mobility of dislocations;

38

(iii)

1 Atomic Interactions

a decrease in the distance between dislocations in pile-ups d = (π μb)/16(1 − v)nσ with σ as applied stress, which increases the number of dislocations n in the pile-up resulting in the increased shear stress at the leading dislocation, τ L = nτ, and causing the earlier opening of a microcrack in front of the leading dislocations in the pile-ups.

This hydrogen effect will be analyzed in Chap. 5, while discussing the electron concept of hydrogen embrittlement of Fe-, Ni- and Ti-based alloys.

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McLellan RB, Alex K (1970) The thermodynamics of nitrogen austenite. Scripta Metall 4(12):967– 970. https://doi.org/10.1016/0036-9748(70)90040-2 McLellan RB, Sutter PL (1984) Thermodynamics of the hydrogen-nickel system. Acta Metall 32(12):2233–2239. https://doi.org/10.1016/0001-6160(84)90165-2 Miwa K, Fukumoto A (2002) First-principles study of 3d transition-metal dihydrides. Phys Rev B 65(15):155114. https://doi.org/10.1103/PhysRevB.65.155114 Moro L, Ferullo R, Brizuela G, Juan A (2000) The electronic structure and bonding of hydrogen near a fcc Fe stacking fault. J Phys D: Appl Phys 33:292–298. https://doi.org/10.1088/0022-3727/ 33/3/317 Morucci VL, Janaak JP, Williams AR (1978) Calculated electronic properties of metals. Pergamon, New York Movchan DN, Shyvanyuk VN, Shanina BD, Gavriljuk VG (2010) Atomic interactions and hydrogen-induced γ* phase in fcc iron-nickel alloys. Phys Stat Sol (a) 207(8):1796–1801. https:// doi.org/10.1002/pssa.200925548 Murnaghan FD (1944) The compressibility of media under extreme pressures. Proc Nat Acad Sci USA, 30(9):244–247. https://doi.org/10.1073/pnas.30.9.244 Muscat JP (1981) The role of H-H interactions in the formation of ordered structures on Ni and Pd single crystals. Surf Sci 110(1):85–110. https://doi.org/10.1016/0039-6028(81)90589-6 Nagasaka M, Yamaschina T (1976) Solubility of hydrogen and deuterium in titanium and zirconium under very low pressure. J Less Common Metals 45(1):53–62. https://doi.org/10.1016/0022-508 8(76)90196-X Naito S, Yamamoto N, Miyoshi T, Mabuchi M, Kimura M (1996) Isotope effect in the diffusion of hydrogen and deuterium in titanium, Ti88 Al12 and Ti3Al. J Chem Soc Faraday Trans 92(18):3407– 3410. https://doi.org/10.1039/FT9969203407 Nazarov R, Hickel T, Neugebauer J (2010) First-principles study of the thermodynamics of hydrogen-vacancy interaction in fcc iron. Phys Rev B 82:224104. https://doi.org/10.1103/Phy sRevB.82.224104 Nishino Y, Kato T, Tamaoka S, Asano S (1987) Internal friction caused by dissolved hydrogen in fcc iron-nickel alloys. Scripta Metall 21(9):1235–1239. https://doi.org/10.1016/0036-9748(87)903 55-3 Novick AS, Berry BS (1972) Anelastic relaxation in crystalline solids. Academic Press, New York and London Petrov YuN (1993) On the carbon distribution at structural imperfections in manganese austenite. Scripta Metall Mater 29(11):1471–1476. https://doi.org/10.1016/0956-716X(93)90339-T Petrov YuN, GavriljukVG BH, Escher Ch (1999) Nitrogen partitioning between matrix, grain boundaries and precipitates in high-alloyed austenitic steels. Scripta Mater 40(6):669–674. https://doi. org/10.1016/S1359-6462(98)00488-6 Pinto H, Korn C, Goren S, Shaked H (1979) Neutron diffraction study of hydrogen in α-titanium. Solid State Commn 32(5):397–398. https://doi.org/10.1016/0038-1098(79)90474-5 Rozin KM, Finkelstein BN (1953) A study of phase transformations using internal friction method (in Russian). Rep Acad Sci. USSR XCI(4):811–812 Rudy ML, Huggins RA (1966) Grain boundary segregation and the cold work peak in iron containing carbon and nitrogen. TMS AIME 236(12):1662–1666 Saravia DR, Juan A, Brizuela G, Simonetti S (2009) Comparative study of H-atom location, electronic and chemical bonding in ideal and vacancy containing FCC iron. Intern J Hydrogen Energy 34(19):8302–8307. https://doi.org/10.1016/j.ijhydene.2009.08.026 Schoeck G (1963) Friccion debido a la interaccion entre dislocacions y atoms solutos. Acta Metall 11(6):617–622. https://doi.org/10.1016/0001-6160(63)90096-8 Seeger A (1979) A theory of the Snoek-Köster relaxation (cold-work peak) in metals. Phys Stat Sol (a) 55(2):457–468. https://doi.org/10.1002/pssa.2210550213 Shanina BD, Gavriljuk VG, Kolesnik SP, Shivanyuk VN (1999) Paramagnetic resonance in hydrogen-charged austenitic steel. J Phys D: Appl Phys 32(3):298–304. https://doi.org/10.1088/ 0022-3727/32/3/018

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Shapovalov and Boyko (1983) On the anomaly of hydrogen solubility in ferromagnetic metals in the vicinity of Gurie temperature (in Russian). Russ Fiz Met Metalloved 55(6):1220–1221 Shapovalov VI, Serdyuk NP (1979) Russian J Phys Chem 53(9):1250–1252 Silva JR, Stafford SW, McLellan RB (1976) The thermodynamics of the hydrogen-iron system. J Less Common Metals 49:407–420. https://doi.org/10.1016/0022-5088(76)90052-7 Simonetti S, Pronsato ME, Brizuela G, Juan A (2003) The electronic effect of carbon and hydrogen in an (1 1) edge dislocation core system in bcc iron. Appl Surf Sci 217(1–4):56–67. https://doi. org/10.1016/S0169-4332(03)00582-8 Sozinov AL, Balanyuk AG, Gavriljuk VG (1997) C-C interaction in iron-base austenite and interpretation of Mössbauer spectra. Acta Mater 45(1):225–232. https://doi.org/10.1016/S1359-645 4(96)00138-3 Sozinov AL, Balanyuk AG, Gavriljuk VG (1999) N-N interaction and nitrogen activity in the iron base austenite. Acta Mater 47(3):927–935. https://doi.org/10.1016/S1359-6454(98)00394-2 Switendick AC (1972) Berichts Bunsenges Physik Chemie 76:535 Teus SM (2007) Effect of hydrogen on electronic structure, phase transformations and mechanical properties of fcc iron-based alloys. PhD thesis, G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, Kiev Teus SM (2018) Hydrogen effect on atomic interactions, phase transitions and dislocation properties in the 3d metal alloys. Doctor hability thesis, G.V. Kurdyumov Institute for Metal Physics, Kiev, Ukraine Teus SM, Gavriljuk VG (2018) Electron structure and thermodynamics of solid solutions in Ni–H system. Material Sci & Eng Int J 2(4):101–109. https://doi.org/10.15406/mseij.2018.02.00042 Teus SM, Gavriljuk VG (2020) On a correlation between the hydrogen effects on atomic interactions and mobility of grain boundaries in the alpha-iron. Stage I. A change in the electron structure of the alpha-iron due to hydrogen. Mater Letts 258:126801. https://doi.org/10.1016/j.matlet.2019. 126801 Teus SM, Shyvanyuk VN, Gavriljuk VG (2006) On a mechanism of Snoek-like relaxation caused by C, N and H in fcc iron-based alloys. Acta Mater 54(14):3773–3778. https://doi.org/10.1016/ j.actamat.2006.04.008 Teus SM, Shyvanyuk VN, Shanina BD, Gavriljuk VG (2007) Effect of hydrogen on electronic structure of fcc iron in relation to hydrogen embrittlement of austenitic steels. Phys Stat Sol (a) 204(12):4249–4258. https://doi.org/10.1002/pssa.200723249 Tsunoda Y (1989) Spin-density wave in cubic γ-Fe and γ-Fe100-x -Cox precipitates in Cu. J Phys: Condensed Matter 1:10427–10438. https://doi.org/10.1088/0953-8984/1/51/015 Ulitchny MG, Gibala R (1973) Internal friction and strain aging of ferrous austenite. Metall Trans 4(2):497–506 Vitt RS, Ono K (1971) Hydrogen solubility in alpha titanium. Metal Trans 2(2):608–609. https:// doi.org/10.1007/BF02663358 Vyatkin AF, Zhorin PV, Tseitlin EM (1983) Russian J Phys Chem 57(2):249–251 Werner VD (1965) On a nature of internal friction peak in interstitial solid solutions having the fcc lattice. Solid State Phys (sov Phys) 7(8):2318–2326 Werner VD, Finkelstein BN, Shalimova AV (1961) A study of nitrogen behaviour in iron alloys using a method of internal friction (in Russian). Solid State Phys (sov Phys) 3(11):3363–3366 Wicke E, Brodowsky H (1978) Hydrogen in palladium and its alloys (chap. 3). In: Alefeld G, Völkl J (eds) Hydrogen in metals II. Springer, Berlin (quoted from Russian edition, Mir, Moscow, 1981, pp. 91–188) Wigner EP, Seitz F (1933) On the constitution of metallic sodium. Phys Rev 43:804–810. https:// doi.org/10.1103/PhysRev.43.804 Wollan EO, Cable JW, Koehler WC (1963) The hydrogen atom positions in face centered cubic nickel hydride. J Phys Chem Solids 24(9):1141–1143. https://doi.org/10.1016/0022-3697(63)900 28-3 Wu TL, Wang CM (1958) Mechanism of carbon diffusion peak in f.c.c. iron-nickel alloys. Acta Phys Sin 14(4):354–368. https://doi.org/10.7498/aps.14.354

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Yutaka H, Masayoshi H (1975) Internal friction of iron cathodically charged with hydrogen. J Iron Steel Inst Jap 61(2):251–257. https://doi.org/10.2355/tetsutohagane1955.61.2_251 Zeng K, Klassen T, Oelerich W, Bormann R (1999) Thermodynamics of the Ni-H system. J Alloys Compounds 283:151–161. https://doi.org/10.1016/S0925-8388(98)00857-3 Zielinski A (1985) Effect of hydrogen charging on internal friction of austenitic stainless steel. Scripta Metall 19(2):173–176. https://doi.org/10.1016/0036-9748(85)90176-0 Zielinski A, Lunarska E (1985) Internal friction of hydrogen charged austenitic stainless steel. J Phys Colloques 46(C10):131–134. https://doi.org/10.1051/jphyscol:19851030 Zielinski A, Hauptmann G, Holzwarth U, Kronmüller H (1996) Internal friction in cold worked and hydrogen charged nickel single crystals. Z Metallkd 87(2):104–110

Chapter 2

Crystal Lattice Defects

As interstitial element, hydrogen causes remarkable distortions in the crystal lattice, which predetermines the affinity of hydrogen atoms with vacancies, dislocations and grain boundaries. This topic will be discussed with a special focus on the nature of interaction between hydrogen atoms and crystal lattice imperfections and its role in mechanical properties.

2.1 Hydrogen-Induced Vacancies A significant energy, of about 2.5–3.0 eV, is needed to introduce a vacancy in the thermodynamically equilibrium metallic crystal. Nevertheless, vacancies are always present in any crystal lattice because their occurrence increases the entropy. If to account only for the configuration part of the entropy, S, its increment in a crystal consisting of N atoms and n vacancies is given by the following expression: S = k B ln

N! , (N − n)!n!

(2.1)

where k B is the Boltzmann constant. The occurrence of vacant lattice sites causes the following change in the Helmholtz free energy, F = nE − TS, with temperature T in K units and E as the formation energy for single vacancy. Using Stirling’s formula for the factorials of large numbers and minimizing F on n, one obtains a thermodynamically equilibrium number of vacancies which increases exponentially with temperature n equi = N e−E/kT .

(2.2)

In fact, the equilibrium concentration of vacancies is very small in metals, no higher than 10–4 to 10–5 at temperatures close to melting point. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. G. Gavriljuk et al., Hydrogen in Engineering Metallic Materials, https://doi.org/10.1007/978-3-030-98550-9_2

45

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2 Crystal Lattice Defects

Along with single vacancies, their clusters, e.g. divacancies, can be created and their concentration becomes important at elevated temperatures. The mobility of divacancies is higher in comparison with that of single vacancies and, for this reason, a positive deviation from the Arrhenius law usually occurs with increasing temperature, see e.g. Bocquet et al. (1996). More complicated clusters, e.g. trivacancies, were supposed to exist by Damask et al. (1959). According to their calculations for copper, the most stable can be a tetrahedral configuration with four vacancies in the corners of a tetrahedron and a Cu atom in its centre.

2.1.1 Hydrogen-Vacancy Interaction in Metals A unique phenomenon related to vacancies in metals is presented by a remarkable increase of their thermodynamically equilibrium concentration in the presence of any interstitials in the solid solution. The first thermodynamic analysis in this respect was performed by McLellan (1988a). He tried to explain the enhanced diffusivity of the host atoms in the presence of dissolved interstitial solutes, namely carbon in γ-iron, which was found earlier in a number of experiments, e.g. by Gruzin et al. (1951) for the Fe–C system. While solving this problem, two main ideas were discussed: (i) vacancies decorated by interstitial atoms acquire higher mobility in comparison with their undecorated counterparts, and (ii) interstitial species cause dilatation in the solid solution, which decreases the free formation and motion enthalpies of undecorated vacancies and, for this reason, enhances the mobility of host metallic atoms (see also McLellan 1988b). Numerical estimations for the fcc FeC solid solution with the carbon content θC = nC /NFe = 0.06 at 1273 K resulted in a five-fold increase of vacancy concentration. Later on, the thermodynamic and kinetic behaviour of metal-vacancy-hydrogen systems was studied by Carr and McLellan (2004) using Fermi–Dirac statistics in order to describe the formation of H-vacancy clusters in Pd, Ni, Fe, Mo and Nb. Similar results were also obtained in theoretical calculations carried out by Smirnov et al. (Smirnov 1991; Bobyr et al. 1991; Bugaev et al. 1997). Moreover, according to their calculations, superabundant vacancies induced by dissolved interstitial atoms can stimulate crystal lattice instability resulting in polymorphic transformations. Fundamental experimental studies of hydrogen-induced vacancies have been performed by Fukai et al. for Ni–H (1993, 2001a, b, 2003a, b), Fe–Pd (1993, 1994, 2000), Fe–H (2003a, b), Mn and Co (2001a), Cu–H and Cr–H (2003a, b) etc. A feature of these experiments was the in situ measurement of X-ray diffraction under high gaseous hydrogen pressures. The authors noted a decrease by ~1.5% of the lattice parameter during hydrogen absorption, which was attributed to vacancy formation. Such a hydrogen effect has been also observed in Ti by Nakamura and Fukai (1995) and in Al by Birnbaum et al. (1997).

2.1 Hydrogen-Induced Vacancies

47

Worth noting is the synergetic effect of hydrogen and plastic deformation on vacancy generation. For example, using positron annihilation, Sakaki et al. (2006) detected a 1.5 increase in the mean positron life-time when commercially pure iron was deformed after hydrogen charging. Along with the life-time component of ~100 ps for positron annihilation in the lattice and that of ~150 ps for dislocations, the authors found a large positron life-time component exceeding 400 ps, which evidenced the existence of vacancy clusters. The same result was obtained by Mikhalenkov et al. (1995) who showed that cold rolling of previously hydrogen-charged nickel increases the positron parameter S far above its value for deformed hydrogen-free samples. Moreover, the recovery of this state started only at temperatures above 400 °C, which pointed to the high thermal stability of vacancy clusters. Among the studies introducing the electron approach to hydrogen-vacancy interaction in metals, remarkable results were obtained by Takeyama and Ohno (2003), Counts et al. (2010), Nazarov et al. (2010) and Metsue et al. (2016) based on the density functional theory. For ambient conditions of hydrogen pressure, Takeyama and Ohno (2003) found stable vacancy-hydrogen atomic configurations in α-iron, VH2 . Moreover, these authors claimed the formation of line-shape vacancy clusters along the atomic planes typical of hydrogen-caused brittle fracture of steels. According to the ab initio calculations performed by Counts et al. (2010), the complex of a single H atom with a monovacancy in α-iron is characterized by the binding energy of 0.57 eV. Experimental measurements of hydrogen-vacancy binding energy in α-iron, e.g. ~0.63 eV, such as those obtained by Besenbacher et al. (1987) in their ion beam experiments, are consistent with these theoretical estimations. Also remarkable is that, according to Counts et al. (2010), substitution solute atoms do not affect hydrogen binding to vacancies provided the size of substitution atoms is not significantly larger than that of iron atoms. In γ-iron, the enthalpy of binding between a hydrogen atom and a single vacancy was estimated by Nazarov et al. (2010) as ~0.2 eV, which seems to be reasonable because of smaller distortions caused by hydrogen atoms in fcc iron in comparison with those in bcc iron. It is also important that a hydrogen atom in its complex with a vacancy does not occupy the vacancy centre. Depending on the magnetic configuration, displacement from the vacancy centre can reach the values of 0.26a to 0.39a, where a is the interatomic distance. This suggests that, using mechanical spectroscopy, namely Snoek-like relaxation caused by hydrogen atoms in metals, one can distinguish between hydrogen atoms in their complexes with vacancies and those in the vacancy-free crystal lattice. For comparison, one can mention the measurements performed by Weller and Diehl (1976) for carbon and nitrogen in irradiated bcc Fe–C and Fe–N solid solutions, where the enthalpies of binding between interstitials and vacancies have been determined. Another important result obtained by Nazarov et al. (2010) is that, in contrast to VH2 configurations in bcc iron, as obtained by Takeyama and Ono, the vacancy in fcc iron can be occupied by up to six H atoms.

48

2 Crystal Lattice Defects

Fig. 2.1 Hydrogen-caused increase in the volume of the unit cell, V, as a function of the hydrogen/metal atomic ratio. According to Baranowski et al. (1971), for hydrogen in the fcc metals (open circles) and Teter et al. (2001) for hydrogen in a bcc titanium alloy (black circles)

The enthalpy of hydrogen binding to vacancies in Ni constitutes 0.44 eV (Meyers et al. 1992). Earlier, the trapping of multiple hydrogen atoms by single vacancies in Ni was calculated by Myers et al. (1986) using the effective-medium theory developed by Nordlander et al. (1984). They obtained a two-stage decrease of trapping energy with an increase in the number of captured hydrogen atoms in a vacancy: 0.52 − 0.47 eV for one and two H atoms and 0.2 − 0.3 eV for 3–6 H atoms. The hydrogen-induced crystal lattice dilatation is presented in Fig. 2.1 as a function of the hydrogen/metal ratio in the fcc metals, as published by Baranowski et al (1971), added by the data obtained by Teter et al. (2001) for hydrogen in the bcc β-Ti alloy Timetal 21S. It is relevant to note that, first found by Baranowski et al. (1971), see also Farrell and Lewis (1981), a negative deviation occurs from the linear correlation between the increment of the volume of the unit cell and hydrogen concentration, starting from the metal/hydrogen ratio of about 0.6–0.7. A possible reason for this may be the increase in the number of hydrogen atoms occupying single vacancies and their clusters.

2.1.2 Hydrogen-Induced Vacancies in Austenitic Steels In relation to vacancies induced by interstitial elements in the fcc substitution solid solution, calculations were performed by Bugaev and Yanchitski (see in

2.1 Hydrogen-Induced Vacancies

49

Gavriljuk et al. 1996) using the mean-field self-consistent approximation developed by Khachaturyan (1983) and Bugaev et al. (1988). The equilibrium concentration of vacancies, C V , was obtained as C V0 CV = exp 1 + CV − C X



 f X C X + f X −X C X2 − Pv , kB T

(2.3)

where C V0 is the vacancy concentration in the substitution solid solution in the absence of interstitials, C x = N x /N is the concentration of interstitials and N x , N are the numbers of interstitial and host atoms in a crystal, respectively, f X describes the effective energy of X-atom injection, which is spent on overcoming the intercrystal field due to lattice relaxation, f X −X is an effective contribution related to chemical and strain-induced interactions between interstitial atoms, P is pressure, V is the volume of the primitive unit cell, k B is the Boltzmann constant and T is absolute temperature. Following from (2.3), the concentration C V increases with the content of interstitial atoms C x . The maximum possible concentration of vacancies can be reached if    f x C x + f x−x C x2 − Pv Cvmax = Cv0 exp (2.4) kB T In general, C v max cannot be really obtained because of the limited solubility of interstitials or the loss of matrix phase stability with respect to polymorphic transformation. At reasonable C x = 0.5, f x = 1.0 eV, k B T = 0.1 eV, a rough estimation of C v in relation to those in the interstitials-free crystals provides the value   1 fx Cx Cv ≈ 300 = exp 1 − Cx kB T C V0

(2.5)

It also follows from (2.3) and (2.4) that pressure P should decrease the concentration of excessive vacancies in the presence of interstitials.

50

2 Crystal Lattice Defects

Fig. 2.2 Dislocation loops in steel containing, mass %, 18.48Cr, 16.3Ni and 9.64Mn: a the contrast of loops in the light of reflection g = (111)γ ; b the condition g · b = 0 is reached when g2 = (422)γ is operating

Experimental tests on vacancies induced by hydrogen in austenitic steels were carried out using transmission electron microscopy, see Fig. 2.2 (Gavriljuk et al. 1996). Numerous plane vacancy discs have been found in austenitic steel Cr18Ni16Mn10 after hydrogen charging, see Fig. 2.2a. To determine the type of dislocations encasing these vacancy discs, a procedure involving the tilting of the sample in the microscope was carried out to reach the relation g · b = 0 between the crystallographic orientations of electron beam g and Burgers vector b at which the image of the loops should disappear, see Fig. 2.2b. From the obtained Burgers vector b = (a/3) < 111 >, one can conclude that the plane vacancy discs are encased in the dislocation loops of the sessile Frank dislocations type. These loops are typical of quenched or irradiated fcc metals where a high density of vacancies occurs resulting in Frank dislocation loops on {111} planes with stacking faults of the vacancy type. For example, one can refer to the studies carried out by Kikuchi et al. (1974) on austenitic nitrogen steels. These authors observed plane quenching defects formed in a CrNi austenitic steel alloyed with 0.5 mass% of nitrogen after ageing at 750 °C leading to nitride precipitation from the solid solution. Moreover, Kikuchi (1985) observed that chromium diffusion in austenitic steels is

2.1 Hydrogen-Induced Vacancies

51

accelerated by dissolved nitrogen. Both of the observed effects can be attributed to nitrogen-induced superabundant vacancies which enhance Cr atom diffusion and become non-equilibrium after nitride precipitation thereby forming planar vacancy clusters. Further on, we will return to the analysis of hydrogen-induced vacancies in metallic materials while discussing a mechanism for hydrogen-accelerated diffusion of metallic atoms, see Chap. 3, and hydrogen-caused localization of plastic deformation, as well as the available hypotheses for hydrogen embrittlement, see Chap. 5.

2.2 Interaction Between Hydrogen Atoms and Dislocations The extremely high mobility of hydrogen atoms in metallic crystal lattice brings about particular effects in hydrogen-dislocation interaction and, consequently, affects the mechanical behaviour of metallic materials. Excluding deep cryogenic temperatures, hydrogen atoms can accompany dislocations in the course of their slip. The value of enthalpy for binding between hydrogen atoms and dislocations is essential for the realization of this phenomenon. Generally, two kinds of interactions, elastic and chemical, result in the formation of, respectively, Cottrell and Suzuki interstitial atom atmospheres around dislocations. The former arises from local lattice distortions caused by interstitial atoms, which are decreased if dissolved interstitials are accumulated in the vicinity of dislocations. The latter is caused by a local change in the interatomic bonds within the stacking faults of split dislocations. Usually, elastic interaction prevails over chemical. The electron contribution to interaction between interstitials and dislocations has often been mentioned but never really proved. At the same time, a local change in the character of interatomic bonds within the clouds of interstitial atoms around dislocations, namely their enhanced metallic or covalent character, is expected to affect the specific energy of dislocations, i.e. their line tension, and, consequently, change their mobility. We shall discuss how the above factors contribute to the enthalpy of hydrogen atom binding to dislocations, as well as to dislocation mobility. If relevant, comparison with the effects of other interstitial elements, carbon and nitrogen in metals, will also be analyzed. Before this analysis, let us describe the dislocation splitting controlled by stacking fault energy, SFE, the hydrogen effect on it and the consequences for dislocation properties.

52

2 Crystal Lattice Defects

2.2.1 Stacking Fault Energy Dislocations in close-packed fcc crystals are split because their Burgers vector b corresponds to rather large atomic displacements on the slip plane. A much smaller applied stress and, consequently, smaller energy are required for dislocation slip via two consecutive shifts performed by partial dislocations (see Figs. 2.3 and 2.4). The leading partial dislocation with Burgers vector bl changes the alternation of atomic planes from an fcc lattice to an hcp one thereby producing a stacking fault, whereas the trailing dislocation bt completes this shift recovering the fcc lattice behind itself. Dislocation splitting is high in stainless austenitic steels having the fcc crystal lattice and rather low in ferritic and pearlitic construction steels and β-titanium alloys with the bcc crystal lattice. In a rather strange way, despite its fcc crystal lattice, nickel is characterized by a high SFE. According to Beeston et al. (1968), who estimated the SFE studying the rolling texture, it exceeds 200 mJ/m2 , which is comparable with that in the bcc iron. Using the weak electron beam technique, Carter and Holmes (1977) obtained ~120–130 mJ/m2 . The SFE of less than about 100 mJ /m2 is conventionally considered to be low, see, e.g., Obst and Nyilas (1991). Fig. 2.3 Atomic displacements in the fcc crystal lattice plane {111}during the slip a → c of a perfect ½[101] dislocation in comparison with the consecutive slips a → b and b → c of leading (1/6)[211] and trailing (1/6)[112] partials, respectively

Fig. 2.4 Split dislocation ½[101] under applied shear stress in an fcc lattice

2.2 Interaction Between Hydrogen Atoms and Dislocations

53

In the absence of applied loading, dislocation splitting is wholly controlled by the interatomic bonds. As first shown by Noskova et al. (1965), an inverse correlation exists between the SFE and the electron structure, namely the density of electron states at the Fermi level in metals, which in turn is proportional to the concentration of free electrons. The higher the concentration of free electrons, the lower the SFE should be. Some exceptions to this prediction occur. Increasing the density of electron states at the Fermi level and, consequently, the concentration of free electrons, see Chap. 1, hydrogen is expected to decrease SFE in accordance with the aforementioned correlation reported by Noskova et al. (1965) Controlling the width of dislocations, the SFE is responsible for a variety of dislocation substructures formed during the straining of metallic materials. Depending on the value of SFE, dislocation slip, deformation twinning or strain-induced phase transitions can be realized. Slip prevails at a high SFE which narrows dislocations and therefore eases the change of the slip plane for screw dislocations in the course of deformation, resulting in the so-called “wave slip”. Some middle SFE values assist a mixed substructure with twinning and dislocation slip. Strain-induced transformations can occur at a sufficiently low SFE, e.g. the γ → ε transformation in fcc iron alloys. It should also be noted that, in order to avoid the mutual influence of stress fields created by neighbouring dislocations, measurements of dislocation splitting and the corresponding estimation of SFE values are correct only under the conditions of low dislocation density. This can be achieved by annealing at elevated temperatures. The obtained “true” stacking fault energy depends only on the chemical composition of metallic materials and serves as a measure of their thermodynamic stability. In the cold worked or quenched states, dislocation splitting depends on the acting internal stresses and does not really characterize the stacking fault energy.

2.2.1.1

Hydrogen Effect on Stacking Fault Energy

Based on X-ray diffraction measurements, the first correct measurement of stacking fault energy γ in hydrogen-charged austenitic steel AISI 304 (18.2Cr, 9.0Ni, 1.2Mn in mass %) was carried out by Pontini and Hermida (1997). For numerical estimations, the authors used an expression proposed earlier by Schramm and Reed (1975): γ =A

2 >111 < ε50 (J/m 2 ), α

(2.6)

where 2 < ε50 >111 is the mean square microstrain over a column 50 Å long in the direction,

α is the intrinsic fault density on the {111} planes, A is a calibration constant.

54

2 Crystal Lattice Defects

Table 2.1 Stacking fault energy γ (mJ/m2 ) in steel AISI 304 (Cr18Ni9) before and after hydrogen charging and its corresponding reduction at three temperatures (Pontini and Hermida 1997)

Temperature (K)

Before

After

Reduction in γ (%)

293

30.4

19.2

37

206

25.7

15.6

39

77

19.5

11.5

41

The obtained values of stacking fault energy before and after hydrogen charging are presented in Table 2.1 for different temperatures. Therefore, hydrogen effect on the SFE is consistent with the aforementioned change in the electron structure. Steel AISI 304 is thermodynamically unstable, which is evidenced by a reduction in the SFE with decreasing temperature even in the absence of hydrogen. The cold work or cooling of this steel down to low temperatures causes the γ → α transformation where the ε-martensite is an interim phase. Thus, decreasing the SFE, hydrogen assists the γ → α transformation in this steel (see Chap. 4 for detail). In a more stable austenitic steel of the AISI 316 (Cr18Ni14) type and even in the stable steel AISI 310 (Cr25Ni20), where neither cold work nor a deep cryogenic temperature causes any phase transitions, hydrogen induces the γ → ε transformation during electrochemical charging and the ε-phase remains stable for a rather long time at RT (e.g. Kamachi 1978, Narita et al. 1982 etc.). Studying in situ the hydrogen effect on dislocation splitting in the transmission electron microscope, Ferreira et al. (1996) have found that the stacking fault energy in the 310 austenitic stainless steel is reduced by approximately 19% under 40 torr of hydrogen. The effect of hydrogen on the SFE in Ni was estimated by Windle and Smith (1968) based on the data obtained by Beeston et al. (1968) and on the analysis of activation energy for the cross slip of dislocations at low temperatures proposed by Haasen (1958). Thereafter, the hydrogen effect on the splitting of screw dislocations in nickel was simulated by Wen et al. (2005) using the embedded–atom potential. They showed that, when uniformly distributed on the slip plane, hydrogen atoms increase separation between partial dislocations. Such a reduction in stacking fault energy should prevent the cross-slip of dislocations, which is consistent with the observations performed earlier by Boniszewski and Smith (1963) and Windle and Smith (1968) about hydrogen-induced planar dislocation slip in nickel.

2.2.1.2

Splitting of Dislocations Under Applied Stress

Discussed below is an unusual hydrogen effect in metallic materials under conditions of their permanent mechanical loading. As mentioned above, the SFE can be correctly measured only in the absence of neighbouring dislocations, i.e. in the annealed state.

2.2 Interaction Between Hydrogen Atoms and Dislocations

55

The stress caused by mechanical loading or by retained stresses changes dislocation splitting. The nature of this effect can be understood if one takes into account the crystallographic texture and different orientation of the Burgers vector for leading and trailing partial dislocations (a/6) in the fcc lattice in relation to the applied stress, which results in the change of actual stresses on the partials (see Copley and Kear 1968 for detail). Consequently, the splitting or narrowing of dislocations can be described by the so-called effective stacking fault energy: γeff = γ0 ± 1/2(m 2 − m 1 )σ b,

(2.7)

where γ 0 is the equilibrium value of SFE, m2 and m1 are the Schmid factors for leading and trailing partials, respectively, σ is the applied uniaxial stress and b is the Burgers vector modulus for (a/6) partial dislocations. The sign ± distinguishes between tensile (+) and compressive (−) stresses. The scheme in Fig. 2.5 illustrates the dependence of mechanical properties of single crystals on their crystallographic orientation. Splitting of dislocations occurs in “soft” and orientations, whereas their narrowing is observed in the “hard” orientation of single crystals along the tension axis of the samples. The inverse result is obtained in the case of compressive tests. Depending on the crystallographic orientation of single crystals or grains in polycrystals, the hatched crystallographic areas correspond to the hard or soft mechanical behaviour of materials. Hydrogen in austenitic steels can strikingly change the response of dislocation splitting on the applied mechanical stress. Corresponding stress-elongation curves

Fig. 2.5 Variation of shear stress on leading and trailing dislocations with a tensile (compressive) axis orientation. Redrawn from Copley and Kear (1968), Elsevier

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Fig. 2.6 Stress-elongation curves of hydrogen-free steel Cr18Ni10N0.2 single crystals differently oriented in relation to the tension axis on the plane {110}

obtained in the tensile tests of the hydrogen-free single crystal austenitic steel Cr18Ni10N0.2 are shown in Fig. 2.6 (Teus et al. 2008). In accordance with the predicted change of tensile properties, as shown in Fig. 2.5, the yield strength and cold work hardening are the highest for the “hard” orientation and the lowest for the “soft” orientation. The highest relative elongation is obtained in the case of the direction, which is explained by the most favourable conditions for the slip of partials (a/6) at sufficiently large splitting of perfect dislocations (a/2). However, after hydrogen charging, the relationship between the mechanical properties of differently oriented crystals becomes contrary to predicted, see Fig. 2.7. Now, the lowest strength is obtained for the originally “hard” direction , whereas higher strengths are observed for the originally “soft” and orientations. Again, single crystals with the orientation acquire the highest plasticity. It follows from this result that, along with dislocation splitting, hydrogen causes an additional effect. A reason for this has been found using X-ray diffraction measurements. Figure 2.8 presents the superimposed fragments of X-ray diffraction patterns from hydrogen-charged single crystals cut on the {110} plane in the and directions. All the samples were deformed by 15% tension prior to diffraction measurements. In the case of hydrogen charging and subsequent tensile deformation of samples with the orientation, X-ray diffraction turned out to be different, namely the (10.1)hcp reflection of εH -martensite was present instead of (111)fcc . No reflections were obtained from the hydrogen-charged deformed samples cut along the direction.

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Fig. 2.7 Stress-elongation curves of preliminary hydrogen-charged steel Cr18Ni10N0.2 single crystals differently oriented in relation to the tension axis on the plane {110}

Fig. 2.8 X-ray diffraction from hydrogen-charged single crystals cut in and directions on the {110} plane. Tension by 15% before diffraction measurements in Fe Kα radiation

These results can be interpreted taking into account the formation of crystallographic texture under plastic deformation, the hydrogen effect on the stacking fault energy of austenitic steels and different splitting of dislocations under retained stresses in hydrogen-charged single crystals deformed in different crystallographic orientations.

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Hydrogen charging decreased stacking fault energy and, moreover, the subsequent tensile deformation enhanced dislocation splitting because of a higher stress on the leading dislocation than on the trailing one in the case of tensile loading in the direction, which resulted in γ → ε transformation. In contrast, despite the Hcaused decrease in SFE, the ratio between retained stresses acting on the leading and trailing dislocations in the oriented samples is such that dislocation splitting decreases. At the same time, the crystallographic texture led to the absence of the expected (002) reflection in the 2 range of 55°–61°. It is the hydrogen-induced ε-martensite that changed the strength of differently oriented single crystals and “hardened” the previously “soft” and directions. Correspondingly, the previously “hard” direction was transformed into a “soft” one. It follows also from the comparison of stress-elongation curves for oriented single crystals in their hydrogen-free and hydrogen-charged states that, in the absence of ε-martensite, hydrogen causes a significant softening regardless of the crystallographic orientation. This effect is obviously caused by the hydrogen-increased concentration of free electrons, i.e. by the enhanced metallic character of interatomic bonds, as shown in Chap. 1.

2.2.2 Hydrogen Softening-Hardening It is generally accepted that interstitial atoms in diluted solid solutions with a bcc crystal lattice are expected to ease the nucleation of kinks on screw dislocations. A possible reason for that is a local change in the Peierls relief of the crystal lattice. In this way, kinks alleviate the gliding of screw dislocations. This is not the case for edge dislocations. A fundamental review of early theories related to this topic was presented by Pink and Arsenault (1979). For illustration, see their computation results in Fig. 2.9 for oxygen in niobium. If all the other obstacles are overcome by a dislocation at constant applied stress, the stress needed for the slip of a screw dislocation can be decreased due to doped oxygen. However, starting from a certain oxygen content, the stress permanently increases and the general situation remains undetermined. The slip of edge dislocations is retarded at any concentration of interstitial atoms. In relation to hydrogen, the idea of two-fold hydrogen enhanced/impeded dislocation mobility has been widely discussed. For example, Deng and Barnoush (2018) studied the hydrogen effect on the nucleation and emission of dislocations at the crack tip and their emission during its growth in a single crystalline FeAl intermetallic alloy subjected to applied stresses. The authors observed hydrogen-caused facilitation of dislocation nucleation followed by subsequent suppression of their mobility when the emitted dislocations could not move from the crack tip. This increased/decreased movement of dislocations was repeated again accompanying crack growth. This

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Fig. 2.9 The stress required to maintain an average dislocation velocity of 10−5 cm/s as a function of oxygen concentration in niobium. Redrawn from Pink and Arsenault (1979), Elsevier

result was confirmed in a similar study performed by Rogne et al. (2018) on the Fe–26Al–0.5Cr alloy. The authors reasonably attributed the case of impeded dislocation mobility to the increasing mutual repulsion of emitted dislocations in the slip plane blocked by some obstacles and/or dislocation locks created with dislocations from other slip planes, i.e. Lomer-Cottrell barriers. This is the well known mechanism for formation of dislocation pile-ups. However, such impediment occurs in any deformed H-free metals, bears no relation to the intrinsic hydrogen effect on dislocation velocity and cannot be interpreted as hydrogen-caused suppression of dislocation mobility. Another experiment with the hydrogen effect on dislocation mobility was carried out by Xie et al. (2016). The authors prepared a thin single-crystal Al pillar with the diameter of ~620 nm transparent for TEM observations, used preliminary ‘cyclic healing’ to reduce the number of dislocations to five, and analyzed the effects of mechanical cycling on the position of each dislocation after electron beam irradiation, hydrogen charging and ageing. As a result, they observed that all five dislocations stood firm despite 85 loading cycles after hydrogenation. Based on this experimental data, and claiming that “vacuum ageing and e-beam irradiation only tend to facilitate dislocation motion”, the authors concluded that “the observed absence of dislocation motion is due to the effect of hydrogen” attributing this phenomenon to a “hydrogen locking of dislocations”. An essential objection against this conclusion is related to the use of electron irradiation. Along with vacancies, electron irradiation produces supermobile selfinterstitial atoms which migrate to dislocations, grain boundaries and free surfaces. On reaching dislocations, these atoms block their mobility, which was first discovered by Karl Lücke and was for many years thereafter demonstrated for visitors at

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the Max Planck Institute in Aachen, Germany. Moreover, combined with hydrogen charging, electron irradiation creates H-V complexes, the mobility of which should be lower in comparison with that of separate vacancies and hydrogen atoms. Bound with dislocations, these complexes are expected to limit their mobility. As a relevant example, one can mention the complexes formed by vacancies with carbon or nitrogen atoms due to bcc iron irradiation, having the binding energy of ~0.8 eV and stable at up to 250 °C, see Weller and Diehl (1976). The formation of vacancy-H complexes in α-Fe was confirmed in the atomistic modeling performed by Zhu et al. (2017) using the embedded atom method and molecular dynamics. A moving edge dislocation was shown to attract these complexes and be pinned by them. In addition, it is worth noting that the hydrogen-increased velocity of dislocations in pure Al has been demonstrated by Bond et al. (1988) in their in-situ TEM observations. The hydrogen- caused softening of aluminium was also found in the macroscopic mechanical tests performed by Zeides (1986). The hydrogen-affected kinking of a screw dislocation in iron was also simulated by Wen et al. (2003) using the nudged elastic band method. The authors found that, if a kink pair is nucleated in the vicinity of a hydrogen atom, the activation energy decreases or increases depending on the transition of the hydrogen atom to a stronger or weaker binding site, respectively. If the kink pair meets a hydrogen atom during kink pair expansion, its sideward motion is impeded by hydrogen. The results obtained from experimental studies concerning the hydrogen effect on dislocation slip are contradictory. Partly, this may have been caused by different experimental conditions. For this reason, let us analyze the studies where tensile tests have been combined with hydrogen charging versus those with separated charging and testing. Synchronised charging and testing. One of the pioneering studies was performed by Bernstein (1974) on hydrogen in α-iron. In contrast to earlier measurements carried out by Adair (1966), where severe hydrogen charging was used, Bernstein worked with hydrogen contents of about 2–7 ppm introduced using cathodic charging at a moderate current density of 1 mA/cm2 . As a result, he observed a decrease of the friction stress σ0 in the Hall–Petch equation σ y = σ 0 + k y d −1/2 with d and k y as the grain size and the unblocking constant, respectively. This result showed unambiguously that hydrogen eases dislocation slip. What was also remarkable in his study is the absence of strain hardening in the hydrogen-charged samples at stresses above yield strength. Later on, in the seventies-eighties, a more detailed analysis was performed by Kimura and colleagues in a large series of measurements. Like Bernstein, they used a combination of tensile tests with synchronised cathodic hydrogen charging. Using this technique, Matsui et al. (1979) have found softening in the stress–strain curves at temperatures above 190 K, whereas hardening occurred below this temperature. The most intriguing in their studies was a sharp decrease in the flow stress down to about 50% of its original level if the charging current has been switched on. On its subsequent switching off, the flow stress began to gradually increase and recover

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to the roughly the same stress level as before charging. This drop-effect was also observed by Lunarska and Wokulski (1982) in their experiments carried out on the iron whiskers using the same technique. Matsui et al. (1979) traditionally interpreted softening in terms of hydrogenincreased mobility of screw dislocations due to some modification of the Peierls relief. Hardening has been attributed to pinning the kinks on screw dislocations if the concentration of hydrogen at the dislocation cores became large and temperature decreases. The edge dislocations were claimed to be always pinned by hydrogen atoms, see also Kimura and Matsui (1987). Of course, one can note that a more simple interpretation of the observed transition from hydrogen-caused softening to hardening with decreasing temperature can be given independently on the dislocation type. One should take into account the increase in the binding of hydrogen atoms to dislocations and delay of hydrogen migration with decreasing temperature. While accompanying the dislocation slip, hydrogen atoms can enhance mobility of dislocations decreasing their line tension, see Sect. 1.5.4 in Chap. 1. However, be immobile at sufficiently low temperatures, they turn out certainly to the pinning points. The migration enthalpy of hydrogen atoms in the bcc iron is uniquely small, see Chap. 3, and they retain diffusivity at sufficiently low temperatures. Consequently, hydrogen softening observed by Kimura and his colleagues could occur at temperatures down to 190 K and to be transformed to hardening at lower temperatures, where H migration has ceased. At the same time, noteworthy are two following features of experiments conducted by Kimura them: (i) the H-induced softening did not occur if the iron samples contained some impurities even in spite of their preliminary refining in the wet or dry hydrogen, (ii) softening was completely absent in the substitutional iron-based solid solutions even if the latter were extremely diluted. Oguri and Kimura (1980) attributed the both these features to formation of hydrogen complexes with impurity atoms. This idea was tested by Oguri et al. (1982) in their studies of hydrogen effect on the flow stress in high purity Fe–C alloys. At temperatures between 170 K and RT, hydrogen induced softening if carbon concentration was smaller than it is needed for the highest solid solution softening in the H-free Fe–C alloys. If the carbon content was beyond that, hydrogen caused hardening. At variance with the mentioned results and derived conclusions, only softening was observed by Kimura and Birnbaum (1987) in the pure iron at temperatures between 77 and 300 K, if hydrogen was introduced into samples using plasma charging. Moreover, the hydrogen-assisted dislocation slip and the hydrogenincreased mobility of dislocations occur in many materials of commercial purity independently of the type of dislocations. Using transmission electron microscopy, the accelerated movement of dislocations was observed due to hydrogen charging of commercial austenitic steels (Ferreira et al. 1998), nickel with varying carbon content (Robertson and Birnbaum 1986), ferritic steels and titanium alloys (Robertson et al. 2015), high-purity aluminium (Ferreira et al. 1998) etc.

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It is also important that, independently of stacking fault energy, the hydrogen effect on dislocation mobility is qualitatively the same in different metallic materials. Therefore, the width of dislocations and the Peierls relief cannot be decisive factors controlling the effect of hydrogen on dislocation mobility. Taking into account this analysis, the following tentative interpretation can be proposed for understanding the inconsistency between results obtained by Kimura et al. and many researchers in the subsequent studies. While interpreting their experiments, Kimura and his colleagues did not take into account the effect of electroplasticity, which is expected in case of stress–strain tests combined with the cathodic hydrogen charging. The electric current in pure metals causes an electron wind dragging the dislocations, which was firstly reported by Troitskii and Lichtman (1963). Later on, electroplasticity has been studied in detail in the experiments relating with the flow stress (Spitsyn and Troitskii 1975), stress relaxation (Troitskii et al. 1980), dislocation generation and their mobility (Zuev et al. 1978) etc., see also the review articles presented by Sprechner et al. (1986) and Conrad et al. (1990). The electron drag coefficient Be can be given by the following expression: ( f /l) = τ b = Be vd ,

(2.8)

where f /l is a force acting on the unit length of dislocation, τ is a shear stress, b is the Burgers vector, vd is dislocation velocity. The experimental data reported by Kimura and colleagues inherently are expected to include the electroplastic effect for the following reasons. First, the hydrogencaused softening has been found by them only in the extremely pure iron, and this is just a feature of electroplasticity, where the effect of electron wind was observed only in metals of high purity. Second, the instantaneous decrease in the flow stress, as observed by Matsui and Kimura (1979), is consistent with the instant response of free electrons and hardly expected for the behavior of hydrogen atoms at dislocations. Separate charging and testing. A rather confused picture of hydrogen effect on the yield strength and hardness of metals has been obtained in case of testing the preliminary charged samples, which became a subject of numerous debates since the fifties. Rogers (1954) studied a hot-rolled commercial steel SAE 1020 after annealing at 600 °C in the dry hydrogen for removing the interstitials, subsequent annealing under vacuum at the same temperature and strain by 15% at −78 °C. A third part of pre-strained samples was aged at 25 °C, and another third part was electrolytically charged with hydrogen at room temperature in 4% H2 SO4 . Thereafter, all three groups of samples, namely the pre-strained, aged and hydrogen-charged ones, were

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undergone the mechanical tests at −150 °C. The yield point has been present in the hydrogen-charged samples and in neither of the others. Remarkably, the yield point was not observed if mechanical tests were carried out above −120 °C. Thereafter, Cracknell and Petch (1955) have reported that cathodic hydrogen charging can eliminate the yield point at room temperature. They studied fifteen different steels, from a well pure iron to a steel with 0.62%C, and compared the annealed state with that after charging in 4% H2 SO4 at current density of 465 mA/cm2 . The yield point occurred in the annealed state and was being progressively removed with increasing time of hydrogen charging. The authors supposed that suppression of the yield point was caused by inhomogeneous stresses arising from the accumulation of hydrogen under high pressure in the internal cavities. In contrast to these observations, using the testing temperature of −150 °C and varying the temperature of pre-strain and ageing between −70 and −150 °C, Adair and Hook (1962) have concluded that the hydrogen-caused yield point, as well as its disappearance and return, are similar to that observed for carbon and nitrogen and can be unequivocally explained by the binding between hydrogen atoms and dislocations. The hydrogen-caused strain hardening of iron is also debatable. Farrell (1965a, 1965b) has found the hydrogen-increased hardening in the mild steel containing of about 0.07%C after charging in 10% HCl solution not depending on the current densities. He attributed this result to the hydrogen gas pressure in some internal voids rather than to the interaction between hydrogen atoms and dislocations. However, earlier Bastien and Azou (1951) reported the hydrogen-decreased strain hardening of the iron. The increase in the flow stress caused by hydrogen has been also found by Yanchishin et al. (1974) and Asano and Otsuka (1976) in the iron, as well as by Ulmer and Altstetter (1991) in the austenitic steel. Along with strengthening, a toughening was observed in the low alloyed ferritic steel by Singh and Sasmal (2004). They observed the hydrogen-caused increase in the yield and ultimate strength along with the increased relative elongation, whereas the effect on the strain hardening was not remarkable. A feature of all the mentioned results was that, with rare exceptions, the measurements were performed using a severe cathodic charging. In contrast, Tobe and Tyson (1977) studied a vacuum melted electrolytic iron and a commercial quenchedtempered steel after gaseous hydrogenation up to several H ppm at hydrogen pressure of 1 bar at elevated temperatures. In both cases they observed the H-caused increased yield stress, strain hardening and serrated flow at testing temperatures of −150 °C up to RT. Some attempts to explain the scattering of experimental data on softeninghardening were undertaken by Birnbaum (1994) and Robertson et al. (2009). Among discussed ideas, the irreversible damage in the form of the voids, gas bubbles and enhanced dislocation densities near the surface have been proposed. In this relation, let us analyze the effect of hydrogenation technique on the softening-hardening. Shown in Fig. 2.10 are the results of nanoindentation tests of a low alloyed steel after charging under hydrogen gas pressure and in the electrolyte (Zhao et al. 2015).

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Fig. 2.10 Hardness as a function of nanoindentation strain rate in the low alloyed steel 0.07C–1.2Mn–0.15Si subjected to hydrogen electrochemical or gaseous charging. A fragment of data obtained by Zhao et al. (2015), Fig. 1, Elsevier

A clear hardening by the electrochemical charging and softening by the gaseous one has been demonstrated. Using thermodesorption spectroscopy, the authors have found that, in contrast to gaseous charging, a significantly higher hydrogen content, more than by one order of magnitude, was absorbed in the electrochemically charged samples by the weak trapping sites (dislocations and grain boundaries). Based on this remarkable difference, they interpreted the obtained results in terms of a change from softening to hardening with increasing hydrogen content. However, one should note that the increased content of trapped hydrogen in the electrochemically charged samples in comparison with the gaseous charged ones can evidence first of all a higher density of dislocations as trapping sites. Additionally, the authors presented data of measurements which allow a quite different interpretation. They detected a sharp gradient of hydrogen concentration in the samples subjected to electrochemical charging and its absence in case of the gaseous one. This result suggests that a higher density of dislocations can be a real reason for the large amount of absorbed hydrogen in the electrochemically charged samples. These dislocations could be generated by plastic deformation because of hydrogen concentration gradient and corresponding stresses. Therefore, one can suppose that cold work hardening accompanies the electrochemical charging. In turn, softening could occur due to the hydrogen-weakened interatomic bonds, which is expected because of the increased concentration of free electrons in the vicinity of dislocations encased in the hydrogen Cottrell’s atmospheres (see Chap. 1). The proposed interpretation is free of the not justified assumption about softening and hardening in dependence of hydrogen content. The occurrence of plastic deformation during electrochemical hydrogen charging and its effect on hardening will be analyzed in more detail in Chaps. 3 and 5. In addition, it is relevant to note that the effect of solute atoms on mechanical behavior of metals with a special focus on hydrogen has been analysed by Kirchheim (2012) who discussed the phenomenon of softening-hardening based on his defactants concept. Term “defactants” includes any solutes which segregate to defects in materials in contrast to “surfactants” denoting the surface-active chemical elements.

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According to Kirchheim, two factors related with solute atoms control the strain rate: time τ g for double kink generation and time τ m necessary to move the kinks to the ends of a dislocation segment. Segregating to the kinks, solute atoms reduce the energy for kinks formation and, therefore, decrease τ g , as it is generally admitted. Under condition τ m  τ g , it leads to the increased strain rate, i.e. to softening. With increasing contents of solutes, they increase the dragging force on the moving kinks, which increases τ m and can reverse the above written condition to τ m  τ g . For this reason, the hydrogen drag on the kinks dominates over hydrogen enhancement of kink formation and results in a decreased strain rate, i.e. in the hardening. Unfortunately, this approach ignores the nature of solutes as chemical elements, interpreting solute atoms just as the point centres of elastic dilatation in the crystal lattice. Beside this, the Peierls barrier is shallow in fcc metals and plays no role in plastic deformation. Consequently, mobility of dislocations under applied stress is controlled by their intersections, not by kink formation, see the theory of yield stress in fcc crystals having low-stacking fault energy (Seeger 1954, 1955) and its verification by Obst and Nyilas, (1991), Nyilas et al. (1993), Gavriljuk et al. (1998) in austenitic steels, and Obst (1998) in Cu, CuNiMn and AlMgMn alloys. Moreover, hydrogen increases dislocation mobility in metals regardless of the type of crystal lattice. An interesting effect of hydrogen softening-hardening in fatigue measurements was detected by Murakami et al. (2010) who observed a non-monotonous dependence of the fatigue life for crack initiation in 304 and 316 type steels on hydrogen concentration. The crack growth was shown to be enhanced with hydrogen content increasing from 2.2 to 23.9 wt ppm and reduced in the samples containing between 70.4 and 89.2 wt ppm of hydrogen. The interpretation proposed by the authors was based on the hydrogen-caused pinning-unpinning of moving dislocations and the blocking of the plastic zone at the crack tip by the surrounding materials having a higher flow stress because of a larger hydrogen concentration. Kirchheim (2012) discussed this phenomenon in terms of the above mentioned τ m < τ g at low H content and reaching τ m > τ g with higher H content. In fact, a possible reason for the Murakami effect can be related to the specific nature of cyclic plastic deformation and the hydrogen effect on slip planarity. The combination of fatigue plastic deformation reversibility and planar slip results in the reverse gliding of dislocations on the same planes, annihilating dislocations of opposite signs. A corresponding softening was observed in nitrogen austenitic steels by Degallaix et al. (1986) and Taillard and Foct (1989) and interpreted as a result of the reverse gliding of dislocation arrays in the opposite direction, which requires a lower applied stress. The point is that hydrogen and nitrogen in austenitic steels are similar in their effect on the electron structure, i.e. an increase in the concentration of free electrons and the initiation of planar slip, see Gavriljuk et al. (1993), Shanina et al (1999), Gavriljuk and Berns (1999). Fatigue crack growth in austenitic steels decreases with increasing nitrogen content, as shown by Vogt et al. (1991) and Nyilas et al. (1993).

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Therefore, it is natural to expect the same hydrogen effect in fatigue experiments on austenitic steels.

2.2.2.1

Hydrogen Elastic and Electron Contributions to Mobility of Dislocations

The temperature-dependent and strain-dependent internal friction, TDIF and SDIF, both affected by the binding of impurity atoms to dislocations, serve as appropriate means to study the effect of solute atoms on dislocation properties. Snoek-Köster relaxation, S-K one in the following, is measured using TDIF and originates from the vibrating movement of dislocations accompanied by migration of interstitial solute atoms. The SDIF represents the internal friction background and also exists in the absence of any relaxation phenomena. Like S-K relaxation, it is caused by stress-induced vibrations of dislocation segments, see Schoeck et al. (1964) and Rivière et al. (1976). In the both, TDIF and SDIF, damping is proportional to the area swept by dislocations in the course of their vibrations. Therefore, at a constant frequency of the applied alternating stress, it characterizes velocity of dislocations. The comparison of effects caused by hydrogen, carbon and nitrogen on the SK relaxation in the bcc iron and the SDIF in the fcc iron allows a possibility to distinguish between the elastic and electron contributions to mobility of dislocations under applied stress. The point is that hydrogen atoms in the iron-based solid solutions are negatively charged, see results of ab initio calculations in Chap. 1. Nitrogen ones also carry a negative electric charge, whereas the carbon ones are positively charged, which follows from the ab initio calculations, see Gavriljuk (2016), and bygone direct experimental measurements performed by Seith and Kubaschewski (1935) for carbon and Seith and Daur (1938) for nitrogen in austenitic steels. It is also important that hydrogen atoms induce much smaller elastic distortions than both nitrogen and carbon ones. At the same time, be oppositely charged, nitrogen and carbon atoms induce nearly the same elastic distortions in the bcc as well as in the fcc iron-based solid solutions, see e.g. Chen and Tang (1990) and Gavriljuk (2016). Therefore, the elastic factor should be smaller for hydrogen and nearly the same for carbon and nitrogen, whereas the electron factor is expected to be the similar for hydrogen and nitrogen and opposite for carbon. Relaxation phenomena. The S-K relaxation has been discovered by Snoek (1941) in the bcc iron and first time studied by Köster with co-workers in terms of its dependence on the interstitial contents and dislocation densities (Köster et al. 1954; Köster and Bangert 1955; Köster and Kampschulte 1961). A remarkable difference between the S-K peaks caused by carbon and nitrogen in the α-iron has been found by subsequent researchers. Kamber et al. (1961) were the first to report that nitrogen causes a higher S-K peak than carbon. To interpret this phenomenon, Mondino and Seeger (1977) referred to complexes created by the C, N atoms and single vacancies V1 . They attributed the higher S-K peak in

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the nitrogen-doped α-iron to the increased temperature for dissociation of C-V1 complexes in comparison with the N-V1 ones, which was earlier found by Weller and Diehl (1976). Therefore, at comparable interstitials content in the α-iron, a larger amount of nitrogen atoms could contribute to the S-K relaxation amplitude. However, as stated by Petarra and Beshers (1967), the Fe–C solid solutions studied by Kamber et al. were not sufficiently purified from nitrogen. The measurements on the iron samples which were highly purified from interstitials before their saturation by carbon or nitrogen have led Petarra and Beshers to a radical conclusion that only nitrogen atoms contribute to S-K relaxation, whereas carbon atoms even suppress it. Among available theoretical approaches to a mechanism of S-K relaxation, two main models proposed by Schoeck (1963) and Seeger (1979) are the most popular and deserve a more detailed analysis. Schoeck was the first to find that the source of relaxation comes from the movement of dislocations, not from migration of interstitials. In his interpretation, the dislocation segments bow-out under applied stress like the vibrating springs, and the transverse drag of interstitial atoms is their response to vibrations of dislocations. In contrast, instead of spring behavior of dislocations, Seeger analyzed vibrations of dislocations due to paired kinks formation on the screw dislocations, γ relaxation, interacting with carbon or nitrogen atoms and on the so-called 71°-dislocations, α relaxation, in presence of hydrogen atoms. The both models give the same expression for the relaxation strength, and the difference between them amounts mainly to the factors contributing to the activation enthalpy, HSK . As mentioned above, the S-K relaxation strength is proportional to the area crossed by dislocations during their vibrations, i.e. to intensity of S-K peaks in the internal friction spectra. If the elastic distortions caused by interstitial atoms play a dominant role in the kinks formation or spring-like bending of dislocations, any interstitials with comparable distortions in the solid solutions should cause the same strength of S-K relaxation. Keeping this in mind, let us analyze the S-K relaxation caused in the bcc iron by hydrogen, carbon and nitrogen. Presented in Fig. 2.11 are the data obtained by Takita and Sakamoto for S-K relaxation in the hydrogen-doped α-iron in comparison with the so-called α-relaxation at ~ 50 K in absence of hydrogen. The both relaxations are caused by the vibrations of the same 71°-dislocations. It is seen that the area under S-K peak is at least by one order of magnitude higher than that of α-relaxation. In other words, hydrogen increases mobility of dislocations in the α-iron. It would not go amiss in this relation to note that, interpreting the data obtained by Takita and Sakamoto, Hirth (1980, 1982) supposed that, along with the α-relaxation, the γ-relaxation caused by hydrogen atoms at screw dislocations in the bcc iron at ~280 K also contributes to the hydrogen S-K peak. If to accept in consistency with Seeger (1979) and Hirth (1982) that S-K relaxation is caused by formation of paired kinks on screw dislocations for carbon and nitrogen and on 71°-dislocations for hydrogen, such an interpretation seems doubtful for the following reason. In case of carbon and nitrogen, at frequencies of ~ 1 Hz, the temperature of SK relaxation in the bcc iron, ~ 230 °C significantly exceeds that for γ-relaxation,

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Fig. 2.11 S-K relaxation caused by hydrogen in the α-iron in comparison with α-relaxation arising from formation of paired kinks on the 71°-dislocations. Modified from Fig. 1 in Takita and Sakamoto (1976), Elsevier

~ 280 K. Exactly so, the temperature of hydrogen-caused S-K relaxation on 71°dislocation is higher than that of α-relaxation. It is relevant to note that both hydrogen and nitrogen increase concentration of free electrons in iron and, as will be shown in the following, their effect on dislocation mobility is similar. Therefore, hydrogen atmospheres at screw dislocations are expected to cause S-K relaxation at temperatures far above RT. However, the binding of hydrogen atoms to dislocations in the bcc iron is rather weak and, correspondingly, hydrogen atmospheres at dislocations are diluted at temperatures above RT so that the hydrogen S-K relaxation on the vibrating screw dislocations cannot be realized. For comparison, presented in Fig. 2.12 is the S-K relaxation in the Fe–C and Fe–N α-iron along with the Snoek relaxation which is caused by diffusion jumps of carbon and nitrogen atoms in the bcc crystal lattice and characterizes the content of interstitials in the solid solution before plastic deformation (see about details Gavriljuk et al. 2005, 2021). The Snoek peak characterizes the carbon and nitrogen content in the α-iron solid solution As seen from the comparison of corresponding relaxation peaks, despite a smaller nitrogen content in the α solid solution, the area under S-K peak is significantly higher in the nitrogen-doped iron alloy, which evidences the increased velocity of dislocations by nitrogen. The same difference between carbon- and nitrogen-caused S-K relaxations occurs in the carbon and nitrogen CrMo martensitic steels, see Fig. 2.13. The S-K relaxation strength is significantly higher if carbon is substituted for nitrogen. Strain-dependent internal friction (SDIF). Hydrogen effect on dislocation mobility in austenitic steels with their fcc crystal lattice can be clarified using measurements of the internal friction background which, as mentioned above, is

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Fig. 2.12 Snoek-Köster relaxation caused by carbon (a) and nitrogen (b) in the α-iron

also controlled by the vibrations of dislocations. Like the case of S-K relaxation, the level of SDIF is proportional to the area swept by dislocations and, at a constant vibration frequency, it is a measure of dislocation velocity. The first theory of the SDIF in the solid solutions containing foreign interstitial atoms has been proposed by Granato and Lücke (1956). It will be shortly described before discussing a rather extended array of results on the impurity-dislocation interactions obtained based on the SDIF measurements. The main idea of this model is that damping of mechanically-induced vibrations under applied stress results in the oscillatory movement of dislocation segments. The triple dislocation nodes block dislocation segments at their ends, whereas interstitial atoms are supposed to be weak pinning points along the segments line. If some external stress causing the strain ε smaller than its critical value εcr is applied to

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Fig. 2.13 Snoek-Köster relaxation caused by carbon and nitrogen in martensitic steels Cr15Mo1C0.6 and Cr15Mo1N0.62, respectively

a crystal, dislocations bow out between the pinning points. As soon as the force concentrated on the impurity atoms exceeds the enthalpy of binding between them and a dislocation, the latter moves away from the pinning points. A further increase in the applied stress should be large enough to initiate the start of dislocation sources followed by dislocation multiplication, i.e. the irreversible strain. This model ignores the temperature-activated character of the break-away of dislocations from the point defects. To improve it, Granato and Lücke (1981) took into account the weakening of interstitial atoms as the effective pinning points with increasing temperature. Serious critical remarks can be made relating to the application of Cranato-Lücke model for SDIF in the interstitial solid solutions. As shown in the experiments performed e.g. by Keh (1963) and Baird (1963), as well as in the theoretical considerations presented by Hirth and Lothe (1983), the stress needed to break the pinned dislocations from their interstitial clouds in the annealed materials is so high that it exceeds the yield stress and even the ultimate strength. Therefore, the emission of fresh dislocations by dislocation sources should occur before dislocation unpinning. As a result, the critical strain εcr , of which above the damping becomes to be strain-dependent, characterizes the start of microplastic deformation, not the break-away of existing dislocations. Just for this reason, the strain-dependent internal friction in the iron-based alloys is irreversible, as shown firstly by Dudarev (1988).

2.2 Interaction Between Hydrogen Atoms and Dislocations

71

Fig. 2.14 Hydrogen effect on the strain-dependent internal friction, Q−1 , in steel Cr25Ni20: 1 hydrogen-free state, 2 after hydrogen charging at 50 mA/cm2 for 48 h, 3 after subsequent hydrogen degassing at 100 °C. Measured at frequency of ~1 Hz and heating rate of 1.5 K/min

The results of SDIF measurements presented in Fig. 2.14 for the hydrogen-charged austenitic steel Cr25Ni20 (AISI 310 type) are consistent with such interpretation (see also Shyvanyuk et al. 2001). It follows from this Figure that hydrogen in the fcc iron solid solution significantly increases damping. In comparison with the hydrogen-free state, it also causes the earlier start of dislocation sources. Hydrogen degassing restores the initial value of damping with some small excess obviously caused by the increased density of dislocations due to severe cathodic charging. An important conclusion follows from the hydrogen-caused increase in the slope Q−1 /ε of the strain-dependent part in the Q−1 (ε) curve. This slope evidences a clear increase in the velocity of dislocations in presence of hydrogen. Remarkable is that, in the absence of hydrogen, additional dislocations created in the course of cathodic charging do not affect either the start stress for their emission or their velocity. These data are also supported by studies of strain-dependent internal friction, SDIF, caused by nitrogen and carbon in austenitic steels. Diffusion of these atoms in the fcc iron in the temperature range above 500 °C proceeds sufficiently fast to follow dislocations at strains of ~10−5 and vibration frequency of ~1 Hz. It is seen in Fig. 2.15 that, in contrast to carbon carbon and like hydrogen, nitrogen in austenitic steel Cr18Ni16Mn10 decreases the start stress for plastic deformation and increases velocity of dislocations. Similar results on dislocation mobility characterised by SDIF were observed in a number of hydrogen-charged austenitic steels. The hydrogen-affected strain-dependent internal friction was also studied in the nickel- and titanium-based alloys (Teus 2017, Teus et al. 2016). Shown in Fig. 2.16 is the SDIF in the nickel-based alloy Inconel 718. Like the SDIF in the austenitic steels, hydrogen decreases the start stress of dislocation sources and increases velocity of dislocations. Hydrogen degassing restores damping with a small residual effect of the increased dislocation density.

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Fig. 2.15 Strain dependence of internal friction in carbon and nitrogen austenitic steels

Fig. 2.16 Strain-dependent internal friction in the nickel alloy Inconel 718 in the hydrogen-free state, after hydrogen cathodic charging and after subsequent hydrogen degassing

2.2 Interaction Between Hydrogen Atoms and Dislocations

73

One can conclude that, like the data on the Snoek-Köster relaxation for the bcc iron, the strain-dependent internal friction presents the unambiguous evidence that hydrogen enhances mobility of dislocations in the fcc iron-based alloys, as well as in the nickel ones. Therefore, the effect of hydrogen and nitrogen on mobility of dislocations and its solutions in the iron and nickel correlates with the increase of concentration of free electrons caused by these interstitial elements. In contrast, the enhanced covalent character of interatomic bonds due to carbon reduces dislocation mobility. The obtained results give the evidence that the role of elastic distortions caused by interstitial elements in the solid solutions on mobility of dislocations is not dominating, which is at variance with the concept of defactants proposed by Kirchheim (2012), where the chemical nature of solute atoms was ignored. Not completely clear is how dislocation properties depend on the binding between interstitial atoms and dislocations. Particularly interesting is the interconnection between migration of hydrogen atoms, their affinity with dislocations and contribution from hydrogen binding with dislocations to their mobility.

2.2.2.2

Binding Between Hydrogen Atoms and Dislocations

The concentration of solute atoms within their atmospheres around the dislocations is described by the following relation (see Cottrell and Bilby (1949) and Hirth and Lothe (1983)):   β sin θ , c = c0 exp − r kT

(2.9)

where c0 is a concentration of solute atoms at distances of r = ∞ from a dislocation and β is proportional to the difference between the atomic volumes of the host and solute atoms in the solid solutions. In consistency with this equation, it is generally accepted that the enthalpy of binding between solute atoms and dislocations is mainly controlled by elastic distortions caused by solute atoms in solid solutions and dilatation in dislocation core. For this reason, the binding should be effective for edge dislocations with a significant hydrostatic component of distortions in their core and smaller in the case of screw dislocations, where no dilatation and only shear displacements occur. An electrochemical contribution arising from the difference between the density of valence electrons within the dislocation core and that at solute atoms is not properly estimated and generally accepted to be secondary. For instance, carbon and nitrogen atoms having identical size in the bcc iron are bound to dislocations with the enthalpy of ~0.8 eV, see e.g. Gavriljuk et al. (1976), although the formers carry a positive electric charge, whereas the latter ones are negatively charged, see e.g. Gavriljuk (2016). Hydrogen atoms cause larger volume distortions in the bcc iron crystal lattice

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in comparison with those in the fcc one. Consequently, as will be shown below, there is a remarkable difference in their binding to dislocations. The distribution of hydrogen atoms around the dislocations in the bcc iron has been studied by Lu et al. (2018) in their atomistic calculations using molecular dynamics. In consistency with the earlier ideas developed within the frame of continuum mechanics, it was revealed that hydrogen trapping occurs due to a hydrostatic stress around the edge dislocations and due to shear stresses in the vicinity of the screw ones. In the experimental studies, it has been first time analyzed for hydrogen in the α-iron by Gibala (1967) and in the austenitic steels by Atrens et al. (1977). Gibala studied the Snoek, S, and Snoek-Köster, S-K, relaxations aiming to clarify partitioning of hydrogen atoms between the solid solution and dislocations. Varying the hydrogen charging conditions, degree of deformation and temperature of ageing, he noticed a correlated change in the intensity of the both peaks and derived the energy H b H to be of ~0.28 eV for hydrogen-dislocation binding in the α-iron from the ratio between the intensities of S and S-K peaks. Later on, it was estimated as 0.22 eV by Sturges and Miodownik (1969) who studied the effect of hydrogen effusion from the deformed iron wire on the intensity of the S-K peak. The values of 0.26 and 0.24 eV were obtained from the frequency shift of the S-K peak by Conophagos et al. (1972) and by Kikuta et al. (1972), respectively. According to the ab initio calculations of hydrogen binding to screw dislocations in the bcc iron performed by Itakura et al. (2013) the binding energy is equal to 0.256 ± 0.032 eV. The highest value of 0.28 eV apparently corresponds to the saturation of dislocation cores by hydrogen. Some details of hydrogen distribution and density of contributing dislocations were discussed by Lunarska and Zielinski (1978) and Miner et al. (1976). It is relevant to note that, among the published data, only Kumnick and Johnson (1980) derived a rather large value of ~0.6 eV for hydrogen-dislocation binding from their measurements of hydrogen permeation through the deformed alpha-iron samples. As discussed later on by Myers et al. (1992), it is highly likely that this value includes a significant contribution from vacancies emitted by the intercrossed screw dislocations during plastic deformation. Studies performed by Atrens et al. (1977) on the austenitic steels were based on the mentioned above Granato-Lücke theory for the strain-dependent internal friction. The authors treated their experimental data using the first version of Granato-Lücke model and obtained H b H ~ 0.14 eV in CrNi austeinitic steels. No detectable effect from the change in the nickel content in these steels has been found. The quite different experimental technique based on the hydrogen-caused change in the temperature dependence of strain-dependent internal friction, Q−1 (ε), was used in the studies of austenitic steels (Gavriljuk et al. 2010), the nickel alloy Inconel 718 (Teus 2017) and the titanium alloy TiV10Fe2Al3 (Teus et al. 2016), see Figs. 2.17, 2.18 and 2.19. As already mentioned, at strains higher than εcr , damping corresponds to the start of plastic deformation and represents the emission of new dislocations. According to measurements of hydrogen Snoek relaxation, see in detail Gavriljuk et al. (2003)

2.2 Interaction Between Hydrogen Atoms and Dislocations

75

Fig. 2.17 Strain-dependent internal friction in the hydrogen-charged steel Cr15Ni25 at different temperatures. The treatment of experimental data in the Arrhenius co-ordinates as ln(Q−1 /ε) = f(T−1 ) is shown in the inset

Fig. 2.18 Strain-dependent internal friction in the hydrogen-charged nickel-based alloy Inconel 718

and Chap. 3, the hydrogen atoms in austenitic steels are mobile at temperatures higher than ~180 K. Therefore, above this temperature, they can follow dislocations during their vibrations. For this reason, as seen in Fig. 2.17, the slope of the Q−1 (ε) curves changes above some critical temperature Tc denoted as that for condensation of hydrogen atoms around the dislocations. With increasing temperature above Tc ,

76

2 Crystal Lattice Defects

Fig. 2.19 Strain-dependent internal friction in the hydrogen-charged nickel-base alloy Ti-10 V2Fe-3Al

these hydrogen clouds become diluted and, correspondingly, the slope Q−1 /ε increases. How quickly this slope increases with raising temperature, depends on the rate of the hydrogen clouds dilution, i.e. on the binding enthalpy between hydrogen atoms and dislocations. Therefore, it can be estimated from the change in the Q−1 /ε ratio with increasing temperature. Transforming formula (2.9), the relation between hydrogen concentrations in the bulk and at dislocations can be expressed using Arrhenius equation: c⊥ = c0 exp(Hb /kT),

(2.10)

where c0 and c⊥ are the hydrogen contents in the bulk and at the dislocations, respectively, Hb is the enthalpy of binding between hydrogen atoms and dislocations. Assuming that c⊥ /c0 ~ Q−1 /ε and treating the experimental data in the Arrhenius co-ordinates (see, e.g., the inset in Fig. 2.17), one can estimate Hb and Tc (Table 2.2). For comprehension, the data on hydrogen diffusion enthalpy, Hd , are also included in this Table, although this topic will be in detail analyzed in Chap. 3. It is seen that binding between hydrogen atoms and dislocations is much smaller in the nickel and titanium alloys in comparison with that in austenitic steels. The data for hydrogen-dislocation binding in nickel of ~0.05 eV has been also calculated by Daw et al. (1986).

2.2 Interaction Between Hydrogen Atoms and Dislocations

77

Table 2.2 Effect of chemical compositions on the enthalpy of binding between hydrogen atoms and dislocations, Hb , in comparison with that of diffusion, Hd , and condensation temperatures, Tc Alloy

Hb ± 0.005, eV

Hd ± 0.005, eV

Tc , ± 3 K

FeCr15Ni25

0.107

0.544

173

FeCr15Ni40

0.096

0.496

163

FeCr25Ni25

0.120

0.589

189

FeCr15Ni25Cu2

0.102

0.517

174

FeCr15Ni25Al2

0.110

0.555

173

FeCr15Ni25Si2

0.112

0.563

186

0.114

0.567

182

FeCr15Ni25Mn15 Ni

~0.08

0.4

–

Inconel 718

0.072

0.42

149

TiV10Fe2Al3

0.035

0.27

–

Presented are the data for austenitic steels (Gavriljuk et al. 2010), nickel (Boniszewski and Smith 1963; Louthan et al. 1975), Inconel 718 (Teus 2017) and β-titanium alloy (Teus et al. 2016)

As follows from Table 2.2, some correlation occurs between diffusion enthalpy Hd of hydrogen atoms, enthalpy Hb of their binding to dislocations and condensation temperature Tc . Nickel in the alloy Inconel 718 enhances migration of hydrogen atoms, weakens the hydrogen-dislocation binding and decreases the condensation temperature. Silicon, manganese and chromium in austenitic steels retard the hydrogen diffusion, enhance hydrogen-dislocation binding and assist the hydrogen condensation at dislocations. Extremely low values of Hb and Hm in the bcc titanium alloy represent a particular case of mobile hydrogen atoms weakly bound to dislocations. The enthalpies of hydrogen diffusion, Hd , and hydrogen binding to dislocations, Hb , control the hydrogen condensation temperature at dislocations, Tc . Below it, the hydrogen clouds at dislocations are condensed and their density does not depend on temperature, which is evidenced by the unchanged slope Q−1 /ε. However, this situation changes above Tc . Remaining bound to dislocations, the hydrogen atoms become sufficiently mobile and their clouds accompany dislocation slip. Simultaneously, their density decreases with increasing temperature. The dilution of hydrogen clouds displays itself in the increased slope Q−1 /ε. The strain-dependent internal friction caused by hydrogen in the nickel-based alloy Inconel 718 is presented in Fig. 2.18, see Teus (2017). Be compared with the data for the austenitic steel in Fig. 2.17, it is characterized by a sharp change in the Q−1 /ε slope with increasing temperature, which reveals a weaker enthalpy of binding between hydrogen atoms and dislocations, as shown also in Table 2.2. Along with a smaller enthalpy of hydrogen diffusion, 0.42 eV against ~0.5 eV in austenitic steels, this explains a low value of Tc of which above dislocations are accompanied by migration of hydrogen atoms in the course of their slip. Even higher mobility of hydrogen atoms is found in the bcc β-titanium alloys, which results in the extremely low temperature position of the hydrogen-caused

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Snoek peak in the β-titanium alloy and prevents to determine Tc temperature, Fig. 2.19. Presumably, Tc in this alloy is located at temperatures of 125 K. The enthalpy of binding Hb ≈ 0.035 eV has been obtained from the slope Q−1 /ε in this experiment. It is seen that, along with the highest mobility of hydrogen atoms, the titanium-based alloys are characterized by the extremely weak binding between hydrogen atoms and dislocations. Just this favorable combination of Hm , Hb and Tc allows the usage of hydrogen as temporary alloying element aiming to increase plasticity of titanium alloys in the course of their technological processing, see e.g. Kolachev et al. (1985), Nosov and Kolachev (1986), Kolachev (1993), Eliaz et al. (2000) and Chap. 6, Sect. 6.1, about details. Summing up, one can conclude that hydrogen binding to dislocations and hydrogen-affected mobility of dislocations analyzed in the previous Section are controlled by two quite different physical factors. Elastic distortions caused by hydrogen atoms in the crystal lattice mainly contribute to hydrogen-dislocation binding forming thereby hydrogen atmospheres around the dislocations. In turn, the hydrogen-caused increase in concentration of free electrons weakens atomic interactions within the hydrogen atmospheres and, consequently, decreases the line tension of dislocations increasing their mobility.

2.3 Hydrogen Effect on Mobility of Grain Boundaries Hydrogen is well known by its strong tendency to segregate at the grain boundaries, see e.g. Ohmisawa et al. (2003) and other similar studies performed using a microprint technique. At the same time, as analyzed in Chap. 1, hydrogen increases the density of electron states at the Fermi level and, correspondingly, concentration of free electrons, which weakens the interatomic bonds. It is reasonable to expect that this weakening eases the hopping of the host atoms across the grain boundaries, which, e.g., is an elementary step in their movement during recrystallization of deformed metals. The molecular dynamics simulations were used by Teus and Gavriljuk (2020) for analysis of grain boundary mobility in the hydrogen-containing α-iron has been performed by the following way. As a base structure, the asymmetric tilt grain boundary 5[001](430)/(100) has been constructed within the framework of the coincidence site lattice (CSL) model, see Fortes (1972). The simulation box having dimensions of ~71 × 287 × 30 Å3 is presented in Fig. 2.20. The periodic boundary conditions were applied in the X and Z directions of the global coordinate system, whereas the boundaries in Y direction were treated as free surfaces to prevent GB’s interaction and minimize forces acting on the GB in this direction. To obtain the equilibrium structure, the energy minimization procedure was applied to the simulation box consisting of the relaxation of atomic positions and the GB internal degrees of freedom.

2.3 Hydrogen Effect on Mobility of Grain Boundaries

79

Fig. 2.20 Schematic presentation of simulation box containing a tilt grain boundary

The following range of hydrogen bulk concentrations was chosen for calculations: 14, 28 and 56 wppm. Details about the used initial hydrogen distribution, temperature stabilization, interatomic potentials and thermodynamic ensembles can be found in Teus et al. (2014). To determine the GB driving force, the theory of elasticity, Zhang et al. (2004), has been used. The chosen level of strain did not exceed 2.5%. As shown by Zhang et al., the comparison of results obtained using the driving force applied in the linear approach with those using the direct stress–strain modeling, the deviation does not exceed 13% at he strain of 2%. For strain smaller than 1%, it could be difficult to separate the GB migration from thermal atomic oscillations. It is also worth noting that simulations have been performed on a dislocation-free crystal, which extends the interval of elasticity. At such conditions, the linear elasticity approach remains to be correct up to 4% deformation in accordance with Schönfelder et al. (1997). The grain boundary migration was calculated each 4 ns during the steps of molecular dynamics. The GB position in the Fe–H system was determined with the following modifications: (i) averaging in the atomic positions, (ii) filtering of atoms according to their energy and (iii) construction of a diagram that describes the number of atoms in the area orthogonal to GB plane. The GB position is a gravity center of such diagram. The change in the GB positions with time as a function of the driving force is shown in Fig. 2.21 for the hydrogen-free and hydrogen-charged iron. It has a linear character, which allows estimation of GB velocity.

80

2 Crystal Lattice Defects

Fig. 2.21 Velocity of grain boundary migration as a function of driving force at different temperatures in: a H-free simulation cell; b cell with CHbulk = 28 wppm. Shown in the insets is a temperature dependence of GB mobility in the Arrhenius co-ordinates

Because of extremely short times used in the molecular dynamics simulations, temperatures chosen for simulation are rather high and, under real conditions, hydrogen atoms should leave the α-iron. However, temperature in this simulation affects only the atomic kinetic energy and not the activation enthalpy which depends on the relative change of temperature, T. In addition, the simulated system is closed for hydrogen escape. The hydrogen atoms can only migrate and redistribute between the solid solution and crystal lattice defects. In reality, such conditions occur under high hydrogen gas pressure at elevated temperatures, where the dissolved hydrogen is in equilibrium with the external surrounding.

2.3 Hydrogen Effect on Mobility of Grain Boundaries

81

Mobility of grain boundaries, M, has been estimated on the slope of curves presented in Fig. 2.21, and its temperature dependence is presented in the Arrhenius co-ordinates for obtaining the GB migration enthalpy. With increasing bulk hydrogen content, its value decreases from 0.99 ± 0.06 eV for the hydrogen-free iron crystal down to 0.83 ± 0.03 eV for the iron having 14 wt ppm H, 0.76 ± 0.03 eV for iron with 28 wt ppm H and 0.73 ± 0.03 eV for the iron with 56 wt ppm H. The obtained results are consistent with experimental data about the hydrogeninduced decrease in recrystallization temperature to be presented in Chap. 6, Sect. 6.2. In the absence of hydrogen, the recrystallization in the cold worked steel 304, as well as in the more stable steel 316, proceeds at significantly higher temperatures of 973 K and 1073 K, respectively, see e.g. Herrera et al. (2007). While discussing the obtained data on GB mobility, an atomic mechanism for grain boundary migration should be taken into account. In the group of models, e.g. Mott (1948) and Turnbull (1951), GB migration is considered as a thermally activated single- or multi-atomic transport through the boundary. Other approach is based on the molecular dynamics, see Rickman et al. (1991), where the GB migration steps consist of local bond rearrangements with formation of domain-like structures and their reordering. An experimental attempt has been also made by Rae and Smith (1980) to relate GB migration with the movement of GB dislocations which contain a component of the step vector out of the GB plane. Based on the ab initio calculations of hydrogen effect on the electron structure in the α-iron, see Chap. 1, Sect. 1.5.1, the hydrogen-increased mobility of grain boundaries is attributed to the change in the atomic interactions. Hydrogen enhances the metallic character of interatomic bonding. Because of strong hydrogen affinity with the grain boundaries, the concentration of free electrons around the GB’s increases, which in turn decreases GB’s surface tension and increases their mobility similar to that in the case of hydrogen at dislocations. Of course, any segregation, e.g. that of carbon, can be also accompanied by some decrease in the GB surface energy despite the carbon-enhanced covalent bonds in the iron. However, decisive is the hydrogen-caused weakening of interatomic bonds, which lowers the energy barrier for atomic jumps across the grain boundary. The proposed interpretation is correct in the case of sufficient mobility of hydrogen atoms to follow the grain boundaries during their migration. A special case of hydrogen-assisted recrystallization and grain refinement will be analyzed in Chap. 6, Sect. 6.2. Summary Formation and properties of crystal lattice defects in metals is discussed based on hydrogen effect on their electron structure. Hydrogen increases the concentration of vacancies and creates vacancy-hydrogen clusters with rather high energy of binding and H/M atomic ratio depending on the type of crystal lattice. In consistency with the change in the electron structure, hydrogen affects the fundamental characteristic of dislocations, namely their stacking fault energy, SFE. Decreasing the SFE, hydrogen reduces thermodynamic stability of austenitic steels

82

2 Crystal Lattice Defects

under mechanical loading assisting formation of ε-martensite and changing relation between the hard and soft crystallographic directions in the textured metallic materials. Increasing the concentration of free electrons and, consequently, weakening the interatomic bonds, hydrogen causes softening of metals through the decrease in the specific energy of dislocations, i.e. their line tension, which enhances their mobility. As will be shown in Chap. 5, the hydrogen-decreased dislocation line tension in combination with a strong affinity of hydrogen atoms with dislocations bounds the hydrogen effect on the electron structure and hydrogen embrittlement of metallic materials. The hydrogen-increased mobility of high angle grain boundaries can contribute to mechanisms of hydrogen effect on the grain refinement.

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Chapter 3

Diffusion

Due to their extremely small size, hydrogen atoms acquire particular diffusivity features in the crystal lattice. For example, their diffusivity is characterized by the occurrence of quantum mechanical effects, namely discrete vibration excitations and hydrogen atom tunnelling. As for mechanical properties, the most important one is that hydrogen is transported throughout the crystal lattice in the presence of crystal lattice imperfections, which results in metal degradation under mechanical loading. Hydrogen-caused embrittlement is particularly dangerous for alloys with a bcc crystal lattice, where hydrogen atoms are particularly mobile. For example, the diffusion coefficient of hydrogen in bcc iron is the highest in comparison with that in many metals. This chapter reviews hydrogen diffusion in Fe, Ni and Ti alloys based on firstprinciple calculations and the available experimental findings. Special attention will be paid to hydrogen traps in the crystal lattice. The role of dislocations and grain boundaries in hydrogen migration will be discussed based on measurements of its permeability which is often used as a simple tool for estimating hydrogen diffusivity.

3.1 Migration Paths and Enthalpies Hydrogen entry into metal bulk starts with the dissociation of H2 gas molecules due to the catalytic effect of the metallic surface, or simply with the adsorption of H atoms from water base solutions. Chemisorbed H atoms diffuse into the surface layer and, thereafter, into the bulk. The activation energy for hydrogen penetration depends on the crystallographic orientation of the metallic surface.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. G. Gavriljuk et al., Hydrogen in Engineering Metallic Materials, https://doi.org/10.1007/978-3-030-98550-9_3

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3.1.1 H in Iron BCC α-iron. The low-index planes (110) and (100) have the smallest surface energy on the iron surface and are the most favourable for the adsorption of hydrogen atoms. Jiang and Carter (2004) studied hydrogen adsorption, absorption and diffusion energetics based on the density functional theory (Hohenberg and Kohn 1964; Kohn and Sham 1965) and using Vienna VASP ab initio simulation package (Kresse and Hafner 1993; Kresse and Furthmüller 1996). They found the H adsorption energy of 0.71 eV/atom on the Fe(110) plane and a smaller energy of 0.3 eV for hydrogen binding to the Fe(100) plane. Further absorption of an H atom in the subsurface of the Fe(110) plane needs additional 0.29 eV in comparison with 0.04 eV for the subsurface of the Fe(100) plane. Thus, to diffuse into the subsurface, a hydrogen atom has to overcome the energy barrier of about 1.0 eV on the Fe(110) plane and of 0.34 eV on Fe(100). This difference is clearly due to the (110) plane being more closely packed in the bcc lattice. As shown in Chap. 1, hydrogen atoms in bcc iron prefer to occupy tetrahedral t sites which have a larger “radius” of 0.36 Å in comparison with 0.19 Å for octahedral o sites. Hydrogen dissolution in a tetrahedral site of iron bulk requires overcoming the energy barrier of ~0.20 eV, which slightly varies with hydrogen concentration as a sign of some negligible H–H interactions. Taking into account the zero-point energy vibrations of a hydrogen atom, this value was corrected to 0.301 eV/atom, which is consistent with the experimental 0.296 eV/atom reported by Hirth (1980). The two possible diffusion paths of a hydrogen atom, amounting to direct hopping between neighboring t sites or to indirect t → o → t hops via an octahedral o site, are presented in Fig. 3.1. The diffusion energy barrier Ea for the direct t → t hop was calculated by Jiang and Carter (2004) as 0.088 eV. This value was confirmed by Hirata et al. (2018) using VASP software. For comparison, Ea of 0.096 eV was obtained by He et al. (2017) based on the ultrasoft pseudopotential with generalized gradient approximation (Perdew et al. 1992) and the exchange–correlation functional (Perdew et al. 1996). Within the random-walk model for interstitial diffusion in the bcc iron lattice, Jiang and Carter also found that the t → t path for hopping between two neighboring Fig. 3.1 Hydrogen atom diffusion paths t → t between tetrahedral sites and t → o → t mediated by an octahedral site on the (100) plane of the bcc iron lattice. Modified from a scheme proposed by Jiang and Carter (2004) and quantum correction performed by Kimizuka et al. (2011), American Physical Society

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t sites 1 and 2 is not linear. It is curved toward the o site located in the centre of the (100) plane, as shown in Fig. 3.1. In contrast, the t → o → t diffusion path between t sites 1 and 3 via an o site as the saddle point is linear and characterized by the diffusion barrier of ~0.12 eV. In fact, this value reflects the energy difference between o sites and t sites, which was presented in Table 1.1 of Chap. 1. It is also worth noting that a smaller energy barrier for hopping between neighbouring tetrahedral sites, 0.059 eV within the temperature range of −40 to 80 °C was mentioned by McLellan (1984) in his thermodynamical analysis of hydrogen diffusion in bcc iron. For diffusion at higher temperatures, larger values, from 0.069 to 0.074 eV, were obtained by this author and attributed to hydrogen migration over octahedral sites. The quantum nature of rapid hydrogen diffusion in bcc iron at low temperatures was mentioned by Jiang and Carter (2004) in order to take into account the discreteness of hydrogen vibration modes in the crystal lattice. According to their estimates, the energy of these vibrations hν H , ν H being the frequency of localized H vibration modes, ranges between 0.12 and 0.24 eV, which significantly exceeds the energy of thermal vibrations k B T at room temperature. Quantum correction was performed in more detail by Kimizuka et al. (2011) who used the path-integral molecular dynamics method along with the ab initio-based potential for calculating localized H vibration modes around the room temperature and their effect on diffusion paths. According to their results, the minimum energy path for hydrogen atom migration between neighbouring tetrahedral sites contains a blurred saddle point S at a minimum distance between the H path and the octahedral o site, as marked in Fig. 3.1. Moreover, as shown in Fig. 3.2, calculations of free energy profiles in the course of H migration along the t–S–t and t–o–t hops demonstrate a striking decrease in the energy barrier with decreasing temperature in both cases, which confirms the possibility of H tunnelling along both paths. Fig. 3.2 Free energy profiles for H migration between t-sites in bcc iron at various temperatures. Redrawn from Kimizuka et al. (2011), American Physical Society

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Fig. 3.3 Free energy profiles for hydrogen diffusion paths o → o (a) and o → t (b) in fcc iron

Taking into account hydrogen quantum tunnelling, the corrected value of activation enthalpy for hydrogen migration in bcc iron, Ea = 0.037 eV, is 58% smaller than the abovementioned t → t energy barrier of 0.088 eV. This result is consistent with the experimental data on hydrogen diffusion enthalpy of 0.035 eV (Hayashi et al. 1989), 0.040 eV (Nagano et al. 1982) and 0.044 eV (Neumann and Domke 1972). It should be added that the possibility of tunnel hydrogen diffusion in bcc iron at ambient temperatures is a unique case among studied metal-hydrogen systems. FCC γ-iron. The “radii” of octahedral and tetrahedral interstitial sites in γ-iron are 0.457 Å and 0.248 Å, respectively, which creates favourable conditions for hydrogen atoms to localize in octahedral sites (see Chap. 1 about details). Similarly to the hopping between t-sites in bcc iron, there are two possible H atom migration paths in fcc iron: o → o and o → t → o. Ab initio calculation results for the non-magnetic fcc iron state, as obtained by Legris and Shyvanyuk (see Shyvanyuk 2014), are presented in Fig. 3.3a, b. It was obtained that direct o → o hops need to overcome the 1.1 eV/atom barrier, whereas, in the case of o ↔ t hopping, 0.62 eV is enough for a direct hop and only 0.18 eV/atom for an inverse one. Therefore, H migration between neighbouring octahedral sites mediated by a tetrahedral one as the saddle point is clearly preferred. Hirata et al. (2018) took into account the antiferromagnetism of fcc iron and performed ab initio calculations for three iron states, see Fig. 3.4: non-magnetic, antiferromagnetic and double-layered antiferromagnetic (see also Chap. 1, Sect. 1.5.1, on the magnetism features in fcc iron). The calculated data for the non-magnetic state with the migration enthalpy of 1.08 eV for o → o and 0.64 eV for o → t → o paths, see Fig. 3.4a, are practically identical with those presented in Fig. 3.3a. As follows from Fig. 3.4b, antiferromagnetism diminishes the energy barrier for both H diffusion paths down to 0.84 eV and 0.44 eV, respectively. Results for the double-layered antiferromagnetic state were practically identical to those for the antiferromagnetic one. The calculated value of 0.44 eV is close

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Fig. 3.4 Free energy profiles for hydrogen diffusion paths o → o and o → t → o with corresponding saddle points S1 and S2 accounting for the quantum tunnelling in fcc iron in its nonmagnetic (a) and antiferromagnetic (b) states. Redrawn from Hirata et al. (2018), Springer

to diffusion enthalpy 0.46 eV for fcc iron, as reported by Mehrer (1990) in the Landolt-Börnstein New Series Tables. However, the only practical way to obtain fcc iron at ambient temperatures is by alloying with austenite-forming elements, and experimental data for hydrogen in austenitic steels is remarkably different from this data. For example, values 0.52– 0.57 eV have been reported for hydrogen in AISI 310 steel by Quick and Johnson (1979) and 0.56 for 316L steel by Tison (1984). A collection of data on hydrogen diffusion enthalpies obtained from measurements of Snoek-like relaxation in austenitic steels demonstrates the different ways in which alloying elements affect the energy barrier for hydrogen atom diffusion jumps in the fcc iron-based lattice, see Table 3.1 and Teus (2007). It decreases with higher nickel content and increases with higher chromium content. Copper has a similar effect to nickel. Aluminium, silicon and manganese moderately slow down hydrogen diffusion. Table 3.1 H diffusion enthalpy in fcc iron-based alloys

Steel

Hd ± 0.01, eV

Cr15Ni25

0.54

Cr15Ni40

0.49

Cr25Ni25

0.59

Cr15Ni25Cu2

0.52

Cr15Ni25Al2

0.55

Cr15Ni25Si2

0.56

Cr15Ni25Mn15

0.57

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HCP ε-iron. An ideal closely packed hexagonal lattice is characterized by the ratio c/a = 1.633, see e.g. Ashkroft and Mermin (1976). Hydrogen dissolution creates lattice distortions, which requires verifying the values of lattice parameters and the ratio between the crystallographic axes after the full relaxation of the crystal lattice. The c/a ratio of 1.58 was obtained in ab initio calculations reported by Shyvanyuk (2014) and Hirata et al. (2018). The energy barriers to be overcome studied according to Hirata et al. for o1 → o2 hydrogen hopping along the c axis, o1 → t → o3 in the basal c plane and o1 → o3 in the basal c plane constitute 0.72 eV, 0.77 eV and 1.26 eV, respectively. Therefore, the most favourable H migration paths are direct hopping between neighbouring octahedral sites along the c axis and indirect hopping between neighbouring octahedral sites located in the basal c plane via a tetrahedral site as the saddle point. Direct hopping between octahedral sites in the c plane is unrealistic. Similar data for abovementioned hops were reported by Shyvanyuk (2014), namely 0.7 eV, 0.68 eV and 1.22 eV, respectively, whereas He et al. (2017) obtained 0.76 eV for migration between neighbouring octahedral sites and 0.8 eV for o → t hops. According to calculations performed by Hirata et al. (2018), the diffusion coefficients in iron decrease in the sequence of its bcc → fcc → hcp lattices. Hydrogen diffusion is the slowest in hcp iron, which should be taken into account in the case of austenitic steels, where hydrogen can cause γ → ε transformation. As the c/a ratio in the hcp iron phase depends on the hydrogen content, one can also expect a different behaviour for hydrogen diffusion during hydrogen dissolution. The anisotropic migration of hydrogen in hcp-iron was obtained in the calculations carried out by Hirata et al. (2018), see Fig. 3.5. The migration path along the basal c plane becomes preferred if the c/a ratio increases due to higher hydrogen content. For this reason, a different behaviour is expected for hydrogen absorption and subsequent desorption in the iron fcc and hcp phases in case of their coexistence in hydrogen-containing austenitic steels. Fig. 3.5 Hydrogen migration energy in hcp iron along the c axis and in the basal c plane as a function of the c/a ratio. Redrawn from Hirata et al. (2018), Springer

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3.1.2 H in Nickel The enthalpy of hydrogen diffusion, EH , and pre-exponential factor, D0 , were obtained ab initio by Wimmer et al. (2008). The calculated migration paths and energy profiles are presented in Fig. 3.6. A feature of these calculations was that vibrations in the host lattice were neglected. The authors obtained the value of hydrogen diffusion enthalpy EH = 0.474 eV, which is rather high in comparison with the available experimental data of, e.g., 0.410 eV (Eichenauer et al. 1965), 0.406 eV (Robertson 1973), 0.405 eV (Lee and Lee 1986), 0.41 eV (Brass et al. 1990) for polycrystals and with 0.414 eV (Ebisuzaki et al. 1967) and 0.408 (Katz et al. 1971) for single crystals. Later, a more realistic value, 0.413 eV, was obtained in the ab initio calculations by Torres et al. (2018). Hydrogen in nickel was chosen as a suitable subject in a number of studies devoted to the anisotropy of diffusion in cubic crystals. In general terms, this task was analyzed by Dederichs and Schroeder (1978) who found the anisotropy of the saddle point configuration to be responsible for the difference in the directions of migration hops. Brass and her colleagues were possibly the first to measure the apparent H diffusion coefficients at RT in their studies of hydrogen permeation in nickel single crystals: H H = 6.2 × 10−14 m2 /s (Brass et al. 1990) and Dapp = 5.6 × Dapp −14 2 m /s (Brass and Chanfreau 1996). 10 Li et al. (2017) measured hydrogen flux in Ni single crystals of different crystallographic orientations, see Fig. 3.7. Consistently with previous data obtained by Brass et al. (1990) for and crystals, hydrogen diffusion was shown to decrease in the → → → sequence. Also remarkable is the positive deviation of the

Fig. 3.6 a Migration hops O1 → T → O2 of a hydrogen atom between two octahedral sites in the fcc unit cell of nickel via tetrahedral site T with two transition states S1 and S2 near the (111) plane. M is the middle point of the direct hop O1 → O2 . b Energy surface for H migration O1 → T → O2 . Modified from Wimmer et al. (2008). American Physical Society

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Fig. 3.7 Hydrogen flux in nickel single crystals of different orientations as a function of charging time. Solid lines show the calculated flux data according to Fick’s law. Redrawn from Li et al. (2017). Springer

experimental hydrogen flux from that calculated using Fick’s law and the shift of this deviation towards longer permeation times in the order of decreased diffusivity. On the account of these experimental data, it seems natural that the crystallographic anisotropy of hydrogen diffusion occurs in the cold-worked states of materials, as demonstrated by Brass et al. (1990) and Cao et al. (2002). In relation to the nature of hydrogen diffusion anisotropy, Torres et al. (2018) made the important observation that, with no imposed stress, hydrogen diffusion in the , and directions does not reveal any significant differences in a nickel single crystal. This suggests the importance of self-stresses caused by the gradient of hydrogen concentration during its flux. As will be shown later, see Sects. 3.3 and 3.4, hydrogen flux anisotropy is prevailingly caused by plastic deformation during electrochemical hydrogen charging. It is also worth noting that the orientation dependence of hydrogen flux in nickel single crystals coincides with that of hydrogen Snoek-like relaxation in the single crystals of austenitic steel with the same fcc crystal structure, see Fig. 1.12 in Chap. 1. During Snoek-like relaxation, hydrogen atom diffusion jumps are initiated by applied alternative mechanical stress, while relaxation strength is controlled by deviation from cubic symmetry in the crystal lattice defect caused by i–s complexes of interstitial and substitution atoms, which depends on the crystallographic direction. In a similar way, Li et al. (2017) analyzed the origin of hydrogen diffusion anisotropy based on elastic interaction between hydrogen atoms and cubic crystal lattice leading to a change in the chemical potential of hydrogen created by its concentration gradient (for comparison, see the general analysis of self-stresses and stress-composition interactions by Larché and Cahn (1982) and Larché (1988)). Two factors cause the orientation dependence of isotropic elasticity Y = 2E/(1 − ν), where E is Young’s modulus and ν is Poisson’s ratio. The first is a self-stress originating from hydrogen atom incorporation into the interstitial site, which leads to the anisotropy of elastic coefficients in nickel. For example, Y is 768 GPa in the and 440 GPa in the orientation. The second factor is qualitatively

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99

described by Li et al. (2017) as an effect of stresses originating from superabundant vacancies induced by hydrogen (see Chap. 2, Sect. 2.1.2, for details), which doesn’t look sufficiently convincing. The point is the extremely low solubility of hydrogen in nickel (see Fig. 1.5 in Chap. 1). A Ni hydride is claimed to be formed in the Ni–H system, see about detail Chap. 4, Sect. 4.2. At current densities of 5 mA/cm2 used by Li et al., the hydrogen content in the Ni–H solid solution exceeds the solubility limit, which causes additional stresses.

3.1.3 H in Titanium and Its Alloys HCP α-titanium. One of the first ab initio studies of hydrogen diffusion in α-titanium was carried out by Han et al. (2009). They pointed to clear anisotropy in the probability of H atom hops on the basal plane and along the c-axis in the hcp titanium lattice. The indirect o → t → o path with the energy barrier of 0.514 eV was found to be preferred for diffusion in the basal plane, whereas the o → o path with the activation enthalpy of 0.694 eV is the most probable for diffusion hops in the c direction. Lu and Zhang (2013) calculated the temperature dependence of hydrogen diffusion. Possible migration paths are presented in Fig. 3.8. The energy barriers for four migration paths o → o, t → t, o → t and t → o were found to be 0.662 eV, 0.042 eV, 0.525 eV and 0.439 eV, respectively. For the o → o and t → t hops, the energy profile displaces a single maximum, and the saddle point is located halfway between the neighbouring sites. In case of o → t or t → o hops, the transition state is close to the t-site.

Fig. 3.8 Energy profiles for hydrogen hopping in α-titanium along (a) O → O, (b) T → T, and (c)O → T and T → O paths. Redrawn from Lu and Zhang (2013), AIP Publishing

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This result was confirmed and essentially refined by Bakulin et al. (2016) who calculated two competitive pathways for o → t → o H-hops along the a axis and o → t → t → o hops along the c axis. The highest energy barrier constitutes 0.514 eV for o → t hops, whereas the barriers for t → o and t → t hops are the smallest (0.332 eV and 0.139 eV, respectively). The average calculated activation enthalpy for H diffusion in alpha-titanium, 0.514 eV, is close to the experimental data of 0.45 eV, as obtained by Miyoshi et al. (1996) at temperatures of 873–1298 K. However, it is at significant variance with the values of 0.128 eV obtained by Wasilewski and Kehl (1954) within the temperature range of 650–1000 K, as well as 0.152 eV by Papazoglou and Hepworth (1968) at temperatures of 610–900 K and 0.145 eV by Johnson and Nelson (1973) at temperatures between 673 and 1073 K. A special case is the value of 0.077 eV obtained by Brauer et al. (1976) in their measurements performed within the significantly lower temperature range of 293–353 K. Bakulin et al. (2016) were also the first to calculate the effect of substitution elements, S, on the energy barriers for diffusion hops in α-Ti (see Fig. 3.9a). They found that transition 3d-metals from the 5th to 10th groups should assist hydrogen diffusion. A possible reason for that is the attractive H–S interaction and the corresponding shift of the H atom towards the S one, which weakens bonding between hydrogen and the neighbouring titanium atoms. As a result, the energy barrier for the o → t hop is decreased by the S elements in the 3d series of transition metals, from vanadium to nickel. Another consequence of the H–S attraction and the consequent H–Ti weakening is the increase in the effective size of interstices occupied by the H atom, which results in a decrease of H absorption energy in the t-sites (Fig. 3.9b). The opposite effect of H–S repulsion, namely an increase in H–Ti bonds, a decrease in the effective size of interstices occupied by hydrogen and an increase in the H absorption energy, as well as of the energy barrier for H atom hops, is predicted

Fig. 3.9 a Effect of group 3–14 substitution atoms, S, on the energy barrier along the o → t path for hydrogen atom, H, in α-Ti; b change in hydrogen absorption energy, E, at the initial o-site with t-site as the saddle point in the presence of a group 3–14 substitution atom in α-Ti. Redrawn from Bakulin et al. (2016). Elsevier

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for the elements from the groups at the beginning or at the end of 3d-series, namely groups 2, 3 and 12–14, e.g. Al, Si, Ga, Ge. The results of these calculations make it possible to understand why the impurities of transition metals from mid-3d-series serve as traps for hydrogen atoms and, for this reason, increase hydrogen solubility and decrease its diffusivity, see e.g. Hu et al. (2002), Spiridonova et al. (2014, 2015). This tendency was also confirmed in the following experiments. Hydrogen diffusion was slowed down by adding Al to Ti (Miyoshi et al. 1996; Naito et al. 1996). The substitution of V by Ti in the V–Ti–Al system decreases hydrogen diffusivity (Dolan et al. 2013). The coefficient of hydrogen diffusion in Ti–V–Cr alloys increases with higher V content (Vyvodtceva et al. 2014) etc. BCC β-titanium. First-principle studies of hydrogen atom diffusion in pure β-Ti are quite rare. Possibly, it is because bcc titanium can be obtained at ambient temperatures only by alloying with β-modificators, of which V and Mo are the most effective in decreasing the temperature of α → β transformation. Hydrogen diffusivity in β-Ti alloys has been thoroughly studied in numerous experiments. Early experimental results were summarized by Wille and Davis (1981). As follows from the comparison of H diffusion parameters in α-Ti with those for βTi alloys, activation enthalpy is halved, and hydrogen diffusion is accelerated by one order of magnitude if the α-Ti is transformed into its β modification by appropriate alloying (see Table 3.2). The EH value of 0.27 eV included in this Table 3.2 was obtained by Teus et al. (2016) in their measurements of Snoek relaxation and characterizes the enthalpy of a single diffusion jump performed by a hydrogen atom at temperatures around 100 K. The effect of alloying elements on the thermodynamic stability of the β-titanium phase and hydrogen diffusion in it was thoroughly studied by Christ and his colleagues. A feature of their results is that the hydrogen diffusion coefficient in the stable β-phase does not depend on the hydrogen content (Christ et al. 2000). At the same time, hydrogen diffusion is accelerated with the increasing content of Table 3.2 Diffusion data, pre-exponential factor D0 and activation enthalpy EH for hydrogen in αand β-titanium (Wille and Davis 1981) Material

Type

D0 , cm2 /s

EH , eV

References

10−2

0.15 eV

Williams (1958)

0.15 eV

Covington (1979)

Comm. pure Ti

Alpha

0.27 ×

Comm. pure Ti

Alpha

0.06 × 10−2 10−2

Iodide Ti

Alpha

1.8 ×

0.13

Wasilewski and Kehl (1954)

Iodide Ti

Beta

1.95 × 10−3

0.07

Wasilewski and Kehl (1954)

Ti-4Al-4Mn

Beta

1.8 × 10−3

0.09

Albrecht and Mallet (1958)

Ti-8Mn

Beta

3.6 ×

10−3

0.07

Williams et al. (1957)

Ti-13V-11Cr-3Al

Beta

1.58 × 10−3

0.05

Holman et al. (1965)

Ti-10V-2Fe-3Al

Beta

–

0.27

Teus et al. (2016)

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Fig. 3.10 Hydrogen diffusion coefficients in Ti–V (Christ et al. 2005) and Ti–Mo (Christ and Schmidt 2009) β-alloys. The temperature border between the α- and β-phases of unalloyed Ti is marked by the vertical solid line. The reference Arrhenius curves for unalloyed α-Ti and β-Ti are shown for Ti–V alloys by dashed and short dashed lines, respectively, and for Ti–Mo alloys by short dashed and dashed lines, respectively. Modified from Christ et al. (2005) and Christ and Schmidt (2009)

β-stabilizing elements, even if stabilization has been already achieved (Prüβner et al. 2002). The last feature is illustrated by the temperature dependence of H diffusion coefficients in the binary Ti–V and Ti–Mo alloys, see Fig. 3.10. The Arrhenius plot for hydrogen diffusion in the Ti-10V alloy nearly coincides with the reference line for pure β-Ti. Its change with increasing vanadium content suggests that hydrogen diffusion becomes faster with the enhanced stability of the β-phase. Similarly, the data for the near α-state of alloy Ti-0.8Mo is consistent with the reference Arrhenius plot of pure α-Ti. Above 800 °C, the α + β alloy Ti-7.7Mo follows the reference line for pure beta titanium. The Arrhenius curves for three alloys with Mo content at 21.45% and higher reveal a decrease in their slope in comparison with the data for pure beta titanium. Consequently, the activation enthalpy for hydrogen diffusion decreases with an increase in V or Mo content, as illustrated in Tables 3.3 and 3.4.

3.2 Hydrogen Trapping by Crystal Lattice Defects Table 3.3 H diffusion enthalpy, E, in Ti–V alloys (Christ et al. 2005)

Table 3.4 H diffusion enthalpy E, in Ti–Mo alloys (Christ and Schmidt 2009)

Alloy, at.%

103 E, kJ/mol

Ti-10V

27.6

Ti-18.7V

26.9

Ti-30V

19.7

Alloy, at.%

E, kJ/mol

Ti-21.45Mo

29.05

Ti-36.1Mo

28.6

Ti-49.66Mo

25.92

3.2 Hydrogen Trapping by Crystal Lattice Defects Perhaps the first indication of hydrogen trapping in metals was made by Darken and Smith (1949) who measured hydrogen permeation, its saturation concentration and diffusivity in steels in their cold worked and annealed states. They suggested that a delay in hydrogen permeation through a sample of cold worked steel is caused by crystal lattice imperfections. This phenomenon was demonstrated clearly by Schumann and Erdmann-Jesnitzer (1953). The authors used a cold rolled unalloyed low carbon steel for measurements and showed that cold rolling leads to a remarkable evolution of hydrogen permeation (Fig. 3.11). This result was attributed by the authors to a change in the microstructure. Later it is found that chaotically distributed tangled dislocations are generated in low carbon steels at small deformation degrees, whereas the shape of grains is not markedly affected. In this case, corresponding retained stresses in the crystal lattice should increase hydrogen diffusivity, which manifests itself in enhanced permeation. Fig. 3.11 Hydrogen permeability of a cold rolled low carbon steel as a function of deformation degree. Redrawn from Schumann and Erdmann-Jesnitzer (1953), John Wiley and Sons

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Fig. 3.12 Effect of annealing temperature on the hydrogen permeability of a cold rolled low carbon steel subjected to 90% rolling deformation. Redrawn from Schumann and Erdmann-Jesnitzer (1953), John Wiley and Sons

With an increasing degree of deformation, an extended cellular dislocation substructure is formed along with crystallographic texture. The grains and dislocation cells are elongated in the rolling direction. For this reason, the trapping of hydrogen atoms by grain and dislocation cell boundaries decreases hydrogen permeation. The strongly deformed steel is practically not penetrated by hydrogen. The contribution of the matrix-carbide interface to hydrogen trapping can be negligible in this case because of the insignificant carbide fraction. Such interpretation is consistent with the permeation behaviour after subsequent annealing of cold worked steel in the quoted experiments. Annealing at 400 °C after weak deformation, of about 10%, led to a small decrease in hydrogen permeability because of stress relaxation caused by the recovery. Annealing at higher temperatures after intensive cold work sharply increased hydrogen permeability (Fig. 3.12). At first glance, these results and their interpretation are at variance with the widely accepted idea of fast hydrogen migration along dislocations. However, they are confirmed by atomistic calculations performed by Lu et al. (2018) who studied hydrogen behaviour near edge and screw dislocations and showed that fast pipe diffusion along the dislocations was absent in both cases. Moreover, hydrogen atoms can only slowly diffuse along oblique paths crossing edge dislocations and on spiral paths around screw dislocations. The next step in understanding the nature of hydrogen trapping was made by Oriani (1970). Based on experimental data available at the time (e.g., Darken and Smith 1949; Hill and Johnsson 1959; Eschbach et al. 1963; Beck et al. 1966; Kim and Loginov 1968), he analyzed the population of trapping sites including dislocations, solid–solid interfaces and microcracks in steel without proposing any specific model and only suggesting a local equilibrium between mobile and trapped H populations. The most striking result of his calculations was the extraordinarily uniform depth of hydrogen traps, i.e. the same enthalpy of about 0.235 eV for hydrogen binding to different kinds of traps. This value is close to that for binding between hydrogen atoms and dislocations, as obtained by Gibala (1967) in his studies of internal friction in hydrogen-charged α-iron, see Sect. 2.2.2.2 in Chap. 2 for detail. This analysis led Oriani to the following conclusions: dislocations are the dominant hydrogen traps in cold worked materials, whereas microcracks surfaces become

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more important with increased cold work and solid–solid interfaces dominate in the case of the annealed state. It should be mentioned that Darken and Smith (1949) made a remarkable observation related to the variety of possible hydrogen traps. They noted that hydrogen effective diffusivity is larger at its high contents than at lower ones, whereas the opposite result should be expected in the case of molecular trapping in voids. This idea of linking hydrogen trapping to a change in effective hydrogen diffusivity as its content increases remained dormant for many years. Johnson and Lin (1980) were perhaps the first to use it for the analysis of experimental data on hydrogen permeation in iron in terms of non-saturable traps (voids) and saturable ones (vacancies, dislocations, impurity atoms, internal interfaces). They wrote the diffusion equation for a system with hydrogen trapping as ∂cT ∂c L + = DL ∇ 2 cL ∂t ∂t

(3.1)

where cL is lattice hydrogen concentration, cT is trapped hydrogen concentration, DL is lattice diffusivity regardless of H concentration. Taking into account the link between trapped and lattice hydrogen concentrations, cT (cL ), the equation on (3.1) was rewritten as ∂ DL ∂c L = ∇ 2 cL ∂t 1 + cT (c L )

(3.2)

T where cT ∼ . = ∂c ∂c L Then, the effective diffusivity was found as

 −1 De f f = D L 1 + cT (c L ) .

(3.3)

For non-saturable traps, cT = αcL m , where α depends on the specific trapping model and m = 1, 2, 3, etc. An m = 2 corresponds to the case of hydrogen trapped as molecules in the voids. In this case, Deff decreases if cL increases. At m > 2, one can imagine trapping in some clusters, whereas m = 1 relates to a significant fraction of trapping by linear defects with Deff independent of cL and smaller than DL by the factor of (1 + α)−1 . These relationships illustrate an important effect of hydrogen lattice and trap concentration on the effective diffusion. Later on, different models for thermal hydrogen desorption from metals were analyzed in detail by Turnbull et al. (1997). Starting with a simple detrapping model by Lee and Lee (1986), where diffusion was neglected, the authors described two types of models, with diffusion for low and high trap occupancy.

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The first type suggests traps of low binding energy and allows the use of effective hydrogen diffusivity. For example, using the internal friction technique, namely measuring hydrogen-caused Snoek relaxation in diluted Ni–Ti alloys, Yoshinary et al. (1991) estimated the binding energy for Ti–H pairs to be smaller than 0.02 eV. Deuterium trapping in the irradiated 316 stainless steel was analyzed by Wilson and Baskes (1978) within the framework of the second model. The obtained trap binding energy of 0.3 eV was attributed to radiation-induced vacancies. Iino (1987) developed a model for hydrogen traps to be irreversible at ambient temperatures and applied it to hydrogen in low carbon sulphur-containing steels. As confirmation, two hydrogen release peaks at 588 and 613 K with the same binding energy of 0.86 eV were observed in the experiment. However, small trap occupancy was implicitly set in his equations, which left this model without a satisfactory rationale.

3.2.1 H in bcc Iron and Plain Carbon Steels Possibly, a first attempt to classify hydrogen traps in α-iron was undertaken by Gibala and Kumnick (1984), mainly based on the experimental data obtained by Pressouyre and Bernstein (1979) for hydrogen in the Fe–Ti and Fe–Ti–C alloys and those presented by Hirth (1980) for iron-based solid solutions. The authors selected hydrogen traps depending on the relationship between their binding energy with hydrogen atoms, Eb , and the heat of hydrogen solution in α-iron, ES ≈ 0.3 eV. The traps are weak if Eb < ES , moderate at Eb ≈ ES , and strong if EB > ES . A collection of available experimental data on trap sites and their binding energies with hydrogen in α-iron is presented in Table 3.5. Weak traps with binding energies smaller than ~0.15 eV were determined by Au and Birnbaum (1978) while studying magnetic relaxation caused by the reorientation of atomic pairs H–H (0.07–0.11 eV), H–C (0.03 eV) and H–N (0.13 eV). A striking difference between H–C and H–N interactions was later confirmed by Au and Birnbaum (1981) in their measurements of hydrogen effect on Snoek relaxation. It is worth noting that a weak H–H attraction exists in bcc iron, whereas a strong repulsion of 0.36 eV was obtained for hydrogen pairs in fcc iron (see Sect. 1.4 in Chap. 1). According to ab initio calculations performed by Counts et al. (2010), weak hydrogen traps with EB smaller than 0.1 eV are formed by substitutional solute atoms of Si, Cr, Mn and Co. It is remarkable that the last three elements are close to Fe in the periodical table. Other substitutional solutes, namely Al, Ti, V, Nb, Ni, Cu, Zn, reveal weak repulsive interaction with hydrogen. As noted by the authors, these substitutional atoms prefer to occupy second neighboring tetrahedral sites in relation to the hydrogen atom. Nevertheless, at variance with these calculations, the binding energy of 0.27 eV was obtained by Pressouyre and Bernstein (1979) in their measurements for Ti substitutional atoms as reversible hydrogen traps in Fe–Ti alloys.

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Table 3.5 Binding energies, HB , of trapping sites with hydrogen in α-iron Trap site

Hb , eV

References

H–H

0.07–0.11

Au and Birnbaum (1978)

C atoms

0.03

Au and Birnbaum (1978)

N atoms

0.13

Au and Birnbaum (1978)

Si, Cr, Mn, Co atoms

Smaller than 0.1

Counts et al. (2010), calculated

Y atoms

0.7–0.9

Myers et al. (1989)

Ti atoms

0.27

Pressouyre and Bernstein (1979)

TiC

0.98

Pressouyre and Bernstein (1979)

Dislocations

0.22 0.28

Sturges and Miodownik (1969), Gibala (1967) et al.

Vacancies

0.63 ~0.48

Besenbacher et al. (1987) Iwamoto and Fukai (1999)

Vacancy-carbon

0.60

Counts et al. (2010), calculated

Grain boundaries

0.08 0.67 0.51 ~0.62

Choo and Lee (1982) Gibala and Kumnick (1984) Ono and Meshii (1992) Iwamoto and Fukai (1999)

Fe3 C interface

0.87 0.58

Gibala and Kumnick (1984) Takai and Watanuki (2003)

Dislocations belong to moderate trapping sites. The corresponding experimental data in Table 3.5 were obtained from measurements of internal friction. These results depend on hydrogen concentration in the iron solid solution and dislocation density. The value of 0.28 eV definitely reflects the saturation of dislocation cores by hydrogen. In more detail, these data were discussed in Chap. 2, Sect. 2.2.2.2. Strong hydrogen trapping is produced by vacancies, see e.g. Besenbacher et al. (1987). Two binding enthalpies, 0.48 and ~0.81 eV, were obtained for deuterium in α-iron (Myers et al. 1979). A remarkable feature of vacancy-hydrogen interaction is the displacement of the hydrogen atom from the vacancy centre for up to 0.04 ± 0.01 nm, as follows from the experiment, and up to 0.06 nm, as predicted by the theory (Myers et al. 1992). Counts et al. (2010) analyzed bonding in the triple vacancy-hydrogen-carbon defect. The total V–C–H binding enthalpy of 0.6 eV was found to be similar with that in V–H complexes and not much different from the V–C binding enthalpy of 0.52 eV, as obtained by the same authors. It is also worth noting that, without a vacancy, the distance between hydrogen and carbon atoms in a stable H–C pair constitutes 3.5 Å, whereas the presence of a vacancy reduces it to 2.4 Å. This may point to repulsive H–C interaction which is to some extent compensated by the attraction of both interstitials to the vacancies. Of particular interest are the studies carried out by Iwamoto and Fukai (1999) on hydrogen desorption in pure bcc iron after heat treatments at 470–870 K under high hydrogen pressure of 1.7 GPa. About 0.1–1.5 at.% trapped hydrogen was desorbed

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in five stages, and the hydrogen amount increased with rising holding temperature. The most intensive desorption peak at 400–440 K was attributed to the release of hydrogen from vacancy-hydrogen clusters VH6 with the binding energy of ~0.46 eV. The other prominent desorption peak at 470–510 K with H binding energy of 0.62 eV was supposed to originate from hydrogen at grain boundaries/dislocations as traps. No clear knowledge has been achieved so far in relation to grain boundaries as trapping sources in α-iron. They are considered as strong traps by Gibala and Kumnick (1984), which is at variance with the experimental data obtained by Choo and Lee (1982). Not much is known, either, about hydrogen trapping by Fe–Fe3 C interfaces. It should be extremely strong, according to Gibala and Kumnick (1984), and is somewhat smaller in the studies performed by Takai and Watanuki (2003). Choo and Lee (1982) were perhaps the first to use thermodesorption analysis, TDA, in their attempt to differentiate between the contribution of grain boundaries, dislocations and microvoids to hydrogen trapping in α-iron (see Fig. 3.13). The grain size was controlled by temperature and recrystallization time. The density of dislocations was changed by varying the cold work degree. A constant

Fig. 3.13 TDA peaks of hydrogen in electrolytic bcc iron depending on the grain boundary area (a), dislocation density (b) and the amount of microvoids estimated on the basis of the relative change in density (c). Spectra were obtained at the constant heating rate of 2.6 °C/min. Redrawn from Choo and Lee (1982), Springer

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degree of preliminary cold drawing, 60%, maintained the same density of dislocations in all the measured samples. A constant fraction of microvoids was controlled by selection of samples having the same relative density of 99.85%. The intensity of the peak at 100 °C, see Fig. 3.13a, grew as the grain boundary area increased, whereas the other part of the TDA spectrum remained unchanged. A peak of 200 °C, the intensity of which grew with the increasing degree of cold work at the same initial grain size and a constant loss in the weight of samples, was attributed to hydrogen trapped by dislocations (Fig. 3.13b). A sharp increase in its amplitude occurred at deformations up to 40%. The subsequent stabilization can be attributed to dynamic recovery and the formation of a cellular dislocation structure in iron during cold drawing. The data in Fig. 3.13c refer to measurements on samples with different relative density obtained at the same grain size but with varying cold drawing from 50 to 70%. The thermal peak at 300 °C increased linearly with the decrease in the relative density of samples, while the intensity of other peaks remained unchanged, and was attributed to hydrogen trapping in the microvoids. The activation enthalpies of hydrogen atom trapping at grain boundaries, dislocations and microvoids were determined as 0.17 eV, 0.28 eV and 0.36 eV, respectively. After subtracting the activation energy of 0.088 eV for H diffusion in bcc iron, 0.08 eV, 0.19 eV and 0.27 eV were obtained, respectively, for the enthalpies of H binding to these trapping sites. Quite different values, 0.51 eV and 0.46 eV, for binding to grain boundaries and dislocations, respectively, were reported for hydrogen in bcc iron by Ono and Meshii (1992). Their model for the analysis of experimental data was based on the effective diffusion coefficient. Nagumo et al. (1999) studied the release of tritium from deformed carboncontaining iron with 0.025 mass% C. In contrast to previous studies, they observed only one broad thermal peak located between 50 and 200 °C (Fig. 3.14a). Its inten-

Fig. 3.14 Tritium thermal desorption from α-iron preliminary deformed at RT with different tensile strain (a) and the desorbed tritium quantity as a function of strain at different deformation temperatures (b). Redrawn from Nagumo et al. (1999), Elsevier

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sity increased significantly if the deformation temperature was decreased to −50 °C (Fig. 3.14b). With increasing deformation degree, the peak amplitude temperature slightly shifted to 140 °C for samples deformed at RT and more significantly, to 170 °C, for those after deformation at −50 °C. The authors emphasized the decisive role of vacancies and vacancy-carbon clusters in their interpretation of this thermal peak. The same hydrogen-induced thermal peak was obtained by Nagumo et al. (2001) in medium-carbon martensitic steel with 0.33 mass% C after quenching, subsequent tempering at 250–350 °C and mechanical preloading or loading in the presence of hydrogen. Its interpretation was also discussed by the authors in terms of point defects. In contrast, along with the peak studied by Nagumo et al. in bcc iron and steel, an additional thermal peak was detected by Takai and Watanuki (2003) in plain carbon steel with 0.84 mass% C, see Fig. 3.15. This peak appeared within the temperature range of 200–420 °C if hightemperature austenite was subjected to isothermal γ → α transformation at 550 °C and subsequent cold drawing for 85% of the reduction in area. Only Nagumo’s peak occurred if isothermal transformation was carried out at 350 °C. It disappeared when 550 °C-85%-specimens were tempered at 200 °C after hydrogen charging. Fig. 3.15 TDA profiles during heating of hydrogen-charged plain carbon steel with 0.84 mass% C subjected to preliminary isothermal γ → α transformations at 350 °C or 550 °C. After isothermal γ → α transformation, the 550 °C samples were cold drawn up to 85% of reduction in area. The dotted curve refers to the 550 °C-85% samples tempered at 200 °C immediately after hydrogen charging to avoid the low temperature TDA peak. Redrawn from Takai and Watanuki (2003), The Iron and Steel Institute of Japan

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Moreover, heat treatment with γ → α transformation at 350 °C led to a significant decrease in the ultimate strength and relative elongation of steel, whereas no degradation of mechanical properties occurred in the case of the 550 °C-85% treatment. The trap activation energies, as determined by Takai and Watanuki, were 0.24 eV and 0.67 eV for the low-temperature and the high-temperature peaks, respectively. Taking into account the H diffusion enthalpy of 0.088 eV in α-iron, the activation enthalpies for H trapping are 0.15 eV and 0.58 eV, respectively. Based on the earlier studies using TDA and ion mass spectrometry, e.g. on cold drawn pure iron (Takai et al. 1998), eutectoid steel (Takai and Nozue 2000) and cast iron (Takai et al. 2002), Takai and Watanuki (2003) identified the trapping sites for the low-temperature peak as vacancies, vacancy clusters, strain fields of dislocations, grain boundaries and ferrite/cementite interfaces. The stable high-temperature peak was attributed to microcracks which formed in the cold drawn pearlitic steels and disappeared after isothermal γ → α transformation. As regards vacancies, such interpretation is close to that proposed by Nagumo et al., although the activation enthalpy data are in conflict with those presented in Table 3.5 for H in pure α-iron. One can finally conclude that TDA experimental data for H in bcc iron and in carbon steels have not yet been properly understood and await their reliable analysis.

3.2.2 H in Austenitic Steels CrNi stainless steel 316 has been predominantly used for studies of hydrogen trapping sites. Measurements of the implanted hydrogen isotope deuterium were carried out by Wilson and Baskes (1978). Deuterium atoms were released from the traps, the H binding enthalpy of which was estimated to be ~0.3 eV. Additional trapping with the binding energy of ~0.14 eV appeared during short periods of ion bombardment. It was suggested that these traps were irradiation-induced vacancies and self-interstitial dislocation loops, respectively. The basis for the latter idea was comparison with the interaction energy of ~0.14 eV between hydrogen atoms and dislocations in CrNi austenitic steels, as determined by Atrens et al. (1977) using internal friction measurements. Hydrogen’s thermal desorption from electrochemically charged 310 and 316L stainless steel was studied by Yagodzinskyy et al. (2011) and Todoshchenko et al. (2013), respectively. A main peak at temperature shifted from 350 to 550 K with increasing charging time was observed in 310 steel, see Fig. 3.16, and attributed to hydrogen diffusion in the crystal lattice. Its complex shape was described in terms of specific hydrogen diffusion in the multicomponent fcc solid solution. The very small peak at higher temperatures was ignored. Two thermal peaks at 420–450 and 550–650 K with binding energies of ~0.1 and ~0.16 eV were detected by Todoshchenko et al. (2013). The first peak was identified

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Fig. 3.16 Hydrogen thermal desorption from steel AISI 310 electrochemically charged in 1 N\H2 SO4 + thiourea at 545 mVSCE and 50 °C, as obtained at the heating rate of 6 K/min (0.1 K/s). Redrawn from Yagodzinskyy et al. (2011), John Wiley and Sons

as caused by hydrogen diffusion in the crystal lattice containing substitutional atoms. Its complex shape was attributed to the inhomogeneous profile of hydrogen distribution in the electrochemically charged samples. The second peak was attributed to vacancies as trapping sites. A weaker interaction between hydrogen atoms and single vacancies in the fcc lattice in comparison with ~0.6 eV in the bcc iron lattice seems to be consistent with the theoretical estimates discussed above in Chap. 2, Sect. 2.1.1, and obviously related to smaller crystal lattice distortions caused by interstitial atoms in the fcc iron lattice. Quite different results were obtained by Shyvanyuk (2014) for the SUS 316L steel. A distinctive feature of his studies was the gaseous hydrogenation under the hydrogen pressure of 100 MPa. Another feature was that the retained hydrogen content in the solution-treated samples was rather large. The TDA spectra of the SUS 316L steel solution-treated before hydrogenation and obtained with two different heating rates are presented in Fig. 3.17. Despite a smaller heating rate in comparison with the spectrum of steel 310 presented in Fig. 3.16, hydrogen desorption was shifted to higher temperatures, which can be attributed to the deeper penetration of hydrogen into the sample and the different size and shape of the samples. The increase in the heating rate caused the hydrogen trapping to shift towards higher temperatures and split the spectrum into two broadened asymmetrical peaks.

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Fig. 3.17 TDA spectrum of solution-treated steel SUS 316L obtained at two heating rates of 0.028 and 0.056 K/s

The fitting of the spectrum obtained at 0.028 K/s was carried out for both solutiontreated and hydrogen-charged states. Four sub-peaks, d1 to d4 , were attributed to hydrogen traps having a different detrapping enthalpy. Charging the same solution-treated steel with high-pressure gaseous hydrogen changed the desorption spectrum, see Fig. 3.18, and shifted the start of desorption down to 300 K in comparison with 400 K in the solution-treated state. The spectra of hydrogen-charged steel have been fitted by 5 subpeaks. Gaseous charging caused an additional low temperature subpeak d5 of hydrogen desorption

Fig. 3.18 TDA spectrum of steel SUS 316L after gaseous hydrogenation

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Table 3.6 Parameters of hydrogen detrapping subpeaks before and after gaseous charging in TDA spectra of steel SUS 316L obtained at heating rate of 0.028 K/s Subpeak number

Solution treated/hydrogen charged Temperature, K

Desorption rate, W ppm/min

d1

525/530

0.003/0.003

d2

625/620

0.007/0.007

d3

740/740

0.01/0/01

d4

840/840

0.005/0.005

d5

– /475

– /0.05

with the temperature of 475 K. Its amplitude is one order of magnitude greater than that of d1 to d4 subpeaks, the temperatures and amplitudes of which are not changed by charging (see Table 3.6). The enthalpy of hydrogen detrapping, Ed , was estimated using a change in the heating rate and the following equation:   ∂ ln Tϕ2 Ed  m = − , R ∂ T1m

(3.4)

where φ is the heating rate, Tm is the temperature of the maximum in K, R is the universal gas constant. The subtraction of hydrogen diffusion enthalpy in the 316L austenitic steel, 0.56 eV (see Tison 1984; Brass and Chéne 2006) from the detrapping enthalpy makes it possible to determine the enthalpy of hydrogen binding with traps. The obtained enthalpies are presented in Table 3.7. Desorption subpeak d5 is obviously related to hydrogen in the solid solution because its activation enthalpy Ed is consistent with that of hydrogen migration in CrNi austenitic steels. The main alloying elements in this steel, chromium and nickel, control the migration of hydrogen atoms and, consequently, the rate of hydrogen desorption. Subpeak d1 can be attributed to dislocations as hydrogen traps because, as follows from Table 2.2 in Chap. 2, the enthalpy of hydrogen binding to dislocations in austenitic steels is equal to ~0.107 eV for the Cr15Ni25 composition and varies Table 3.7 Enthalpies of hydrogen desorption, Ed , and binding with traps, Eb , in 316 type austenitic steel Subpeak

d1

d2

d3

d4

D5

Ed , eV

0.65

0.83

1.02

1.2

0.56

Eb , eV

0.09

0.27

0.46

0.64

0

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between ~0.09 eV, in the case of increased Ni content, and ~0.12 eV if Cr content increases. Hydrogen-caused distortions in the crystal lattice of austenitic steels are smaller in comparison with those in bcc iron alloys. Therefore, hydrogen binding to grain boundaries, GB, is expected to be less significant. Based on the abovementioned value of ~0.08 eV for H binding with GB in α-iron, as obtained by Choo and Lee (1982), the contribution of grain boundaries to subpeaks d2 to d4 seems to be doubtful. Taking into account the rather high enthalpy, about 0.2 eV, of hydrogen binding with monovacancies in fcc iron, as well as the hydrogen-caused increase in the thermodynamically equilibrium concentration of vacancies (see Sect. 2.1) and their strong inclination to form clusters, i.e. microvoids, one can suggest that deep hydrogen traps in austenitic steels with binding energies of 0.27 up to 0.64 eV are created by vacancies and their clusters. This interpretation of hydrogen desorption in austenitic steels is consistent with the results obtained from autoradiography (Braun et al. 1971; Zouev et al. 2000). Both scientific groups studied the tritium distribution in the 304 steel in its annealed and cold worked states. It was found to be uniform after annealing, whereas the cold work resulted in tritium trapping by the slip bands. In both states, no visible tritium was recognized at the grain boundaries. These observations exclude any significant role of grain boundaries as trapping sites in austenitic steels. At the same time, they are not in conflict with the decisive role of vacancies because hydrogen atmospheres at dislocations in the slip bands produce superabundant vacancies. Forming complexes with hydrogen atoms, these vacancies cannot be removed by pipe diffusion along dislocations. The evolution of vacancy-hydrogen complexes was modelled in detail for bcc iron using molecular and cluster dynamics modelling (Li et al. 2015). Vacancyhydrogen complexes cannot be absorbed by dislocations. For this reason, they exist with concentrations of 10−5 –10−3 and can grow, thereby forming nanovoids. This modelling correlates with the earlier ab initio calculated stable vacancy-hydrogen clusters along close-packed atomic planes in iron (see Takeyama and Ohno 2003).

3.2.3 H in Nickel Louthan et al. (1975) observed a remarkable difference in the hydrogen flux through annealed and heavily cold rolled pure nickel with flux ratio of 0.8 in the former and 0.2 in the latter. The corresponding enthalpy of hydrogen permeability for the cold rolled state was equal to 0.57 eV, which remarkably exceeds that of hydrogen diffusivity, ~0.41 eV. Hydrogen trapping was attributed to dislocations in nickel. In a number of subsequent studies, preference was given to vacancies as hydrogen trapping sites. The estimation of ion-implanted deuterium binding to traps in nickel was carried out by Besenbacher et al. (1982) using ion-beam analysis techniques. In relation to the untrapping solution site, two kinds of traps were found, with trapping binding enthalpies of ~0.24 and ~0.43 eV. The first trap was associated with vacancies,

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Fig. 3.19 TDS spectra of nickel hydrogen-charged in different ways: a under high hydrogen gas pressure at 1223 K, b commercial electrolytic production and subsequent ageing for more than 30 years. The spectra are obtained at the heating rate of 5 K/min (0.083 K/s). Redrawn from Fukai et al. (2003), Elsevier

whereas a multiple-vacancy defect was suggested to be responsible for trapping with the binding enthalpy of 0.43 eV. In this connection, convincing experimental data for hydrogen trapping by vacancies in nickel were obtained by Fukai et al. (2003), see Fig. 3.19. Presented are the thermal desorption spectra obtained in the measurements carried out using the following methods: (a) holding at 1223 K for 2 h under hydrogen pressure of 3 GPa and immediate transfer for TDS measurements, (b) commercial electrolytic production and subsequent ageing for more than 32 years. In case of high-pressure gaseous hydrogen charging, Fig. 3.19a, a giant first peak is located at 380 K. It disappears after holding for several days after sample preparation and clearly belongs to hydrogen in the interstitial sites of the nickel crystal lattice. Two other peaks at 624 and 763 K were identified as desorption from vacancyhydrogen clusters. A relative amount of hydrogen in these two desorption stages was estimated as x = 6.8 × 10−2 . Two similar peaks of high intensity with the extracted hydrogen amount of 1.5 × 10−3 were observed in electrolytic nickel, see Fig. 3.19b. Their amplitudes are shifted to lower temperatures, which can be attributed to extremely long ageing before measurements. Both spectra offer evidence of the high stability of vacancy-hydrogen clusters as trapping sites. Taking into account the temperature of the first peak attributed to hydrogen desorption from the solid solution and using the value of 0.45 eV for hydrogen diffusion in nickel reported by Völkl and Alefeld (1975), the authors estimated the binding enthalpies for H in the vacancy clusters as 0.28 eV and 0.45 eV, respectively. Although these data can be corrected based on the more realistic experimental and theoretical data of ~0.41 eV for hydrogen migration enthalpy in Ni, see Sect. 3.1.3, they are consistent with the results of the first-principles calculations performed by

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Connétable et al. (2014) and Tanguy et al. (2014). In their studies, the “segregation energy” of −0.26 eV was obtained for the single-vacancy trapping of a hydrogen atom in its octahedral or tetrahedral position with some preference for the octahedral ones. Divacancies have been shown to trap hydrogen atoms with the energy gain of −0.41 eV. It is also worth noting that no hydrogen trapping was obtained for selfinterstitials in nickel, which is at variance with some previous studies, e.g. Norskov et al. (1982). In contrast, only two hydrogen thermal desorption peaks similar to those presented in Fig. 3.16 for austenitic steel 310 were observed by Todoshchenko et al. (2013) who used electrochemical hydrogen charging of pure nickel. One of the peaks was identified by the authors as belonging to hydrogen degassing from the sites of the nickel crystal lattice, which matches the low temperature peak of Fukai et al. (2003) in Fig. 3.19a. The other was attributed to hydrogen in traps with the binding enthalpy of 0.22 eV. Referring to Myers et al. (1984), dislocations in the nickel surface layer introduced due to electrochemical charging were supposed by the authors to be these traps. Such interpretation seems to be doubtful because the enthalpy of hydrogen binding to dislocations in nickel does not exceed of 0.08 eV, see Table 2.2 in Chap. 2. Generally, because of dislocation splitting, the binding of interstitial atoms with dislocations in the fcc crystal lattice is smaller than in the bcc lattice. For example, it constitutes ~0.28 eV for hydrogen in bcc iron, see Gibala (1967), and about 0.10 eV in stainless steels with the fcc iron lattice, see Table 2.2. Therefore, it is more likely that the desorption peak with binding enthalpy 0.22 eV obtained by Todoshchenko et al. (2013) is caused by hydrogen in single vacancies, as established by Fukai et al. (2003) and supported by the ab initio calculations. Possibly, because of smaller hydrogen contents resulting in the insignificant concentration of hydrogen-induced superabundant vacancies, the third desorption peak observed by Fukai et al. did not appear in the spectrum obtained by Todoshchenko et al., despite comparable heating rates.

3.2.4 H in Titanium Alloys Hydrogen desorption from α-titanium complicated by the dissociation of the δhydride formed during hydrogen charging was studied by Takasaki et al. (1995) who used X-ray diffraction, thermodesorption spectroscopy (TDS) and differential thermal analysis (TDA). At temperatures near 600 K, the δ-hydride was found to be completely decomposed into the α + β system, which pointed to an eutectoide reaction of hydride formation. At the same time, the hydride dissociation was not accompanied by any accelerated hydrogen evolution from the sample. It was concluded that hydrogen escaping from the hydride had diffused into the sample. The authors estimated the activation enthalpies for hydride dissociation and hydrogen evolution to be about 1.09 eV and 0.51 eV, respectively.

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Comparing the value of 0.51 eV for hydrogen evolution with available experimental data about the enthalpy of hydrogen diffusion in α-Ti of ~0.13 eV (Wasilewski and Kehl 1954), ~0.15 eV (Papazoglou and Hepworth 1968), ~0.14 eV (Johnson and Nelson 1973), ~0.15 eV (Covington 1979), and an even smaller one in β-Ti (see Table 3.2), one can suggest rather strong hydrogen trapping in α-titanium at temperatures where the δ-hydride is dissociated. Some light can be shed on this uncertainty by the results of positron annihilation in commercially pure α-titanium charged with 1 mass % of hydrogen from the H2 gas atmosphere at high pressure and temperature, followed by thermodesorption analysis, see Bordulev et al. (2014). The authors observed a peak of hydrogen evolution from the samples at 620 °C with its shift to 660 °C due to increasing heating rate. The activation enthalpy of hydrogen evolution was estimated as 1.04 eV, which pointed to hydride formation. The TiH1.5 hydride was identified using X-ray diffraction, and its volume fraction on the surface was measured as ~40%. This hydride disappeared during heating above 600 °C. In contrast to the results of Takasaki et al. (1995), no β-phase was formed, which is possibly related to a smaller hydrogen content in the case of saturation from gaseous hydrogen. Two positron lifetimes τ were determined in the H saturated samples: τ 1 = 148 ps and τ 2 = 235 ps with their intensities as 92.4% and 7.6%, respectively. Be a bit higher than the lifetime in non-saturated Ti samples, the τ 1 component was identified to result from the superposition of positron annihilation in the bulk and in single vacancies. The latter are stronger traps for positrons in comparison with interstitial sites. The long-lived τ 2 component was attributed to vacancy clusters. The average positron lifetime, about 155 ps, was used as a robust statistical parameter in subsequent experiments. A striking decrease in the average positron lifetime occurred above 600 °C in correlation with the start of hydrogen evolution from the samples and hydride decomposition at this temperature. The electrical resistivity had been already partly decreased before the start of hydrogen evolution. A reason for that is the relaxation of compressive stresses caused by the formation of titanium hydride during hydrogen saturation. At the same time, remarkable is the subsequent delay in the decay of the average positron lifetime with increasing temperature in relation to that of electrical resistivity. Therefore, one can conclude that the free volume of vacancy clusters responsible for the increased positron lifetime is not immediately reduced after hydrogen evolution. Certainly, these vacancy clusters are irreversible hydrogen traps with a high activation evolution enthalpy in hydrogen-saturated α-titanium, as measured by Takasaki et al. (1995) and Bordulev et al. (2014). Hydrogen trapping from β-titanium alloys was studied by Pound (1994, 1997). Using the potentiostatic pulse technique, he measured an apparent trapping characteristic and hydrogen entry flux in a number of different β-Ti alloys in their solutiontreated and aged (~500 °C) states and analyzed the relationship between the traps and hydrogen embrittlement.

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The lowest irreversible trapping was observed in the Ti-15-3 (Ti-15V3Cr-3Al-3Sn) alloy, increasing in the order of Beta-C (Ti-3.0Al-8.0V-6.0Cr3.9Mo-3.8Zr-0.1Nb-0.093O-0.01C-0.018N-0.06Fe), Beta-21S (Ti-15Mo-2.7Nb3Al-0.2Si-0.15O) and Ti-13-11-3 (Ti-13V-11Cr-3Al). The last was found to have the highest trapping constant and hydrogen flux. It was concluded that reversible hydrogen trapping by vacancies and dislocations can be ignored in β-Ti alloys, whereas the irreversible traps created by the α-phase precipitated at the boundaries of β-grains during ageing are essential. This irreversible trapping was thought to be responsible for the intergranular cracking of aged β-Ti alloys along α + β interfaces. Using thermal desorption spectroscopy together with X-ray diffraction and electron microscopy, hydrogen trapping was studied in detail by Eliezer and colleagues in β-21S alloys, see Eliezer et al. (2006). They focused on the ways of hydrogen penetration into the alloys. Electrochemical cathodic charging for 48 h led to an increase of the bcc lattice parameter without any phase transformations. Subsequent hydrogen evolution occurred at 515–584 °C at heating rates of 0.05–0.12 °C/s, respectively (Fig. 3.20a). In comparison with the available hydrogen migration enthalpies, see Table 3.2, the obtained activation enthalpy of 0.28 eV points to rather weak trapping sites, the role of which can be played by vacancies, dislocations and even grain boundaries. Very weak reflections of the α-phase appeared after thermal hydrogen desorption. In contrast, gas-phase hydrogenation under the pressure of about 5 bar at 500 °C resulted in the formation of the tetragonal TiH2 hydride with c/a > 1 and intergranular cracking. A rather large amount of the α-phase appeared after hydrogen desorption accompanied by the dissociation of the hydride. The hydrogen desorption spectrum was quite different from that of cathodic charging, see Fig. 3.20b. A low-intensity peak, the temperature of which increased from 249 to 315 K with increasing heating rate, was characterized by the hydrogen evolution activation enthalpy of 0.12 eV. Its nature was obviously the same as in the case of the electrochemical charging. The activation enthalpy of the broad second peak with amplitudes at 484–508 K was estimated to be equal to 1.06 eV, which is close to the 1.09 eV for δ-hydride dissociation found by Takasaki et al. (1995) in hydrogenated pure α-titanium. Its nature is clearly related to hydrogen evolution from the intergranular cracks which are irreversible traps. Moreover, this peak is decomposed into two subpeaks at the top heating rate. The authors suggested two phenomena responsible for this two-stage hydrogen release: the precipitation of hydride and its dissociation with increasing temperature. Hydrogen desorption from two-phase (α + β) titanium was studied by TalGutelmacher et al. (2007) using the example of the Ti-6Al-4V alloy which has a bi-modal structure with 60 vol.% α- and 40 vol.% β-phase formed using a special thermomechanical treatment described in detail by Tal-Gutelmacher et al. (2004). The cases of electrochemical and gaseous hydrogen charging were compared. A single desorption peak centred at temperatures of 548–584 °C depending on the heating rate and characterized by the H evolution activation enthalpy of ~1.12 eV was observed after electrochemical charging. It was attributed to hydrogen desorption

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Fig. 3.20 Hydrogen evolution from β-21S alloy charged electrochemically (a) and from the gas phase (b). Redrawn from Eliezer et al. (2006)

from the (α + β) interface referring to Young and Scully (1993), who were the first to suppose such an irreversible hydrogen trap. The X-ray diffraction measurements revealed hydride formation during charging and its dissociation in the course of hydrogen desorption. In contrast, in the case of gaseous hydrogen saturation, a single desorption peak was located at lower temperatures of 404–431 °C with the activation enthalpy of about 1.04 eV. Similar to electrochemical charging, hydrogen evolution was accompanied by hydride dissociation. The variance in the temperatures and activation enthalpies was attributed to a different initial microstructure. The α- and β-phases along with the Ti hydride were present after electrochemical charging, whereas only the δ-hydride existed after gaseous hydrogenation.

3.3 Hydrogen Transport by Dislocations

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3.3 Hydrogen Transport by Dislocations Measuring internal friction at room temperature in hydrogen-free and hydrogencharged cold worked iron, Bastien and Azou (1951) showed that hydrogen increases the damping of introduced mechanical vibrations. The observed phenomenon was attributed to the segregation of hydrogen atoms at moving dislocations, and this, in fact, was the first observation that hydrogen atoms accompany dislocations during their slip. This surprising result and its proposed interpretation did not find any remarkably quick response. However, in time there was a growing number of experimental data which could not be simply interpreted in terms of hydrogen lattice diffusion. Boniszewski and Smith (1963) demonstrated a hydrogen-caused sharp yield point and the Portevin–Le Chatelier effect during the deformation of nickel. With reference to Bastien and Azou, they interpreted both phenomena as the manifestation of hydrogen segregation to stationary and moving dislocations, respectively. Moreover, by claiming in conclusions that “hydrogen embrittlement occurs in nickel at temperatures and strain rates at which hydrogen atoms can segregate to moving dislocations”, the authors anticipated the underlying idea behind the phenomenon of hydrogen enhanced localized plasticity phenomenon, HELP, responsible for hydrogen embrittlement of metals (see Chap. 5). Developed further by Wilcox and Smith (1965), the concept of hydrogen transport by sliding dislocations was applied to studies of the intercrystalline fracture in hydrogen-charged nickel. Their interpretation suggested the movement of dislocations together with their hydrogen clouds into the grain boundary. Louthan et al. (1972) demonstrated the important role of hydrogen interaction with moving dislocations in hydrogen migration throughout the crystal lattice, in their experiments with the uptake of tritium in the 304L stainless steel. Tritium penetration was deeper in the plastically strained region of tensile specimens compared with that in the elastically strained region (see Fig. 3.21). These measurements were continued by Donovan (1976) who demonstrated a higher concentration of tritium absorbed during plastic deformation in preliminary annealed nickel samples in comparison with their non-deformed zone. At the same time, the quantity of absorbed hydrogen and its distribution were not affected if the nickel samples were previously deformed. In other words, stationary dislocations do not accelerate hydrogen atom migration. Hydrogen transport by dislocations was also suggested as a reason for the accelerated fatigue crack growth in the hydrogen environment. For example, studying crack growth in thoria-dispersed nickel and nichrome, Frandsen et al. (1973) observed that little or no crack growth occurs under internally charged hydrogen. At the same time continual supply with hydrogen from the gas phase during fatigue tests increased the crack propagation rate by a factor of two. Chu et al. (1979) studied hydrogen-induced delayed plasticity and cracking in high-strength steels and came to conclusion that hydrogen alone was responsible for the enlargement of the plastic zone. Analyzing this result, Tien et al. (1980)

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Fig. 3.21 Tritium penetration into 304L steel exposed in hydrogen at 22 °C for 15 days under tension loading. Redrawn from Louthan et al. (1972), Elsevier

substantiated the critical role of hydrogen dislocation transport in this phenomenon, which directly controls the rate of intergranular cracking. Kinetic models of hydrogen transport by dislocations were proposed by Johnson and Hirth (1976) and Tien et al. (1976) for the supersaturation of solid solutions with hydrogen and for hydrogen enrichment at interfaces and voids as stronger traps. The former is based on the suggested annihilation of H-transporting dislocations in the absence of traps and excessive hydrogen leaks from the annihilation sites to the nearest hydrogen sinks. According to the latter model, internal traps strip hydrogen atmospheres from dislocations. The resulting local hydrogen enrichment depends on hydrogen-trap binding and the time balance between the arrival of swept hydrogen to the traps and its departure by diffusion into the surrounding matrix. Nair et al. (1983) analyzed both models as competition between hydrogen diffusivity and hydrogen-trap binding. The strip model was estimated to be valid both in the case of slow and fast hydrogen diffusion, as well as for weak and strong hydrogen traps. In the case of weak hydrogen diffusivity (e.g., in austenitic steels), dislocation annihilation supports enrichment if the distance between annihilation events does not exceed ~10 μm, whatever the trap type. Hydrogen transport was also analyzed by Sofronis and McMeeking (1989) for the case of hydrogen distribution ahead of a blunting crack tip. Based on the large elastic–plastic deformation, they predicted that hydrogen is trapped by dislocations rather than concentrating at normal interstitial lattice sites, which should result in its preferential distribution near the crack surface. These studies were continued by Taha and Sofronis (2001). The prevailing hydrogen trapping at the surface of the crack tip

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123

was confirmed with some refinement related to the types of materials and kinds of mechanical loading. For example, hydrogen trapping in pre-cracked steel specimens should dominate regardless of steel strength. In pre-cracked niobium strained under yielding, trapped hydrogen dominates at its initial small concentrations and accumulates at the crack tip surface. However, at large initial hydrogen concentrations, normal interstitial lattice sites take priority, and hydrogen atoms are localized ahead of the crack tip. Some specificity appears in the case of bending mechanical tests. Later, a revised model for hydrogen transport by dislocations was proposed by Dadfarnia et al. (2015) in order to interpret copious plasticity in a large volume afield from a crack tip before the fracture. This model accounted for hydrogen transport by moving dislocations along with stress-driven diffusion. In an attempt to clarify the specific role of the dislocation type in hydrogen transport, a unique experiment was carried out by Hwang and Bernstein (1986). The authors used three different sections of a nickel single crystal along three tensile axes, allowing the initiation of slip systems with dominating screw, edge or mixed dislocations. The hydrogen flux during plastic deformation was estimated for all types of dislocations from their egress on the monitored crystal surface. A discontinuous hydrogen flux was obtained for the egress of screw dislocations. In the case of outgoing edge and mixed dislocations, the crystal surface was intersected by kinks sliding along the screw dislocations, which resulted in a continuous flux of hydrogen. With increasing strain rate, the hydrogen flux decreased because hydrogen atoms left dislocations once some critical breakaway velocity was achieved. This effect strongly appeared in the case of edge and mixed dislocations where the kink velocity is the fastest. At low strain rates, the edge kinks revealed the highest capacity for hydrogen transport. A weak transport dependence on the lattice hydrogen concentration was observed and attributed to the kinetic nature of this phenomenon. An interesting feature of hydrogen transport by dislocations was found by Takasawa et al. (2010). They observed this phenomenon in high-strength low-alloy steel at applied stresses below yield strength, i.e. during elastic strain. At the same tensile strains, lower-strength steels absorbed more hydrogen. Remarkably, the activation enthalpy of hydrogen desorption did not depend on the strength of the steels, which is a sign of the same kind of trap sites. The enhancement of hydrogen absorption was attributed to moving dislocations initially contained in the steels. Somewhat consistent with this study are the data on hydrogen desorption from pure iron and Inconel 625 during elastic and plastic deformations studied by means of mass spectrometry (Takai and Shoda 2009). The authors did not detect hydrogen desorption during the elastic deformation of Inconel 625 due to its high yield stress and a distinct boundary between the elastic and plastic zones in the stress–strain curve. In contrast, slight hydrogen desorption during elastic deformation occurred in pure iron due to its low and not clearly resolved yield stress. Therefore, the pinning of dislocations was weak, allowing them to easily move and transfer hydrogen atoms to the specimen surface. Above the yield stress, hydrogen desorption sharply increased,

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quickly reached its maximum and then gradually decreased with plastic strain. Important was also the increase in the quantity of desorbed hydrogen with a decreasing strain rate. This phenomenon was obviously controlled by the balance between dislocation velocity, hydrogen diffusivity and the binding between hydrogen atoms and dislocations. Hydrogen diffusion in Inconel 625 is six orders of magnitude lower, and the enthalpy of hydrogen-dislocation interaction in fcc nickel, ~0.08 eV, is much smaller than in pure iron, ~0.28 eV. Therefore, the effect of the strain rate on hydrogen desorption should be stronger in metals with the fcc lattice. Another way to detect hydrogen transport by dislocations in combination with hydrogen dislocation trapping was proposed by Yi (2017) who used permeation measurements in a commercial X80 pipeline steel during its tensile tests. In the case of tension with a slow strain rate, current density was found to increase with elastic deformation and then sharply decrease with the start of plastic deformation. The latter was linked to the trapping of hydrogen by the emitted dislocations. After some trapping stage, the permeation current increased with increasing plastic deformation and reached a steady stage, pointing to a balance between the trapping of dislocations and their movement. A new idea for studies of hydrogen trapping/transport phenomena was implemented by Pu and Ooi (2019) using the microprint technique which does not require radioactive hydrogen isotopes. It is based on the reaction of silver with hydrogen, Ag+ + ½H2 = Ag0 + H+ . As a result, hydrogen diffuses out of the sample, reducing deposited Ag atoms at the hydrogen-rich sites on the sample surface. The authors studied hydrogen visualization at the surface of a 304 type steel in three cases: (i) H charging + deformation by compression + microprint; (ii) H charging + ageing at RT + compression + microprint and (iii) compression + H charging + microprint. With some silver atom background throughout the surface, a clear preferential deposition of silver particles in the deformation slip bands was observed in the first case. The ageing before deformation in the second case led to hydrogen diffusion out of the sample, so that the microprinted surface was free of silver. At the same time, silver deposition on the slip bands still occurred and was even more distinctive. This observation appears to evidence strong hydrogen trapping in the slip bands by dislocations or vacancies which were produced within the hydrogen atmospheres at dislocations. Predominant trapping by vacancies seems to be more probable because of higher H-binding enthalpy. In the third case, silver was distributed homogeneously, without its preferential deposition on the slip bands. Therefore, hydrogen atmospheres at dislocations mainly contributed to its distribution on the surface sample. Acting as hydrogen traps, they transported hydrogen atoms during plastic deformation and, along with the vacancies, caused hydrogen location within the slip bands in the first case. The hydrogen left after ageing in the solid solutions was trapped by moving dislocations, which resulted in the absence of hydrogen throughout the surface and its localization within the slip bands, where it was held by both dislocations and vacancies. Dislocations located in the slip bands

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at the surface in the third case did not take part in hydrogen trapping and, for this reason, did not prevent hydrogen degassing.

3.4 Hydrogen Migration Along Grain Boundaries It is still widely accepted that grain boundaries, GB, are the fast diffusion paths for solutes in metals. This idea is traditionally used for both migrating substitutional and interstitial solute atoms. At the same time, in relation to hydrogen diffusivity, the available experimental data are rather controversial. Two features were common in studies where accelerated hydrogen diffusivity along the grain boundaries has been observed: (i) measurements were carried out using the hydrogen permeation technique with electrochemical charging, (ii) quantitative estimations revealed a huge scattering. For example, based on the data of measuring the tritium concentration profile in the 304 and 316 type austenitic steels, Calder et al. (1973) reported that the GB diffusion coefficient was 8 orders of magnitude higher than that for bulk diffusion. Using secondary ion mass spectrometry (SIMS) for hydrogen in nickel, Tsuru and Latanision (1982) analyzed hydrogen permeation in polycrystalline nickel. Applying a standard model proposed earlier by Devanathan and Stachurski (1962) for the treatment of H permeability data, they obtained 60–100 fold enhancement in GB diffusion. It was also noted that diffusion coefficients in the bulk and GB did not depend on sulfur segregation at the grain boundaries, which seems unexpected. In their studies of hydrogen permeability, Brass and Chanfreau (1996) reported hydrogen diffusion in nickel to be 2–7 times faster along grain boundaries than in the bulk. Measurements on nickel bicrystals were undertaken by Ladna and Birnbaum (1987) for the analysis of the H distribution profile and its dependence on the grain boundary structure. In this case, diffusivity enhancement by a factor of 8–17 occurred only for the high energy 9 boundaries and was absent in the case of the low energy 11 boundaries. Fast hydrogen diffusion along the grain boundaries in nickel was also claimed by Kimura and Birnbaum (1987). Studying the kinetics of hydrogen-caused intercrystalline fracture, they found the hydrogen penetration depth to be remarkably larger than expected for lattice diffusion and attributed this effect to enhanced hydrogen GB diffusion. The estimated enhancement of diffusion was only by a factor of 2. Scattering of experimental data on the H diffusion enhancement level for the same materials is typical in such studies. It is not trivial, either, that the observed increase of hydrogen GB diffusion depends on the type of materials, regardless of the enthalpy of hydrogen migration in the bulk. It is several orders of magnitude higher in austenitic steels than in nickel, although the enthalpy of hydrogen diffusion in nickel, 0.4 eV, is much lower in comparison with 0.49–0.57 eV in CrNi austenitic steels (see Sect. 3.2.3 and Table 3.1, respectively).

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In contrast to the above results, the enhancement of hydrogen diffusion along the grain boundaries was not confirmed in several studies. Moreover, according to Beck et al. (1966), the H diffusion coefficient obtained from hydrogen permeation measurements in the zone-refined iron single crystal is 30% larger in comparison with that in the polycrystal. No grain boundary effect was reported by Chew and Fabling (1972) who measured the hydrogen diffusion coefficient at temperatures of RT to 200 °C in mild steel with coarse and fine grain structures. In both cases, the diffusion coefficients were indiscernible and significantly lower than the values extrapolated from higher temperatures. The latter evidenced the role of grain boundaries as trapping sites. A similar result was obtained by Robertson (1973) in his measurements of hydrogen permeability and diffusion coefficient within the temperature range of RT to 500 °C in pure nickel with the grain size of 30–104 μm. Hagi et al. (1979) measured the hydrogen diffusion coefficient at RT in the iron single and polycrystal and also failed to find any effect of the grain boundaries. Contradictory results were reported by Sidorenko and Sidorak (1973) who studied the hydrogen permeability of commercial iron. The measured activation enthalpy for hydrogen diffusion along the grain boundaries was twice as large as for bulk diffusion, whereas hydrogen diffusivity in the bulk turned out to be 3 times smaller. The authors explained this discrepancy as the greater contribution of the pre-exponential factor D0 to the coefficient of GB hydrogen diffusion compared to that of the activation enthalpy. Later, Sidorenko and Sidorak (1975) reported that the lattice hydrogen flux prevails in nickel and copper, whereas GB flux is dominant in iron. The attempt to solve the acceleration-deceleration inconsistency in hydrogen GB diffusion was made by Yao and Cahoon (1991a). Using a simple model of a polycrystalline metal with a varied uniform grain size and taking into account hydrogen segregation at grain boundaries, they analyzed the effect of the grain size and segregation factor on the breakthrough time for hydrogen penetration to be determined by the monitoring system in experiments on hydrogen permeation. Based on these studies, a precondition has been formulated that “for most materials, an average grain size of 10 μm should be sufficient to reveal enhanced grain boundary transport of hydrogen”, even when the ratio DGB /DL between the grain boundary and lattice hydrogen diffusivities is small and the lattice diffusion is more dominant. The obtained theoretical estimations were tested in the experiments on polycrystalline nickel using the electrochemical hydrogen permeation and silver decoration method (Yao and Cahoon 1991b). As a result, no grain boundary enhancement for hydrogen transport was detected. It was concluded that hydrogen atoms can cross grain boundaries overcoming their binding energy, but migration along GB is retarded by some trapping sites in the GB structure. A common feature of experimental studies presented in this Section is the implicit preconceived idea about grain boundaries being the fast diffusion paths for any solute, whether interstitial or substitution, atoms. The occurrence of some free space within the grain boundaries constitutes the background to this idea. The same is considered to be true for pipe diffusion along dislocations.

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However, this fails to take into account the fact that the only available mechanism for this kind of diffusion enhancement is related to vacancies the concentration of which increases within the grain boundaries and dislocation pipes. Therefore, this mechanism is acceptable only for substitution solute atoms, whereas the atoms of interstitial elements like hydrogen, carbon, nitrogen etc. form complexes with vacancies and, for this reason, are expected to have limited diffusivity. In general terms, the transfer of interstitial atoms from solid solutions to grain boundaries or dislocations decreases the elastic term in their gradient of chemical potential as the driving force for diffusion. One of the first experimental proofs of binding between interstitials and vacancies was obtained for carbon and nitrogen in irradiated bcc iron by Weller and Diehl (1976) who measured Snoek relaxation using the internal friction technique. They showed that complexes C(N)-V1 of N and C atoms with single vacancies in α-iron having the binding enthalpy of ~0.8 eV and dissociation enthalpy of ~1.6 eV remain stable up to 200 °C and 250 °C, respectively. The diffusion hops of interstitial atoms in these complexes are shifted to higher temperatures in comparison with their diffusion on the interstitial sites in the lattice. Hydrogen-vacancy complexes in metals are described in Chap. 2, Sect. 2.1.1. Therefore, diffusion of interstitials in the presence of crystal lattice defects should be analyzed in detail in order to understand contradictory experimental data about the enhancement of hydrogen diffusion along grain boundaries.

3.4.1 Grain Boundary Diffusion of Interstitial and Substitution Solutes In an attempt to shed light on the fundamental difference between the diffusion mechanisms of these two kinds of solutes, let us as discuss, for example, the experimental data obtained using radioactive carbon and cobalt. One of the earliest studies of iron and iron-based solid solutions was carried out by Bockstein et al. (1961) who investigated how radioactive carbon from deposited BaCO3 migrates along the grain boundaries and in the bulk within the temperature ranges of bcc and fcc iron. The measurement technique included the assessment of carbon concentration at the grain boundaries and in the bulk on the autoradiographic replicas obtained using the sectioning method at different depths below the surface. The data for carbon in bcc iron are presented in Fig. 3.22. It is seen that carbon penetration in the bulk approaches zero at the depth of about 9 × 10−3 mm, whereas its amount at the grain boundaries remains remarkable at a significantly larger distance from the surface. Based on the obtained data, the authors concluded that carbon diffusion in the α- and γ-iron phases proceeds at a much faster rate along the grain boundaries in comparison with lattice diffusion. The carbon grain

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Fig. 3.22 Density of blackening in autoradiographic replicas as a function of carbon diffusion depth in the bulk and on the grain boundaries of bcc iron at 550 °C. Bockstein et al. (1961), Springer

boundary diffusion coefficient in α-iron was estimated to be 3–4 orders of magnitude larger than in the bulk. Unfortunately, a methodical error occurred in this study. The more often carbon atoms cross the grain boundary, the more carbon should remain segregated at GB. GB-carbon binding energy should be spent on its return to the bulk. Therefore, with increasing distance from the surface on which radioactive carbon is deposited, the carbon content in the bulk should decrease and approach zero, whereas its remarkable part is doomed to migrating along the grain boundaries, regardless whether its diffusion is enhanced or retarded. This was the very phenomenon observed by Bockstein et al. in their experiments. Using the same technique of the surface deposition of radioactive elements, Teus et al. (2014) compared carbon and cobalt diffusion in iron. The grain size was varied in order to investigate the effect of the GB area on the penetration depth of radioactive atoms. Measurements of the autoradiography profile orthogonal to the surface of samples and the sectioning method were used for carbon and cobalt, respectively, to estimate their total content as a function of the distance from the surface. As follows from the data in Fig. 3.23, the penetration depth of cobalt atoms is enhanced with decreasing grain size, whereas the carbon penetration is delayed.

Fig. 3.23 Migration depth of 820 μm

60 Co

(a) and

14 C

(b) in the α-iron having grain size of 170 and

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129

Fig. 3.24 Processing of autoradiography and sectioning method results using the graphical differentiation technique for the case of 14 C (a) and 60 Co (b) in α-iron

In other words, as the area of the grain boundaries increases, cobalt diffusion is accelerated, whereas carbon diffusion is reduced. Based on these measurements, the so-called diffusivity parameter P = Dgb sδ was calculated, where Dgb is the grain boundary diffusion coefficient, s is the segregation factor and δ is the grain boundary width. The diffusion characteristics are presented in Fig. 3.24 using the graphical differentiation technique. Here the penetration parameter C = N/Y is used with N as the pulse count and Y as the penetration depth. Based on the analysis performed by Claire (1963), the grain boundary diffusivity parameter could be calculated using the following formula:  P = DG B sδ = n

∂ ln c ∂ y 6/5

−5/3 

4D t

1/2 ,

(3.5)

where D is the bulk diffusion coefficient, t is the time, n is a coefficient that depends on the relationship between the diffusivity parameter and the bulk diffusion value, and tgα = ∂ ln c/∂ y 6/5 is the slope angle in Fig. 3.24. A reasonable value of the grain boundary width δ is about 0.5 nm, see e.g. Inoue et al. (2007). At the same time, there is some uncertainty as to the grain boundary segregation factor s, which makes direct calculation of the grain boundary diffusion coefficient difficult. For this reason, the diffusion parameter P for samples with different grain size was obtained from the slope angle of the curves in Fig. 3.24. The obtained ratio PGB 170 /PGB 820 = DGB 170 /DGB 820 characterizes the change in the diffusion of solute elements with varying total grain boundary area. These data are summarized in Table 3.8. As the grain boundary area increases, diffusion is accelerated in the case of substitution Co atoms and slowed down for interstitial C atoms. For each element, the penetration distance corresponds to grain sizes 170/820 μm.

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Table 3.8 Results of 14 C and 60 Co diffusion in α-iron obtained using the autoradiography profile and sectioning technique Radioactive element 14 C

→ Fe

60 Co

→ Fe

Penetration distance, μm

P = DGB 170 sδ, m3 /s

P = DGB 820 sδ, m3 /s

DGB 170 /DGB 820

24/15

2.54E−15

1.93E−14

0.13

413/600

5.61E−22

3.42E−22

1.64

One should add that the same is true for the pipe diffusion of interstitial atoms along dislocations. As established in a number of studies, carbon diffusion is accelerated during plastic deformation, which can be easily interpreted in terms of carbon transport by moving dislocations. At the same time, it is generally accepted that carbon pipe diffusion is accelerated in cold worked metals, i.e. no distinction is made between interstitial atom diffusion during and after deformation. Meanwhile, this matter was resolved conclusively back in the 1970s. Using sectioning autoradiography to study carbon diffusion in cold worked iron and nickel, as well as in iron-silicon and iron-chromium alloys, Matosyan and Golikov (1970) convincingly demonstrated that prior cold rolling with 10–75% reductions in area retards carbon diffusion. It is also relevant to quote the above experimental data obtained by Schumann and Erdmann-Jesnitzer (1953) about the effect of prior cold work on the permeability of hydrogen in cast steel, see Fig. 3.11. With up to 20% of deformation, hydrogen permeability increases because the retained stresses enhance interstitial atom diffusion. At plastic strain higher than 60%, hydrogen permeability approaches zero because the well-developed dislocation cell structure is formed parallel to rolling direction and retards interstitial atom diffusion.

3.4.2 Thermodynamic Simulation of Hydrogen Atom Diffusion Hydrogen diffusion in α-iron and the interaction of H atoms with grain boundaries were simulated by Teus et al. (2014) using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package, Plimpton (1995). In view of different approaches used in molecular dynamics, the simulation technique is described below in some detail. For the case of hydrogen in α-iron, a single crystal of pure iron with a bcc crystal structure and dimensions of 143 × 143 × 143 Å3 was constructed with crystallographic axes of , and . It contained approximately 250,000 atoms. For carbon, the cell size of 115 × 115 × 115 Å3 contained 128,000 iron atoms. Symmetric tilt grain boundaries were generated within the framework of the coincidence site lattice theory (CSL), Fortes (1972).

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131

According to this theory, a symmetric tilt grain boundary is created by rotating two parts of the single crystal around the tilt axis and connecting them along the boundary. The rotation axis was chosen and the grain boundary planes were (310), (410) and (710). An energy minimization procedure was applied to get an equilibrium configuration with a minimum energy value. The simulation cells for each case had a rectangular shape, and the side lengths were chosen to satisfy the CSL conditions. For all cells, the periodic boundary conditions were applied. Hydrogen atoms were homogeneously distributed over the entire volume of the cells taking into account the well known data that hydrogen atoms thermodynamically prefer to occupy tetrahedral interstitial sites in the bcc lattice. For all the simulations, the hydrogen concentration did not exceed 2 mass ppm, which can be obtained experimentally. To characterize atomic interactions, a potential developed for α-iron by Ramasubramaniam et al. (2009) was used. An extensive database of energies and atomic configurations obtained using density functional theory (DFT) calculations was analyzed in order to fit the cross-interaction between Fe and H atoms. Initially, hydrogen atoms were homogeneously distributed over the simulation cell. During relaxation, hydrogen atoms segregated at grain boundaries, as shown in Fig. 3.25. This result is in agreement with the experimental data reported by Wang (2001) and Ohmisawa et al. (2003). The diffusion coefficient of hydrogen has been calculated using the mean square displacement parameter (MSD). According to the Einstein expression, 1 M S D, 6t  M S D = |r (t) − r (0)|2 , D=

(3.6) (3.7)

where t is a time interval, r(t) − r(0) is a distance traveled by an atom over the time interval t.

Fig. 3.25 Schematic view of hydrogen atom redistribution in the presence of a grain boundary in comparison with the bulk

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Fig. 3.26 Time dependence of the mean square displacement of hydrogen atoms in bulk α-iron at different temperatures. The Arrhenius dependence of the hydrogen diffusion coefficient on the inverse temperature is shown in the inset

The MSD variation with time for hydrogen in α-iron is shown in Fig. 3.26. The linear part of the curves allows the diffusion coefficient to be determined. The inverse temperature dependence of the hydrogen diffusion coefficient is shown in the inset. The data obtained for bulk hydrogen diffusion in α-iron at room temperature, D = 0.83 × 10−8 m2 /s, is 2.8 times higher than the results given by other classical molecular dynamic studies, but is consistent with the experimental data reported e.g. by Nagano et al. (1982). The discrepancy with other calculations can be attributed to a different potential used. The potential used in our case describes the Fe–H and H–H interactions more correctly. It should be noted that, in some cases, the used temperature range exceeds 1185 K, i.e. is above the transition point from the bcc to the fcc phase in iron. At such temperatures, the bcc structure was retained in order to decrease statistical deviations in the calculated diffusion coefficient. Taking into account the fact that temperature affects only migration velocities in the simulation, i.e. the kinetic energy of particles, such approximation is considered to be reasonable. It is also important that, in comparison with real-life experiments, the calculated system is closed to hydrogen escape, and hydrogen atoms can only migrate and redistribute between crystal lattice defects. To some extent, such conditions are realized during high pressure gaseous hydrogenation at elevated temperatures where dissolved hydrogen is in equilibrium with the external environment. The temperature dependence of hydrogen diffusion in α-iron is presented in Fig. 3.27 in the Arrhenius co-ordinates for three types of special grain boundaries.

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133

Fig. 3.27 Arrhenius dependence of hydrogen (a) and carbon (b) diffusion coefficients on the inverse temperature for three types of special grain boundaries

All the data are summarized in Table 3.9. As follows from it, the angle dependence of the grain boundary energy repeats the trend previously reported by Shibuta et al. (2008) who performed molecular dynamics simulations using the Finnis–Sinclair potential, and Jaatinen et al. (2010) who used the phase field crystal model. Therefore, it is confirmed that some energy cusps occur in such a dependence, which could be explained by special atomic ordering which causes a change in the grain boundary energy.

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Table 3.9 Results of molecular dynamics simulation of hydrogen diffusion in bcc iron Iron

Misorientation angle, θ°



Energy, mJ/m2

Activation enthalpy, eV

Bulk

–

–

–

0.037 ± 0.04

(310)[001]

36.87

5

1073

0.314 ± 0.017

(410)[001]

28.07

17

1102

0.341 ± 0.011

(710)[001]

16.26

25

1023

0.244 ± 0.001

Perfect agreement is obtained between the calculated data and the experimental measurements of activation enthalpy for hydrogen diffusion in the bulk, as measured by Nagano et al. (1982) and Dufresne et al. (1976) in bcc iron. Diffusion of interstitials in the vicinity of grain boundaries clearly needs a higher activation enthalpy in comparison with that in the bulk. The simulation of hydrogen permeation is presented in Fig. 3.28, and the graphical analysis of these data is given in Fig. 3.29. Starting from a homogeneous distribution of hydrogen atoms on the side of a crystal containing the grain boundary, the concentration profile is significantly modified with time. The average penetration distance of hydrogen atoms along the grain boundary is smaller than in the bulk, which corresponds to different hydrogen diffusion coefficients in these two areas. A simple physical substantiation can be proposed for the retarded diffusion of interstitial atoms along grain boundaries. If interstitial atoms in the solid solution approach the grain boundary, the elastic term disappears from the chemical potential gradient or significantly decreases because of the excessive volume within the GB. Thus, the grain boundary diffusion of such atoms should be slow in comparison with that in the bulk. Fig. 3.28 Schematic presentation of hydrogen atom redistribution in an iron sample with the 5(310) grain boundary after the time interval of 70 ps

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Fig. 3.29 Steps of hydrogen penetration in iron crystal with the 5(310) boundary. Initially, hydrogen atoms were homogeneously distributed on the surface of the simulated crystal. Crystal size is 90 × 180 × 85 Å3

Therefore, a huge increase in hydrogen diffusion along the grain boundaries, as reported, e.g., by Calder et al. (1973), Brass et al. (1990), Brass and Chanfreau (1996) etc., needs a more appropriate interpretation.

3.4.3 A Mechanism for Enhanced Hydrogen Flux Along Grain Boundaries As mentioned above, a feature of the experiments on hydrogen diffusion in metals performed using the hydrogen permeation technique is electrolytical hydrogen charging. A simple reason for that is to do with the significantly longer time required for measurements in the case of gaseous hydrogenation. The well-known significant gradient of hydrogen concentration appearing during electrolytical charging can be the key to understanding the observed distinction in the bulk and grain boundary hydrogen diffusion. Mogilny et al. (2020) were the first to use the method of rocking curves to shed light on a possible hydrogen-caused change in the crystal structure during its permeation measurements using electrochemical versus gaseous hydrogenation. The method of rocking curves also known as the ω scan is used for X-ray diffraction studies of crystallographic orientations in polycrystalline metals, see Fig. 3.30.

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Fig. 3.30 Rocking curves in (111) reflection at 2θ = 43.62° of the Fe-36Ni sample after annealing (a) and electrochemical hydrogen charging in the 1 N H2 SO4 + 125 mg/l NaAsO2 solution at the current density of 50 mA/cm2 for 15 min (b), 4 h (c) and 24 h (d)

It amounts to simultaneous measurements of the same diffraction reflection from different grains. In fact, the rocking curve is a radial section of the full pole figure. Presented in Fig. 3.30 are results of measurements on the Fe-36Ni alloy after its annealing and subsequent electrochemical charging for different durations. The rocking curve provides a set of isolated (111) diffraction peaks from a number of grains, which corresponds to the polycrystalline state of the annealed alloy. Their broadening occurs already after hydrogen charging for 15 min (Fig. 3.30b), which is evidence of plastic deformation resulting in the increase of dislocation density. The broadening is strengthened with increasing time of charging (Fig. 3.30c). Along with broadening, the intensity of reflections is changed, which is a sign of a crystallographic texture forming. Both tendencies intensify with longer charging times. After charging for 24 h, see Fig. 3.30d, reflections from different grains are not distinguished, and no remarkable change occurs with further increase in hydrogenation time. The rocking curves of samples subjected to charging for 24 h in comparison with those for the annealed state are shown in Fig. 3.31 for reflections (111) and (200). A feature of these data is that hydrogen enhances diffraction from (111) planes and decreases it from (200) planes, which confirms that a strong crystallographic texture has been formed.

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Fig. 3.31 The same as in Fig. 3.30 after annealing and electrolytic charging for 24 h in reflections (111) at 2θ = 3.62° (a) and (200) at 2θ = 50.82° (b)

The same series of measurements was performed on samples subjected to gaseous hydrogen charging, see Fig. 3.32. Gaseous hydrogenation at 350 °C made sure that hydrogen distribution throughout the sample was homogeneous. The ω scan diffraction is identical in both H-free and H-charged samples, which points to the absence of any plastic deformation. The data in Figs. 3.31 and 3.32 clearly show that, in contrast to gaseous hydrogenation, electrochemical hydrogen charging is accompanied by strong plastic deformation resulting in the increase of dislocation density and the formation of a crystallographic texture. Stresses caused by the hydrogen concentration gradient seem to be the only possible reason for the induced plastic deformation.

Fig. 3.32 Rocking curves of the annealed Fe-36Ni sample subjected to gaseous hydrogen charging at 350 °C for 30 h at hydrogen pressure of 12 MPa

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One of the first calculations and measurements of the hydrogen concentration gradient formed by electrochemical hydrogen saturation of the samples was performed by Atrens et al. (1979) who calculated the concentration profiles resulting from hydrogen charging of iron austenite and showed that hydrogen concentration falls by a factor of 10 within the surface layer of 5 μm. Farrell and Lewis (1981) carried out similar calculations and measurements using nuclear microanalysis for austenitic steel AISI 310. Zhao et al. (2015) compared the hardness of a low carbon steel subjected to electrochemical or gaseous charging. In comparison with the uncharged state, hardness was increased by cathodic and decreased by gaseous charging. The authors interpreted the obtained results in terms of a difference in the absorbed hydrogen amount and its increased concentration at the sample surface in the case of cathodic charging. Neither study raised the possibility of plastic deformation. Studying silver decoration evolution in experiments with hydrogen permeation through iron, Koyama et al. (2017a) observed that silver particles first appeared at grain boundaries before their identification in the grain interior, and concluded that grain boundaries are the sites with maximum hydrogen flux. However, as mentioned in Sect. 3.4.3.1, the retarded diffusion of hydrogen atoms along grain boundaries in iron was demonstrated by Teus et al. (2014) and Gavriljuk and Teus (2017) based on molecular dynamics simulation. The discrepancy with available experimental data on enhanced GB hydrogen diffusion was attributed in those studies to strong plastic deformation which occurs during electrolytic hydrogen charging and can be accompanied by microcracking in the vicinity of grain boundaries segregated by hydrogen. Koyama et al. (2017b) claimed the absence of microcracks in their experimental observations but confirmed the occurrence of dislocations at grain boundaries and proposed the following correlation between hydrogen GB segregation and appearing dislocations: (i) slight plastic deformation caused by hydrogen charging; (ii) strainpromoted enhancement of GB hydrogen segregation; (iii) repetitive plastic deformation caused by enhanced H segregation; (iv) the increased amount of segregated hydrogen at GB resulting in a high hydrogen flux along them. Nevertheless, as discussed in Sect. 3.4.1, the accelerated hydrogen flux in the polycrystalline samples with decreasing grain size cannot be attributed to increased GB hydrogen segregation alone as the driving force for grain boundary diffusion. Therefore, based on the data on plastic deformation during hydrogen permeation measurements, one can suggest that hydrogen transport by dislocations is the most probable mechanism for the apparent acceleration of hydrogen diffusion in polycrystalline metals. Plastic deformation occurs in a direction parallel to the hydrogen concentration gradient, and, for this reason, the moving dislocations encased in hydrogen atmospheres are expected to increase the hydrogen flux. The density of dislocations involved in the plastic deformation of polycrystalline metals particularly increases at grain boundaries, see e.g. Ashby (1970). Additionally, hydrogen segregation at GB causes stresses, which also locally enhances plastic deformation. Therefore, enhanced hydrogen flux can be observed particularly in

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the vicinity of grain boundaries, which was a fixture in the experiments with silver decoration. The proposed mechanism is also applicable to apparent hydrogen-enhanced diffusion along dislocations. Using the silver decoration method, Tseng et al. (1988) observed silver particles to be predominantly precipitated within the area of high dislocation density in nickel subjected to cathodic charging at current densities of 10–50 mA/cm2 . Due to rather strong conditions of hydrogenation, there is a high probability that hydrogen transport by dislocations occurred in this case. Finally, sufficiently strong plastic deformation can be accompanied by the formation of microcracks within grain boundaries. Molecular hydrogen recombination in these cracks with its repetitive dissociation and subsequent diffusion along grain boundaries is also expected to accelerate hydrogen flux. It should be noted in this respect that hydrogen-induced cracking was previously suggested by Harris and Latanision (1991) to be responsible for enhanced grain boundary hydrogen migration in nickel and nickel-based alloys.

3.5 Hydrogen Effect on Metallic Atom Diffusion in the Crystal Lattice and Short-Range Atomic Order It is natural to expect that hydrogen-induced superabundant vacancies can affect selfdiffusion of the host metallic atoms and diffusion of substitutional atoms at lattice sites in the crystal lattice. The first experimental data about the effect of interstitial elements on the diffusion of metallic atoms over crystal lattice sites has been obtained by Gruzin et al. (1951) who measured parameters of iron self-diffusion in fcc ironcarbon sold solutions and detected a remarkable decrease in the activation enthalpy and a corresponding increase of the iron diffusion coefficient with increasing carbon content. The first attempt to explain this carbon effect was undertaken by McLellan (1988) in his thermodynamic calculations resulting in the conclusion that there is significant carbon-induced generation of vacancies in fcc iron. According to his numerical estimations, the concentration of vacancies increases five-fold at the atomic ratio of nC /NFe = 0.06 and the temperature of 1273 K. Similar theoretical results were also obtained by Smirnov and his colleagues who developed a general theory for vacancies in interstitial solid solutions without specifying the type of atoms in the lattice and interstitial sites, see Smirnov (1991) and Bobyr et al. (1991). Possibly, the first statement about the hydrogen-caused acceleration of metallic atom diffusion was made by Sidorenko et al. (1977) who demonstrated the hydrogenassisted formation of superstructures FeNi and CrNi3 during annealing of invar-type and heat resistant Ni-based alloys, respectively. A remarkable contribution to this problem was later made by Fukai and his colleagues who carried out thorough studies of vacancy formation under high gaseous hydrogen, see Sect. 2.1.1 in Chap. 2 for detail. Particularly interesting is the data

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Fig. 3.33 Concentration profiles of Cu after diffusion annealing for 30 min at 600 ± C (a), 700 ± C (b), 750 ± C (c), and 800 ± C (d) under hydrogen pressure of 5 GPa, and 700 ± C (e) under a mechanical pressure of 5 GPa. Redrawn from Hayashi et al. (1998), American Physical Society

obtained by Hayashi et al. (1998) and Fukai et al. (2001), where hydrogen-caused diffusion enhancement was demonstrated in Cu-Ni couples, see Fig. 3.33. Measurements of Cu-Ni concentration profiles were performed after annealing at different temperatures under hydrogen pressure of 5 GPa and at the same pressure in vacuum. It is seen that hydrogen enhances the mutual penetration of two elements. The interdiffusion coefficient is increased by ~104 in the Ni side and only by ~10 in the Cu side, which is due to higher H solubility in Ni in comparison with that in Cu. Partial diffusion coefficients are also sharply increased. For example, for diffusion T = 4.1 × 10−7 e−1.26 eV/kT m2 s−1 in the presence of hydrogen and of Cu into Ni DCu T −5 −2.66 eV/kT m2 s−1 in its absence. The diffusion of metallic atoms DCu = 6.1 × 10 e is enhanced due to decrease in the activation enthalpy. The hydrogen-caused enhancement of metallic atom diffusion was put into practice by Ivasishin et al. who developed a new technology of low cost titanium hydride powder metallurgy, see Ivasishin et al. (2000, 2007, 2012) and Fig. 3.34. A key feature of this technology is using of titanium hydride TiH2 powder instead of titanium powder, and it was found that the sintered density exceeded 98% of theoretical value. The hydrogen-caused enhancement of metallic atom mobility has been also observed in the alloys of noble metals, resulting in the short-range atomic order in their atomic distribution. It is relevant to note in this respect that, rather oft, the scientists do not distinguish between short-range order and short-range ordering. The point is that the term “short-range atomic order” suggests any deviation from the random distribution of solute atoms in metals and nothing more. In turn, it suggests two kinds of such deviation, short-range atomic ordering and short-range atomic

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Fig. 3.34 Density of Ti-6Al-4V compacts after pressing and sintering of hydrogenated and non-hydrogenated powder. Courtesy of professor Ivasishin, G.V Kurdyumov Institute for Metal Physics, Kiev, Ukraine

decomposition. The preferred neighborhood of different kinds of atoms occurs in the former case and that of the same kind of atoms is typical of the latter case. For example, PdMn alloys are prone to short-range atomic ordering, even forming the Pd3 Mn superstructure at high Mn concentrations. As observed by Phutela and Kleppa (1981), hydrogen solubility is higher in the ordered state in comparison with the disordered one. Using measurements of hydrogen solubility, Flanagan et al. (1986) observed hydrogen-accelerated ordering in Pd–Mn alloys. The H-enhanced short-range decomposition was found in Pd–Rh alloys by Noh et al. (1991, 1992). A homogeneous state of the Pd0.8 Rh0.2 alloy was obtained after its heating at 873 K in vacuum, whereas the same heat treatment under hydrogen pressure of 5.5 MPa led to this alloy’s transformation into two phases, Pd0.88 Rh0.12 and Pd0.14 Rh0.86 , with their atomic fractions of 11% and 89%, respectively. The thermodynamics of this phenomenon has been not clarified by the authors. They merely suggested that hydrogen-caused crystal lattice expansion allows metal atom mobility in the vicinity of the expanded lattice. But in fact, the Gibbs free energy of thermodynamic systems like Pd–Rh inherently contains a positive excessive term Ge in addition to its entropy term RT(XPd lnXPd + XRh lnXRh ). This term flattens the concentration dependence of the Gibbs energy in the part with the highest numbers of Pd–Rh pairs, which results in the formation of two negative hills and the corresponding miscibility gap in the phase diagram responsible for decomposition of the solid solution. The role of hydrogen amounts mainly to the increase in vacancy concentration, which accelerates metal atom diffusion if a thermodynamic stimulus for that is present. These studies were further extended by Noh et al. (1996) who took into account a miscibility gap in the Pd–Rh system, and hydrogen charging was used as a diagnostic technique for phase diagram determination. The hydrogen-caused enhancement of lattice atom diffusion resulting in the short-range decomposition of solid solutions was also detected by Noh et al. (1995) in Pd–Pt and Pd0.9 Pt0.1 alloys. Short-range

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decomposition into Pd-rich and Pt-rich regions occurred under gaseous hydrogen pressure of 5.5 MPa at 448 K, and the initial homogeneous state was restored after annealing above the consolute temperature Tc . Flanagan and Noh (1995) reported hydrogen-induced lattice atom migration during technological processing of Pd–Pt and Pd–Ni alloys. It was shown based on experiments with cold worked and annealed alloys that H solubility enhancement caused by dislocations in the cold work state disappears after annealing, nevertheless its enhancement due to H-induced compositional variations still largely remains. The role of short-range atomic order in hydrogen distribution over the crystal lattice will be analyzed further in Chap. 4, Sect. 4.1.4, in relation to the nature of the so-called γ*-phase in CrNi austenitic steels. The effect of short-range atomic order on the hydrogen embrittlement of austenitic steels and nickel superalloys will be discussed in Chap. 5, Sect. 5.1.8.4. Summary Migration paths of hydrogen atoms and corresponding energy barriers affecting diffusion enthalpies in iron, nickel and titanium are analyzed based on the ab initio calculations of the electron structure. The smallest activation enthalpy, ~0.04 eV, is found in the experimental measurements of H diffusion in the bcc iron, which is consistent with calculations accounting for the hydrogen quantum tunneling. It is significantly higher, about ~0.5–0.6 eV, for hydrogen diffusion in austenitic steels and the highest in the hcp iron changing with increasing c/a ratio in its crystal lattice from 0.8 to 0.65 eV for diffusion in the basal c plane and from 0.55 to 0.95 eV in the c direction. Consequently, the diffusion coefficients in iron decrease in the sequence of its bcc–fcc-hcp crystal lattices. The value of ~0.4 eV for H diffusion in nickel was obtained in the experiment, as well in theoretical estimations. A feature of hydrogen flux in the electrochemically charged nickel is its dependence on the crystal lattice orientation, namely its increase in the → → sequence, which is interpreted in terms of hydrogen-induced self stresses and, more realistic, the occurrence of plastic deformation during electrochemical charging. The experimental data on the activation of diffusion enthalpy in titanium vary in the range of 0.13–0.15 eV in the hcp α-Ti and 0.05–0.09 eV in the bcc β-Ti alloys of different chemical compositions. Measurements of Snoek relaxation enthalpy for single hops of hydrogen atoms in a β-Ti alloy gives the value of ~0.27 eV. Hydrogen trapping by crystal lattice imperfections strongly depends on their type. The most effective for trapping in the bcc iron are dislocations and vacancy complexes with binding enthalpies of ~0.27 eV and ~0.46 eV, respectively. Dislocations and microvoids are found to be main hydrogen traps in the austenitic steels with binding energies of ~0.19 eV and ~0.4 eV to ~0.6 eV, respectively, whereas only ~0.08 eV is a realistic value for H trapping at the grain boundaries. Hydrogen trapping in nickel is characterized by two kinds of traps with binding energies of ~0.2–0.26 and ~0.4 eV which are attributed to single vacancies and their clusters. A rather weak hydrogen trapping by crystal lattice defects is observed in the α- and β-titanium.

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The hydrogen transport by dislocations occurs at the strain rates allowing the hydrogen atoms to follow dislocations. As will be shown in Chap. 5, this unique phenomenon plays a dominant role in hydrogen embrittlement of metals. A feature is the discontinuous hydrogen flux during transport of screw dislocations in contrast to edge dislocations. The increased hydrogen flux along the grain boundaries is observed in the case of electrochemical hydrogen charging, which is caused by the enhanced plastic deformation near the grain boundaries and, consequently, by more intensive hydrogen transport by dislocations. Increasing the concentration of vacancies in the solid solutions, hydrogen significantly intensifies diffusion of metallic atoms, which is expected to accelerate sintering of metallic powder and is successfully used in the recent technology of low cost powder metallurgy.

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Chapter 4

Phase Transformations

A fundamental criterion for the thermodynamic stability of solid solutions and compounds is the density of electron states, DOS, at the Fermi level, EF , which determines cohesion energy in the crystal lattice. The higher the DOS, the less stable any thermodynamic system. As shown in Chap. 1, hydrogen in iron, nickel and βtitanium increases DOS at EF . Therefore, hydrogen dissolution is expected to make these metals prone to forming new phases. A non-monotonous hydrogen concentration dependence of DOS at EF in nickel and titanium is a clear sign that some phase transformations do occur. As mentioned in Chap. 2, DOS at the Fermi level controls a special characteristic responsible for the thermodynamic stability of metallic solid solutions, namely stacking fault and SFE, and hydrogen decreases it. The situation can be complicated further by additional factors, e.g. external pressure during gaseous hydrogenation and the occurrence of crystal lattice imperfections. The aim of this chapter is to analyze hydrogen-induced phase transformations in the iron-, nickel- and titanium-based alloys.

4.1 Hydrogen-Induced Phases in Iron-Based Alloys Vaughan et al. (1963) were perhaps the first to detect a hydrogen-caused phase transformation in a type 304 stainless steel subjected to holding in a MgCl2 -H2 O solution at 154 °C. Using X-ray diffraction and transmission electron microscopy, they found the formation of a “highly strained ferrite or bcc martensite”. This hydrogenstrained ferrite differed from an unstrained one by a smaller lattice parameter. Subsequent ageing at room temperature led to the decomposition of this phase into normal austenite and “hexagonal hydride phase”. Holzworth and Louthan (1968) identified the “strained ferrite” and the “hexagonal hydride” as α - and ε-martensites similar to those formed under cold work. Confusing was only the increased volume ratio of α and ε fractions in comparison with that © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. G. Gavriljuk et al., Hydrogen in Engineering Metallic Materials, https://doi.org/10.1007/978-3-030-98550-9_4

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caused by cold work. Hydrogen charging was also found to increase dislocation density and induce stacking faults. The latter can be clearly attributed to a hydrogencaused decrease in stacking fault energy, as described in Chap. 2, Sect. 2.2.1. A number of further studies on hydrogen-charged low stable austenitic steels confirmed these previously obtained results (see e.g. Kamachi 1978; Inoue et al. 1979; Eliezer et al. 1979; Hänninen and Hakarainen 1980 etc.). Their authors mainly dealt with the morphology of α- and ε-phases, their stability after hydrogen degassing and the supposed harmful effect on mechanical properties. An intercorrelation between the formation of hydrogen-induced α- and ε-phases was well demonstrated by Kamachi (1978) using the X-ray diffraction of steel SUS 304 (Cr18Ni9) subjected to cathodic charging of different durations at room temperature, see Fig. 4.1. Reflections of ε-martensite appeared with the start of charging, whereas those of α-martensite were screened by the broad ε peak and could be detectable only after about 3 h of charging when the ε peak was shifted to higher angles due to a decrease in the ε lattice parameter c. In the course of subsequent heating up to 300 °C, Fig. 4.1 X-ray diffraction pattern of steel SUS 304 after hydrogen charging at RT for different durations. According to Kamachi (1978), The iron and Steel Institute of Japan

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the ε-martensite gradually disappeared whereas the α-phase remained stable up to 700 °C. The abovementioned shift of ε reflections occurred despite continued hydrogen charging and was attributed by Kamachi to elastic interactions between the grown large α bands encroaching upon the ε bands which in turn remained narrow stringers. Many years later, Koyama et al. (2018) observed a non-homogeneous shift of the ε peak to higher angles resulting in its splitting during hydrogen desorption from stable austenitic steel Cr10Ni8Mn15 at 193 K, whereas no α-phase was formed due to hydrogen charging. The interpretation proposed by these authors amounts to hydrogen atoms temporarily entering tetrahedral positions in the ε-phase during γ → ε transformation, which causes non-homogeneous lattice distortions. Using transmission electron microscopy, Tanino et al. (1982) studied hydrogeninduced microcracks in steels of the 304 type. Microcracking was found located along the α lath boundaries and at the ε/α interfaces. Some features of α- and ε-phase formation in the presence of cracks in the previously notched and then cathodically charged samples of 304-type steel were also analyzed by Inoue et al. (1979). Both α and ε phases were found to be located near the developed cracks. The cracks in the α-phase advanced on a complex zigzag path by expending a large energy, whereas their straight propagation occurred along the α/ε interface. At higher hydrogen contents, which has been achieved due to an increase in current density, the volume fraction of the α-phase near the crack decreased and the only enhanced straight crack propagation occurred along the α/ε interface. Based on these observations, Inoue et al. concluded that, with increasing hydrogen content in the vicinity of cracks, γ → α transformation is suppressed, whereas γ → ε transformation is promoted because of a hydrogen-caused decrease in stacking fault energy. This observation is somewhat contradicted by the studies performed by Eliezer et al. (1979), where a large amount of α-martensite, about 17%, was detected on the fracture surface of cathodically charged 304 steel. It was interpreted in terms of the autocatalytic character of γ → α transformation: the α-phase accelerates hydrogen entry, which in turn aids its formation. Among other features of hydrogen-caused phase transformations in low stable austenitic steels, one should note a decrease in the fractions of α- and ε-phases if cold work precedes hydrogen charging, see e.g. Holzworth and Louthan (1968) and Bentley and Smith (1986). The orientation dependence of hydrogen-induced transformations was detected by Tähtinen et al. (1986) who performed TEM studies on the single crystals of the more stable AISI 316 type steel. Only ε plates were formed in the foils on their surface having the (310) plane, whereas the α-phase appeared additionally on the (211) planes. Higher Ni content increases the thermodynamic stability of austenitic steels and, consequently, their resistance to hydrogen-caused γ → α and γ → ε transformations is enhanced. For example, according to Rozenak et al. (1984), the α-phase is absent after cathodic charging of AISI 316 steel containing ~12% of Ni, whereas its occurrence was detected in steels AISI 347 and AISI 321 with Ni contents of ~9 and ~10%,

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respectively. No α-phase was also observed by Narita et al. (1982) after cathodic charging of steel AISI 310 having 25% of Ni. The ε-phase was found in all these steels, although its fraction decreased with increasing Ni content because of the Ni-increased stacking fault energy. The effect of the hydrogen concentration gradient caused by electrochemical hydrogen charging on the thermodynamic stability of austenitic steels was profoundly analyzed by Rozenak and Bergman (2006). While changing the X-ray wavelength, they investigated the distribution of hydrogen-induced phases in a thin surface layer of the following AISI steels: 347 with 9.09%Ni, 321 (10.1%Ni), 304 (9.95%Ni) and 316 (12.09%Ni). The content of the α-phase in the surface layer decreased with increasing Ni content from 25% in AISI 347 to 16% in 321, 4% in 304 and 2% in 316 steel. The effect of nickel on the amount of the ε-phase was not so definite, varying from 77% in steel 321 to 45% in 347, 56% in 304 and 51% in 316. Measured in steel 316, the relative strain was found to increase with charging time, which points to a rather high level of hydrogen-induced stresses at the surface. In addition, a decrease in spacing between the atomic planes was obtained for the (200) reflection peak, which evidenced the non-homogeneity of the stressed state. The results of these studies were summarized by Rozenak and Shani (2012) and Rozenak (2013) who additionally investigated the role of the ε- and α-phases in the mechanical behaviour of steels subjected to deformation in situ in the electron microscope. Cracks originated from deformation were observed to propagate through the ε-plates, whereas the α-phase was found at both sides of crack propagation. The overall conclusion derived from a number of these and similar studies, including also those on binary Fe–Ni austenitic alloys, was that hydrogen-induced stresses decrease the stability of the γ-phase and can induce both γ → α and γ → ε transformations. This statement was also supported by the earlier observations that the morphology of a hydrogen-induced ε-phase is close to that after cold work or cryogenic treatment, see Rigsbee (1978). In both cases of cold work or hydrogen charging, subsequent holding at room temperature led to the final ε → α transformation. At the same time, quite a different behaviour was found in stable austenitic steel of AISI 310 type with typical Cr25Ni20 composition, where no transformation occurs under either cold work or deep cooling. Nevertheless, severe cathodic hydrogen charging leading to an increase in hydrogen content of up to several tens at.% induces partial transformation of fcc austenite into hcp martensite (e.g., Mathias et al. 1978; Narita et al. 1982; Ulmer and Altstetter 1993; Gavriljuk et al. 1994). Moreover, in contrast to less stable CrNi steels, the inverse ε → γ transformation during subsequent ageing occurs without the intermediate ε → α transformation. Taking into account this uncertainty in the effects of cold work and hydrogen charging on the thermodynamic stability of austenitic steels, it is expedient to compare the hydrogen effect on the electron structure of γ and ε iron phases in an attempt to search for some physical factors affecting their stability in addition to the impact of stresses.

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4.1.1 Atomic Interactions in Hydrogen-Charged γ and ε Phases Cohesion energy was determined as a difference between the total crystal energy  per elementary cell and the sum of energies of constituting atoms, Ec = Etotal − i Ei . The effect of hydrogen on it in a FeCrNi solid solution was calculated ab initio by Vakhney et al. (1998), see Fig. 4.2. As expected, the cubic crystal lattice γ is more stable than the hexagonal ε in the hydrogen-free state. If hydrogen is added with the metal/hydrogen atomic ratio H/M of 1/2, thermodynamic stability is nearly ambivalent for both phases. With the H/M ratio increasing to 1/1, the hcp crystal lattice acquires higher stability than the fcc one. Such a high hydrogen content in austenitic steels, particularly within the hydrogen atmospheres around dislocations, can be obtained using electrochemical charging or under high gaseous hydrogen pressure. More complicated is the hydrogen effect on atomic interactions in the CrMn austenitic steels, as studied by Movchan et al. (2013), see Fig. 4.3a, b. In the case Fig. 4.2 Cohesion energy in γ and ε phases in austenitic steel Cr25Ni25 at different hydrogen contents. Swz is the Wigner–Seitz radius (half of the interatomic distance)

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Fig. 4.3 Cohesion energy versus elementary cell volume: a configurations Fe2 Cr1 Mn1 and Fe6 Cr3 Mn3 in the fcc and hcp phases, respectively, b configurations Fe2 Cr1 Mn1 H1 with 20 at.% of H and Fe6 Cr3 Mn3 H4 with 25 at. % of H in the fcc and hcp phases, respectively

of 20–25 at.% H, the hcp phase acquires higher stability in comparison with the fcc phase. It remains also more stable at hydrogen contents up to about 35 at.%. However, at higher H concentrations, the γ-phase restores its stability (Fig. 4.4). Two conclusions follow from the comparison of nickel and manganese effects on the hydrogen concentration dependence of cohesion energy in γ-iron base alloys: (i) CrNi austenitic steels are more prone to hydrogen-induced γ → ε transformation than CrMn steels, (ii) hydrogen effect is non-monotonous in CrMn steels. Let us compare the calculated data with those obtained in experiments using electrochemical or high pressure gaseous hydrogenation. For example, γ → ε transformation under cathodic charging was studied in binary FeNi alloys by Kamachi (1978), ternary Fe2 Ni1−x Mnx alloys with 0 < x < 1 (Asano et al. 1990), CrNi austenitic steels with different Ni contents (Kamachi 1978; Inoue et al. 1979; Narita et al. 1982; Han et al. 1998) and CrNiMn austenitic steels (Shivanyuk et al. 2003; Teus et al. 2008). Hydrogen-free binary FeNi alloys acquire a fully austenitic structure at Ni concentrations above 28 mass %. However, hydrogen cathodic charging causes partial γ → α transformation in these alloys at Ni contents up to 32% (e.g., Kamachi 1978). With a further increase in nickel content, these alloys acquire stability in relation to hydrogen-induced γ → α transformation.

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Fig. 4.4 Hydrogen effect on the concentration dependence of cohesion energy in the fcc and hcp phases of the Fe50Cr25Mn25 solid solutions

The Cr effect on the stability of austenitic steels under hydrogen cathodic charging was studied by Gavriljuk et al. (1995), Shyvanyuk et al. (2007) and Teus (2007), see Figs. 4.5 and 4.6. These steels were hydrogen-charged up to H/M ratios of 0.4–0.6, which is consistent with the range of hydrogen contents used in the above ab initio calculations. At the content of 25%Ni remaining unchanged, an increase in Cr content intensified hydrogen-induced γ → ε transformation, compare Fig. 4.5a, b. In contrast, if the Ni content is increased up to 40% at chromium content unchanged, steel acquires stability against γ → ε transformation, see Fig. 4.5c. Such a stabilization of the γ-phase occurs also in binary FeNi alloys at nickel contents above 32% (Kamachi 1978). The ε-phase is favoured if manganese is added to the Cr15Ni25 composition at the amount of 15% (Fig. 4.5d), although the manganese effect is much weaker in comparison with that of chromium. A significantly larger fraction of the ε-phase is induced by hydrogen if manganese is substituted for silicon (Fig. 4.5e). The manganese effect becomes the opposite if it is added to the chromium-rich Cr25Ni20 composition (Fig. 4.6a, b). In this case, manganese increases the stability of the γ-phase and retards the formation of the ε phase. In contrast, combined alloying with silicon and chromium enhances ε-phase formation (compare Figs. 4.5b and 4.6c). Moreover, a large broadening of γ reflections in Fig. 4.6c and their shift to smaller angles points to the Si-increased hydrogen content in the crystal lattice of γ solid solution. It seems logical to analyze the obtained results in terms of a change in stacking fault energy because, as mentioned above, being derivative of the density of electron

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Fig. 4.5 X-ray diffraction patterns of steel Cr15Ni25 (a) with increased Cr (b) or Ni (c) content or additionally alloyed with Mn (d) or Si (e). Charging in 1 N H2 SO4 solution for 72 h at current density of 50 mA/cm2 . Designations γ* and γe are used for split austenitic reflections from the hydrogen-rich and hydrogen-exhausted solid solutions, respectively (see about the nature of this splitting in Sect. 4.1.4)

states at the Fermi level, it is the SFE that controls thermodynamic stability of phases in solid solutions. Hydrogen assists γ → ε transformation in iron-based fcc alloys because it decreases the SFE, see Pontini and Hermida (1997). Alloying elements can change the intensity of this transformation in accordance with their effect on the SFE in hydrogen-free solid solutions. For example, chromium is known to decrease the SFE

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Fig. 4.6 Effect of manganese and silicon on hydrogen-induced γ → ε transformation in austenitic steel Cr25Ni20. Charging in 1 N H2 SO4 solution for 72 h at current density of 50 mA/cm2

in austenitic steels, whereas nickel increases it (Schramm and Reed 1975). Therefore, one can derive from Figs. 4.5b and 4.6a that the chromium effect prevails over that of nickel in the Cr25Ni25 and Cr25Ni20 compositions. The effect of manganese can be interpreted based on studies performed by Schumann (1967) who was the first to show that the manganese effect on the thermodynamic stability of the iron γ-phase in binary Fe–Mn alloys is non-monotonous. Corresponding reactions are presented in Fig. 4.7a based on dilatometric measurements. With Mn content increased to 10 mass %, the α-phase is partly substituted for the γ phase. A further increase in Mn content leads to the replacement of the γ-phase by the ε phase, and the highest ε fraction is reached at ~18% of Mn, whereas the content of the α-phase approaches zero. Thereafter, the opposite change in the ε/γ balance occurs and the ε-phase completely disappears at ~27% of Mn. The effect of manganese on stacking fault energy in binary Fe–Mn alloys was studied by Volosyevich et al. (1976), see Fig. 4.7b. A clear correlation exists between SFE behaviour and the γ → ε → γ transformations in the critical range of Mn contents of 10–30%. Of course, adding Cr, Ni etc. to Fe–Mn alloys can bring certain features to the discussed correlation. Nevertheless, one can state that X-ray diffraction data in Figs. 4.5 and 4.6, as well as the quoted data in Fig. 4.7 confirm a non-monotonous Mn effect on the thermodynamic stability of γ- and ε-phases in hydrogen-charged

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Fig. 4.7 Effect of Mn content in binary Fe–Mn alloys on the length change during α → γ, γ → ε, ε → γ and γ → ε transformations, according to Schumann (1967) (a); corresponding change in stacking fault energy, curve 2, according to Volosyevich et al. (1976) (b). The dashed curve 1 in figure b is a schematic SFE change proposed by Schumann (1974), John Wiley and Sons

CrNi austenitic steels, as follows from the results of ab initio calculations presented in Figs. 4.3 and 4.4. In these terms, the Si-enhanced formation of the ε-phase under hydrogen charging, as demonstrated in Figs. 4.5e and 4.6c, can be also linked to the Si effect on the SFE, which is consistent with Schramm and Reed (1975). As austenite formers, carbon and nitrogen are expected to prevent hydrogeninduced γ → ε transformation. The ε-fraction is shown in Fig. 4.8 to disappear with Fig. 4.8 Diffraction patterns of Cr18Ni16Mn10 steel consisting of 0.07, 0.22 or 0.56 mass %N subjected to cathodic charging in 1 N H2 SO4 , Co Kα radiation. Si has been used for calibrating diffraction patterns

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nitrogen content increasing up to 0.56 mass % in austenitic steel (see Gavriljuk et al. 1993 for details). Like the influence of substitution alloying elements, this nitrogen effect can be attributed to the increase in stacking fault energy within the framework of its concentration in the studied steel, see Gavriljuk et al. (2006). It is difficult to test the effect of carbon in the experiments because corrosion-resistant CrNi austenitic steels contain it in small amounts as an undesirable element. Less stable against hydrogen-induced γ → ε transformation is the high-nitrogen Cr19Mn190.9N steel, see Vogt (2001) because the replacement of nickel by manganese significantly decreases γ-phase stability. Thus, in agreement with the results of ab initio calculations of the electron structure, the analysis of available experimental data reveals the important role of stacking fault energy in the thermodynamic stability of austenitic steels subjected to cathodic hydrogen charging. However, this interpretation is seriously damaged by the results obtained using high pressure gaseous hydrogenation. The X-ray diffraction studies of austenitic steel Cr18Ni16Mn10 gaseously charged at 200 °C under hydrogen pressure of 3.5 GPa and reaching the extremely high hydrogen content of H/M = 0.8 did not reveal any ε-phase, see Fig. 4.9 and Gavriljuk and Shyvanyuk (2003) for detail. At the same time, cathodic charging of this steel causes γ → ε transformation, as shown in Fig. 4.10. The induced ε-phase remains stable even after subsequent ageing at 300 K for 12 h.

Fig. 4.9 X-ray diffraction of steel Cr18Ni16Mn10 before (a) and after (b) hydrogenation at 200 °C under hydrogen gaseous pressure of 3.5 GPa and subsequent measurements at −100 °C. The experiment was performed in the Laboratory of High-Pressure Physics, Institute for Solid State Physics, Chernogolovka, Russia. The expected position for reflection εH (10.1) is marked as ↑ε

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Fig. 4.10 X-ray diffraction of steel Cr18Ni16Mn10 after hydrogen cathodic charging at current density of 50 mA/cm2 for 72 h and subsequent holding at different temperatures for 10 min. Measurements are carried out at 100 K. The εH -phase is induced by cathodic charging and remains stable even after lengthy hydrogen degassing at RT

The absence of γ → ε transformation in steel Cr25Ni20 (AISI 310) charged up to H/M = 1.0 under hydrogen gas pressure of 7 GPa has also been mentioned by Hoelzel et al. (2004). While studying the less stable austenitic steel 304 after gaseous charging up to H/M = 0.56 under hydrogen pressure of 3 GPa, the authors found the ε-phase with its fraction of 16%. These experimental results look even more intriguing, considering that high pressure itself stabilizes the ε-phase in iron, see, e.g., Bundy (1965), and decreases stacking fault energy, see Galkin et al. (1976). A probable interpretation proposed by Bugaev et al. (1997) is based on the increased concentration of equilibrium vacancies due to hydrogen dissolution claiming to stimulate the loss of thermodynamic stability. If so, the increase in pressure should retard the formation of vacancies, see also Chap. 2, Sect. 2.1.2. However, such explanation is at variance with a number of studies performed by Fukai with his colleagues about hydrogen-induced vacancies in metals under high hydrogen gaseous pressure (see Chap. 2, Sect. 2.1.1). Summing up, one can state that, as a whole, the γ → ε transformation of austenitic steels is basically controlled by their stacking fault energy. However, the role of stresses accompanying cathodic charging and absent in the case of gaseous hydrogenation needs more detailed analysis.

4.1.2 Hydrogen-Caused Stresses and Plastic Deformation as a Reason for γ → ε Transformation The inhomogeneous hydrogen distribution during electrochemical charging of metals was analyzed in Chap. 3 as a reason for hydrogen-induced stresses resulting in plastic deformation. As shown for the first time by Mogilny et al. (2015), its effect on the thermodynamic stability of the γ-phase can be even more significant. A change of the

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ε/γ phase ratio in austenitic steels subjected to cathodic hydrogen charging followed by subsequent mechanical tension tests is presented in Table 4.1 along with the lost plasticity index (δ0 − δH )/δ0 . It is seen that three studied steels acquired different hydrogen content in the surface layer despite the same time of charging. The difference in the hydrogen content of steels Cr15Ni25 and Cr15Ni40 is certainly due to higher Ni content in the latter, which decreases hydrogen diffusion enthalpy and assists their diffusion from the surface layer into the bulk (compare with hydrogen diffusion enthalpies in Table 3.1, Chap. 3). However, the decrease of hydrogen content due to Si added to steel Cr15Ni25 is surprising because Si increases hydrogen diffusion enthalpy in austenitic steels and, therefore, detains hydrogen in the solid solution. This is clearly demonstrated by the comparison of austenitic diffraction reflections in Fig. 4.6a for hydrogen-charged steel Cr25Ni20 and Fig. 4.6c for steel Cr25Ni20Si3. Probably, a change in the content of substitutional solute elements affects their atomic distribution in multicomponent solid solutions, i.e., causes their short-range atomic ordering or decomposition, which in turn changes the distribution of interstitial hydrogen atoms and, consequently, hydrogen solubility. Some examples of such effects will be analyzed in the next Section. Except for the ε-free steel Cr15Ni40, γ → εH transformation occurs in the other two steels during hydrogen charging, as well as in the course of subsequent mechanical tests. Besides this, and consistently with the X-ray diffraction patterns in Fig. 4.6a, e for steels Cr15Ni25 and Cr15Ni25Si2, the hydrogen-caused increase in the fraction of εH -martensite is not proportional to the hydrogen concentration in the surface layer. It is obviously a sign of the important role of stacking fault energy in γ → εH transformation. Also remarkable is that the increment of the ε fraction due to mechanical tests is higher in steel Cr15Ni25 than in steel Cr15Ni25Si2, although it was smaller before tension. A reason for this ambiguity is change in the crystal structure estimated using stereographic pole figures, see Fig. 4.11. After hot rolling, all the steels had a typical sheet crystallographic texture. Annealing at 1100 °C causes recrystallization. As a result, narrow peaks of separated grains are clearly resolved in the pole figures, although their distribution is close to the texture after hot rolling, see Fig. 4.11a for steel Cr15Ni40. Table 4.1 H/M, εH /γ ratio and hydrogen embrittlement after hydrogen charging at current density of 50 mA/cm2 Steel

Charging time, h

H/M

εH/ γ after charging

ε/γ after charging + deformation

(δ0 − δH )/δ0 , %

Cr15Ni25

48

0.41

0.10

0.62

54.8

Cr15Ni40

48

0.14

–

–

99.8

Cr15Ni25Si2

48

0.28

0.66

0.71

89.3

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Fig. 4.11 (111)γ X-ray pole figures of studied steels: a steel Cr15Ni40, annealed at 1100 °C; b Cr15Ni40, hydrogen-charged for 48 h; c Cr15Ni25, hydrogen-charged for 48 h; d Cr15Ni25Si2, hydrogen-charged for 48 h

In the absence of γ → ε transformation in this steel, an axisymmetric (fibre) texture is formed due to hydrogen charging, as presented in Fig. 4.11b. In contrast, two texture components are observed in the hydrogen-charged steels Cr15Ni25 and Cr15Ni25Si2, where the εH -martensite was formed in the course of cathodic charging (Fig. 4.11c, d). These components are the following: (i) an axial texture, the intensity of which decreases with an increasing in the ε-martensite fraction, (ii) blurred reflections remained from the recrystallized grains of the initial texture in the annealed austenite. Like the data for the binary Fe–Ni alloy demonstrated in Fig. 3.32, see Sect. 3.4.3 in Chap. 3, the occurrence of crystallographic texture suggests that cathodic charging of austenitic steels is accompanied by extensive plastic deformation. Along with a hydrogen-caused decrease in the stacking fault energy, it gives an additional thermodynamic stimulus to γ → ε transformation, and this is why strain-induced and hydrogen-induced ε-martensites are so similar in their morphology. From the comparison of Fig. 4.11b–d one can conclude that γ → ε transformation decreases the intensity of plastic deformation. In other words, the formation of ε-plates limits dislocation slip. For this very reason, the ε-free steel Cr15Ni40 having the highest plasticity in the annealed state loses most of it due to plastic deformation in the course of hydrogen charging. In contrast, γ → ε transformation imparts higher resistance to hydrogen embrittlement

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for steel Cr15Ni25 in comparison with steel Cr15Ni40 despite the higher hydrogen content in its surface layer. Also of interest is the observed lower resistance of steel Cr15Ni25Si2 to hydrogen embrittlement, which seems to be at variance with the decrease in the hydrogen content in the surface layer and with a positive Si effect on the plasticity of hydrogencharged high chromium steels, as will be shown later in Chap. 5. This contradiction can be removed if one considers that plastic deformation is accompanied by additional γ → ε transformation during mechanical tests, see Fig. 4.12. It is seen that the fraction of ε-martensite formed due to charging was significantly increased due to tensile deformation in the process of mechanical testing. The quantitative data on the ε fraction after mechanical tests on hydrogen-charged steels Cr25Ni25 and Cr15Ni25Si2, as presented in Table 4.1, demonstrate a significant TRIP effect during mechanical tests of steel Cr15Ni25. For this reason, its resistance to hydrogen embrittlement is improved in contrast with that in steel Cr15Ni25Si2, where a large fraction of ε-martensite was obtained during hydrogen charging and only slightly increased due to tensile plastic deformation. Obviously, the plasticity resource of this steel was depleted by the plastic deformation accompanying the γ → ε transformation in the course of charging. Moreover, the change in the profile of austenitic reflections in Fig. 4.12 after mechanical tests, namely their shift to higher angles, clearly confirms that γ → ε transformation has proceeded in the hydrogen-rich areas of the austenite. For this reason, the hydrogen content within the surface layer of austenite in the hydrogencharged steel Cr15Ni25Si2 is smaller in comparison with that in steel Cr15Ni25.

Fig. 4.12 X-ray diffraction patterns of steel Cr15Ni25 after hydrogen charging (curve 1, black squares) and after electrochemical charging followed by mechanical tests (curve 2, open circles)

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Fig. 4.13 Hydrogen embrittlement, HE = (δ0 − δH )/δ0 as a function of the fraction of the hydrogeninduced ε-martensite in austenitic steels

It is worth noting that a recent study of hydrogen-induced γ → ε transformation in austenitic steel Mn15Cr10Ni8 performed by Koyama et al. (2019) contains some new statements about thermodynamic factors controlling the nucleation of ε-martensite and the growth of its plates. The authors claimed that hydrogen increases the critical stress, i.e. the required elastic strain energy for martensite nucleation, but eases its nucleation in terms of the plastic strain needed for its formation during mechanical tests on hydrogen-charged samples. Further studies are needed to distinguish the role of hydrogen itself in the thermodynamics of γ → ε transformation and its effect on the formation of ε-martensite in the course of plastic deformation. Finally, it is relevant to note that mechanical tests of austenitic steels hydrogencharged and containing the ε martensite disprove the widespread idea of harmful ε effect on hydrogen resistance. Presented in Fig. 4.13 is the hydrogen-caused degradation of relative elongation in the tension tests as a function of ε fraction of hydrogencharged austenitic steels of which phase composition was analyzed in Sect. 4.1.1 using X-ray diffraction. A decrease in the distance of dislocation slip due to ε plates and initiation of new slip planes can serve as possible interpretation of the obtained effect.

4.1.3 Hydrogen-Induced γ *-Phase and Short-Range Decomposition of the Solid Solution The first information about this phase appeared from pioneering studies performed by Wayman and Smith (1971) on Ni–Fe alloys with iron content of up to 60%. The

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authors detected a splitting of γ reflections starting from 20% of Fe and claimed that, along with the Ni β-hydride discovered earlier by Baranowski et al. (1958), a new iron γ-hydride is formed. Later, Kamachi (1978) observed the same effect in Fe–Ni alloys with Ni content from 29 to 32%, as well as in stainless austenitic steels of AISI 304 to AISI 310 type and interpreted it as formation of a new Y-hydride. These findings were supported by Szummer and Janko (1979) who studied CrNi steels 18-8 and 25-20 and stated that the fcc Fe hydride is characterized by an expanded crystal lattice with the lattice constant larger by 5% in comparison with the hydrogen-free state. The γH designation was proposed later for this phase by Asano et al. (1990). However, within the same time interval, some doubt as to the existence of this new hydride was expressed by Mathias et al. (1978) investigating the time relaxation of the crystal lattice after hydrogen charging. In contradiction with the abovementioned statements, they demonstrated a continuous shift of γ* reflections towards higher angles during hydrogen degassing, i.e. a permanent decrease in hydrogen content, which is at odds with the expected behaviour of chemical compounds, of which hydrides are a type. Nevertheless, Narita et al. (1982) claimed that the γ*-phase lattice parameter only slightly decreases immediately after charging, from 5.2 down to 4.6%, and remains unchanged in the course of further hydrogen degassing. They found also that the γ*-phase is ferromagnetic with Curie temperature below 300 K. In contrast and in agreement with Mathias et al., the continuous nature of lattice contraction in the γ*-phase during hydrogen diffusion out of the specimen was confirmed by Rozenak and Eliezer (1988). Following the data obtained by Narita et al., Ulmer and Altstetter (1993) described the splitting of γ reflections in terms of the miscibility gap in the solid solution of hydrogen-charged steel 310S, where hydrogen-diluted γe and hydrogen-rich γ* solid solutions coexist creating thereby a crown in the binary phase diagram. In the case of miscibility gap, two hydrogen solid solutions should keep their concentrations when the total hydrogen content is changed. Possibly, some uncertainty could arise in these interpretations of X-ray diffraction patterns due to hydrogen degassing during measurements at ambient temperature where the hydrogen solid solution is unstable. To ensure unchanged total hydrogen content in the solid solution during measurements, these were carried out at low temperatures by Gavriljuk et al. (1994) after successive heating at higher temperatures (Fig. 4.14). Reflections of the γ*-phase (γH in figure) along with those of the εH -phase are presented within the diffraction angle range of 46° to 116° after holding at 230– 300 K with subsequent measurements at 100 K. It is seen that hydrogen degassing is accompanied by a gradual shift of γH and εH reflections to higher angles, which is consistent with the observations made by Mathias et al. (1978). This result suggests that the γ*(γH )-phase is not a chemical compound. Instead, it is a hydrogen solid solution in γ-iron, and the origin of hydrogen-caused reflection splitting must be quite different. Seeking to solve this puzzle, Movchan et al. (2010) calculated ab initio the atomic interactions in the Fe–Ni–H system, where γ* reflections are distinctly observed in

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Fig. 4.14 X-ray diffraction of steel Cr25Ni20 after hydrogen charging in 1 N H2 SO4 + 250 mg/l NaAsO2 solution at current density of 50 mA/cm2 for 72 h. Measurements were carried out at 100 K immediately after charging and subsequent holding for 10 min at temperatures within 230–300 K. The Si reflection was used for calibration of diffraction patterns

the X-ray diffraction patterns and, at the same time, calculations are made easier by the smaller number of bonds between neighbouring atoms in comparison with that in CrNi austenitic steels. The energies of interatomic bonds were obtained as parts of cohesion energy per elementary cell. Its minimum value was determined using variation of interatomic distances to obtain the equilibrium lattice parameter of the relaxed crystal lattice. The obtained energies EFe–Fe , ENi–Ni , EFe–Ni , EH–H (Fe), EH–H (Ni), EFe–H , ENi–H are presented in Tables 4.2 and 4.3. Table 4.2 Energies (eV) of interatomic bonds Me–Me in nickel, iron and iron-nickel solid solutions

Element

Element Ni

Fe

Ni

−0.93

−0.72

Fe

−0.72

−1.3

4.1 Hydrogen-Induced Phases in Iron-Based Alloys Table 4.3 Energies of interatomic bonds Me–H and H–H in hydrogen-charged nickel and iron

Energy, eV EMe–H EH–H

171 System Ni-based

Fe-based

−0.592

−0.647

0.267

0.361

One can see that all Me–Me interactions are of the attractive type. However, the Fe–Fe and Ni–Ni interactions, −1.3 eV and −0.93 eV, respectively, are stronger than the Fe–Ni ones (−0.72 eV), which points to short-range decomposition of the Fe–Ni solid solution with formation of iron- and nickel-rich areas. These data are consistent with studies of the neutron-, ion- or electron-irradiated fcc Fe–Ni (Russel and Garner 1992) and fcc Fe–Cr–Ni (Rotman et al. 1990) alloys, where spinodal-like decomposition was found into the areas enriched in Fe (or in Fe and Cr, respectively) and depleted in Ni. The role of irradiation amounts to an increase in the concentration of superabundant vacancies, which accelerates metallic atom diffusion. The inherent thermodynamic nature of this process was proven by Wiedenmann et al. (1989) in their measurements of small angle neutron scattering in Fe-34 at.% Ni alloy within the temperature range of 625–725 °C. The authors detected oscillating Ni concentration fluctuations between 28.5 and 36.5 at. Ni. As follows from Table 4.3, Ni–H interaction, −0.592 eV, is weaker than Fe–H (−0.647 eV). In other words, hydrogen dissolved in FeNi solid solutions should prefer the iron neighborhood and, hence, hydrogen-caused dilatation of the crystal lattice is expected to be larger in Fe-rich areas than in Ni-rich ones. The obtained results allow the unambiguous interpretation of the γ*-phase nature. The splitting of γ-phase reflections in the X-ray diffraction patterns of hydrogencharged Cr–Ni austenitic steels, as well as in binary Fe–Ni alloys, is due to the inherent short-range decomposition of corresponding hydrogen-free solid solutions. The role of hydrogen merely amounts to manifesting this effect because of the difference in Fe–H and Ni–H interatomic bonds and consequent non equal hydrogen distribution in the decomposed solid solution between the two types of different in their dilatation submicrovolumes. This is the reason for reflection splitting and continuous recovery during subsequent H degassing, as demonstrated in Fig. 4.15. As soon as hydrogen decreases the stacking fault energy in Fe-based alloys, see Ferreira et al. (1996), Pontini and Hermida (1997) and Sect. 2.2.1 in Chap. 2, and this effect depends on the hydrogen content, hydrogen charging can serve as a tool for studying short-range atomic order in metallic solid solutions, see Gavriljuk et al. (2011). It is generally known that solid solutions are far from ideal and reveal a tendency to short-range atomic order, SRO, of two types: ordering or decomposition. Cowley (1950) was the first to characterize SRO in an AB solid solution using the following equation: αilmn = 1 − Plmn i /c A ,

(4.1)

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Fig. 4.15 X-ray diffraction of Fe-50.8%Ni alloy after cathodic charging and subsequent holding at RT. Reflections γ* and γe belong to the submicrovolumes in the solid solution enriched in Fe and Ni, respectively

where Pi lmn is the probability of finding the atom A with co-ordinates lmn in the ith coordination sphere on condition that the atom B is located in the co-ordinates origin, cA is the concentration of A atoms. In other words, the Cowley parameter α is determined by the relationship between the numbers of AB pairs in the real solid solution and in the ideal one with random atomic distribution. Within the framework of this definition, α = 0 corresponds to the ideal solid solution, α > 0 suggests short-range decomposition where atoms of the same name (AA, BB) are predominantly the nearest neighbours, and α < 0 characterizes short-range atomic ordering with an increased number of differently named atoms (AB) as the nearest neighbours. The occurrence of a short-range atomic order in FeNi solid solutions was discussed in literature. A miscibility gap below 400 °C should exist in the Fe–Ni system according to thermodynamic calculations performed by Hertzman and Sundman (1985). A number of experimental studies on the intensively irradiated FeNi alloys (e.g., Reuter et al. 1989) and meteorites (e.g., Petersen et al. 1977) contain evidence of a miscibility gap and even formation of a Fe50 Ni50 superstructure below 400 °C. Annealing of these alloys above this consolute point destroys the superstructure, but retains short-range decomposition, which results in non-homogeneous hydrogen distribution and should be accompanied by a difference in stacking fault energy leading to different dislocation splitting. Measurements of the dislocation triple node radius are one of the generally used methods of studying dislocation splitting and obtaining SFE values. The frequency curves of such measurements are presented in Figs. 4.16 and 4.17 for a hydrogen-free and a hydrogen-charged Fe-50.8%Ni alloy, respectively.

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173

Fig. 4.16 Frequency curve for values of the dislocation nodes radius in the Fe-50.8% Ni alloy after annealing at 900 °C

Fig. 4.17 Frequency curve for values of the dislocation nodes radius in the Fe-50.8% Ni alloy after annealing at 900 °C and subsequent hydrogen charging at RT in the 1 N H2 SO4 solution containing 0.01 g/l NaAsO2 at current density of 50 mA/cm2 for 72 h

Statistical data for the hydrogen-free alloy in Fig. 4.16 have a maximum at about 7 nm, which corresponds to the SFE of ~62 mJ/m2 . In contrast, two peaks of dislocation splitting occur in the hydrogen-charged alloy with the maximum at 6.3 and

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9.3 nm, see Fig. 4.17. The corresponding stacking fault energies are equal to 69 and 47 mJ/m2 , respectively. Therefore, short-range decomposition results in decreased SFE in Fe-rich areas and in increased SFE in Ni-rich areas. The observed short-range decomposition can hardly be caused by the hydrogenincreased concentration of superabundant vacancies which are expected to enhance diffusion as in the case of neutron or electron irradiation. Both hydrogen charging and measurements are carried out at room temperature which is too low for a remarkable migration of Ni and Fe atoms.

4.2 Nickel Hydride or Miscibility Gap?! The formation of nickel hydride declared by Baranowski et al. (1958), see also Baranowski (1959), was a prominent step in studies devoted to the Ni–H system. This conclusion was based on observations of the non-diffusion character of hydrogen desorption kinetics after electrochemical charging interruption. Using X-ray diffraction, Janko (1960) and Cable et al. (1964) showed that this new phase inherits the fcc structure of the parent nickel, but with the lattice parameter increased by about 6%. The history of this discovery, including its stimulating effect on the subsequent studies of metal–hydrogen systems was described on its 45th anniversary, see Baranowski and Filipek (2005). Since 1958, a number of experiments have been devoted to the Ni–H system and the obtained results have created a considerable basis for discussion. For example, three different regions in potential-composition curves were distinguished by Baranowski and Szklarska-Smialowska (1964) in their measurements of nickel penetration by hydrogen. These regions were interpreted as corresponding to the so-called α-phase existing up to the hydrogen-to-metal ratio H/Ni ≈ 0.03, to the β-phase with H/Ni of about 0.6 and to a mixture of two phases. As a consequence, a hydrogendepleted Ni–H solid solution, a hydrogen-rich nickel hydride and an intermediate zone were claimed, respectively. Among numerous XRD studies, the in situ experiments during cathodic hydrogen charging carried out by Juskenas et al. (1998) stand out. The authors found some variations in the stoichiometric coefficient x from NiH0.7 to NiH0.76 and ascribed it to the formation of “a hydrogen ordered solid solution” on the basis of a nickel hydride. No other possible interpretations were analyzed. It was also shown by Janko (1960) and Rashkov et al. (1982) that nickel hydride decomposition follows first order kinetics. The opposite result was obtained by Tomov et al. (1992) who observed non-linear behaviour of the desorption rate and attributed it to the effect of microstructure on the phase transition mechanism. Subsequent studies of the “nickel hydride” were concerned with the hydrogen saturation of nickel under high hydrogen pressures, e.g. Ponyatowsky et al. (1976) and Antonov et al. (1977). Using measurements of electroresistivity, they built a phase diagram in a broad range of temperatures and hydrogen concentrations. As in the case of electrochemical hydrogen saturation performed by Baranowski

4.2 Nickel Hydride or Miscibility Gap?!

175

and Szklarska-Smialowska (1964), the three detected T-P areas were ascribed to a hydrogen-depleted γ1 -phase, a hydrogen-rich γ2 -phase and a mixed area, see Fig. 4.18. In fact, the data for both phases overlap at temperatures above 300 °C and a crown would be expected if these data were to be presented in the concentration-temperature co-ordinates. Such a crown was found in the Ni–H phase diagram obtained from in situ X-ray diffraction measurements at high hydrogen pressures, see inset in Fig. 4.18 according to Shizuki et al. (2002) and Fukai et al. (2004). These authors claimed spinodal-type two-phase separation. Two intriguing points in these diagrams attract particular attention if analyzed in terms of nickel hydride. First, the existence of a phase denoted as “nickel hydride” over the extended range of hydrogen concentration could be natural for solid solutions and can hardly be imagined for chemical compounds, of which hydrides are a type. Second, the occurrence of the crown can be interpreted as a sign for a miscibility gap in the solid solution, but is not consistent with the formation of chemical compounds. In this connection, let us analyze the thermodynamics of the Ni–H system based on atomistic calculations combined with measurements of X-ray diffraction and discuss the experimental data within the framework of two possible precipitation reactions in solid solutions, as proposed by the father of thermodynamics, Gibbs, see Teus and Gavriljuk (2018) for detail.

Fig. 4.18 T-P phase diagram Ni–H constructed using high gaseous hydrogen pressures and measurements of electroresistivity, according to Antonov et al. (1977). Inset shows the same diagram obtained using in situ X-ray synchrotron radiation and diffraction measurements at different temperatures and high hydrogen pressures, as obtained by Fukai et al. (2004), Elsevier

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4 Phase Transformations

4.2.1 Atomic Interactions in the Ni–H System The solution enthalpy of hydrogen atoms in the nickel lattice can be presented by the following equation: Hs = E tot (N i Hn ) − E tot (N i) − n/2E H 2 ,

(4.2)

where E tot are total energies of corresponding cells after all types of relaxation (volume, shape and atomic positions), E H2 is the total energy of a hydrogen molecule, which is calculated by putting two hydrogen atoms in a cubic box with quite a large length (20 Bohr) to exclude any possible interactions which can arise because of periodic boundary conditions. These calculations resulted in the bond length distance of 0.751 Å, binding energy of 4.70 eV and vibration frequency of 4270 cm−1 , which is in good agreement with the available experimental values of 0.741 Å, 4.75 eV and 4395 cm−1 , see Huber and Hertzberg (1979). To include the effects related to phonons, a dynamical matrix has been constructed. The elements of such a matrix are the force constants that were obtained from the ab initio calculations according to the direct method proposed by Kunc and Martin (1982) and Yin and Cohen (1982) and modified by Parlinski et al. (1997). The comparison of possible positions for hydrogen atoms in the nickel lattice in terms of energy revealed that they prefer to occupy octahedral interstitial sites in the Ni fcc lattice in the entire range of studied hydrogen concentrations. This result is consistent with a huge array of experimental data obtained by X-ray diffraction measurements, see e.g. Wollan et al. (1963) and Cable et al. (1964). The calculated cohesion energy for Ni–H ensembles with variable concentrations of hydrogen atoms is presented in Fig. 4.19 as a function of hydrogen concentration. It characterizes the potential energy of all the interatomic bonds in the studied structure and, consequently, the thermodynamic stability of the Ni–H system. As seen, it monotonically increases in its module with increasing hydrogen concentration in the nickel lattice, which is due to the formation of new bonds between hydrogen and metallic atoms. The calculated enthalpy of hydrogen dissolution is presented in Fig. 4.20a. As follows from its concentration dependence, the solution enthalpy increases with the H/Ni ratio rising to 0.25 and decreases thereafter. As shown in Fig. 4.20b, the second derivative of this solution enthalpy acquires a negative sign in the concentration range of H/Ni between 0.03 and 0.75. The obtained solution enthalpy per hydrogen atom in the nickel lattice amounts to ~0.14 eV, which is consistent with available experimental data, see Robertson (1973), Yamakawa and Fujita (1977) and Papastaikoudis et al. (1983). Of course, measurements of solution enthalpy are usually carried out at elevated temperatures, and extrapolation of experimental data to low temperatures is needed for correct comparison with the ab initio calculated data. A large array of experimental data was

4.2 Nickel Hydride or Miscibility Gap?!

177

Fig. 4.19 Total cohesion energy as a function of H/Ni atomic ratio in the Ni–H system

Fig. 4.20 Variation in hydrogen solution enthalpy for the Ni–H system with increasing hydrogen content (a); second derivative of the solution enthalpy as a function of hydrogen content (b)

analyzed by Zheng et al. (1999) who showed that the heat of hydrogen solution in nickel tends to increase with increasing temperature. The calculated total density of electron states, DOS, for spin up and spin down electrons in the NiHx system having different hydrogen content was discussed in Chap. 1 in comparison with that in pure nickel, see Fig. 1.33. Also remarkable is the effect of hydrogen on DOS at the Fermi level (see insets in Fig. 1.33). With increasing hydrogen content, it increases moderately and monotonously for the majority spin channel (Fig. 1.33a), whereas its behaviour is non-monotonous in the case of the minority spin channel (Fig. 1.33b).

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Fig. 4.21 Total density of states at Fermi level and those for different spin orientations as functions of hydrogen concentration

The corresponding concentration dependences of spin up and spin down electron state densities and their total values are presented in Fig. 4.21. Up to the H/Ni ratio of about 0.27, both DOS at the Fermi level for the minority channel and the total DOS increase, however, they decrease above this hydrogen content. Such a substantial decrease in DOS at the Fermi level is caused by the filling of the antibonding electron states. It explains the magnetic behaviour of H-saturated nickel which becomes paramagnetic at high hydrogen contents according to the experimental data obtained by Bauer and Schmidbauer (1961). The phonon contribution calculated within the framework of harmonic approximation is presented in Fig. 4.22. With increasing hydrogen content, it does not change the general behaviour of free energy within the studied temperature range. This is an indication that the precipitation reaction in Ni–H solid solutions has an electron nature.

4.2.2 Thermodynamics of Ni–H Solid Solution According to the classical theory of solid solutions, and in line with Gibbs, two types of precipitation reactions are possible, see e.g. Doherty (1996). In the first type, Fig. 4.23, the Gibbs energy of an oversaturated solid solution with concentration C* cannot be spontaneously reduced to its minimum Cγ at given temperature T1 because the curvature of free energy versus the composition curve is always positive.

4.2 Nickel Hydride or Miscibility Gap?!

179

Fig. 4.22 Temperature dependence of Helmholtz free energy for different hydrogen concentrations in Ni–H system

Fig. 4.23 Gibbs energy and the corresponding fragment of a phase diagram as function of solute atoms concentration and temperature in the case of a chemical compound precipitation in the solid solution. Cγ —equilibrium concentration, C*—oversaturation concentration, Cβ —concentration in the precipitation phase

For this reason, the Gibbs energy can be decreased only if a new distinctly different phase β with concentration Cβ having a lower energy and different crystal lattice is nucleated, and g is the energy gain of this reaction. This type of precipitation reaction is characterized by some energy barrier which should be overcome to initiate the nucleation process. For example, this very reaction occurs during the saturation of iron with gaseous nitrogen at high pressures resulting in the precipitation of γ´-nitride Fe4 N, see the phase diagram in Hansen and Anderko (1958). In the second type of precipitation reactions, Fig. 4.24, the Gibbs energy is characterized by a common curve for both phases with one maximum and two local

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4 Phase Transformations

Fig. 4.24 The same as in Fig. 4.23 for the case of miscibility gap in the oversaturated solid solution

minima. This case is caused by some positive energy term added to the free Gibbs energy of an ideal solid solution, which results in the immiscibility of solid solutions. Phases belonging to this single curve have the same type of crystal lattice and differ only in the concentration of solute elements. As a result, below some critical temperature called the consolute point, the system decomposes into two solid solutions of fixed compositions which are changed only with varying temperature. In the concentration range between the inflection points on the free energy curve, a mechanism of such reaction is the spinodal decomposition. As follows from the concentration dependence of the total cohesion energy presented in Fig. 4.19, its module monotonically increases with increasing hydrogen content in nickel. The absence of any deviations from its linear behaviour suggests that the precipitation reaction proceeds without any energy barrier. The absence of the energy barrier and the identity of the crystal structures in the “nickel hydride” and the parent nickel suggest that the dependence of free energy on the hydrogen content should be described by a single curve belonging to both phases, like it occurs in Fig. 4.24. Moreover, the non-monotonous behaviour of hydrogen solution enthalpy with increasing hydrogen content, as presented in Fig. 4.20a, and its negative second derivative within the H/Ni ratio in between the values of 0.03 and 0.75, see Fig. 4.20b, are important signs that the precipitation reaction occurs via spinodal decomposition. Within this concentration range, the oversaturated hydrogen solid solution is decomposed into a modulated structure of hydrogen-rich and hydrogen-depleted solid solutions. It is interesting to compare the presented calculation results with the experimental data demonstrated by Baranowski and Filipek (2005), where the electrical resistance of nickel was measured as a function of gaseous hydrogen pressure. A significant change in the electroresistivity was observed if hydrogen pressure exceeded 6 kbar, which was attributed by the authors to the formation of the hydride phase. Using the expression for temperature dependence of hydrogen concentration in Ni derived by San Marchi et al. (2007) and taking into account the hydrogen solution enthalpy

4.2 Nickel Hydride or Miscibility Gap?!

181

obtained in the calculations presented here, the H/Ni ratio corresponding to the start of such sudden decrease in electroresistivity can be estimated as C H = αsqr t(F)ex p(−H/RT )

(4.3)

where α is a constant, F is a fugacity, R is the gas constant, H is the enthalpy of hydrogen atom dissolution in metal, and T is temperature. The H/Ni ratio of 0.07 obtained from this estimation falls into the above concentration range calculated for the existence of two solid solutions formed via spinodal decomposition. It was shown earlier by Jones (1962), Smirnova et al. (2001), Olsson et al. (2006) and Alling et al. (2008) that spinodal decomposition has an electron origin. Consequently, a correlation should exist between some parameters describing the electron structure of a thermodynamic system and its inclination to spinodal decomposition. Within the rigid electron band approximation, the second derivative of the solution enthalpy correlates with DOS at the Fermi level via the following equation: d 2 Hs /dc2 ∼ 1/n(F),

(4.4)

where n(F) is density of states at the Fermi level, H s is solution enthalpy. Generally, the rigid band model fails to describe a change in DOS with varying composition of solid solutions. Nevertheless, an inverse proportionality between solution enthalpy and DOS at the Fermi level was confirmed to exist, e.g. by Jones (1962) and Alling et al. (2008). The identical character of the concentration behaviour for the second derivative of the solution enthalpy and DOS at the Fermi level, see Figs. 4.20b and 4.21 respectively, is consistent with the inverse proportionality between the components in Eq. 4.4 for the Ni–H system. X-ray diffraction was frequently used in studies of “nickel hydride” mainly seeking to determine the crystal lattice type and lattice parameters, see e.g. Janko (1960), Cable et al. (1964), Juskenas et al. (1998) etc. The evolution of the intensity of “hydride” diffraction reflections in the course of hydrogen degassing should be useful for clarifying its nature in terms of the abovementioned precipitation reactions proposed by Gibbs. For these experiments to be reliable, it is important to avoid hydrogen degassing in the course of measurements. For this reason, the X-ray diffraction patterns presented in Fig. 4.25 were obtained in situ at −155 °C after subsequent heating procedures carried out in the diffractometer. The intensive peak (111)γa and the rather small peak (111)γ1 exist just after hydrogen charging and sample installation. The first and second heating at 295 K,

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4 Phase Transformations

Fig. 4.25 Evolution of X-ray diffraction in hydrogen-charged nickel measured at −155 ± 5 °C in situ after successive intermediate holdings at higher temperatures. Charging was performed in the 1 N H2 SO4 solution containing 0.01 g/l NaAsO2 with the current density of 50 mA/cm2 for 72 h

each for 10 min, shift the initial (111)γa peak to the positions (111)γb and (111)γ2 , respectively, whereas the intensity of peak (111)γ1 remains unchanged within the error of measurements. Further steps of hydrogen degassing at temperatures of 319 K to 363 K result in the exchange of peak intensities between γ2 and γ1 . Finally, the sample was heated up to 90 °C for 10 min and held for two weeks at RT thereafter. The γ2 peak disappeared. Any possible change in the position of peak (111)γ1 was within the margin of error. Corresponding lattice parameters were estimated as 3.725 Å for γa , 3.715 Å for γb , 3.710 Å for γ2 and 3.514 Å for γ1 . Using the data for hydrogen effect on the dilatation of metals with the fcc crystal lattice proposed by Baranowski et al. (1971), see Fig. 2.1, one can estimate the atomic ratio H/Ni as 0.73 for γa , 0.69 for γb , 0.67 for γ2 and 0.02 for γ1 with the accuracy of ± 0.005. The resulting H/Ni ratio nγ1 is close to H/Ni = 0.03 obtained in our ab initio calculations, see Fig. 4.20b. Just after hydrogen charging and the first two steps of hydrogen degassing, the diffraction pattern contains the γ1 peak, in a position close to that of pure nickel, and peaks (111)γa and (111)γb belonging to H solid solutions with the hydrogen contents above those within the crown. After subsequent series of heating, diffraction patterns reveal the coexistence of two hydrogen solid solutions in nickel, γ1 and γ2 , within the crown, as obtained by Fukai et al. (2004), see Fig. 4.18. In other words, hydrogen degassing is accompanied by a change in the fractions of these solid solutions, whereas their hydrogen concentrations remain unchanged. Consequently, in the course of hydrogen degassing, a corresponding figurative point in the Ni–H phase diagram shifts along the conode towards decreased total hydrogen

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183

content in the system within the crown which borders the T-C area of the miscibility gap. A number of available theoretical calculations and experimental studies suggest that, because of extremely limited hydrogen solubility in nickel, see e.g. Fig. 1.5 in Chap. 1, both the depleted H solid solution and the H-free nickel contribute to the reflection γ1 in the experiment within the limits of error. The data in Fig. 4.25 are not in contradiction with the three different regions in the potential-composition curves detected by Baranowski and Szklarska-Smialowska (1964) and attributed to formation of the α-phase with H/Ni of about 0.03 and the β-phase with H/Ni of about 0.6. Essentially, the difference is in their interpretation. Based on the presented atomistic calculations and experimental data, one can state that Ni hydride does not really exist. It is also relevant to note that a similar phase diagram is found for the Pd-H system, and its interpretation is also proposed in terms of “Pd hydride”, see e.g. Maeland and Gibb (1961), Goltsova et al. (2002), Zhirov et al. (2006). The β-phase, i.e. “Pd hydride”, is claimed to exist in a region of high hydrogen contents, whereas the αphase, or “α-hydride”, with the same crystal lattice, is claimed to exist at low hydrogen contents, and both phases coexist within the crown with the consolute temperature Tc of about 300 °C. Above Tc , the α- and β-phases coexist in the phase diagram without any phase borders and without acceptable thermodynamic substantiation, similarly to the T-P Ni–H diagram. Indicative results have been obtained in the experiments where the saturation of palladium with hydrogen was carried out at temperatures below and above Tc (Goltsova et al. 2002; Zhirov et al. 2006). While changing hydrogen content, the authors observed a strong hardening and even surface relief during the intersection of the two-phase region at temperatures below Tc , whereas the absence of both hardening and surface relief occurred above Tc . Really, this effect is caused by a difference in specific volumes of two solid solutions within the area of miscibility gap and disappears within the area of a homogeneous solid solution. As hydride formation results in brittle fracture, it is relevant to test dislocation mobility in nickel with the H/M ratio of about 0.7 corresponding to “nickel hydride” in comparison with dislocation mobility in H-free nickel. Metal hydrides are brittle compounds and play a distinctly negative role in the hydrogen embrittlement of hydride-forming metals. As shown in Chap. 2, Sect. 2.2.2.1, the strain-dependent internal friction, SDIF, used for this test is caused by dislocation vibrations under applied stress. Moreover, the emission of new dislocations occurs at stresses exceeding that for the start of dislocation sources. The intensity of SDIF is proportional to the area swept by dislocations in the course of their vibrations and slip. SDIF behaviour in hydrogen-free and hydrogen-charged nickel with H/M of about 0.7 is presented in Fig. 4.26. As seen, SDIF occurs in both H-free and H-charged nickel, i.e. “Ni-hydride” is not brittle. However, in contrast to that in austenitic steels and nickel superalloys, see Figs. 2.14 and 2.16 in Chap. 2, respectively, dislocation mobility is decreased by hydrogen if its concentration is within the area of miscibility gap. This effect can be

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Fig. 4.26 Strain-dependent internal friction in H-free compared to H-charged nickel contents and, correspondingly, different specific volumes

related to stresses caused by two coexisting solid solutions with strikingly different hydrogen.

4.3 H-Induced Transformations in Ti Alloys Hydrogen effect on the phase transformations in titanium alloys has been extensively studied in the seventies to the nineties of the past century. Subsequent studies aimed mainly to use hydrogen as interim alloying element for improving technological plasticity of titanium alloys or refine the grain microstructure, see Chap. 6 about details. Hydrogen belongs to the eutectoid forming β-stabilizers. The eutectoid transformation β → α + δ(γ) in the Ti–H solid solution occurs at ~300 °C: 319 °C at the heating with the rate of 1 °C per minute (point Ac1 ) and 281 °C at the cooling with the same rate (point Ar1 ), see Fig. 1.6 and Lenning et al. (1954). The single-phase areas β and α are separated by the two-phase α + β region. Hydrogen decreases temperatures of β/α + β and α/α + β equilibrium and decreases temperature of β → α + δ(γ) reaction, which substantially expands the concentration-temperature range of β phase. For example, hydrogen in the α alloy Ti-5Al decreases the temperature of β/α + β equilibrium by 290 °C at the H content of 1.1 at.%, see Ilyin et al. (2002). At the H concentrations more than 0.15 at.%, the α + β area is replaced by the narrow-width three-phase α + β + γ, and only the α and γ phases are stable below this area. The alloying of this alloy by Sn shifts the equilibrium boundaries to higher temperatures.

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185

In the pseudo-α alloy Ti-6.5Al-2Zr-1Mo-1V, temperatures of β/α + β equilibrium are also decreased by hydrogen. However, the α + β + γ and α + γ areas containing hydrides are shifted to significantly higher hydrogen concentrations. The α + β alloys, e.g. the Ti-6.5Al-0.7Mo-4Zr-2.5Sn-1Nb-0.2Si one, are characterized by precipitation of the ordered α2 phase at high concentrations of hydrogen, which can be explained by a smaller number of β-stabilizing elements and the higher total content of Al and Al-equivalent elements like Sn and Zr. Beside this, hydrogen causes the redistribution of alloying elements over the phases, which results in the increase of the Al content in the α phase. The eutectoid β → α + γ transformation is partially or even completely suppressed by hydrogen in the α + β alloys. For example, at H concentrations higher than 0.3%, this transformation in the alloy Ti-6Al-4V proceeds but is not completed. It does not occur in the hydrogen-charged alloy Ti-6.5Al-1.8 Sn-3.8Zr-4Mo-1W-0.2Si and neither γ hydride nor the α2 phase are formed in the alloy Ti-5.5Al-2Mo-4.5V-1Cr0.6Fe. The β/α + β equilibrium in the alloy Ti-6Al-4V is shifted by hydrogen from 1000 °C down to 800 °C, see Qazi et al. (2001, 2002) and Fig. 4.27a. Starting from Fig. 4.27 Phase equilibrium in the alloy Ti-6Al-4V doped with hydrogen (a) and diagram T-τ of β decomposition at H content of 30 at.% (b). Redrawn from Qazi et al. (2002), Springer

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hydrogen concentration of ~15 at.%, the δ hydride is formed in this alloy and the equilibrium is established between the β, β + δ, and α + β + δ areas. With decreasing temperature, the metastable β phase decomposes revealing a typical TTT kinetics of isothermal decomposition with the time nose at 600 °C (Fig. 4.27b). The sequence of hydrogen-induced phase transformations in the alloy Ti-6Al-4V obtained by electron beam melting was studied in situ by Pushilina et al. (2018) using synchrotron XRD during hydrogenation at 650 °C. The following phase transformations were detected with increasing hydrogen content. The increase in the lattice parameter of the β phase and no change in the α lattice parameter occur at the initial stage of hydrogenation. Then, the volume fraction of β phase grows at expense of the α phase and, along with α → β transformation, the α2 phase based on the intermetallic compound Ti3 Al appears. A reason for the α → α2 transformation is the redistribution of Al in Ti leading to its local accumulation above 7 mass %, see Kim et al. (2016). Formation of α2 phase was also observed by Sun et al. (2015) at similar conditions of hydrogenation. After hydrogenation to 0.29 mass % of H, the Ti3 Al particles having plate morphology were found inside the α2 plates. Generally, the following features are typical for hydrogen effect on the phase transformations and phase equilibrium in the titanium alloys. Temperatures of β/α + β equilibrium are decreased by hydrogen regardless of the Ti alloy chemical composition. The hydrogen-containing α and α + β alloys are characterized by the decreased temperature of the eutectoid β → α + γ transformation. This transformation does not go to the end in the α + β alloys and is fully suppressed if the so-called Kβ coefficient characterizing the β-stabilizing effect of alloying elements exceeds its value of 0.4, see Ilyin et al. (2002) for details. An increase in the cooling rate leads to the diffusionless transformation of the β phase into the martensitic hexagonal α -phase. In the pure titanium and its alloys with the eutectoid-forming stabilizers, as well as with α-stabilizers, the only β → α martensitic transformation is realized. It also occurs in the Ti alloys moderately alloyed with the β-stabilizing elements. Above their critical concentration, the orthorhombic α martensite is obtained instead of α . The main difference between the mechanisms of these transformations is the combined uniform deformation and homogeneous shear in the first case and the only uniform deformation in the second one (Ilyin et al. 2002). These features of H-induced transformations were confirmed by subsequent researchers, see e.g. Wen et al (2020) who studied hydrogen concentration dependence of phase transformations and evolution of microstructure in metastable β-Ti alloy β-21S. Relating to martensitic transformation, the hydrogen-enhanced stability of the β-phase is accompanied by two important effects. First, the start and finish temperatures of the α transformation, Ms and Mf , decrease with increasing hydrogen content, so that it proceeds below the ambient temperature in the alloy Ti-12V doped with 0.2 mass % of H and the microstructure in the as-quenched state is represented by the only metastable βm phase, see Fig. 4.28. Second, the critical cooling rate for martensitic transformation, vcr , decreases with increasing hydrogen content. For example, if the diffusionless β → α transformation

4.3 H-Induced Transformations in Ti Alloys

187

Fig. 4.28 Hydrogen effect on the temperature of α + β/β equilibrium Ac3 and temperatures for the start, Ms , and finish, Mf , of martensitic transformation in the Ti-12V alloy. Redrawn from Ilyin (1987)

in this alloy with 0.003% H occurs only at the cooling rates vcr higher than 34 K s−1 , its value of 1 K s−1 is sufficient to prevent the diffusion β → α + β transformation even at ambient temperature. A reason for that is obviously related with a difference in the hydrogen effect on the temperature dependence of free energy in the β and α phases. A feature of martensitic transformation in the hydrogen-charged titanium alloys is also a decrease of main strains in the ellipsoid of deformations, whereas one of them even approaches zero. As a result, the habit plane acquires a more perfect structure and higher mobility. Moreover, the coherence of interface boundaries is conserved within the range of β → α martensitic transformation, which causes the nearly complete shape memory effect, see Ilyin et al. (1995) about details. In contrast to other β-stabilizing elements, a unique peculiarity of hydrogen as a β-stabilizer forming the interstitial solid solutions is its effect on stability of α martensite and ω phase. For example, hydrogen charging of Ti–V alloys eases transition of α -martensite to the α -martensite, which is not the case of other β-stabilizers. The α -martensite is formed in the Ti-8Al alloy due to quenching from the temperature area of β phase, whereas the quenching of the same alloy doped with 0.05% of H results in the β → α transformation (Kolachev et al. 1982). Debatable is the hydrogen effect on stability of the ω-phase which is formed under hydrostatic compression in the pure Ti and due to quenching of Ti alloyed by β-stabilizing elements in their critical concentration range, see e.g. Collings (1984) and Ilyin (1994). Hydrogen dissolution in the Ti alloys having the β + ω structure destabilizes the ω phase and initiates the ω → β transformation. Like β → α transformation, it is reversible during hydrogen degassing. A feature of hydrogen is also that it allows to decrease the concentration of βstabilizing elements needed for obtaining the βm + α structure due to quenching and, at the same time, fully suppresses formation of ω phase. Therefore, the

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hydrogen dissolution allows to change the phase composition of titanium alloys and, consequently, their microstructure. In relation to decomposition of metastable phases, the alloying with hydrogen does not significantly change its mechanisms. The H-containing phases α , α and βm are decomposed at temperatures below 550 °C due to diffusive redistribution of alloying elements leading to formation of enriched and depleted submicroscopic areas which in turn are transformed into more stable phases via the diffusionless mechanisms, see Ilyin (1987). Because of increased hydrogen diffusivity in comparison with other β-stabilizing elements, it changes temperatures and times of some decomposition stages. For example, despite the equivalent phase composition of alloys Ti-16V0.15H and Ti-20V, the hydrogen redistribution proceeds at smaller temperatures and for shorter times than that of vanadium. As a result, a larger fraction of ω phase is formed in the former alloy at the same thermal treatments. At the same time, hydrogen accelerates decompositions of α (α ) martensites and retards decomposition of βm phase. Decomposition of the H-containing β phase at temperatures above 550 °C proceeds via diffusionless mechanism. Like other martensitic phase transitions, because of a large volume effect of β → α transformation, the α phase is formed as coarse plates, see e.g. Glazunov and Kolachev (1980). Usually, this undesirable structure is retransformed into the globular one by means of thermo-mechanical treatment at temperatures of α + β area. As shown by Kerr et al. (1980), Kolachev and Nosov (1984), Kolachev et al. (1985) and Kerr (1985), hydrogen charging of titanium alloys and subsequent annealing allow to transform the coarse plates into fine particles in the α + β alloy Ti-6Al-4V (Kerr et al. 1980; Kerr 1985) or refine the grains in the cast α alloy Ti-5Al-2.5Sn (Kolachev et al. 1985), see Chap. 6, Sect. 6.2 about details. In the quoted studies, the disperse α + β structure and recrystallization in the α phase were attributed to the volume effect of eutectoide β → α + β transformation leading to hardening. However, the same change in structure can be obtained at the zero volume effect due to controlling the decomposition of β phase and the nucleation of α phase, as it is proposed by Ilyin (1987), see Fig. 4.29. Two competitive factors, the surface energy and elastic deformation, determine the plate or globular geometry of nucleated phases. In the case of large volume effect of nucleation, the energy of elastic deformation prevails and, consequently, the new phase has morphology of thin plates, like it occurs during martensitic transformations in steels. At the insignificant volume change, the nuclei acquire the globular form reducing thereby the surface energy. Because of the preferential hydrogen dissolution in the β phase, the atomic volume is insignificantly changed in the α phase of the Ti-12V alloy and markedly increases in the β phase, see curves 2 and 3 in Fig. 4.29. For this reason, along with decreased fraction of β phase, the hydrogen degassing is accompanied by a decrease of its atomic volume. Hence, at some critical hydrogen concentration, e.g. 0.2 mass % in Fig. 4.29, the volume effect of β → α transformation in the Ti-12V alloy approaches zero or is so insignificant that prevailing is the contribution of the surface energy in the change of free energy during the

4.3 H-Induced Transformations in Ti Alloys

189

Fig. 4.29 Hydrogen effect on the fraction Qβ of β phase (1), atomic volumes  in α (2) and β (3) phases and the volume effect of β → α transformation in the annealed alloy Ti-12V. After Ilyin (1987)

phase transformation. Consequently, the precipitated α phase acquires the globular morphology. Subsequent studies of hydrogen-induced phase transformations in Ti alloys with βeutectoid stabilizers were mainly related with searching for strengthening using intermetallic compounds. For example, a mechanism for the hydrogen-induced appropriate phase composition in Ti-Cr alloys was analyzed by Skvortsova et al. (2006). As alloying element in titanium, chromium is characterized by a high solubility in the β phase, whereas its content in the α phase does not exceed 0.5%. It increases hardness due to solid solution hardening, as well as by a structural change due to an appropriate heat treatment. A feature is the chromium-increased stability of the β phase and its decrease in relation of TiCr2 compound in the α phase. The phase composition of as quenched binary pseudo-β Ti-Cr alloys doped with hydrogen, as high as 0.4%, is characterized by the following features. At the Cr content up to 5%Cr, hydrogen decreases temperature of α → β transformation and increases stability of β phase. If the chromium content exceeds 6%, hydrogen induces the TiCr2 precipitation in the β phase. This hydrogen effect occurs also in the TS alloy (Ti-3.2Al-6.7V-4.2Mo-11.3Cr0.9Zr) with the only difference in the chemical composition of Tix Cry precipitates containing additionally Al, Mo, V and Zr. Moreover, during the annealing hydrogenation, the spinodal decomposition of the β phase occurs into the Cr-rich/H-depleted and Cr-depleted/H-rich submicrovolumes accompanied with the redistribution of hydrogen and substitutional β-stabilizing elements. During this procedure, the Crrich and hydrogen-depleted β phase transforms into the Tix Cry compound, whereas stability of hydrogen-rich β phase decreases with respect to the compound.

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4.3.1 Titanium Hydrides The crystal structure of titanium hydride is complicated given there are three types. Precipitated in the α-Ti phase at temperatures below 300 °C, non-stoichiometric hydride has an fcc CaF2 -type crystal structure with hydrogen atoms randomly occupying tetrahedral interstitial sites. With increasing hydrogen content, some uncertainty appears, caused by unchanged lattice parameters within the range of hydrogen content up to H/Ti = 1.6. One can suggest that, within this concentration range, the fcc hydride volume fraction increases with increasing hydrogen content without any remarkable change in hydride composition. Starting from the H/Ti ratio of about 1.6, the lattice parameter of this cubic hydride increases, see Irving and Beevers (1971) and Millenbach and Givon (1982), indicating the increasing filling of tetrahedral sites by hydrogen atoms. In addition to these X-ray diffraction observations and using transmission electron microscopy, Numakura and Koiwa (1984) identified face-centred tetragonal hydride, as well as deuteride, with c/a = 1.09 in α-titanium having a low concentration of hydrogen of 1–3 at.% H or D. The distinct features of this fct hydride are two modes of its precipitation with different habit planes and superlattice reflections indicating an ordered arrangement of hydrogen. The authors explained the observed deviation from cubic symmetry by a volume misfit between the hydrides and the α-matrix and a large stress in the α-matrix around hydride precipitates. Hydride precipitation in α-titanium is accompanied by an increase in the volume lattice of 15–21%, which causes coherent stresses at the matrix-hydride interface (see Yan et al. 2006). The decisive role of stresses in the deviation of the crystal lattice from cubic symmetry was also convincingly demonstrated by Zhang and Kisi (1997) who obtained even the fct hydride TiH1.73 due to ball milling titanium powders under hydrogen atmosphere. Another distortion of the cubic lattice in titanium hydride occurs when the hydrogen content approaches the stoichiometric composition of TiH2 . As found for the first time by Sidhu et al. (1956) and Yakel (1958), below a critical temperature of 310 K, the cubic face-centred hydride is transformed into the face-centred tetragonal hydride with the c/a < 1.0. The same occurs with titanium “deuteride” (see Fig. 4.30). Transition from cubic to tetragonal distortion proceeds via continuous expansion of the crystal lattice in two directions, the a and b axes, and contraction in the third one, the c axis. At 79 K, the c/a ratio reaches its minimum value of 0.943. Later, this phenomenon was found to be common to all compounds MHx near the stoichiometry x = 2 in the IVB group of the periodical system. It is also accompanied by a change in the temperature dependence of magnetic susceptibility, specific heat (Stalinski and Bieganski 1960), the Hall coefficient and resistivity (Cesi et al. 1963), etc. While measuring the electron specific heat, magnetic susceptibility and thermoelectric power of TiHx and ZrHx compounds, Ducastelle et al. (1970) revealed a clear correlation between the change of electron properties and the fcc → fct transformation of crystal structure and ascribed it to the Jahn–Teller effect. Its essence

4.3 H-Induced Transformations in Ti Alloys

191

Fig. 4.30 Variation of lattice parameter (a) and c/a ratio (b) with temperature in titanium deuteride Ti/D1.98 . After Yakel (1958), International Union of Crystallography

amounts to a lift of degeneracy in electron states at the Fermi level, which lowers the total energy of the system and is accompanied by atomic displacements, thereby decreasing the crystal symmetry. This interpretation has been confirmed by Gupta (1979) who calculated the electron structure of titanium hydride TiH2 , see Fig. 4.31. In comparison with the DOS of pure α-titanium, hydrogen induces bound Ti–H states below the left side of the metal d-band (0.44 Ry) and a high peak of electron states at the Fermi level (0.611 Ry). The DOS at the Fermi level in the cubic TiH2 phase is equal to 1.73 states/eV per Ti atom. Using measurements of the electron heat capacity of the tetragonal phase of TiH1.97 , Ducastelle et al. (1970) obtained D(EF ) = 0.95 states/eV per Ti atom. Therefore, the fcc → fct transformation originates from a change in the electron structure, namely from a decrease in the total electron energy. Based on the analysis of the above experimental data, transformations of the hydride crystal structure with increasing hydrogen content in the Ti–H system can be presented as shown in Fig. 4.32. At small hydrogen contents, stresses in hcp α-titanium in the vicinity of the precipitated fcc hydride cause tetragonal distortions in the hydride crystal lattice resulting in the c/a > 1 (γ-hydride). With hydrogen content in the alloy increasing up to H/Ti

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Fig. 4.31 Total density of electron states (solid line) and number of electrons (dased line) per unit cell in fcc titanium hydride TiH2 After Gupta (1979), Elsevier

Fig. 4.32 Lattice parameters of Ti hydrides measured at RT as a function of hydrogen content: black circles—fct γ-phase with c/a > 1 (Numakura and Koiwa 1984), semifilled circles—fcc δ-phase (Millenbach and Givon 1982), open squares—fct ε-phase with c/a < 1 (Irving and Beevers 1971)

of ~1.6, the volume hydride fraction increases without any remarkable change of hydrogen content in the hydride and, consequently, its lattice parameter remains unchanged (δ-hydride). The increase in the lattice parameter of fcc δ-hydride starts within the concentration range of a single δ-phase when hydrogen atoms fill the available empty tetrahedral sites. At compositions close to TiH2, tetragonal distortions with c/a < 1 appear arising from atomic displacements caused by the above change in the electron structure and transforming the fcc δ-hydride into an hcp ε one. Hydrogen occupation of the tetrahedral sites was also established for titanium hydrides having the fcc (δ-phase), as well as fct (ε-phase) crystal lattice (e.g. Wipf et al. 2000). This suggests that the above distortions at the H/Ti ratio close to 1.0 resulting in the fcc → fct transformation hardly change hydrogen distribution on the interstitial sites.

4.3 H-Induced Transformations in Ti Alloys

193

4.3.2 Metal Pseudo-Hydrides and Thermodynamics In view of the growing interest in phase transformation induced by hydrogen in metals under high gaseous pressures, it would not go amiss to comment on the available data on metal hydrides claimed to be formed in a number of metals, e.g., Cr, Mn, Fe, Co, Ni, Mo, Tc, Rh, Pd, Re etc., see e.g. Ponyatowsky and Belash (1976), Somenkov et al. (1987), Antonov (2002), Antonov et al. (2002) etc. All these hydrides have been shown to exist within a broad range of hydrogen contents. In cobalt, rhodium and palladium they have crystal lattices identical with those of the parent metals, as in the case of the “Ni hydride” analyzed above. In contrast, the hydrides in Ti, Zr, Ta, Nb and V have definite stoichiometric chemical compositions. Their crystal lattices are different from those of the parent metals, in line with the abovementioned first type of Gibbs’ precipitation reactions. Hydrogen dissolution under the high gaseous hydrogen pressure of chromium, manganese, and molybdenum induces γ → ε transformation, as is the case in iron. Again, these “ε-hydrides” with the hcp crystal lattice are shown to exist in the wide concentration range. Indicative in this respect is the comparison of hydrogen and nitrogen dissolution in iron. According to the Fe–N phase diagram, see Hansen and Anderko (1958), the ε-phase having the hcp crystal structure is stable at nitrogen contents of 20– 35 at.%. The long-range atomic ordering occurs at 33 at.% of nitrogen resulting in a superstructure conventionally denoted as ζ-Fe2 N nitride. Nevertheless, so far, no attempts have been made to apply the term “nitride” to the whole concentration range of the hcp Fe–N solid solution. In many aspects, nitrogen and hydrogen in metals are similar in their effect on the crystal structure, phase transformations and properties. Both elements increase the density of electron states at the Fermi level, and, consequently, increase the concentration of free electrons, cause γ → ε transformation and affect iron’s mechanical properties in a similar way, see e.g. Gavriljuk (2016). Like hydrogen, nitrogen is a volatile element, and they both are characterized by remarkably low solubility in iron. Like the Fe–H phase diagram, the Fe–N one is constituted not for pN2 = 1 bar, but for different partial pressures of nitrogen and, in fact, it is a projection of various equilibrium states in the temperature–pressure– concentration diagram onto its temperature–concentration plane. Therefore, there are no convincing arguments to denote as hydrides the oversaturated hydrogen solid solutions obtained under high hydrogen pressures, decomposed immediately under normal hydrogen pressure and without the inherent features of chemical compounds. Summary Ab initio calculations of change in the interatomic cohesion energy in the fcc and hcp iron phases give evidence of the hydrogen-decreased thermodynamic stability of austenitic steels in relation to the γ → ε transformation. However, this effect is observed mainly using electrochemical hydrogen charging and, with rare exceptions,

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does not occur in the case of gaseous hydrogenation under high hydrogen pressure. Among the discussed possible reasons for that, the hydrogen-caused plastic deformation taking place during electrochemical charging and absent at gaseous hydrogenation is a factor assisting formation of ε-martensite. It is shown that this phase does not initiate hydrogen embrittlement and, on the contrary, improves hydrogen resistance. The existence of hydrogen-caused formation of the fcc γ*(γH ) phase in austenitic steels, as declared in a number of available studies, is disproved based on the ab initio calculations of interatomic bonding energies and low temperature X-ray diffraction measurements. It is shown that, in fact, due to different affinity with the atoms of substitution alloying elements, hydrogen is non-homogeneously distributed in the fcc multicomponent iron-based solid solutions and, for this reason, makes visible their inherent short range atomic decomposition. Reality of the widely believed formation of nickel hydride is disputed by means of theoretical analysis of Ni–H cohesion energy. It is shown that, instead, a miscibility gap occurs in the Ni–H thermodynamic system in consistency with Gibbs’ thermodynamics of precipitation reactions forming thereby the crown in the Ni–H phase diagram under which coexist two solid solutions having stable lattice parameters. Hydrogen-induced phase transformations in titanium including Ti-based solid solutions and hydrides are discussed based on the theoretical and experimental studies of the hydrogen-caused change in the titanium electron structure.

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Ponyatowsky EG, Belash IT (1976) Formation and decomposition of chromium hydride at temperatures up to 400 ºC and pressures up to 20 kbar. Rep USSR Acad Sci 229:1171–1173 (in Russian) Ponyatowsky EG, Antonov VE, Belash IT (1976) Phase T-P diagram of Ni-H system at temperatures up to 630 K and pressures up to 18 kbar. Rep USSR Acad Sci 229:391–393 (in Russian) Pushilina N, Panin A, Syrtanov M, Kashkarov E, Kudiiarov V, Perevalova O, Laptev R, Lider A, Koptyug A (2018) Hydrogen-induced phase transformation and microstructure evolution for Ti6Al-4V parts produced by electron beam melting. Metals 8(5):301. https://doi.org/10.3390/met 8050301 Qazi JI, Senkov ON, Rahim J, Genc A, Froes FH (2001) Phase transformations in the Ti-6Al-4V-xH alloys. Metall Mater Trans A 32(10):2453–2463. https://doi.org/10.1007/s11661-001-0035-8 Qazi JI, Rahim J, Senkov ON, Patankar SN, Froes FH (2002) Phase transformations in the Ti-6Al4V-H system. JOM 54:68–77. https://doi.org/10.1007/BF02701081 Rashkov S, Monev M, Tomov I (1982) Electrochemical formation and disintegration of the Ni-H phase in bright nickel coatings. Surf Technol 16(3):203–208. https://doi.org/10.1016/0376-458 3(82)90110-8 Reuter KB, Williams DB, Goldstein JI (1989) Determination of Fe-Ni phase diagram below 400 ºC. Metall Trans A 20(4):719–725. https://doi.org/10.1007/BF02667589 Rigsbee JM (1978) TEM observations of hydrogen-induced ε-hcp martensite. Metallography 11(4):493–498. https://doi.org/10.1016/0026-0800(72)90074-2 Robertson WM (1973) Hydrogen permeation, diffusion and solution in nickel. Z Metallk 64:436– 443. https://doi.org/10.1515/ijmr-1973-640606 Rotman F, Gilbon D, Dimitrov O (1990) Periodic decomposition of electron-irradiated pure austenitic Fe-Cr-Ni alloys. In: Russel KC, Smith DF (eds) Physical metallurgy of controlled expansion invar-type alloys. TMS-AIME, Warendale, PA, pp 145–158 Rozenak P (2013) Stress induced martensitic transformations in hydrogen embrittlement of austenitic steels. Metall Mater Trans A 45(1):162–178. https://doi.org/10.1007/s11661-0131734-7 Rozenak P, Bergman R (2006) X-ray phase analysis of martensitic transformations in austenitic steels electrochemically charged with hydrogen. Mater Sci Eng A 437:366–378. https://doi.org/ 10.1016/j.msea.2006.07.140 Rozenak P, Eliezer D (1988) Nature of the γ and γ* phases in austenitic stainless steels cathodically charged with hydrogen. Metall Trans A 19(33):723–730. https://doi.org/10.1007/BF02649288 Rozenak P, Shani E (2012) Analysis of phase distribution in thin surface layers comparable to the penetration depth of X-rays. Metall Mater Trans A 43(11):4028–4042. https://doi.org/10.1007/ s11661-012-1203-8 Rozenak P, Zevin L, Eliezer D (1984) Hydrogen effects on phase transformations in austenitic stainless steels. J Mater Sci 19(2):567–573. https://doi.org/10.1007/BF02403244 Russel KC, Garner FA (1992) Thermal and irradiation-induced phase separation in Fe-Ni based invar-type alloys. Metall Trans A 23(7):1963–1976. https://doi.org/10.1007/BF02647544 San Marchi C, Somerday BP, Robinson SL (2007) Permeability, solubility and diffusivity of hydrogen isotopes in stainless steels at high gas pressures. Int J Hydrogen Energy 32(1):100–116. https://doi.org/10.1016/j.ijhydene.2006.05.008 Schramm RE, Reed RP (1975) Stacking fault energy of seven commercial austenitic stainless steels. Metall Trans A 6(7):1345–1351. https://doi.org/10.1007/BF02641927 Schumann H (1967) Die martensitischen Umwandlungenin Kohlenstoffarmen Manganstählen. Archiv Eisenhüttenw 38(8):647–656. https://doi.org/10.1002/srin.196704234 Schumann H (1974) Einflu der Stapelfehlerenergie auf den kristallographischen Umgitterungsmechanism der/-Umwandlung in hochlegierten Stählen. Kristall und Technik. 9(10):1141–1152. https://doi.org/10.1002/crat.19740091009 Shivanyuk VN, Foct J, Gavriljuk VG (2003) On a role of hydrogen-induced ε-martensite in embrittlement of stable austenitic steel. Scripta Mater 49(6):601–606. https://doi.org/10.1016/S13596462(03)00338-5

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Wayman ML, Smith GC (1971) Hydride formation in nickel-iron alloys. J Phys Chem Solids 32(1):103–118. https://doi.org/10.1016/s0022-3697(71)80012-4 Wen J, Fleury E, Cao F, Allain N (2020) Hydrogen concentration dependence of phase transformation and microstructure modification in metastable titanium alloy β-21S. J Mater Sci. https://doi. org/10.1007/s10853-020-05568-5 Wiedenmann A, Wagner W, Wollenberger H (1989) Thermal decomposition of Fe-34at.% Ni between 625°C and 725°C. Scripta Metall 23(4):603–605. https://doi.org/10.1016/0036-974 8(89)90459-6 Wipf H, Kapesser B, Werner R (2000) Hydrogen diffusion in titanium and zirconium hydrides. J Alloys Compd 310(1–2):190–195. https://doi.org/10.1016/S0925-8388(00)00945-2 Wollan EO, Cable JW, Koehler WC (1963) The hydrogen atom positions in face centered cubic nickel hydride. J Phys Chem Solids 24(9):1141–1143. https://doi.org/10.1016/0022-3697(63)900 28-3 Yakel HL (1958) Thermocrystallography of higher hydrides of titanium and zirconium. Acta Cryst 11(1):46–51. https://doi.org/10.1107/S0365110X58000098 Yamakawa K, Fujita FE (1977) Diffusion of hydrogen in hydrogen-quenched nickel. Jpn J Appl Phys 16(10):1747 Yan L, Ramamurthy S, NoëL JJ, Snoesmith DW (2006) Hydrogen absorption into alpha titanium in acidic solutions. Electrochim Acta 52(3):1169–1181. https://doi.org/10.1016/j.electacta.2006. 07.017 Yin MT, Cohen ML (1982) Theory of lattice-dynamical properties of solids: application to Si and Ge. Phys Rev B 26(6):3259–3272. https://doi.org/10.1103/PhysRevB.26.3259 Zhang H, Kisi EH (1997) Formation of titanium hydride at room temperature by ball milling. J Phys Condens Matter 9(11):L185–L190. https://doi.org/10.1088/0953-8984/9/11/005 Zheng K, Klassen T, Oelerich W, Bormann R (1999) Thermodynamics of the Ni-H system. J Alloys Compd 283:151–161. https://doi.org/10.1016/S0925-8388(98)00857-3 Zhirov GI, Goltsov VA, Shatalov GE, Glyakov DA (2006) Mechanical properties and fine structure of annealed and hydrogen-phase-hardened palladium. Fiz Metall Metalloved 101:103–112 (in Russian)

Chapter 5

Hydrogen Embrittlement

Hydrogen-induced degradation of iron and steel was discovered by Johnson in 1874 and first published in 1875. In time, it was confirmed for any metallic materials, and, in fact, no metals are free of this dangerous phenomenon, which is also diverse in its outward signs. Finding a correlation between the strength of metallic materials and their predisposition to hydrogen brittleness was the first step in searching for its nature. In the case of carbon steels, some doubt in this respect was expressed by Thompson and Bernstein (1980) in their discussion of the results obtained by Zmudzinski et al. (1977), see Fig. 5.1. The latter carried out 465 mechanical tests on 34 grades of low and medium strength steels. The huge scattering of experimental data demonstrates that strength itself may not be a reliable factor and, therefore, the nature of hydrogen embrittlement, HE, should be investigated at a more sophisticated level. Possibly, one of the first attempts to summarize different kinds of hydrogen-caused damage and their manifestations in metals was undertaken by Hirth and Johnson (1976). According to their classification, hydrogen environmental embrittlement, HEE, is degradation of the mechanical properties of plastically deformed samples in contact with external gaseous hydrogen. Hydrogen stress cracking, HSC, where hydrogen atoms are free to migrate under loading below yield strength in the direction of their concentration or stress gradients, is ascribed to internal hydrogen embrittlement. A reduction in the strength of carbon steels under high hydrogen pressure at elevated temperatures caused by methane formation is designated as hydrogen attack, HA. Remarkable external signs characterize the next group of hydrogen-caused damage: (i) blistering produced from molecular hydrogen formed at some lamellas or bands of non-metallic inclusions in metals; (ii) shatter cracks, flakes and fisheyes formed in the course of heavy forging and conceivably resulting from hydrogen pick-up during melting with subsequent segregation at the voids and discontinuities in the process of solidification; (iii) microperforation by high-pressure hydrogen in steel products at near ambient temperatures. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. G. Gavriljuk et al., Hydrogen in Engineering Metallic Materials, https://doi.org/10.1007/978-3-030-98550-9_5

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Fig. 5.1 Index of hydrogen embrittlement (δH − δ0 )/δH in %, where δ0 and δH are relative elongations before and after tensile tests, as a function of yield strength for 34 steels in 436 tension tests. According to Thompson and Bernstein (1980)

Separately designated is the hydrogen-caused loss in tensile ductility characterized by the percentage decrease of elongation and reduction in area during tensile tests, as well as the hydrogen-enhanced degradation of flow properties during steady state creep under constant loading. Closing this classification is embrittlement due to hydride formation in metals like Ta, Nb, V, Zr, Ti and their alloys. Later on, Birnbaum (1978) reviewed hydrogen-induced failures related to mechanisms of fracture. First, he distinguished metals forming stable hydrides with high hydrogen contents of nearly stoichiometric metal-hydrogen ratios in contrast to nonhydride formers where the hydrogen concentration can constitute a few parts per million. Distinctive features of the first and second metal groups are, respectively, the negative and positive heats of hydrogen solution from the gas phase, respectively. Second, Birnbaum divided sources of hydrogen into external and internal ones, underlying at the same time that mechanisms of hydrogen embrittlement are not basically different, and only its kinetics depends on the source of hydrogen. Consequently, the proposed kinds of failure were grouped into the following classes: (a) high pressure bubble formation, (b) surface adsorption effects, (c) plastic deformation effects, (d) decohesion and (e) hydride precipitation. Some redetermination of this classification was made by Kolachev (1985) who analyzed six types of hydrogen brittleness. The first one covers hydrogen-caused fracture of metals like copper, silver, nickel etc., which are not sufficiently free of oxygen, including also hydrogen attack on carbon steels. In the first case, the absorbed hydrogen interacts with oxygen at elevated temperatures forming high-pressure water vapor. In the second, hydrogen interacts with carbon forming methane and leading to decarbonization and cracking even in the absence of external mechanical loading.

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The second type is concerned with molecular hydrogen, like the abovementioned high-pressure bubble formation. With decreasing temperature, hydrogen pressure in the microvoids can reach hundreds of thousands MPa. Hydride formation is attributed to a third type of hydrogen brittleness. It is typical of III and IV group metals in the periodic table and dangerous even in the case of negligible hydrogen solubility, e.g. ~ 0.003 mass % in titanium and ~ 0.00003 mass % in zirconium. The fourth type of brittleness is caused by dissolved hydrogen. It is developed in hydride-forming elements, e.g. in titanium (α + β)- and β-alloys, in niobium and vanadium, as well as in aluminium-based alloys at concentrations much smaller in comparison with those for hydride formation. It includes also hydrogen segregation at the grain boundaries and interfaces with the following special features: (i) plasticity remains unchanged with increasing hydrogen content up to its certain value and then abruptly falls down to its small values; (ii) this certain hydrogen content decreases with decreasing temperature. Surplus hydrogen remaining in the solid solution after rather fast cooling to ambient temperatures, e.g. in Ti–Al, Zr–Nb alloys etc., is supposed to be a reason for the fifth type of brittleness as a consequence of hydrogen precipitation or formation of non-hydride phases. This hydrogen brittleness is not reversible. Reversible brittleness caused by diffusively mobile hydrogen constitutes the sixth type of brittleness. This most complicated and dangerous phenomenon is often denoted as true hydrogen brittleness. Its typical features are the following: (i) (ii) (iii) (iv) (v)

plasticity decreases in a certain temperature range; the worst embrittlement occurs at certain strain rates and can disappear at sufficiently fast straining; the drop in plasticity is shifted to higher temperatures with increasing strain rate; the temperature range of brittleness is expanded with increasing hydrogen content; it manifests itself at smaller hydrogen contents in comparison with any other type of hydrogen failure.

This type of hydrogen embrittelement will be described below in its hypotheses and experimental data.

5.1 Available Hypotheses 5.1.1 Hydrogen Pressure Expansion Among a number of attempts to clarify a mechanism of hydrogen embrittlement, hydrogen pressure expansion, also titled as the hydrogen bubble theory, was one of the earliest. Zapfe (1947) believed that pressure generated by hydrogen gas located

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in small cavities increases with a growing amount of precipitated hydrogen. Under critical pressure, the metal lattice is expanded under hydrostatic forces and, then, fracture is caused by applied mechanical stress. The role of plastic deformation preceding the fracture remained unclear within this approach. Based on the model developed by Stroh (1954) for the stability of a microcrack in equilibrium with the dislocation pile-up that creates it, Garofalo et al. (1960) suggested that a critical internal pressure of hydrogen gas in the Stroh microcracks can upset their stability, as is the case with increasing shear stress or continuing crack propagation even in the absence of external stresses. According to performed estimations, such an event could occur in iron or steel at rather small hydrogen contents of 2 cm3 per 100 g of metal, i.e. near 2 ppm. Some correction of this model as performed by Bilby and Hewitt (1962) amounts to the re-assessment of the effect of hydrogen adsorption and the statement that a smaller quantity of the lattice dissolved hydrogen is sufficient to cause embrittlement due to gas internal pressure in the cracks. It was also additionally suggested that much of hydrogen is bound in some traps. Tetelman and Robertson (1963) performed direct observations of microcracks produced by hydrogen in iron-3% silicon single crystals after cathodic charging or high-temperature gaseous hydrogen saturation. Their theoretical analysis determined the slip planes taking part in plastic deformation around the tip of a crack and confirmed discontinuous crack growth under hydrogen internal pressure. Critical arguments in relation to the pressure expansion model were obtained by Morlet et al. (1958) in experiments with plastic straining of hydrogen-charged medium-carbon steel in liquid nitrogen, followed by holding for different times at 65 °C and final tensile measurements at RT. The observed initial increase in ductility with ageing time and its subsequent decrease were in contradiction with the expectation of a steady decrease in hydrogen pressure inside the cracks. At variance with the pressure expansion model was also the experimental evidence that gaseous hydrogen at pressures of ~ 1 bar causes greater embrittlement in high strength steels than electrolytic charging despite partial hydrogen pressure in the latter case being higher by several orders of magnitude, see Johnson (1969). Moreover, plastic deformation and, consequently, the formation of microcracks accompanying cathodic charging should make the pressure-expansion mechanism more probable. This result was supported by Williams and Nelson (1970) who observed embrittlement of steel 4130 under gaseous hydrogen with pressure under 1 bar. Remarkable in that study was an unusual change in the rate of crack growth with decreasing temperature, namely its enhancement in the temperature range of 80–25 °C and its slowdown if the temperature decreased from 0 to − 80 °C. The authors attributed this result to the adsorption of hydrogen atoms at the crack surface as a diffusion rate-controlling step in crack growth, which does not relate to hydrogen pressure in the cracks. A serious critical analysis of the expansion theory was provided by Birnbaum (1978). According to his remarks, this theory does not describe how the fracture mode changes from a ductile to a brittle one under high pressure internal hydrogen. The point is that, without some additional source of hydrogen, its pressure in the

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microcracks should permanently decrease in the course of crack growth. Second, Birnbaum referred to Oriani and Josephic (1974) in whose experiments on the highstrength AISI 4340 steel a threshold hydrogen pressure for crack propagation varied insignificantly with changing the stress-intensity factor and was too small to form high pressure bubbles. Therefore, other sources of crack instability should be at work to induce the growth of microcracks. Hydrogen transport by dislocations was proposed by Tien et al. (1976) as a source for local enhancement of hydrogen fugacity related to crack growth. According to these authors, hydrogen atoms can be stripped off dislocations while passing inclusions via cross slip thereby forming voids which expand with increasing internal gas pressure. As a result, hydrogen should induce a loss of ductility. However, a kinetic model developed by Johnson and Hirth (1976) for local hydrogen supersaturation due to its transport by dislocations and its deposition at sinks predicts that hydrogen supersaturation enhances with increasing strain rate, which is at variance with the well-known decrease in hydrogen embrittlement if the strain rate increases. As also noted by Birnbaum (1978), the embrittlement of material occurs in front of a growing crack, which needs lower hydrogen pressures and cannot be attributed to the expansion theory. Finally, the formation of high gaseous hydrogen pressure in the cracks or voids suggests the endothermic heat of hydrogen solution, which, as mentioned above, is expected only in hydride-forming metals.

5.1.2 Hydrogen Surface Adsorption The model of hydrogen adsorption at the crack surface or at its tip was proposed by Petch (1952, 1956). His main idea was a decrease in the surface energy γ of the crack due to hydrogen, which should ease crack propagation and decrease the fracture stress σ f in agreement with the Griffith criterion σ f = (2Eγ/πc)1/2 , with E as the Young modulus and c as crack length. Using Stroh criterion τ = 12γ/nb for crack production by dislocation pile-up, where the shear stress τ produces the array of n dislocations with their Burgers vector b, and the formula n = π(1 − ν)τL/μb for the number of dislocations in pileups as derived by Eshelby et al. (1951) with Poisson coefficient ν, shear modulus μ and the length of dislocation array L, Petch (1956) obtained the equation  σ f = σ0 + 4

3μγ π(1 − ν)L



where σ0 is a lattice friction stress for dislocation slip and L is equal to the grain size in polycrystalline materials.

(5.1)

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As hydrogen is a very mobile solute, its adsorption can easily occur on the formed crack, and the final Petch’ equation includes the equilibrium pressure of hydrogen. It follows from this model that hydrogen embrittlement should disappear at sufficiently high strain rates in agreement with the experiment. Applying the obtained relationship to the case of iron demonstrated the lowering of surface energy by hydrogen adsorption and the consequent decrease of (σf – σ0 ) on the scale of two to ten times depending on the increase in the fractional coverage of the surface by hydrogen. At the same time, the Hall–Petch relationship between strength and grain size d, σ f = σ 0 + k y d −1/2 , was shown to remain true, except for hydrogen-caused reduction in the slope of the unblocking constant k y and the stress of lattice friction σ 0 . However, the surface adsorption mechanism met serious objections. First, a number of chemical elements and compounds like nitrogen, oxygen and water vapor decrease the surface energy of metals, whereas, e.g., oxygen prevents hydrogen embrittlement, see Hancock and Johnson (1966). Moreover, the use of hydrogendecreased surface energy as a criterion for hydrogen effect on mechanical properties ignores the energy of plastic deformation preceding the fracture, which is larger by several orders of magnitude than the surface energy of cracks. Crucial for testing the hydrogen-adsorption theory were also experimental data on reversible mechanical behaviour of hydrogen-charged steels, see Morlet et al. (1958). Plastic deformation of hydrogen-charged steels in liquid nitrogen did not affect their ductility because of the virtual absence of hydrogen diffusion. At the same time, it increased the volume of cracks lowering thereby the hydrogen pressure. Subsequent ageing at − 100 °C allowed hydrogen diffusion to redistribute its concentration between the lattice and the cracks and thereby increase hydrogen pressure in the latter. However, regardless of hydrogen pressure, the embrittlement was diffusioncontrolled at all temperatures of ageing. In a similar way, Barth and Steigerwald (1970) detected reversibility of the incubation time preceding the delayed fracture of hydrogen-containing high-strength steel, in contradiction with adsorption theory predictions. Both these studies supported the idea that a source of hydrogen embrittlement should be searched for in the crystal lattice of solid solutions, namely in the region of severe triaxial stress state, not in the cracks.

5.1.3 Hydrogen-Induced Lattice Embrittlement This concept was developed by Troiano and his coworkers, see Troiano (1960) and Steigerwald et al. (1960). Its feature is that hydrogen in the crystal lattice, not within the crack, creates conditions for embrittlement. The ideas of hydrostatic stress in the region ahead of the crack tip and the weakening of interatomic bonds due to hydrogen-caused repulsive forces between the atoms constitute the core of this model. The combination of applied stress and hydrogen concentration in the solid solution initiates a crack, followed by its discontinuous propagation due to a localized increase

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in hydrogen concentration in front of the crack tip, where the hydrostatic stress field should be expected. An opened initial crack is stopped when leaving the region of increased hydrogen concentration. Thereafter, stress-induced hydrogen diffusion and localized crack formation have to be repeated. The incubation time for step-wise crack propagation is controlled by hydrogen diffusion towards the area of triaxial stress state. The analysis of a critical hydrostatic stress for hydrogen-caused failure led the authors to the conclusion that it diminishes with increasing strength of materials, which was brought into correlation with the experimentally observed increased sensitivity of high-strength steels to hydrogen embrittlement. Troiano was the first to suppose that hydrogen-caused change in the interatomic bonds causes a decrease in the fracture strength. According to his idea, electrons supplied by hydrogen atoms into transition metal solutions fill the d electron band and cause repulsive forces, which increases the interatomic distances and promotes microcracking under hydrostatic stress pressure. This electron approach was illustrated by comparing the hydrogen embrittlement of Fe–Ni and Ni–Cu alloys, Fig. 5.2, with their catalytic activity for the hydrogenation of styrene on the one hand, and both with the characteristics of electron structure on the other, Fig. 5.3. Fig. 5.2 Hydrogen effect on ductility of Fe–Ni and Ni–Cu alloys. According to Blanchard and Troiano (1959), Springer

Fig. 5.3 Change in activity for hydrogenation of styrene versus the composition of Fe–Ni and Ni–Cu alloys, curves A and B (Emmet 1959). Number of d-band vacancies, curve C, and low temperature electron heat capacity, curve D, according to Dowden and Reynolds (1950), American Chemical Society

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The ductility of hydrogen-charged fcc Fe–Ni alloys decreases with increasing Ni content. The embrittlement reaches nearly maximum in pure nickel and decreases, approaching zero, if copper is added to nickel. Exactly the same behaviour has been observed for the catalytic activity of Fe–Ni and Ni–Cu alloys used for the hydrogenation of styrene, Emmett (1959). Moreover, some correlation exists between both hydrogen caused failure and change in activity versus composition and the filling of electron vacancies in the 3d-band due to nickel in iron and copper in nickel. The evolution of low-temperature electron heat capacity characterizes the corresponding change in the concentration of free electrons. The hydrogen-induced crystal lattice embrittlement model was further substantiated by Tong and Knott (1991) and Knott (1996) who gave a more detailed description of hydrogen-caused cracking: (i) (ii)

(iii)

(iv)

(v)

an initial microcrack appears due to plastic deformation, and the effect of hydrogen dissolved in the crystal lattice is not decisive in this stage; in the course of plastic deformation, hydrogen atoms are transported by moving dislocations into the formed microcrack, and hydrogen pressure inside it increases; hydrogen is re-dissolved in the region at the crack tip characterized by maximum hydrostatic stress and, at the same time, hydrogen atoms dissolved in the lattice diffuse to this region; cohesive forces in the triaxial stressed region in front of the crack tip are weakened by hydrogen, which results in the opening of a separate satellite microcrack which joins the main crack; this process is repeated, creating discontinuous propagation of the growing crack.

5.1.4 Hydrogen-Enhanced Decohesion, HEDE The starting point in this model is the idea of hydrogen-caused weakening of interatomic forces at the tip of an already existing crack. A decrease of atomic cohesion in iron across the cubic planes and grain boundaries due to hydrogen was first supposed by Pfeil (1926). As a model for embrittlement, it was declared by Oriani (1972) for bcc iron alloys and suggested to be also applicable to fcc steels. Essential similarities link this hypothesis with the abovementioned concept of hydrogen surface adsorption and that of crystal lattice embrittttlement. In respect of the former, the Oriani’s analysis starts with the argument that hydrogen adsorption is not only necessary for embrittlement but both necessary and sufficient. In contrast to Troiano’s idea with its step-wise hydrogen-induced crack propagation, Oriani’s model considers it to be intrinsically continuous, whereas any jerking in crack growth is attributed to chemical and structural inhomogeneities in the solid solution. Based on the Griffiths thermodynamic criterion for crack growth in some ideally elastic solid, Oriani claims that “the crack grows when the local tensile elastic stress normal to the plane of the crack equals to local maximum cohesive force per unit area

5.1 Available Hypotheses

209

as reduced by the large concentration of hydrogen”. This statement suggests that an initial atomically sharp crack tip is not subjected to blunting by dislocations and the shielding of the sharp crack tip occurs due to hydrogen-increased slip localization at the crack tip. A positive hydrostatic component of elastic stresses at the tip of a crack is thought to be caused by locally increased hydrogen concentration, which was substantiated earlier in the theoretical analysis carried out by Li et al. (1966). Thus, a local threshold tensile stress σ z  normal to the crack plane is controlled by a cohesive atomic force F m reduced by hydrogen: σz = n Fm (cH ),

(5.2)

where n is the number of hydrogen atoms per unit area of the crystallographic plane, cH  is a critical hydrogen concentration at the crack tip. The equilibrium and kinetic aspects of this model were analyzed by Oriani and Josephic (1972, 1974, 1977). For the equilibrium state, they supposed a correlation between the threshold hydrogen pressure p, below which the crack does not propagate, and the threshold stress-intensity factor K below which the crack will halt. This equilibrium balance was demonstrated by the authors in an experiment, where the crack was restarted either by increasing the environing hydrogen gas pressure or achieving higher K values. In the authors’ opinion, this result eliminates all the models based on the dislocation mechanisms of cracking and is consistent only with the decohesion mechanism modified by Petch’s adsorption criterion. Therefore, under low-pressure gaseous hydrogen, crack propagation is asserted to be an atom-to-atom process with only small scattering caused by an intrinsic heterogeneity of solid solutions and by a noise in the measuring system. Discussing the advantages and disadvantages of hydrogen decohesion theory, one can note that it is unambiguously true only in the statement about hydrogendecreased interatomic forces. The first experimental evidence of hydrogen-increased concentration of free electrons, which enhances the metallic character of interatomic bonds and, consequently, weakens them, was obtained by Shanina et al. (1999) in their measurements of electron spin resonance in hydrogen-charged austenitic steel, see Fig. 1.25 in Chap. 1. Later, it was confirmed by ab initio calculations of electron structure in hydrogen-containing gamma and alpha iron, showing the increase in the density of electron states at the Fermi level which is proportional to the concentration of free electrons, see Sect. 1.5 in Chap. 1 and also Teus et al. (2007), Gavriljuk et al. (2013), Teus and Gavriljuk (2020) for detail. One should also mention ab initio calculations of hydrogen effect on atomic bonding within the grain boundaries in nickel (Geng et al. 1999) and bcc iron (Zhong et al. 2000). It was shown that, in comparison with the bulk, hydrogen in the 5 nickel grain boundary expands the H–Ni bonds, which attenuates the chemical interaction

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between the H and host Ni atoms. The H–Fe bond length was also found to be greater at the grain boundary than at the Fe(111) free surface. Consequently, the calculated valence electron charge at the H atom and the Fe–H binding energy are smaller at the grain boundary than at the surface, despite the fact that one of the three vertical bonds is broken in the latter. These results were used by the authors for the interpretation of intergranular hydrogen embrittlement. It is relevant to mention that, according to experimental data of hydrogen effect on atomic cohesion in the metals of group V in the periodic table, namely vanadium, niobium and tantalum, hydrogen increases the shear constants c44 , see Fisher et al. (1975) and Magerl et al. (1976). Consequently, one can conclude that the decohesion theory is a priori incapable of explaining hydrogen embrittlement in the hydride forming metals at hydrogen concentrations smaller than is needed for hydride formation. At the same time, it does not follow from hydrogen-decreased interatomic bonds that preexisting microcracks with ideally sharp tips can grow due to atom-to-atom bonds breaking under some critical normal component of the stress state. First, the idea that a growing crack retains its sharp tip needs more detailed substantiation. Conditions for shielding an atomically sharp crack tip in metals with bcc and fcc lattices by the spontaneous emission of dislocations around the crack were analyzed by Rice and Thomson (1974) and Rice (1992). According to their calculations, the crack tip is expected to remain sharp in bcc metals if the dislocation cores are narrow and the value of μb/γ = 7.5 to 10, where μ is the shear modulus, b is the Burgers vector and γ is some true surface energy of the crack plane. In contrast, fcc crystals are shown to be unstable against dislocation emission. Although the modelling of interatomic bonds in these calculations using Young’s modulus and Poisson’s ratio was rather idealistic, the applicability of the decohesion theory seems to be limited only to metals with the bcc crystal lattice. Moreover, Gerberich et al. (2008) have shown that dislocations in the presence of hydrogen do not shield the crack tip as effectively in Fe-3wt%Si alloy as is the case with dislocations in its hydrogen-free state. Second, discontinuous hydrogen-assisted subcritical crack growth was found in many metals, e.g. by scaling with 1 μm extensions in Fe-3wt%Si crystals using fractography, as observed e.g. by Chen et al. (1990). Therefore, it can hardly be exclusively ascribed to chemical inhomogeneity. Third, a positive hydrostatic component of elastic stresses supposed to be responsible for a critical normal stress depends on the thickness of specimens. As shown by Yokobori et al. (2002), the hydrostatic pressure decreases if the stress field meets the plane strain conditions. Based on this result and following the decohesion theory, these authors predicted that hydrogen embrittlement should be sensitive to the thickness of specimens and even disappear in those sufficiently thin. Meanwhile, in its mechanical behaviour and fracture morphology, hydrogen embrittlement of the Feand Ni-based amorphous ribbons with thickness of about 20 μm is essentially the same as in massive samples, see Nagumo and Takahashi (1976), Ashok et al. (1981), Slavin and Stoloff (1984).

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211

In their analysis of decohesion theory, Birnbaum et al. (1978) noted the incompatibility of the ignorance of the role of dislocations with fractographic observations of plasticity traces on the fracture surface. The transgranular fracture of hydrogencharged steels always reveals clear signs of plasticity preceding the fracture, e.g. Beachem (1972). The same is true for hydrogen in nickel and its alloys, e.g. Ladna and Birnbaum (1987) and Eastman et al. (1980), whereas both types of these materials were suggested by Oriani and Josephic as candidates for hydrogen degradation via the decohesion mechanism. According to Birnbaum (2003), a possibility for realization of HEDE mechanism amounts to simultaneous fracture and a very high H segregation on the newly formed surfaces, which could be valid only during very slow fractures. Even in this case, the plasticity preceding the fracture surface formation would not be significantly decreased. The cases where the hydrogen-caused decohesion is likely the operating mechanism were addressed by Birnbaum to the intergranular fracture of FeSi alloys and high temperature transgranular cleavage of NbH alloys at high hydrogen contents. Unique examples of fracture surface evidencing the occurrence of dislocation slip preceding the fracture were presented by Hänninen and Hakkarainen (1979) and Ulmer and Altstetter (1991) for hydrogen-charged austenitic steels. A saw-tooth profile has been found in steel AISI 316 (Fig. 5.4). Facets of this profile obviously correspond to dislocation slip on a set of parallel crystallographic planes resulting in the opening of microcracks along these planes and their following integration. The most probable mechanism of such a fracture can be imagined as a slip of screw dislocations on the intersecting (111) planes resulting in the formation of the LomerCottrell barriers, locking the slip and opening assimilated microcracks, see e.g. Hirth and Lothe (1983) and Schoeck (2010). Another example of slip bands blocked by the grain boundary in stable austenitic steel 310S, Fig. 5.5a, or by the twin in unstable austenitic steel 304, Fig. 5.5b, resulting in formation of microcracks and their fusion along these obstacles was presented by

Fig. 5.4 Thansgranular crack propagation in an AISI 316 steel tensile tested after cathodic hydrogen charging. Hänninen and Hakkarainen (1979), Springer

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5 Hydrogen Embrittlement

Fig. 5.5 SEM view of side surface of failed hydrogen-charged austenitic steels 310S (a) and 304 (b) showing slip band formation resulting in grain and twin boundary cracking, respectively. Ulmer and Altstetter (1991), Elsevier

Ulmer and Altstetter (1991). The saw-tooth relief was also clearly observed by these authors in their SEM studies of intergranular cracking. A similar phenomenon was observed by Lynch (1986) in hydrogen-charged nickel single crystals. The fracture surface in his studies was close to a {100} plane, whereas the crack grew sometimes in different directions in the adjacent regions. Remarkable for further discussion is that, using the Laue X-ray back reflection technique, Lynch obtained proof of extensive plastic deformation beneath the fracture surface. The same {100} hydrogen-assisted cracking in nickel single crystals was found earlier by Vehoff and Rothe (1983). In time, in view of evident signs of plastic deformation accompanying crack growth, the hydrogen decohesion theory saw some change, with the inclusion of plasticity in combination with embrittlement. First, while measuring the crack tip opening in a steadily growing crack in FeSi- and Ni-single crystals at different hydrogen gas pressures and temperatures, Vehoff and Rothe (1983) observed that cracks grow under fully plastic conditions. The crack front was left behind enclaves of material deformed in an ideally ductile manner. Moreover, isolated microcracks were nucleated along the crack front encircling the uncracked material. Thereafter, the necessity of both plasticity and brittleness in the decohesion model was studied for hydrogen in Fe-3wt%Si single crystals by a group headed by Gerberich. Using the acoustic emission technique during sustained load tests combined with SEM observations, Lii et al. (1990) detected a discontinuous crack advance consisting of separated groups of microcracking. The computational analysis of the stress state ahead of a crack tip showed that, directly at the tip, the stress is slightly compressive, whereas a maximum stress close to theoretical strength is located ahead of the crack tip resulting in slip bands operating within a distance of

5.1 Available Hypotheses

213

about 3–30 μm away from the tip and controlling the instability of crack growth. The ductile–brittle behaviour resulted in initiation, arrest and reinitiation processes accentuated by hydrogen. Gerberich et al. (1991) performed a crack/dislocation simulation according to which plastic relaxation ahead of the crack tip is caused by a large number of dislocations leading to the increased hydrogen concentration in this region and consequent normal stresses which initiate atomic decohesion. According to Gerberich et al. (2009), because of dislocation shielding at the crack tip, HEDE can control at least separate stages of fracture, namely hydrogen-enhanced cleavage, microvoid growth or shear instability. In addition, according to the decohesion mechanism, the intergranular fracture should occur exclusively along grain boundaries. However, TEM fracture studies of hydrogen-charged polycrystalline iron and nickel unambiguously revealed that, except for the case of grain boundary segregation with embrittling elements, cracks can propagate along grain boundaries, but only a part of them may lie within, see, e.g., Robertson et al. (1984). Thus, a number of experimental and theoretical data are at variance with the decohesion theory in its version formulated by Oriani and ignoring any role of dislocations in hydrogen embrittlement. Perhaps a unique engineering material where pure decohesion is claimed to unambiguously occur is the bcc β-titanium alloy Timetal 21S, see Birnbaum et al. (1997) and Teter et al. (2001). A feature of β-titanium alloys is their plasticity at rather high contents of dissolved hydrogen. At extremely high hydrogen concentration of up to H/M = 0.21, dislocation mobility was shown to be enhanced by hydrogen, and fracture was ductile, which is a unique case in comparison with other metallic materials which reveal brittleness at insignificant hydrogen contents, e.g. ~ 2 ppm in austenitic steels. A further increase in hydrogen content in Timetal 21S led to a cleavage-like fracture without any traces of plasticity on the fracture surface, except for slip traces on the transverse surfaces evidencing that dislocations were involved in crack nucleation. At the same time, even in case of H/M = 0.27, fractographs revealed small voids as well as curved and bent edges on the cleavage steps as a sign of plasticity. Moreover, in the alloy with H/M = 0.33, a high density of dislocations and rings in the electron diffraction patterns were detected within several hundred nanometers beneath the fracture surface. The hydrogen enhanced velocity of dislocations was also observed in situ in the transmission electron microscope, in agreement with mechanical tests showing that hydrogen decreases the 0.2% yield strength at it contents up to H/M = 0.27. Despite this clear evidence of plastic deformation preceding cleavage-like fracture, the authors interpreted their observations as a case of a pure decohesion mechanism at work. It is reasonable in this respect to compare cracking in hydrogen-charged β-titanium alloys with a similar phenomenon observed by Tomota et al. (1998) in nitrogen austenitic steels.

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5 Hydrogen Embrittlement

Like hydrogen, due to increase in the concentration of free electrons, nitrogen enhances metallic character of interatomic bonds in austenitic steels. In contrast to hydrogen, nitrogen improves their ductility and fracture toughness, see e.g. Gavriljuk and Berns (1999). Nevertheless, ductile–brittle transition and quasi-cleavage occur in case of the impact tests at cryogenic temperatures where relaxation of stresses is impeded, see Fig. 5.6. Paired intrusions and extrusions having pyramidal or tang-like forms occur along the traces of slip bands at the fracture surface, which evidences formation of microcrackes ahead of the blocked slip bands. The interpretation given by these authors includes dislocation slip on the intersecting {111} planes, formation of microcracks at the Lomer-Cottrell locks and a zig-zag propagation of the opened crack along nonactive {111} planes. Using transmission electron microscopy, the authors detected a high density of dislocations directly under fracture surface like it was observed by Martin et al. in the β-titanium alloy. Therefore, there is no sufficient substantiation to link the cleavage caused by extremely high hydrogen contents in β-titanium alloys only with atomic decohesion ignoring the preceding localized plastic deformation.

Fig. 5.6 Matching fractured surfaces of nitrogen austenitic steel Cr18Mn18N0.5 subjected to impact tests at 77 K. Interpretation is schematically presented at the right hand side. Tomota et al. (1998), Elsevier

5.1 Available Hypotheses

215

A possible interpretation can be also given in terms of decrease in plasticity accompanying the decrease in bonding referring to Jokl et al. (1980). The theory developed by these authors describes a rather unique case of the brittle fracture in deformable solids when, during the propagation of a crack, the energy is consumed by simultaneous emission of dislocations from the crack tip and breaking the bonds. A further development of this theory has been made by Jok et al. (1989), where the cases of pre-existing crack and that appeared in the loaded deformable solid were analyzed. In recent years, the HEDE hypothesis acquired a new interpretation in terms of the cohesive zone model. The essence of this approach amounts to the accumulation of hydrogen atoms between close-packed cleavage planes, as well as at grain boundaries, which is supposed to reduce cohesion between atomic planes and grain boundaries, leading to brittle intra- or intergranular fracture, respectively. Following the previous descriptions of hydrogen-induced decohesion across (111) planes in bcc iron, e.g. Hirth and Rice (1980), Mishin et al. (2002), Van der Ven and Ceder (2004), and using the quantum–mechanical approximation to interatomic forces, Katzarov and Paxton (2017) found the reduction of the ideal cohesive strength from 33 GPa down to 22 GPa at bulk hydrogen concentrations within the range of 0.1–10 appm, which should result in significantly decreased toughness. The authors underlined that their approach is applicable to both intragranular and interfacial decohesion, for example, the interface between ferrite and carbide particles in steel. In contrast, using the density functional theory, Tahir et al. (2014) studied hydrogen effect in the  5 (310)[001] symmetric tilt grain boundary, STGB, and obtained a mere 6% decrease in the work of separation in the GB plane caused by a full H monolayer, whereas no change was found for the theoretical strength. An insignificant—only 0.4%—hydrogen-caused decrease of the strength in  3 (112)[110] STGB by a full H monolayer was also obtained by Momida et al. (2013). However, they assumed that hydrogen can promote quite a different mechanism of intergranular brittle fracture, namely forming complexes with vacancies at the GB. Different hydrogen effects at the GB and in the bulk were attributed to different local atomic structures affecting sensitivity to the H effect on atomic bonds and the consequent difference in the physical aspects of interatomic cohesion. For example, according to Psiachos et al. (2011), hydrogen decreases the elasticity moduli in bcc iron, which causes a detrimental volumetric effect. Geng et al. (2005) attribute the role of solute atoms in GB cohesion to a decrease in the segregation energy and separate chemical and mechanical contributions. As obtained by Yuasa et al. (2015), the electron charge density in the  3 (111) GB of bcc iron decreases with increasing strain induced by hydrogen, whereas Tian et al. (2009) describes H-caused embrittling merely as a chemical effect. A novel approach to the atomistic calculations of the mechanism for intergranular hydrogen embrittlement was proposed by Alvaro et al. (2015) based on the density functional theory and finite element modeling combined with nanoscale experiments. Nickel was chosen in these studies as the simplest relevant model system. The intensity of hydrogen accumulation by grain boundaries and, consequently, their cohesive strength, were shown to strongly depend on the damage caused by them in the crystal

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lattice. For example, below certain hydrogen content,  3 (111) GB does not attract hydrogen from H2 gas, or from the bulk Ni lattice, while the weaker  5 (012) GB accumulates hydrogen both from gas and bulk Ni. Hydrogen also negligibly reduces the cohesive strength of  3 (111) GB in comparison with the (111) plane in bulk Ni, whereas  5 (012) GB loses about 40% of the strength compared to that of the (012) plane in the bulk. The hydrogen-facilitated transition from transgranular to intergranular fracture was further analyzed by Ding et al. (2021) using atomistic modeling of a uniaxially strained Ni bi-crystal with a  5 (210)[001) grain boundary. The authors found a specific mechanism amounting to the formation of a hydrogen atmosphere near the grain boundary, which induces stress concentration locally and prevents subsequent stress relaxation during deformation. This local stress concentration is shown to promote the emission of dislocations and the generation of vacancies, and therefore to facilitate nanovoiding. Finally, the growth of nanovoids leads to intergranular fracture as opposed to transgranular fracture in the absence of hydrogen. A revisited first-principles cohesive zone model proposed by Guzman et al. (2020) claims to “elucidate the HEDE mechanism in iron and explain discrepancies between the bulk cleavage and GB planes”. Following the traditional analysis of decohesion on the atomic scale, the authors started with the so-called ab initio tensile test. They calculated cohesive energy at different displacements taking into account subsequent relaxation due to which the displacement is distributed among several atomic layers and the cohesive zone extends up to the tip of the crack. The work of separation and the cohesive strength were calculated for both bulk Fe and grain boundaries with different misorientations. The obtained extraordinary result amounts to higher hydrogen resistance to fracture on the part of grain boundary structures in comparison with the bulk atomic plane, see Fig. 5.7. For example, the cohesive strength across (111) atomic planes decreases by 45% at the hydrogen coverage of 0.29 atom/Å2 , and a reduction of 36% was obtained for the (001) plane at 0.25 atom/Å2 . The loss of 3% in the cohesive strength of  5 (310)[001] GB and 6% for  3 (112)[1 1 0] GB were obtained at the H coverage of 0.08 atom/Å2 and 0.05 atom/Å2 with the values of 12% and 21%, respectively, after extrapolation to 0.29 atom/Å2 .

Fig. 5.7 Cohesive strength as a function of specific hydrogen concentration (Guzman et al. 2020)

5.1 Available Hypotheses

217

More space for the H atom in the grain boundary is proposed as an interpretation of smaller sensitivity to H-induced intergranular embrittlement in agreement with the linear decrease of elastic constants in bcc iron with increasing hydrogen concentration, as calculated ab initio by Psiachos et al. (2011). Summing up, one should note that atomic decohesion occurs at different stages of plastic deformation, from the nucleation of microcracks to their growth and final fracture. However, the HEDE hypothesis does not take into account the role of dislocations preceding all of these stages, regardless of the fracture type.

5.1.4.1

Electron Version of HEDE Hypothesis for Intergranular Brittle Fracture

First-principles studies of GB hydrogen embrittlement began with the pioneering ab initio calculations performed by Freeman and colleagues on the electron charge transfer during the GB segregation of interstitial and substitutional elements resulting in brittle fracture along grain boundaries. As shown by Zhong et al. (2000), the free energy of hydrogen segregation at the free surface is more negative than it is in the grain boundary, which points to a weakening of iron interatomic bonds within grain boundaries. The same result was obtained by Geng et al. (1999) for hydrogen in nickel. The effect of hydrogen on grain boundary cohesion is remarkable in comparison with that of other interstitials, namely carbon and nitrogen. As obtained by Wu et al. (1996), carbon is a strong enhancer of interatomic bonds in bcc iron, whereas nitrogen weakens iron interatomic bonds within grain boundaries. Among the studied substitutional impurity elements, boron enhances atomic cohesion within grain boundaries in bcc iron, whereas phosphorus weakens it, see Wu et al. (1993). The same difference occurs between boron and phosphorus in nickel (Geng et al. 1999). Based on the abovementioned ab initio studies, Jiang and Carter (2004b) proposed an ab initio assessment of ideal fracture energies in iron and aluminum doped with hydrogen, which can be considered as the first approach to the electron theory for intergranular hydrogen embrittlement. The ideal fracture energy is that for opening the crack in the absence of preceding or accompanying plastic deformation. A model used by the authors for calculating fracture energy 2γ as a function of hydrogen content (H) is based on the Born-Haber thermodynamic cycle (Fig. 5.8). Hydrogen atoms in this model are considered to be mobile impurities which segregate at the arising crack surface in the initial state of equilibrium with hydrogen distribution in the bulk. This equilibrium continues with hydrogen covering each slowly formed crack surface until the final state. Three preconditions make it possible to rely less on kinetics and more on thermodynamics as the dominant factor. Firstly, the heat of the hydrogen solution does not vary significantly with hydrogen concentration, e.g. only ~ 0.02 eV over 0.9–3.0 at.%H in bcc Fe, see Hirth (1980). Secondly, hydrogen diffuses sufficiently quickly in a metal solid solution, e.g. the H diffusion barrier is of ~ 0.04 eV in bcc Fe, see

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Fig. 5.8 Born-Haber cycle used for calculating ideal fracture energy along a certain plane in a single crystal. Hs is the solution enthalpy of H2 in bulk metal, γ(0) is the metal surface energy free of hydrogen, Ead is the adsorption energy of H2 to form adsorbed hydrogen on the metal surface. According to Jiang and Carter (2004b), Elsevier

Jiang and Carter (2004a). Thirdly, hydrogen prefers to diffuse out easily to the Fe surface, e.g. with a diffusion barrier of ~ 0.02 eV, and this process is exothermic with the energy release of ~ 1.0 eV, see Jiang and Carter (2004a). The first step in the calculations amounted to removing dissolved hydrogen from the metal with the reverse of H2(g) dissolution enthalpy from the gas, –Hs , of 0.20 eV/H atom. The second step consisted of cleavage energy in pure metal to form the most stable surface without hydrogen. The surface energy of the hydrogen-free Fe(110) atomic plane as the closest-packed surface in bcc iron was calculated as 2.43 J m−2 , which is consistent with the experimental data of ~ 2.41 J m−2 obtained by Tyson and Miller (1977). The energy of dissociative hydrogen adsorption on the Fe(110) plane of − 0.52 eV/H for (H) ~ 0.11–0.50 ML (monolayer) was calculated within the final third step in good agreement with the experimental value of − 0.525 ± 0.05 eV, see Kurz and Hudson (1988). Its dependence on the hydrogen coverage of fracture plane Fe(110) is shown in Fig. 5.9. A dramatic decrease of fracture energy is considered to be the driving force for intergranular hydrogen embrittlement because grain boundaries serve as preferred places for hydrogen adsorption. The calculated energy of an ideal fracture differs from that of a real fracture by the absence of plasticity which was not included in the described calculations. The ab initio results presented were further used as input in the continuum model of hydrogen embrittlement proposed by Serebrinsky et al. (2004) who additionally analysed a stress-assisted hydrogen diffusion with certain boundary conditions accounting for the hydrogen environment and intermittent crack growth with its initiation time depending on stress intensity and yield strength. The ignorance of plastic deformation preceding to opening the crack is the common drawback of HEDE hypothesis in its application to both intra- and intergranular hydrogen-induced fracture. Moreover, the break of atomic bonds occurs at

5.1 Available Hypotheses

219

Fig. 5.9 Decrease of normalized surface energy γ(H )/γ(0) of Fe(110) plane with its increased hydrogen coverage. Fragment of the data obtained by Jiang and Carter (2004b), Elsevier

subsequent stages of plastic deformation including the growth of cracks and final fracture. However, HEDE hypothesis does not take into account the role of dislocations in the all these stages regardless of the fracture type.

5.1.5 Adsorption-Induced Dislocation Emission, AIDE Hydrogen-assisted crack propagation by dislocations emitted from the crack tips was declared by Lynch (1988) based on metallographic and fractographic observations of similarity between hydrogen-assistant cracking, stress-corrosion cracking and liquid–metal embrittlement in a number of studies, e.g. Williams and Nelson (1970), Lynch (1977, 1979, 1984, 1985), Funkenbusch et al. (1982), Stoloff (1983), Price and Fredell (1986), Galvele (1987) etc. Earlier, based on field ion microscopy observations, Clum (1975) suggested that hydrogen adsorption on the metal surface alters energy parameters, such as the surface energy or stacking-fault energy, which should result in the decrease of critical shear stress for the creation of dislocation loops and, consequently, ease the nucleation of dislocations. Lynch applied this idea to hydrogen adsorbed at the crack tip, in combination with the weakening of interatomic bonds facilitating the nucleation stage of dislocations as a consequence. An important point in this hypothesis is that, once nucleated, dislocations “can readily move away from the crack tip under applied stress”, see Lynch (2012). Thus, hydrogen was declared not to play any essential role in the embrittlement process in the solid solution and at dislocations. Another postulate is that the crack grows due to alternating dislocation slip along suitably inclined crystallographic planes and coalescence with microvoids formed at

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5 Hydrogen Embrittlement

second phase particles, slip band intersections or any other sites created in the plastic zone ahead of it. Very close to these ideas are the abovementioned results obtained by Vehoff and Rothe (1983), which provide evidence that hydrogen atoms act directly at the crack tip and the crack grows due to micro-cleavage accompanied by dislocation emission from the tip (see previous Section). To some extent, hydrogen surface adsorption, as well as the weakening of interatomic bonds at the crack tip, link this hypothesis with those developed by Petch (1952, 1956) and Oriani (1972), respectively. Evidence of surface hydrogen adsorption was also found in studies performed by Christmann (1995), Pundt and Kirchheim (2006) etc., where the hydrogen concentration at the crack tip surface, namely in interstitial sites between the first to third atomic layers, was shown to be higher than in the normal crystal lattice. Some reconstruction of the surface lattice at the crack tip has been analyzed by Lynch with reference to Van Howe (1991), Kuk et al. (1987) and Stumpf (1997). Small surface lattice perturbations were supposed to produce shear movements of atoms and facilitate dislocation emission. This effect should occur even in the course of crack growth at high velocities. The effect of hydrogen on crack tip configuration was modelled in atomistic calculations performed by Hoagland and Heinisch (1992). Using the embedded-atom method, these authors studied two types of models with different cracking directions in nickel. Within the framework of the so called “brittle model”, it was obtained that a crack propagates in the [100] direction on the plane (010) and its tip does not lie in the {111} slip plane. In this case, hydrogen enhances crack propagation approaching the crack tip from the nickel lattice, not from the crack surface, and dislocation emission is difficult. Crack propagation can occur only due to energy release if hydrogen is transferred from the crack tip to its surface. The situation becomes unclear in the “ductile model” with a [111](110) orientation where the crack is unstable, regardless whether hydrogen is at its tip or not. In the absence of hydrogen, there is some critical value of the stress intensity factor K below or above which the crack retreats or emits dislocations, respectively. It is qualitatively shown that, in the presence of hydrogen, the crack first evolves, allowing the hydrogen atom to escape to the crack surface, after which two partial dislocations can be emitted on a new slip plane. As a result, the slip plane will accompany the moving crack tip. As experimental evidence of the AIDE mechanism for hydrogen embrittlement, typical features of the fracture surface in hydrogen-charged nickel (Lynch 1986), tempered martensitic steel (Lynch 1984) and Al-Zn–Mg alloys (Lynch 1988, 2008) etc. have been presented, including tear ridges, isolated dimples, and coarse and fine slip lines. Critical to this hypothesis were studies of dislocation structure in the region beneath the quasi-cleavage fracture surface of carbon pipeline steels subjected to tension tests in a high-pressure hydrogen gas environment, see Martin et al. (2011a, b). A high dislocation density including dislocation lines and loops was observed in the region at depths up to 1500 nm from the fracture surface. Important is the absence of any gradient in the dislocation density with distance from the surface,

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221

which should exist in the case of dislocation emission by the growing crack. Moreover, no dislocation half-loops emanating from the fracture surface were observed. The occurrence of grain boundaries and cementite particles did not affect the density of dislocations or the topology of dislocation structure. Lynch (2011) commented on these unfavourable to his hypothesis results by claiming that, in order to heat-tint fracture surfaces produced by hydrogen action, the samples studied by Martin et al. were heat-treated at ~ 275 °C after hydrogen charging and prior to the final fracture tests. In his opinion, this treatment affected the fracture surface and the dislocation arrangements beneath it. However, mechanical tests on hydrogen-charged samples were performed by Martin et al. (2011a) under high gaseous hydrogen pressure, and the resulting quasi-cleavage fracture surface with ridges and highly localized deformation bands is typical of hydrogen embrittlement. Therefore, the above details, such as high dislocation density without its visible gradient and the absence of half-loops indeed characterise the substructure beneath the fracture surface of hydrogen-charged steel.

5.1.6 Hydrogen-Enhanced Strain-Induced Vacancies, HESIV This hypothesis posits that “deformation-induced vacancies and their clusters, being enhanced and stabilized by hydrogen, play the primary role in HE”, whereas “the role of hydrogen in embrittlement is indirect and rather subsidiary”, see Nagumo (2001). In fact, it rules out hydrogen itself as the reason for the brittle fracture of metallic materials and attributes its role only to facilitating vacancy formation during straining. It was developed based on the analysis of cases where strain-induced vacancies were supposed to be involved in the fracture mechanism (Nagumo et al. 2001, 2004). For example, attention was focused on the microvoid arrays formed by vacancies at the intersection of striations visible in the fracture surface of Fe-3wt.% Si alloy embrittled by hydrogen, see Terasaki et al. (1998). These authors concluded that the voids were initiated by hydrogen vacancies at slip bands or cell walls. Similar patterns were also observed by Marrow et al. (1996) and linked to dislocation loops formed in front of propagating cracks. Another observation sees vacancies playing a role in void initiation ahead of a growing crack, which usually occurs at second-phase particles. At the same time, such dimple patterns on the crack surface were also found without particles and attributed to vacancy agglomerations, e.g. Wilsdorf (1982) and Cuitino and Ortiz (1996). These vacancy clusters are proposed by Nagumo (2004) to be the main reason for the hydrogen-caused decrease in crack growth resistance. Based on TDA studies of hydrogen absorption due to straining, he declared a correlation between susceptibility to failure and the capacity of trapped strain-induced hydrogen. The shift of hydrogen desorption peak to higher temperatures with increasing hydrogen content

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was interpreted as the formation of trap sites having a higher binding energy with hydrogen, i.e. the vacancy agglomerates. As a result, the tendency to vacancy creation, rather than hydrogen itself, was proposed to be decisive in hydrogen failure. Thus, this model shifts the viewpoint from hydrogen to vacancies, the formation of which hydrogen merely enhances. The following theoretical and experimental data were presented as supporting this model. Essmann and Mughrabi (1979) analyzed the formation of point defects during tensile and cyclic deformation in fcc and bcc metals due to the annihilation of screw and non-screw dislocations, and came to the conclusion that the concentration of vacancies in persistent slip bands can reach the values of 10−3 . According to estimates performed by Mecking and Estrin (1980) based on experimental data for Al, strain-induced excess vacancy concentration in the slip bands can be effective for plasticity at temperatures below 0.4 Tmelting . Strain-induced voids in the absence of particles in stainless steels were observed by Bauer and Wilsdorf (1973) in their in-situ experiments in a high voltage electron microscope. Clusters of nanovoids with diameters of less than 2 nm were also detected by Chen et al. (1995) in situ in dislocation-free zones of stainless steel 310 under applied stress in the electron microscope. These authors came to the conclusion that a stable nanovoid with the critical radius of ~ 0.5 nm can be formed under a high stress concentration close to cohesive strength. Studying tritium thermal desorption, Nagumo et al. (2000) revealed the enhanced formation of vacancy-type defects due to plastic deformation. A review of studies performed as part of the HECIV hypothesis was presented by Nagumo (2012). In summary, this model suggests localised mechanical degradation due to superabundant vacancies as a mechanism of hydrogen embrittlement and ignores the second important part of this phenomenon, namely hydrogen-enhanced dislocation mobility. For this reason, it cannot explain other important features observed in the experiments, e.g. the increased velocity of dislocations, the strain rate dependence of hydrogen embrittlement and the hydrogen-decreased distance between dislocations in pile-ups causing microcracks to open sooner. A Hadfield-type austenitic steel having the carbon content of 1.2 mass% (θC = nC /Nmetal = 0.06) could be used as an appropriate test of the HESIV hypothesis. As in the case of hydrogen in the solid solution, carbon atoms increase the equilibrium concentration of vacancies (up to its five-fold increase at 1273 K in Fe–C austenite with θC = nC /NFe = 0.07, see McLellan 1988). Therefore, according to the HESIV model, severe plastic deformation of this steel should lead to the formation of straininduced vacancies and their clusters as the primary reason for brittleness, whereas carbon-induced vacancies should play a subsidiary role, merely increasing vacancy concentration. Meanwhile, Hadfield-type steel is characterized by excellent plasticity and fracture toughness and does not reveal any sign of localised plasticity under mechanical loading. Even hydrogen charging does not cause any remarkable mechanical degradation in this steel, see Michler et al. (2012b).

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5.1.7 Nanoscale Hydrogen Embrittlement The main idea of this hypothesis proposed by Song and Curtin (2011) based on their modelling of hydrogen in nickel amounts to the formation of a so-called “nanohydride” due to sufficiently high local hydrogen concentration near the crack, which prevents dislocation emission or absorption at the crack tip. As a consequence, the blunting of the crack is suppressed, thereby inhibiting ductile fracture mechanisms and promoting cleavage failure. By means of the atomistic simulation of hydrogen distribution around the crack tip in Ni under increased applied loading, the authors analysed the kinetics of “nanohydride” formation as a function of H chemical potential and diffusion coefficient, temperature, the level of loading and its rate. The kinetic analysis was combined with that of deformation/fracture in order to construct a mechanism map showing that the formed “nanohydride” prevents dislocation emission and leads to cleavage fracture. Similar calculations were also carried out by these authors describing the evolution of a nanoscale crack tip in α-iron, see Song and Curtin (2012). This model is put in serious doubt if one is to compare the proposed crack evolution with the available theoretical studies of hydrogen effect on the electron structure of metals and corresponding experimental data. A “nanohydride” formed in the vicinity of the crack, which could prevent dislocation emission or absorption, would suggest the occurrence of covalent bonds between neighbouring hydrogen atoms in the solid solution as a feature of chemical compounds. However, as follows from ab initio calculations for hydrogen in Ni, e.g. Teus (2016), and in Fe, e.g. Teus and Gavriljuk (2020), hydrogen increases the density of electron states at the Fermi level of these metals, i.e. increases the concentration of free electrons assisting the metallic character of interatomic bonds. Beside this, a strong repulsion with its energy of ~ 0.36 eV occurs between hydrogen atoms in the iron-based solid solution, see Sect. 1.4 in Chap. 1. The same is true for hydrogen in nickel. Moreover, according to the “nanohydride” model, crack propagation is accompanied by hydride reformation via short-range hydrogen diffusion. However, the physical reason for hydride reconstruction in this simulation remains unclear, because it would require the breaking of interatomic bonds in order to allow hydrogen atom hops. Meanwhile, remarkable dislocation mobility occurs in hydrogen-charged nickel even at the H/M ratio of ~ 0.7, see Teus and Gavriljuk (2018), which is not consistent with the assertions of suppressed dislocation emission and cleavage fracture. A direct comparison with experimental measurements is at variance with the results of the simulation performed by Song and Kurtin. If the formation of a “nanohydride” prevents the emission or absorption of dislocations, the fracture surface should correspond to full embrittlement. The cleavage-like fracture of nickel single crystals in notched, and fatigue-precracked specimens tensile tested under gaseous hydrogen have been studied e.g. by Vehoff and Rothe (1983), Lynch (1988) and Vehoff (1997). Their SEM studies revealed a cleavage fracture surface with regions of tear ridges,

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isolated dimples and coarse slip lines. Moreover, transmission electron microscopy of replicas showed rumpled areas due to fine slip markings, whereas optical microscopy revealed extensive slip on the {111} planes intersecting the crack tips. Thus, these experimental results confirm the role of dislocations in the fracture. Recently, Tehranchi et al. (2020) carried out studies complementary to the discussed “nanohydride” model. Simulations on a nickel crystal showed that the presence of a 3-layered “nanohydride” alone ahead of the crack tip can reduce surface energy to nearly zero. This is sufficient for embrittlement, and a cleavage fracture is predicted along the {111} planes. Again, according to the above experimental studies, local plasticity accompanies hydrogen-caused fracture. In addition, as shown by Lynch (1988) and Vehoff and Rothe (1983), fracture planes in nickel occur near the {100}, not the {111} planes.

5.1.8 Hydrogen-Enhanced Localized Plasticity, HELP A pioneering idea was expressed by Beachem (1972) based on his observations of microscopic plasticity accompanying different fracture modes. Its essence amounts to the suggestion that a sufficiently high concentration of hydrogen ahead of the crack tip assists any deformation process and subsequent fracture mode, namely intergranular, quasi-cleavage, microvoid coalescence, etc. In this respect, Beachem analysed four basic hydrogen-related processes: (1) hydrogen enters the metal via electrolytic charging or gaseous hydrogenation and is located at the crack tip, (2) hydrogen gas dissociates at the deformed surface and is brought into the metal matrix e.g. by moving dislocations, (3) hydrogen atoms migrate to areas of triaxial tensile stresses and (4) hydrogen dissolved in the metal matrix aids plastic deformation. Any additional processes previously discussed in the literature were rather ambitiously claimed to be unnecessary. Three types of experiments on different steels were performed by Beachem to test his idea. Stress corrosion and hydrogen attack cracking were studied on AISI 4300type carbon steels using a 3 pct NaCl solution. As a result, the fracture modes had the same features as in the absence of hydrogen, namely microvoid coalescence in the case of large microscopic plastic deformation and quasi-cleavage or intergranular fracture at small degrees of plastic deformation. Localised plasticity was detected in all the experiments. Torsion tests on electrolytically charged samples of AISI 1020 steel revealed that hydrogen atoms were trapped by plastic deformation. Gaseous hydrogenation was studied using high-strength AISI 4340 steel. The typically brittle fracture surface contained traces of significant plasticity which did not appear in the absence of hydrogen. Some observations analyzed by Beachem could be also interpreted in terms of earlier hypotheses. At the same time, he was the first to clearly state that, instead of locking dislocations as is accepted in traditional embrittlement theories, hydrogen

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assists their multiplication and, moreover, causes their movement at reduced applied stresses. The first experimental observation of the hydrogen effect on dislocation mobility was published by Tabata and Birnbaum (1983) using an HVEM environmental cell facility for a transmission electron microscope, see its subsequent description by Lee et al. (1991). It was shown that hydrogen decreases the stress needed for dislocation slip. It is important that any other gases in the environmental cell did not cause this phenomenon. Further on, the hydrogen-enhanced mobility of dislocations was confirmed for a number of metallic materials, e.g. in Ni (Robertson and Birnbaum 1986), Al (Bond et al. 1988), Ti (Shih et al. 1988), austenitic stainless steel 310 (Rozenak et al. 1990), iron (Sofronis and Robertson 2002), etc. It is remarkable that this hydrogen effect does not depend on the type of dislocation: edge, screw or partial. The discovered phenomenon was first denoted by Sirois and Birnbaum (1992) as hydrogen-enhanced localised plasticity, HELP. The authors compared the effects of hydrogen and carbon on the activation of dislocation slip in nickel using measurements of stress relaxation and differential temperature tests. The results obtained provided evidence that hydrogen increases the rate of stress relaxation, whereas carbon decreases it. At the same time, the activation enthalpy of stress relaxation was decreased by hydrogen in both Ni and Ni-C alloys. The essence of the HELP model, as proposed by Birnbaum and Sofronis (1994), see also Sofronis and Birnbaum (1995), amounts to hydrogen redistribution within their dislocation atmospheres. It is changed due to a linear superposition of stress fields around neighbouring dislocations (Fig. 5.10). This redistribution increases with decreasing distance between dislocations and creates a shielding effect on the stress fields of neighboring dislocations. Consequently, the repulsion force exerted by the neighboring dislocations decreases, which in turn reduces the applied stress needed to move dislocations with their hydrogen atmospheres. It is particularly important that, at high hydrogen concentrations and short distances between dislocations, repulsive stresses can become attractive at the leading dislocations in the pile-ups, which can result in formation of a crack. These calculations have been successfully validated by the abovementioned direct TEM observations of hydrogen-enhanced dislocation mobility and hydrogendecreased distance between dislocations in their planar ensembles in 310S stainless austenitic steel and high-purity aluminium (Ferreira et al. 1998). Detailed reviews of experimental studies confirming the HELP phenomenon as applied to hydrogen embrittlement of metallic materials were published by Robertson (1999), Sofronis and Robertson (2002), Robertson et al. (2015), Nagao et al. (2018), and Martin et al. (2019).

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Fig. 5.10 Contours of normalised hydrogen concentration c/c0 in Nb around two parallel edge dislocations having identical Burgers vectors and located on the same slip plane at c0 = 0.1, temperature 300 K and dislocation distances of 10b (a) and 6b (b). According to Sofronis and Birnbaum (1995), Elsevier

5.1.8.1

Localisation of Plastic Deformation

The hydrogen-enhanced dislocation mobility is expected to improve plasticity. Consequently, hydrogen in metallic materials should assist their ductility. Unfortunately, except for rare cases, this is not the case because plastic deformation, as a rule, is localised. This feature constitutes the second part of the HELP phenomenon. It is not well substantiated within the framework of the HELP theory, and its nature remains debatable. In fact, shear localization is the inherent property of many metallic alloys, while hydrogen merely enhances its detrimental effect on macroplasticity via increased dislocation velocity. Hwang and Bernstein (1986) were perhaps the first to detect hydrogen-enhanced planar slip and strain localisation in iron single crystals around silicon-rich particles. Similarly, Le and Bernstein (1991) observed a dense dislocation structure emanating from carbide particles in hydrogen-charged spheroidized steel and the strain localization “tails” associated with them. However, the role of precipitates cannot be dominant in localised dislocation slip because the latter occurs also in single phase solid solutions, e.g. in austenitic steels. A model for macroscopic shear localization was proposed by Sofronis et al. (2001) based on hydrogen-induced softening and lattice dilatation. According to their quantitative estimates, macroscopic strains of up to 80–117% and locally decreased yield

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stress of ~ 69% should be sufficient for localised plastic flow if the H/M ratio is ~ 0.3. Ulmer and Altstetter (1991) were perhaps the first to suppose that hydrogen affects the ability of dislocations to cross-slip, thereby assisting slip planarity. A reason for that could be the stronger hydrogen binding in the elastic field of an edge dislocation than that of a screw dislocation because of the absence of the normal stress component in a screw dislocation. This idea was verified by Ferreira et al. (1999) in their TEM studies of hydrogen effects on the character of dislocations in aluminium, where hydrogen atoms were found to stabilise the edge segments of dislocations, thereby inhibiting cross slip. The hydrogen-caused increase in the propensity towards the edge character of dislocations in hydrogen-charged 310 s austenitic steel was also observed by Robertson (2001). Subsequently, Robertson et al. (2009) supposed three possible reasons for Hinduced shear localisation: (i) inhomogeneous hydrogen distribution; (ii) hardening due to hydride or hydrogen cluster formation and (iii) hydrogen-induced volume dilatation which can cause shear localisation even with uniform hydrogen distribution and in the absence of stress concentrators or second phases. It is also relevant to mention a general mechanism for shear localisation denoted by Ashby and coworkers as “void sheeting”, see Teirlinck et al. (1988). Its essence amounts to the preferential occurrence of any voids along active slip planes, which decreases their load-carrying area: d Ab = −4rv3 Nv dγ , Ab

(5.3)

where Ab is the slip area, rv is the void radius and N v is void density per unit volume. A decrease in the load-carrying area dAb /Ab corresponds to shear increment dγ, so the slip localises there. This model could be applied to hydrogen in metals because hydrogen-induced vacancies, see Sect. 2.1.1.1, are microscopic voids, the preferential occurrence of which in the hydrogen atmospheres around dislocations moving in the slip planes is expected to assist the localisation of their slip, see the scheme in Fig. 5.11. The mechanism of localised plasticity is often discussed in terms of stacking fault energy, SFE. Due to the splitting of dislocations having a large Burgers vector, their partials acquire higher mobility due to their smaller Burgers vectors. At the same time, to change their slip planes, split dislocations should be locally transformed by the formation of constrictions, which requires an increase in applied stress. Hydrogen decreases SFE in iron-based alloys, see Sect. 2.2.1.1 in Chap. 2, and this is often thought to be the reason for slip planarity and, consequently, shear localisation. However, split dislocations can move in their parallel slip planes and it remains unclear why they should be accumulated into separate bands. On the other hand, as shown by Lu et al. (2001) in their calculations of dislocation displacement density in aluminium, the hydrogen-caused decrease of SFE by 40% does not lead

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Fig. 5.11 Scheme for shear localisation caused by increased concentration of vacancies in hydrogen clouds around dislocations in the slip plane as imagined based on the general model proposed by Teirlinck et al. (1988)

to the dissociation of dislocations into partials, while the core width of dislocations is significantly increased causing their enhanced mobility. This theoretical result is consistent with the TEM studies performed by Ferreira et al. (1999), where no dislocation partials were observed in Al despite the high hydrogen concentration. At the same time, it is claimed that hydrogen atmospheres are formed only at edge dislocations, which prevents their transformation into screw dislocations and, for this reason, retards cross slip. Strikingly different dislocation structures in deformed carbon and nitrogen austenitic steels can demonstrate how ambiguous the effect of stacking fault energy on slip localisation is. Carbon in CrNi austenitic steels is known to increase SFE, see e.g. Charnock and Nutting (1967). Its non-monotonous change with increasing carbon content occurs in manganese austenitic steels, see Fig. 5.12. Non-monotonous SFE concentration behaviour occurs for nitrogen in CrNiMn and CrMn austenitic steels, see Fig. 5.13. These carbon and nitrogen effects are Fig. 5.12 Stacking fault energy as a function of carbon content in austenitic steel having 13.0 mass % of Mn (Volosevich et al. 1972)

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Fig. 5.13 Stacking fault energy γ (white circles and squares) and density of electron states at the Fermi level DF (black circles and squares) as functions of nitrogen content in austenitic steels Cr18Ni16Mn10 and Cr15Mn17 (Gavriljuk et al. 2006)

controlled by the electron structure, which is evidenced by the corresponding change in the density of electron states at the Fermi level. The SFE varies from 25 to 50 mJ/m2 in MnC steels and from 20 to 65 mJ/m2 in CrNiMnN and CrMnN steels. Nevertheless, irrespective of the SFE and in the whole area of its concentration, carbon assists the formation of tangled dislocations during cold work, whereas nitrogen always facilitates planar dislocation slip and localisation of plastic deformation, see e.g. Gavriljuk et al. (2008b). This distinctive difference between carbon and nitrogen occurs in steels of varied basic compositions. Therefore, some other, more fundamental characteristic than SFE, controls dislocation slip. A mechanism for the localisation of plastic deformation that is closer to physical reality was proposed by Gerold and Karnthaler (1989) who considered short-range atomic order, SRO, to be the main reason for planar slip in fcc alloys, thinking low SFE or high yield stress to be of minor significance. The passage of the first dislocation at the start of plastic deformation in ordered solid solutions needs energy spent to destroy the atomic order locally. Therefore, subsequent dislocations can easily follow the same way resulting in the formation of their slip bands. In these terms, the character of dislocation slip, particularly at ambient temperatures, cannot be affected by hydrogen because it does not change the distribution of metallic atoms in the crystal lattice. At elevated temperatures, e.g. in the course of technological processing, hydrogen can assist the localisation of plastic deformation because it accelerates the diffusion of metallic atoms, see Sect. 3.5 in Chap. 3, and therefore contributes to short-range atomic order.

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5.1.8.2

5 Hydrogen Embrittlement

Pros and Cons in HELP Theory

The main achievement of the HELP theory is its theoretically and experimentally substantiated statement of hydrogen-increased dislocation mobility. The slip of dislocations escorted by hydrogen atmospheres can be considered as a precondition for reversible hydrogen embrittlement and displays itself within its temperature and strain rate ranges. One of the early relevant observations was made by Popov (1969) in plain carbon steel charged with 2 cm3 per 100 g of hydrogen, see Fig. 5.14. As follows from these experimental data, an increase in the strain rate causes the HE phenomenon to shift to higher temperatures, and brittleness disappears at some threshold rate. It is also seen that the greatest embrittlement occurs with the appropriate combination of temperature and strain rate, where hydrogen atom mobility is consistent with dislocation velocity. At increased temperatures and high strain rates, brittleness diminishes because hydrogen atmospheres are diluted and released by dislocations. With decreasing temperature, hydrogen atoms lose their mobility, and embrittlement can be realised only at smaller strain rates. Similar results were obtained by Gabidullin et al. (1971) in titanium alloys. Fournier et al. (1999) also observed the weakening and disappearance of hydrogen embrittlement in Inconel 718 with increasing strain rate. Such a display of hydrogencaused degradation of plasticity within a definite range of temperatures and strain rates follows from hydrogen binding to dislocations, as analysed in Chap. 2, which causes their compatible movement. Criticism concerning the applicability of the HELP theory is mainly related to the role of solute or absorbed hydrogen in crack growth and in the increase of ductility. For example, it is claimed that the crack velocities, as presented by Lynch (1987) for a series of hydrogen-charged metals and alloys, can be higher than the diffusion rate of solute hydrogen. Compared with the results of calculations performed by Tien et al. (1976), they are claimed to be too high even if hydrogen atoms are transported by dislocations. Fig. 5.14 Combined effect of temperature and strain rate on the plasticity of hydrogen-charged (solid lines) and hydrogen-free (dashed line) plain carbon steel doped with 0.5%Cr. Strain rates (mm/min): 1—0.045, 2—0.6, 3—20, 4—200. According to Popov (1969)

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The question is how reliable the results of these calculations are and their comparison with the experiment. The maximum crack velocity of 10−1 cm s−1 , as measured by Lynch (1986) in nickel, is much higher than the critical rate of ~ 10−3 cm s−1 quoted from Tien et al. (1976) for dislocations accompanied by hydrogen atmospheres. However, according to Hirth and Johnson (1983), core hydrogen atmospheres at dislocations in nickel can be transported at velocities of ~ 100 cm s−1 , which is higher than crack velocity by 3 orders of magnitude. Moreover, the critical dislocation rate of ~ 10 cm s−1 calculated for iron alloys exceeds by one order of magnitude the maximum crack velocity of 1 cm s−1 quoted by Lynch (1987) for martensitic steels. Another point of criticism concerns the temperature range of hydrogen-caused degradation. According to Livne et al. 1986, hydrogen-assisted crack growth in hydrogen-charged high-strength AISI 4340 steel does not occur at temperatures above ~ 70 °C. This observation was interpreted by Ransom and Ficalora (1980) in terms of a correlation between the crack growth rate and the decrease in the concentration of hydrogen adsorbed at the iron surface but not dissolved in the crystal lattice. Based on these data, Lynch (2008) claimed that “hydrogen-dislocation interactions resulting in HELP should occur up to about 200 °C, and hence, the absence of cracking above 70 °C suggests that solute hydrogen is relatively innocuous compared with adsorbed hydrogen.” To eliminate this misunderstanding, it is sufficient to note that the temperature of ~ 200 °C is specific to interaction between carbon or nitrogen atoms and dislocations in bcc iron, resulting e.g. in Snoek-Köster relaxation, while this is not the case for hydrogen. Such interaction for hydrogen and dislocations occurs at about − 25 °C, see Takita and Sakamoto (1976) and Fig. 2.11 in Chap. 2. Therefore, hydrogencaused degradation of mechanical properties in bcc iron alloys is expected to be quickly diminished with temperature increasing above RT. Particularly representative of interaction between hydrogen atoms and dislocations and the role of solute or adsorbed hydrogen atoms in HE is hydrogen in bcc β-titanium alloys. According to Lynch (2008), “the ductile behaviour of a hydrogencharged β-titanium alloy with quite high hydrogen concentrations with H/M ratio up to ~ 0.21, see Teter et al. (2001), suggests that solute hydrogen is not a potent embrittler in this material”. However, while analysing hydrogen embrittlement, particularly its temperature and strain rate range, it is useful to take into account the diffusivity of hydrogen atoms in the crystal lattice and their binding to dislocations, see Chaps. 2 and 3. Let us compare the enthalpies of hydrogen binding to dislocations, 0.035 eV, and of hydrogen migration, 0.27 eV, in β-titanium with those in nickel, 0.072 and 0.42 eV, or in austenitic steels, ~ 0.1 and ~ 0.5 eV, respectively, see Table 2.2 in Chap. 2. It follows from this comparison that the hydrogen brittleness of β-titanium alloys should be expected at temperatures far lower than RT. The extremely weak hydrogen binding to dislocations, as well as high diffusivity of its atoms, suggest formation of hydrogen atmospheres around dislocations at rather low temperatures and their quick dilution with increasing temperature. Along with the absence of localised plasticity, this feature is responsible for the ductile behaviour of β-titanium alloys at RT at

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high hydrogen contents and even allows the use of hydrogen as a temporary alloying element for technological processing, see Chap. 6 for detail. The hydrogen-caused shielding of elastic stresses within the distance between neighboring dislocations constitutes the essence of the HELP theory developed by Birnbaum and his school within the framework of continuum mechanics. The shielding effect depends on the concentration of hydrogen in its atmospheres at dislocations and, therefore, is controlled by the binding enthalpy. Hydrogen-dislocation binding arises from elastic stresses caused by hydrogen atoms dissolved in the crystal lattice and the stress field around the dislocation with the hydrostatic stress component significant for edge dislocations, whereas only shear stress prevails in the case of screw dislocations. It is remarkable that the shielding effect in the HELP theory is obtained only for interaction between hydrogen and edge dislocations, whereas screw dislocations are ruled out from the analysis, see Birnbaum and Sofronis (1994). The other feature of the elasticity approach to the HELP phenomenon is that hydrogen is not determined as a chemical element, which ignores the change in interatomic bonds due to the overlapping between hydrogen electrons and those of metallic atoms. In fact, a hydrogen atom in the HELP theory is presented as merely a point defect inducing elastic distortions in the crystal lattice. If so, under the condition that the atoms of interstitial elements accompany dislocations during plastic flow, any interstitials, e.g. carbon and nitrogen, are expected to affect dislocation velocity, as in the case of hydrogen. Particularly interesting is the comparison of carbon and nitrogen effects because their atoms have nearly the same effective size in α-iron, see Chen and Tang (1990), and quite a comparable size in γ-iron, see Gavriljuk and Berns (1999). Therefore, the shielding effect is expected to be nearly the same for these elements in iron-based solid solutions and, consequently, the dislocation properties should be comparable. Nevertheless, as follows from studies of Snoek-Köster relaxation, see Chap. 2, Sect. 2.2.2.1, nitrogen enhances dislocation mobility, as is the case of hydrogen, whereas carbon depresses it, see Figs. 2.12 and 2.13 for bcc iron and martensitic steels, respectively. The same is true for nitrogen and carbon in austenitic steels, see Fig. 2.15. Therefore, it seems that the shielding effect is overestimated in the HELP theory. Some additional mechanisms should exist, according to which chemical elements change the properties of dislocations, namely their specific energy, i.e. line tension, which affects dislocation mobility.

5.1.8.3

Atomistic Modelling of the HELP Phenomenon

Attempts to describe interaction between hydrogen atoms and dislocations and the hydrogen effect on interaction between dislocations were undertaken mainly using models based on experimental data with some parameters determined by ab initio calculations.

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For example, Lu et al. (2001) analysed the hydrogen effect on dislocation properties in Al using a pseudopotential proposed by Vanderbilt (1990) and the semidiscrete variational Peierls-Nabarro model revisited by Bulatov and Kaxiras (1997) and Lu et al. (2000). It was obtained that hydrogen with its concentration of 4 at.% decreases stacking fault energy by up 50%, which allowed the prediction that dislocations could be emitted more easily from a crack tip, based on the analysis performed earlier by Rice (1992). This prediction is consistent with previous results of atomistic calculations for H in Ni, where the H-accelerated emission of dislocations from a crack tip was obtained by Daw and Baskes (1987) using the embedded atom method developed by Daw et al. (1986). Additionally, Lu et al. (2001) studied the properties of dislocation core for screw (0°), edge (90°) and mixed (30°, 60°) dislocations and found a decrease by more than one order of magnitude in the Peierls stress needed for moving a stationary dislocation. This result underlines the prevailing role of individual hydrogen-dislocation interaction in the increase of dislocation mobility and is at variance with the fundamental point in HELP theory that hydrogen-affected elastic interaction between dislocations is responsible for their H-increased velocity, as it was presented in Fig. 5.10. Another part of their calculations concerned binding between individual dislocations and hydrogen atoms. In agreement with generally accepted ideas about elastic dilatation in the core of dislocations mainly contributing to their binding with impurity atoms and previous TEM observations, see Ulmer and Altstetter (1991), Ferreira et al. (1999) and Robertson (2001), the authors obtained that edge dislocations possess a significantly larger binding energy with hydrogen atoms than screw dislocations. Consequently, a conclusion was derived that, by inhibiting cross slip, hydrogen promotes slip planarity resulting in the localisation of plastic deformation. Its verification will be further discussed while analysing experimental data on hydrogen embrittlement. The atomistic simulation of the hydrogen effect on the mobility of edge dislocations in bcc iron was performed by Taketomi et al. (2008) and Taketomi et al. (2017), whereas Wang et al. (2013) studied hydrogen-caused change in the core of both edge and screw dislocations. In both cases, the authors used the empiric embedded-atom potentials for hydrogen in bcc iron developed on the basis of the density functional theory by Wen et al. (2001), Lee and Jang (2007), Ramasubramaniam et al. (2009). Taketomi et al. (2008) found that shear stress distribution along the slip plane near the core of edge dislocations is not changed by hydrogen even if the number of hydrogen atoms per unit length of dislocations increases up to 7.35 nm−1 and again, in contrast to the HELP theory, elastic interaction between dislocations is not significantly changed by hydrogen. Under the low hydrogen concentration of 2.24 mass ppm and the corresponding number of hydrogen atoms per unit length of dislocation line 0.49 nm−1 , a decrease in the energy barrier for the movement of individual dislocations was mentioned. However, Taketomi et al. (2017) obtained that, at hydrogen concentration of 1.24 nm−1 , the energy barrier increases, which suggests a decrease in dislocation mobility.

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According to Wang et al., hydrogen assists the movement of edge dislocations in a form similar to classic kink-pair motion, which the authors denoted as hydrogen induced broaden-core. In contrast, the core of the screw dislocation is split by hydrogen, which is expected to decrease the Peierls barrier for moving dislocations. However, this quasi-splitting has the character of broadening in the dislocation core, i.e. it is of the single-hump, not the camel-hump type. This short-range change in the core denies the isotropic strain field of H atoms, as assumed in the HELP theory. The hydrogen effect on screw dislocation mobility has been studied by Itakura et al. (2012, 2013) using first-principles calculations. They analysed preferred hydrogen positions around the dislocation with the subsequent determination of the energy of hydrogen binding to the screw dislocation. The incorporation of the obtained interaction energy into the line tension model of a curved dislocation line developed by Edagawa et al. (1997) and Rodney and Proville (2009) made it possible to estimate the hydrogen effect on the kink nucleation enthalpy and the hydrogencaused trapping effect during kink movement. The upper/lower critical values of temperature and shear stress for hydrogen-caused softening were also established. Qualitatively, the resulting predictions of lower critical temperature needed for the softening/hardening transition are in the agreement with the experimental observations of Matsui et al. (1979). The quantitative disagreement could be attributed to the static approach and inability to incorporate the dislocation motion coupled with hydrogen migration into the model. In general, the hydrogen-caused decrease of the Peierls barrier is a common result in the studies of hydrogen effect on the properties of screw dislocations based on atomistic calculations. At the same time, it is relevant to note that the Peierls relief is shallow in fcc metals and plays no role in dislocation movement. In spite of this, the hydrogen-enhanced mobility of dislocations remains a distinctive feature of dislocation slip, which makes doubtful any significant role of kinks in hydrogen embritlement.

5.1.8.4

Electron Concept of the HELP Phenomenon

Studies of hydrogen-caused change in the electron structure of iron, nickel and titanium, as presented in Chap. 1, show that hydrogen atoms are encased in valence electron clouds. Moreover, hydrogen increases the concentration of free electrons, which is confirmed by the measurements of electron spin resonance in hydrogen-charged austenitic steels, see Fig. 1.25. This result is consistent with the hydrogen-increased density of electron states, DOS, at the Fermi level, see Figs. 1.19 and 1.22 for bcc and fcc iron. Similarly, hydrogen increases DOS in nickel and titanium, see Fig. 1.26 for fcc nickel and Fig. 1.29 for bcc titanium. The increase in the concentration of free electrons suggests the enhancement of the metallic character of interatomic bonds, i.e. their softening, which in turn changes fundamental properties of dislocations, see Sect. 1.5.4 in Chap. 1, namely the start of dislocation sources at smaller applied stresses, the decrease in the line tension of dislocations and in the distance between dislocations in their planar assemblies.

5.1 Available Hypotheses

235

The latter increases the number of dislocations in pile-ups and the stress at leading dislocations, thereby decreasing the stress required for microcrack opening. The hydrogen-induced softening of interatomic bonds should particularly appear in the vicinity of dislocations encased in hydrogen atmospheres if the latter escort dislocations during plastic deformation. As mentioned in Sect. 5.1.8.2, this combined movement of dislocations and hydrogen atoms is a precondition of hydrogen embrittlement, the reversibility of which is a distinctive feature in comparison with other numerous dramatic hydrogen effects in metals. It can be seen that, unlike in the aforementioned models of hydrogen embrittlement, where the initial crack exists a priori appearing like Aphrodite from sea foam, in the electron concept of the HELP phenomenon the hydrogen-assisted crack nucleation directly follows from the earlier start of dislocation sources and dislocation emission under smaller applied stresses. Crack opening can occur via any operating mechanism, e.g. crack nucleation in front of a pile-up, as proposed by Stroh in the fifties, see Stroh (1954, 1957), or at the Lomer-Cottrell locks caused by intersecting screw dislocations, e.g. Schoeck (2010) etc. It is also relevant to note that atomic decohesion is naturally and reconcilably included in the electron model of HELP phenomenon as a result of weakening in the interatomic bonds not due to hydrogen-assisted normal stresses in front of an a priori existing crack, as proposed in the original HEDE hypothesis and its subsequent variants, but because of the hydrogen effect on the electron structure resulting in changed dislocation properties, corresponding dislocation emission and microcrack opening. The similarities in the hydrogen and nitrogen effects and the opposite effect of carbon on the electron structure of iron can serve as an appropriate illustration of the dominant role of electron structure in the properties of dislocations and, consequently, in the mechanical properties of metallic materials, see Fig. 5.15. As in the case of hydrogen, compare Figs. 1.19 and 1.22 in Chap. 1, nitrogen increases the density of electron states at the Fermi level in iron, whereas carbon decreases it. As a result, carbon atoms supply their valence electrons to states below the Fermi level. The distance on the energy scale between the bound states caused by these interstitial elements at the bottom of the valence band is smaller for carbon, which points to stronger bonds between carbon and iron atoms in comparison with those between iron and nitrogen. Consequently, iron-carbon bonds in fcc iron are characterised by the enhanced covalent component in contrast to their prevailing metallic character if carbon is substituted for nitrogen. These calculations were supported by free electron concentration measurements, Fig. 5.16 (see Gavriljuk et al. 1993 and Shanina et al. 1995 for detail). Like hydrogen, see Fig. 1.25 in Chap. 1, nitrogen increases the concentration of free electrons in the fcc iron lattice, whereas it remains nearly unchanged in the case of carbon in accordance with the filling of electron states below the Fermi level and the corresponding reinforcement of covalent bonds. As a consequence, the covalent character of interatomic bonds is particularly prevalent within carbon clouds around the dislocations, whereas nitrogen and

236

5 Hydrogen Embrittlement

Fig. 5.15 Density of electron states per elementary cell in fcc iron and iron-based solid solutions Fe32 C and Fe32 N. The situation at the Fermi level is shown in the upper-left inset

Fig. 5.16 Concentration of free electrons in austenitic steel alloyed with carbon or nitrogen

hydrogen locally enhance metallic interatomic bonds in their dislocation atmospheres and thereby increase the velocity of dislocations in their slip planes. The identical effects of nitrogen and hydrogen on the electron structure in iron-based solid solutions allow a better understanding of similarities in dislocation properties of hydrogen- and nitrogen-containing austenitic steels in comparison with the carbon ones. Any interstitial atoms pose obstacles to moving dislocations and should prevent dislocation slip. This is the case for carbon austenitic steels, where plasticity and

5.1 Available Hypotheses

237

fracture toughness continuously decrease with increasing carbon content, whereas yield stress increases. In contrast, with nitrogen content increasing up to 0.8 mass%, yield stress increases, however the values of plasticity and fracture toughness remain unchanged, see Gavriljuk and Berns (1999). The point is that the nitrogen-increased concentration of free electrons compensates the embrittling effect of nitrogen interstitial atoms in austenitic solid solutions. Due to this effect, nitrogen austenitic steels are characterised by an excellent combination of strength, plasticity and fracture toughness. Only at certain critical nitrogen contents, the nitrogen-enhanced metallic character of interatomic bonds no longer compensates the embrittling effect of interstitial atoms. The same is true for hydrogen in metals. Due to the hydrogen-enhanced metallic character of interatomic bonds, plasticity is enhanced or at least retained until the counterbalance between the interstitial location of hydrogen atoms retarding dislocation slip and the hydrogen-assisted mobility of dislocations is broken. Remarkable in this relation is the aforementioned case of ductile fracture of titanium alloy Timetal 21S at H/M ratio of ~ 0.21. The hydrogen-enhanced metallic character of interatomic bonds and the absence of localized plasticity provide goood plasticity despite so high concentration of interstitial atoms. Comparable is also the brittle fracture of hydrogen austenitic steels during room temperature tensile tests, see Figs. 5.4 and 5.5, and quasi-cleavage in nitrogen austenitic steels during impact mechanical tests at cryogenic temperatures, see Fig. 5.6. In both cases, intensive plastic deformation under fracture surface precedes pseudo-brittle fracture. The hydrogen-enhanced localisation of plastic deformation caused by dislocations escorted by hydrogen atmospheres is responsible for brittleness in the first case, whereas the abnormal transfer of nitrogen atoms by moving dislocations occurs in the second case, as it does during impact deformation, see e.g. Larikov et al. (1975), Hertsricken et al. (1999), Nemoshkalenko et al. (2001) and Filatov et al. (2015), which creates conditions for quasi-cleavage. Hydrogen-increased plasticity does not occur in hydrogen-charged austenitic steels because hydrogen-enhanced plastic flow is localised. At the same time, as will be discussed below, it can be realised in β-titanium alloys if the localisation of plastic deformation is absent, see Chap. 6. Summing up, one can state that due to the increase in the concentration of free electrons, hydrogen in metals is expected to improve their plasticity and toughness if plastic deformation is not localised. In the case of localised plastic deformation, hydrogen should enhance it because of easy dislocation emission and increased dislocation velocity, thereby assisting embrittlement.

5.1.8.5

HELP + HEDE and HELP-Mediated HEDE Models

Both these concepts have been proposed in the previous decade of this century based on the earlier attempts to find an interconnection between the HELP and HEDE models accounting for the occurrence of plastic deformation preceding brittle

238

5 Hydrogen Embrittlement

fracture. Along with studies performed by Gerberich and his colleagues analysed in Sect. 5.1.4, it is appropriate to mention those belonging to Katz et al. (2001), Delafoss and Magnin (2001), Birnbaum (2003), Komaragiri et al. (2008) etc. Hydrogen-dislocation and hydrogen-fracture plane interactions in a metastable austenitic steel and Cu/Ti/SiO2 /Si interfaces, respectively, were studied by Katz et al. (2001) using nanomechanical tests combined with surface probe microscopies. It was obtained that hydrogen-induced formation of martensite due to electrolytic charging increases yield strength, whereas subsequent hydrogen degassing removes this effect. These data were interpreted as evidence of hydrogen-impeded dislocation mobility. However, the authors ignored plastic deformation accompanying electrolytic hydrogen charging and resulting in γ→ε transformation and corresponding hardening which disappeared with the reverse ε→γ transformation during hydrogen degassing. The hydrogen-caused reduction by at least 50% in strain energy release at thin film interfaces was also demonstrated as hydrogen-enhanced decohesion. Both experiments added new information about hydrogen interaction with crystal lattice imperfections, although they hardly offer any real evidence of HELP + HEDE synergy. A model for periodic microfracture along the {111} slip planes in austenitic steels was developed by Delafosse and Magnin (2001) in relation to hydrogen’s role in stress corrosion cracking. According to their model, hydrogen-caused local softening at the crack tip creates dislocation emission and subsequent pile-up formation, whereas the hardened zone is previously formed by forest dislocations under applied stress. At this obstacle, a certain role is played by the interface between H-softened and H-free hardened zones. As a result, the microcrack is nucleated via mechanism proposed by Stroh (1954). Hydrogen decreases cohesion energy along the {111} slip planes and a crack opens on these under normal stresses. The emission of dislocations on symmetric slip planes shields the tip of the formed crack, and the process is repeated periodically, changing crack planes. Thus, it claims that a synergy of HELP and HEDE can occur. One can only remark that necessity of normal stresses for cracks opening at the inresecting slip planes is not substantiated and looks rather artificial. Moreover, formation of pile-ups in these slip planes, which occurs also in the absence of hydrogen, does not mean that hydrogen impeded dislocation mobility. Using finite element simulations, Komaragiri et al. (2008) calculated hydrostatic stress distribution under the condition of large gradients in the plastic strain caused by increased dislocation density. In this case, the consequent strain hardening creates crack tip stresses which are claimed to be sufficient for the initiation of local atomic decohesion. The HELP + HEDE concept is described in detail by Djukic et al. (2014, 2015, 2016a, 2016b, 2019). Referring to Komaragiri et al. (2008) and, as in the case of the original HEDE model developed by Oriani (1972), a central role in the fracture is assigned to hydrostatic stresses at the crack tip caused by hydrogen localisation in the fracture process zone, see Djukic et al. (2019). The hydrogen-enhanced mobility of dislocations combined with localised plasticity is considered only as a possible previous phenomenon preparing necessary conditions for HEDE to be activated. The hydrogen-impeded mobility of dislocations, the validity of which was

5.1 Available Hypotheses

239

analysed in Chap. 2, Sect. 2.2.2, is claimed to lead to HEDE as an independent mechanism of hydrogen embrittlement (Djukic et al. 2016a). Moreover, hydrogen-impeded localized plasticity is also stated to occur. One of the early studies in this relation was performed by Djukic et al. (2014) and in more detail by Djukic et al. (2015) on samples of a low-carbon steel taken from the boiler tubes of fossil power plants damaged by hydrogen attack and hydrogen embrittlement. Based on the uneven distribution of hardness and impact toughness attributed to different hydrogen contents, as well as on the analysis of fracture surface, the authors claimed simultaneous action of the HEDE and HELP mechanisms, where HEDE is responsible for brittle transgranular fracture, whereas the local ductile features of microvoid coalescence fracture are attributed to HELP. The HELP mechanism is considered to be dominant at low hydrogen concentrations. If hydrogen concentration reaches a critical value, “relatively sudden HEDE mechanism manifestation” occurs. The statistical micro-mechanical model proposed by Novak et al. (2010) for the hydrogen embrittlement of martensitic steels was presented by Djukic et al. (2019) as an example of a HELP mediated HEDE mechanism for hydrogen-induced brittle fracture. High-strength low-alloyed carbon steel AISI 4340 tempered at 200 °C after quenching and containing needle-like carbides at the grain boundaries was studied by the authors after saturation with gaseous hydrogen under its increasing pressure. The fracture strength was found to dramatically decrease with increasing hydrogen concentration, accompanied by transition from ductile microvoid coalescence fracture in H-free steel to the brittle intergranular fracture of H-doped steel. The latter was associated with the interface cracking of grain-boundary carbides. However, as shown by the authors, hydrogen atoms accumulated at the carbide/matrix interface did not control cracking because, regardless of the pressure of hydrogen, it fully saturated both grain boundaries and carbides (more than 99%) throughout the entire course of the test. According to the proposed model, brittle fracture occurred under stress created by dislocation pile-up blocked in ferrite at the carbide surface, see Fig. 5.17. Hydrogen atmospheres at dislocations reduce repulsive stress between dislocations, which increases the number of dislocations in the pile-up, thereby enhancing impingement on the carbide/matrix interface and ultimately resulting in the opening of a crack at the interface and consequent brittle fracture. This model is consistent with the interpretation of hydrogen-induced intergranular embrittlement of martensitic steels given by Kameda and McMahon (1983), McMahon (2001) and with previous works performed by these authors, where it was shown that hydrogen transport by dislocations during continued plastic flow is predominantly responsible for hydrogen accumulation sufficient for nucleating a microcrack at an inclusion. It was underlined that hydrogen-caused cracking is a dynamic rather than a static process because crack-tip hydrogen concentration would be several orders of magnitude lower in the case of a static hydrogen distribution model. Nevertheless, in fact, the fracture scheme presented in Fig. 5.17 is identical to the generally accepted mechanism of microcrack nucleation by dislocation pile-up

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5 Hydrogen Embrittlement

Fig. 5.17 Hydrogen-saturated dislocation pile-up locked at the grain-boundary carbide and responsible for microcrack nucleation and consequent brittle intergranular fracture. Red circles denote hydrogen atoms in the solid solution, green circles—H atoms at the carbide/matrix interface, blue circles—H atoms at dislocations. Redrawn from Novak et al. (2010), Elsevier

locked for slip by any obstacle, as proposed by Stroh (1954, 1957). Under applied stress τ, the stress τL at the leading dislocation increases as τL = nτ until it reaches the threshold value needed for the local breaking of interatomic bonds and microcrack nucleation. It is particularly important that the microcrack is nucleated in the iron matrix under stress τL because of the hydrogen-increased number of dislocations in the pile-up, and not in the interface apart from the active slip plane. As mentioned in Sect. 5.1.8.4, the role of hydrogen amounts to a local increase in the concentration of free electrons within the hydrogen atmosphere at dislocation in the pile-up leading to the local decrease of the shear modulus and a consequent increase in the number of dislocations in the pile-up, which results in the nucleation of a microcrack under applied stresses lower than in H-free metal. Therefore, the model proposed by Novak et al. (2010) is consistent with the electron approach to HELP phenomenon described above, if one were to substitute the idea of hydrogen-induced elastic shielding of repulsive stresses between dislocations in the pile-up for the hydrogen-increased concentration of free electrons within hydrogen atmospheres around dislocations locally enhancing the metallic character of interatomic bonds. This mechanism for hydrogen-induced brittle fracture should be operating in the absence of particles in the case of any obstacle to dislocation slip. The model proposed by Novak was also applied to the brittle fracture of lath martensitic steels by Nagao et al. (2012, 2014) and presented as a HELP-mediated HEDE model. Hydrogen embrittlement of a middle-carbon martensitic steel having the same carbon content as the aforementioned AISI 4340 steel subjected to quenching and tempering at 500 °C with subsequent gaseous hydrogen charging under high pressure was studied by Nagao et al. (2012). Flat and quasi-cleavage features of the fracture surface were observed using scanning electron microscopy. Intense slip bands were detected beneath both fracture surfaces. Parallel laths under the flat fracture surface were interpreted as corresponding to intergranular fracture along prior austenitic grains, whereas dislocation slip along the martensitic

5.1 Available Hypotheses

241

lath boundaries was detected under the quasi-cleavage surface. A conclusion was made about the hydrogen-enhanced and plasticity-mediated decohesion mechanism of brittle fracture. In further studies, Nagao et al. (2018) analyzed the hydrogen-caused fracture of Ti-free and Ti-added lath martensitic steels in an attempt to macroscopically quantify their hydrogen embrittlement. The obtained results amounted to the statement about the weakening of hydrogen segregation at the high-angle grain boundaries by dislocation pile-ups so that, instead, hydrogen is deposited on the boundaries by impinging dislocations. The Ti(Mo)C carbides trap much hydrogen diminishing thereby its segregation at grain boundaries and martensitic laths. For this reason, their precipitation enhances resistance to hydrogen embrittlement. In the overall assessment of the HELP + HEDE and HELP mediated HEDE models, one can ascertain that they both initiated a number of useful experimental studies. On the other hand, they can hardly claim conceptual significance. First, the acronym HEDE is not used correctly when analysing cases where cracking has a purely dislocation-related nature and has nothing in common with the breaking of interatomic bonds under applied stress alone. The original HEDE model suggests this breaking when “the local tensile elastic stress normal to the plane of the crack” exceeds the “local maximum cohesive force per unit area as reduced by the large concentration of hydrogen”. This essence of the HEDE concept remains unchanged in the subsequent attempts to improve it by Gerberich et al. (1991, 2009), see Sect. 5.1.4, and in the statements made by Djukic (2019) about the central role of hydrostatic stresses at the crack tip caused by hydrogen localisation in the fracture process zone. Second, atomic decohesion is implicit in the HELP theory and explicit in the electron approach to HELP phenomenon, where the earlier opening of a microcrack results from a hydrogen-caused decrease in the shear modulus and the consequent weakening of interatomic bonds initiating the start of dislocation sources, decreasing the specific energy of dislocations and thereby enhancing their mobility and diminishing the distance between dislocations in pile-ups. Based on these arguments, it may be better to follow Occam’s razor in that “entities should not be multiplied without necessity”. Finally, one can state that hydrogen embrittlement is a complicated phenomenon resulting from a number of competing and, at the same time, mutually complementary processes. Among these, the hydrogen effect on the electron structure seems to be dominant. On the other hand, the phenomena inherent in metallic alloys, namely short-range atomic ordering or the short-range decomposition of metal solid solutions, both arising from interaction between the atoms of constituting elements, interfere with the effects induced by hydrogen, which complicates the correlation between atomic interactions and mechanical properties of hydrogen-charged materials.

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5.2 Hydrogen Embrittlement of Fe-, Ni- and Ti-Based Alloys Taking into account the whole complex of phenomena accompanying hydrogen in metallic solid solutions, this analysis will take into account the following parts of the HELP phenomenon: (i) decrease in the start stress for dislocation emission, (ii) increase in dislocation mobility and (iii) localisation of plastic deformation. The first part arises from the hydrogen-increased concentration of free electrons, whereas the second can be interpreted in terms of hydrogen-shielded interaction between neighbouring dislocations or a decrease in the dislocation line tension due to the above mentioned hydrogen effect on the electron structure. The third part is essentially controlled by the short-range order of atomic distribution in metallic solid solutions and depends on the interaction between constituent atoms.

5.2.1 Austenitic Steels It is relevant to choose austenitic steels in the case of Fe-based alloys since a number of studies have been performed recently, e.g. in relation to hydrogen-resistant steels for containers in the automotive industry. Long-distance hydrogen transportation via pipelines is of current significance. Under consideration will be the following factors: chemical compositions affecting interatomic bonds and the type of hydrogen charging. The effects of electrochemical and gaseous hydrogenation are expected to be different because of plastic deformation accompanying electrochemical charging and absent in the case of gaseous hydrogenations, see Sect. 4.1.2 in Chap. 4. Accompanying hydrogen charging, plastic deformation reduces the plasticity resource of hydrogenated steels during subsequent mechanical loading. The effect of chemical compositions on the thermodynamic stability of austenite including stacking fault energy will be also taken into account. A correlation between the chemical composition of austenitic steels and their electron properties has been studied by Shanina et al. (1995, 1998, 2002, 2007) see Table 5.1. One can see that the substitutional elements located to the right of iron in the periodic table (Ni, Cu, Si, Al) increase the concentration of free electrons nf , whereas those on the left of it (Cr, Mn, Mo) decrease it. Among the interstitial elements, nitrogen significantly increases nf and carbon acts in the opposite direction. At the same time, combined alloying with carbon and nitrogen results in the highest concentration of free electrons, which was, e.g., used for the development of austenitic steels characterized by an excellent combination of high strength and fracture toughness, see Berns et al. (2013). Mechanical properties of hydrogen-free austenitic steels and those electrochemically charged with hydrogen are presented in Table 5.2.

5.2 Hydrogen Embrittlement of Fe-, Ni- and Ti-Based Alloys

243

Table 5.1 Concentration of free electrons nf in austenitic steels (Shanina et al. 1998) Steel

nf , 1022 cm−3

Cr15Ni15

0.14

Cr15Ni20

0.30

Cr15Ni20Mn5

0.16

Cr25Ni20

0.10

Cr15Ni20Mn10

0.09

Cr15Ni20Mo1.3

0.09

Cr25Ni20Cu2.5

0.31

Cr15Ni20Si2

0.90

Cr15Ni20Al2

0.45

Cr18Ni16Mn10N0.4

2.6*

Cr18Ni16Mn10C0.3

0.19*

Cr13Mn18N0.7

1.1**

Cr13Mn18C04N0.4

3.7**

Cr18Mn18C035N0.6

2.9***

* Shanina et al. (1995), ** Shanina et al. (2002), *** Shanina et al. (2007) Table 5.2 Hydrogen effect on the mechanical properties and the embrittlement index HE = [(δH − δ0 )/δ0 ] × 100% of austenitic steels charged for 72 h at 50 mA/cm2 (Gavriljuk et al. 2010)a Steel composition

Hydrogen-free

Hydrogen-charged

HE, %

σ0.2 , MPa

σu , Mpa

δ, %

σ0.2 , MPa

σu , MPa

δ, %

Cr15Ni25

125

378

29.0

211

228

1.6

94.5

Cr15Ni40

147

442

45.2

192

195

0.34

99.2

Cr25Ni20

149

393

6.4

166

277

2.5

65

Cr25Ni20Si3

197

389

7.4

192

356

4.5

39.2

Cr15Ni25Cu2

131

374

32.1

199

212

1.0

96.9

Cr15Ni25Al2

203

468

33.6

297

350

1.6

95.2

Cr15Ni25Si2

136

351

28.0

260

291

4.4

84.3

Cr15Ni25Mn15

152

386

27.3

274

316

5.5

79.9

Cr18Ni18Mn10

139

359

8.7

182

233

2.7

68.2

Cr18Ni16Mn16

164

414

23.8

206

351

9.6

59.7

Cr12Ni18Mn16

143

269

10.4

205

253

4.1

60.6

Cr18Ni12Mn17

166

381

19.3

215

334

9.9

48.7

Cr18Ni18Mn10Mo2

156

371

15.1

219

284

5.3

65.4

Cr18Ni16Mn10Si2

227

339

4.2

219

332

2.8

32.5

a

The H/M ratio is equal to ~ 0.6

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5 Hydrogen Embrittlement

As follows from the presented data, copper, aluminum and particularly nickel assist hydrogen embrittlement. Manganese and molybdenum moderately decrease it, whereas the positive effect of chromium and silicon on HE resistance is significant. Silicon increases the concentration of free electrons, which is expected to assist hydrogen brittleness in the presence of localized plastic deformation. It decreases also the stacking fault energy in austenitic steels, which is often claimed, but has never really been proven, to be responsible for the localisation of plastic deformation. The obtained Si-increased resistance to hydrogen embrittlement could be attributed to the increased fraction of the ε-martensite induced by plastic deformation during electrolytic hydrogen charging, see Sect. 4.1.2 and Fig. 4.5e in Chap. 4. However, according to Weber et al. (2011), significantly increased resistance to hydrogen embrittlement is obtained in silicon-containing steel Cr16Ni8Si2C0.1 after the gaseous hydrogenation, which excludes the formation of ε-martensite. The straininduced ε-martensite was also not detected in the quoted study after mechanical tests, although tensile deformation causes γ → ε transformation in the electrochemically charged stable austenitic steel Cr15Ni25, see Fig. 4.12 in Chap. 4. Weber et al. supposed that inverse ε → γ transition could take place in the less stable Cr16Ni8Si2C0.1 steel due to hydrogen effusion from the samples after mechanical tests before X-ray diffraction measurements. Another reason why silicon improves the hydrogen resistance of austenitic steels can be linked to increased hydrogen concentration in the solid solution, as follows from Fig. 4.6c, Chap. 4. The Si atoms serve as traps for H atoms in the crystal lattice, impeding their migration and thereby retarding hydrogen embrittlement. Chromium improves the resistance of stable austenitic steels to hydrogen embrittlement in the case of severe electrochemical charging, see Table 5.2. This result is consistent with the significantly decreased concentration of free electrons, see Table 5.2, on the condition of localized plastic deformation, and the retarded diffusion of hydrogen atoms in the fcc iron crystal lattice, see Table 2.2 in Chap. 2. At the same time, chromium increases the enthalpy of binding between hydrogen atoms and dislocations, see Table 2.2, assisting the formation of hydrogen atmospheres at dislocations. This should stimulate hydrogen-caused increase of dislocation velocity if one is to accept that hydrogen shielding is dominant, or prevent it if the Cr-decreased concentration of free electrons is decisive, thereby increasing the line tension of dislocations. A positive effect of chromium was observed in the low stable Cr18Ni8 austenitic steel subjected to gaseous hydrogen charging at the pressure of 40 MPa, see Martin et al. (2011c). Because of an insignificant increase in Cr content in this steel compared to the reference steel, this result could hardly be attributed to an increase in the stability of the austenitic structure. Chromium decreases stacking fault energy in austenitic steels, see e.g. Schramm and Reed (1975). Low stacking-fault energy is considered in a number of studies as the reason for planar dislocation slip and the consequent localisation of plastic deformation leading to hydrogen embrittlement. For example, Symons (1997) demonstrated a correlation between the calculated stacking fault energy, the observed planar

5.2 Hydrogen Embrittlement of Fe-, Ni- and Ti-Based Alloys

245

slip and the hydrogen-caused degradation of the mechanical properties of Ni-XCr8Fe alloys under gaseous hydrogen pressures of 13 and 34 MPa. However, his analysis ignored the occurrence of short-range atomic order and its dominant effect on dislocation structure and the localisation of plastic deformation in the Ni–Cr–Fe system, which will be analysed below for high-nickel austenitic steels and Ni superalloys. Manganese. A moderate decrease in hydrogen embrittlement due to manganese follows from Table 5.2 and is consistent with the decreased concentration of free electrons, see Table 5.1., taking into account localization of plastic deformation. However, the positive effect of manganese was also confirmed by Martin et al. (2011c) in AISI-type 304 steel subjected to gaseous hydrogen charging at the pressure of 40 MPa and was attributed to the increased stability of austenite. Michler et al. (2012a) have also mentioned good resistance to hydrogen embrittlement in steel Cr18Ni8Mn6N0.25 charged with gaseous hydrogen at the pressure of 10 MPa. This result cannot be attributed to a change in stacking fault energy because, at these contents of manganese and nitrogen, they affect SFE in opposite directions. The manganese effect on the hydrogen embrittlement of low-nickel CrNi steels was discussed in a number of studies, initially by Louthan and Gaskey (1976). They demonstrated the excellent ductility of steel Cr21Ni6Mn9 under the gaseous hydrogen pressure of 69 MPa. Nevertheless, about half of ductility was lost in the samples subjected to preliminary thermal hydrogen charging and thereafter tested in the air at room temperature. The incresed temperature of charging should cause short range decomposition of the solid solution. Later, the same effect was obtained by West and Louthan (1982) who compared the properties of this steel after preliminary thermal charging and subsequent testing under hydrogen pressures of 120(172) MPa with those of uncharged steel tested under the same hydrogen pressure conditions. As a result, the uniform elongation decreased from 49(43)% down to 6(5)%, whereas the relative reduction in area degraded from 57(65)% down to 23(21)%. The authors concluded that preliminary thermal charging makes this steel sensitive to hydrogen-induced cracking at grain boundaries. The very probable change of metallic atom distribution in the solid solution during thermal charging, i.e. short range atomic order, was not mentioned. Molybdenum improves the hydrogen resistance of austenitic steels subjected to both electrochemical charging in the case of stable austenitic steels and gaseous hydrogen charging in the case of unstable steels, see data in Table 5.2 and Martin et al. (2011c), respectively. For the case of electrochemical charging, as it was done with chromium, this effect can be attributed to the Mo-decreased concentration of free electrons. Similar Mo and Cr effects on short range atomic order, namely shortrange decomposition in fcc iron solid solutions, are also worth noting. This positive effect is not significant, particularly taking into account increased costs. Copper in CrNi austenitic steels increases the concentration of free electrons, see Table 5.1, and stacking fault energy, see Dulieu and Nutting (1964), causing wavy slip during plastic deformation. All these effects are similar to those occurring in nickel. A feature of pure copper is that wavy slip is observed only at cold rolling

246

5 Hydrogen Embrittlement

up to 50% of reduction in thickness and is substituted for shear bands at higher deformation (Smallman and Lee 1994). Copper enhances hydrogen embrittlement of CrNi austenitic steels in the case of electrochemical charging, see Table 5.2. Its harmful effect is also confirmed by mechanical tests on steels Cr18Ni10Cu3 and Cr18Ni12.7 subjected to gaseous hydrogen charging under pressures of 10 and 40 MPa, see Michler et al. (2012a). According to their data and in contrast to those for CrNi steels, planar slip traces are clearly seen on the fracture facets in CrNiCu steels, whereas in Cu-free steel they appear only slightly with a decrease in temperature of mechanical tests. In contract to nickel, the harmful effect of copper on the resistance of austenitic steel to hydrogen embrittlement is combined with the Cu-assisted localisation of plastic deformation despite an increase in stacking fault energy. The point is that copper in steel acts as a surface active element and causes both liquid and solid metal embrittlement, see e.g. Vigilante et al. (2012). Nitrogen in austenitic steels increases the concentration of free electrons, see Table 5.1. According to the electron approach to the HELP phenomenon, it is not desirable in the case of electrochemical hydrogen charging. At the same time nitrogen austenitic steels are prone to the localisation of plastic deformation, which should makes them also not applicable in the case of gaseous hydrogenation. Nebertheless, a positive effect of alloying with 0.28% N of electrochemically charged AISI type 316, 321 and 347 austenitic steels containing 13.2, 10.7 and 11.2% of Ni, respectively, has been reported by Rozenak (1990). In contrast, the negative effect of 0.1–0.3 mass% of nitrogen added to austenitic steel Cr15Mn15Ni4 has been also observed by Kim et al. (2020) who also used electrochemical charging and attributed the obtained result to the nitrogen-decreased diffusivity of hydrogen atoms. At the same time, a negligible effect of high-pressure 10 MPa hydrogen on the ductility of nitrogen austenitic steel Cr18Ni8Mn6N0.25 has been observed by Michler et al. (2012a). Earlier, a positive nitrogen effect in the electrochemically charged steel Cr21Ni6Mn9 containing less than 0.25 mass% of nitrogen was demonstrated by Odegard et al. (1976). The increase in nitrogen content above 0.3 mass % led to detrimental H-caused degradation of mechanical properties. Based on these experimental data, one can suppose that a positive nitrogen effect on resistance to hydrogen embrittlement occurs in not sufficiently stable austenitic steels and is linked to the stabilization of the fcc crystal lattice. Using gaseous hydrogenation at pressures of 10 MPa, Michler and Naumann (2010) have shown that, added to CrNi steels or in combination with manganese in the CrMnN steels, nitrogen decreases their resistance to HE within its concentrations of 0.25–0.84 mass%. It is worth noting that the authors performed their tensile tests at − 50 °C, which is a temperature of highest hydrogen-caused mechanical degradation, as found earlier by Han et al. (1998) and Fukuyama et al. (2003). Such a definite temperature for the most harmful hydrogen effect on ductility is obviously controlled by a balance between hydrogen diffusivity in the crystal lattice and hydrogen binding to dislocations, see Table 2.2 in Sect. 2.2.2.2 of Chap. 2.

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247

As mentioned above, despite the increase in stacking fault energy, nitrogen facilitates planar dislocation slip amd assists the localisation of plastic deformation. It is the nitrogen-caused short-range atomic ordering in the distribution of metallic atoms that predominantly controls the type of dislocation structure, see Gavriljuk et al. (2000a, 2008b). This nitrogen effect occurs even in martensitic steels, see Gavriljuk (1996). Therefore, nitrogen has a harmful effect on the hydrogen resistance of stable austenitic steels subjected to both electrochemical and gaseous charging. Carbon is expected to retard the hydrogen embrittlement of electrochemically charged austenitic steels, judging on the decrease in the concentration of free electrons, see Table 5.1. A moderate improvement in hydrogen resistance due to carbon in austenitic steels was first discussed by Bernstein and Thompson (1976). Supplying its valence electrons to the states below Fermi level, carbon strengthens covalent interatomic bonds, which should prevent any tendency towards enhanced ductility. However, in contrast to nitrogen, carbon does not assist the localisation of plastic deformation. A possible reason for that is that carbon atoms themselves in pure iron are prone to clustering, whereas nitrogen atoms demonstrate short-range atomic ordering. Such a different behaviour was first demonstrated in bcc iron by Cheng et al. (1988) for Fe–C and Cheng and Mittemmeijer (1990) for Fe–N martensites. Moreover, in contrast to the generally accepted idea of carbonitrides in tempered Fe–C–N martensite, it was shown by Cheng et al. (1992) that the ε/η-carbide and the transition α -nitride are precipitated separately from carbon clusters and ordered nitrogen-rich areas appear during the low-temperature ageing of martensite. Later, a strikingly different atomic distribution in binary Fe–C and Fe–N martensites inherited from the high temperature austenitic phase was demonstrated using Mössbauer spectroscopy, see Gavriljuk et al. (2000b). As shown in Fig. 5.18a, carbon distribution in Fe–C martensite freshly formed due to quenching in liquid nitrogen, and even after ageing below 223 K, is characterized by the occurrence of single carbon atoms in the solid solution (component Fe1 from iron atoms with one C atom in the neighbouring interstitial site) and carbon pairs (component Fe2 from iron atoms with two C atoms as nearest neighbours), whereas component Fe0 represents iron atoms free of the carbon neighbourhood. In contrast, only components Fe0 and Fe1 are present in Fig. 5.18b, which confirms that nitrogen atoms do not occupy neighbouring sites in freshly formed Fe–N martensite. Instead, they form dumbbell-like atomic configurations around iron atoms. Such C and N atomic distribution occurs also in Fe–X–C and Fe–X–N solutiontreated alloys. Moreover, nitrogen assists short range atomic ordering in the atomic distribution of substitutional elements in multicomponent fcc iron-based solid solutions, see e.g. Gavriljuk (1996) and Gavriljuk et al. (2000a), whereas the clustering of carbon atoms does not remarkably change the distribution of substitutional metallic solutes. This difference in interatomic bonds and the consequent atomic distribution

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Fig. 5.18 Mössbauer spectra of freshly formed and aged martensites in alloys Fe-9at.%C (a) and Fe-9.3at.%N (b) subjected to preliminary quenching in liquid nitrogen. Shown are the outer lines of Zeeman’s sextets (nuclear transition − 1/2 → −3/2). Measurements were carried out at 80 K

of nitrogen- and carbon-containing solid solutions results in different dislocation structures formed under mechanical loading. Tangled dislocations and twinning are observed in the structure of cold worked C1.2Mn12 Hadfield steel characterized by the stacking fault energy of ~ 50 mJ/m2 , see Gavriljuk et al. (2008b). As a consequence, the hydrogen-caused degradation of mechanical properties is not significant in the 1.3C-12Mn Hadfield steel under the gaseous pressure of 40 MPa, see Michler et al. (2012a). The situation is different in carbon austenitic steels with higher Mn content. At its contents of up to 25 mass% in binary Fe–Mn alloys, stacking fault energy drops below 20 mJ/m2 , see Fig. 4.7b in Chap. 4. Added to such steels, carbon increases SFE, as is the case with carbon steel containing 13%Mn, see Fig. 5.12. Simultaneously, Mn-enhanced twinning progressively occurs with a further increase in Mn content, and this is the reason for catastrophic reduction in resistance to HE, as demonstrated for the TWIP steel C0.6Mn23 by Michler et al. (2012a). Carbon + nitrogen combination in austenitic steels causes the highest increase in the concentration of free electrons, see Table 5.1, which leads to a more uniform spatial distribution of free electrons in the crystal lattice, see Fig. 5.19.

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Fig. 5.19 Projection of the spatial distribution of valence electron density on the (100) plane in the atomic ensemble Fe20 Mn8 Cr4 corresponding to austenitic steel Mn25Cr12.5 in at.%, doped with C, N or C + N. The electron density in the interatomic area increases in the sequence of a Fe20 Mn8 Cr4 C2 → b Fe20 Mn8 Cr4 N2 → c Fe20 Mn8 Cr4 C1 N1 . Plane (100) is chosen in order to demonstrate how alloying with C + N increases electron density even in the vicinity of carbon atoms (compare Figures a and c)

In turn, a correlation exists between the distribution of nitrogen and carbon atoms over interstitial sites, the enhanced atomic ordering in the (C + N) substitution solid solution and the increased thermodynamic stability of the austenitic phase in these steels, see Gavriljuk and Berns (1999) and Shanina et al. (2002, 2007). The quoted studies formed the basis for the development of high interstitial stainless austenitic steels characterized by a combination of high strength and fracture toughness, see Gavriljuk et al. (1999) and Berns et al. (2013). However, because of enhanced short-range atomic ordering, C + N austenitic steels demonstrate pronounced planar slip of dislocations during plastic deformation, see Gavriljuk et al. (2008b). Therefore, the extremely high concentration of free electrons in these steels combined with the strongly pronounced localisation of plastic deformation does not leave any chance for resistance to HE. This tendency is confirmed in the studies performed by Martin et al. (2011c) on steel Cr18Mn19C0.32N0.63 subjected to gaseous hydrogen charging under the pressure of 40 MPa, where hydrogen decreased the relative elongation from 67 to 21% and the relative reduction in the area from 63 to 13%.

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Aluminium Success in the design of a hydrogen-resistant austenitic steel was achieved by Martin et al. (2013) who used aluminium for alloying a low-nickel steel. In their alloying concept, the authors tried to strike a balance between low cost and a fully stable austenitic structure, moderate corrosion resistance and the formation of an appropriate dislocation substructure where the increase in stacking fault energy was claimed as a core requirement. In comparison with available CrNi steels of the AISI 304 and 316 type, Ni content was kept at its minimum possible level of 8%, whereas the content of Cr was reduced to 13% in combination with the addition of 10% of Mn to compensate the ferritestabilizing effect of Cr and Al. Giving priority to an increase in stacking fault energy, alloying with ~ 2.5% of Al was a novelty in the chemical composition of leanalloyed CrNi steel. Mechanical tests at − 50 °C under hydrogen pressure of 40 MPa demonstrated its excellent resistance to environmental hydrogen embrittlement. Some comments can be made on the interpretation of the obtained results and the substantiation of the chosen chemical composition. First, based on the data of low hydrogen solubility in Al-based alloys obtained by Louthan and Gaskey (1976), it is expected that adding Al to Fe-based alloys can decrease hydrogen permeation. Therefore, measurements of hydrogen content in the studied steel could be desirable. Second, claiming that aluminum assists the highest stacking fault energy in austenitic steels, the authors referred to Dumay et al. (2008) and Ronevich et al. (2012). However, the former authors merely predicted the SFE value of 45 mJ/m2 in the Mn22C0.6 steel alloyed with 4% of Al, which does not seem to be a high value for SFE. The latter authors studied only the hydrogen effect on the delayed fracture of electrochemically charged steel Mn18C0.6 doped with 1.5%Al without analysing SFE. According to calculations performed by Ogata et al. (2002), the SFE in pure aluminum constitutes ~ 158 mJ/m2 , whereas SFE of 135 mJ/m2 was measured by by Charnock and Nutting (1967). For comparison, Carter and Holmes (1977) obtained ~ 120–130 mJ/m2 for pure nickel using the weak electron beam technique, whereas Howie and Swann (1961) obtained the value of 150 mJ/m2 using the measurements of dislocation nodes radius. Therefore, statements about the highest SFE in aluminium need more precise substantiation. Direct measurements of SFE in the Al bearing austenitic steels would be desirable. Third, it would be also interesting to clarify the role of aluminium in the shortrange atomic order of austenitic steels to explain the reason for the absence of localised plastic deformation in Al-alloyed austenitic steel. Short-range atomic order in Fe–Al solid solutions has been studied in detail a long time ago and summarised in a number of monographs, see e.g. Iveronova and Kaznelson (1977). It was shown, see also Houska and Averbach (1962), that Fe and Al atoms prefer to be the nearest neighbours in solid solutions, creating short-range atomic ordering and even local areas of superstructures. Particularly interesting is the so-called K-state, i.e. submicroscopic non-homogeneous areas of local long range atomic order with increased Al concentration first detected in the Fe–Al solid solution having nothing but 4 at.% Al.

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Therefore, it would be promising to explore factors that would make it possible to avoid localised plastic deformation, as has been done by alloying low-nickel austenitic steel with aluminium despite the expected enhanced short range atomic ordering. Nickel. Intriguing is the strong negative Ni effect on the ductility of austenitic steels subjected to electrochemical hydrogen charging, see Table 5.2, because in the case of high-pressure gaseous hydrogenation Ni significantly improves their hydrogen resistance (see, e.g., Michler and Naumann 2008; Michler et al. 2012a). It is appropriate in this relation to compare the results presented in Table 5.2 with those in the diagram of the Ni effect on the hydrogen degradation of CrNi austenitic steels and nickel superalloys subjected to gaseous hydrogenation, as presented by Gaskey (1985), Fig. 5.20a, and corrected by Lee (2012), Fig. 5.20b. According to both diagrams, the retained ductility of CrNi steels in tension tests under gaseous hydrogen pressure of 69 MPa sharply increases up to 100% if the Ni content exceeds 10 mass%, which is obviously due to the stabilisation of the fcc austenitic structure. As inserted in Fig. 5.20a, the data from Table 5.2 on the retained ductility of CrNi steels subjected to electrochemical charging demonstrate its permanent decrease with increasing Ni contents. It is evident that this striking decrease in ductility is caused by plastic deformation accompanying electrochemical charging, which decreases the resource of plasticity during subsequent mechanical tests, see Sects. 3.3 and 3.4 in Chap. 3 and Sect. 4.1.2 in Chap. 4. Because of their low yield strength, high-nickel austenitic steels are easily subjected to plastic deformation at rather small applied stresses. At the same time, it is relevant to note that the ductility data presented in Fig. 5.20 refer to CrNi austenitic steels subjected to solution treatment at high temperatures and rapidly cooled down to ambient temperatures. For this reason, atomic distribution in solid solutions should be tentatively uniform. However, any sensibilisation treatment before hydrogen charging is expected to cause the precipitation of intermediate phases and the short-range atomic order, causing decreased hydrogen resistance. These features of CrNi Fe-based and Ni-based alloys will be analysed in the next Section. Based on the presented experimental data, one can conclude that hydrogen resistance of austenitic steels is significantly affected by their chemical compositions. The coresponding change in the electron structure controls properties of dislocations in the hydrogenated steels and localization of plastic deformation. The latter is determined by the atomic interactions in the multicomponent solid solutions and is essentially independent of hydrogen.

5.2.2 Nickel-Based Superalloys The term “superalloys” covers heat-resistant metallic materials. Among their three main classes, namely Ni-based, Co-based and Fe-based, the first possesses the highest strength at temperatures up to 1050 °C, occasionally 1200 °C, in combination with

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Fig. 5.20 a Effect of nickel content on the retained ductility of austenitic CrNi alloys under the gaseous hydrogen pressure of 69 MPa, according to Gaskey (1985), black circles, and after cathodic charging from Table 5.2, open circles; b Gaskey’s diagram corrected by Lee (2012), Elsevier

good toughness and resistance to oxidation and corrosion, see e.g. Schafrik and Sprague (2004). The Ni–Cr–Fe system forms the basis of their design. The strengthening of the fcc γ matrix is achieved due to ageing at elevated temperatures up to ~ 800 °C. It is linked to two kinds of precipitated phases. Alloying with aluminium and titanium results in the precipitation of spherically shaped γ intermetallic compounds Ni3 Al and Ni3 Ti having the fcc L12 crystal structure coherent with the matrix phase. Alloying with niobium in the presence of iron forms the discshaped bct DO22 Ni3 Nb γ phase which is also coherent, but causes giant coherent

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stresses of about 2.9% at the interface with the γ phase. Prolonged holding at intermediate temperatures leads to the transformation of the γ phase into the plate-shaped semicoherent δ phase which is an orthorhombic DOa structure with Ni3 Nb stoichiometry, see Sundararaman et al. (1988) and Galliano et al. (2014) for detail. The δ phase is used for stabilising grain size and improving high-temperature properties. In the course of their growth, δ precipitates form an intersecting network, see Sundararaman et al. (2010). Other phases, particularly fcc carbonitrides (Nb, Ti)CN, are usually present in the microstructure. At Ni contents above 30%, the hydrogen resistance of Ni-based alloys decreases. A single point at ~ 55% of Ni in Gaskey’s diagram, Fig. 5.20a, reflects the results of mechanical tests on superalloys Inconel 700, Inconel 718, Hastelloy X, Waspalloy etc., as collected earlier by Louthan and Gaskey (1976). Data for the Ni superalloys added in Fig. 21b by Lee to Gaskey’s diagram have been obtained on Incoloy 800, 801, 802, 825, Inconel 600, 706, 825, X750 and Carpenter 20-Cb3. Similar data on the degradation of mechanical properties in Ni-based gaseous hydrogen-charged Ni superalloys were obtained in the case of electrochemical hydrogen charging by Mummert et al. (1996) who studied hydrogen embrittlement, HE, and stress corrosion cracking, SCC, in the Incoloy and Inconel-type alloys. These authors showed that, with Ni content increasing from 33 to 73%, hydrogen embrittlement rises, whereas stress corrosion cracking is reduced. Based on the idea of HE as a bulk phenomenon and SCC as a surface one, they interpreted the obtained results in terms of the Ni-enhanced diffusion of hydrogen atoms, which decreases hydrogen content within the surface layer and increases it in the bulk. The available studies of the effect of precipitated phases on hydrogen embrittlement were mainly performed using electrochemical hydrogen charging, which should cause pre-damage before subsequent mechanical tests because of the plastic deformation initiated by a sharp gradient of hydrogen concentration, see Figs. 3.33 and 3.34 in Chap. 3 and Fig. 4.11 in Chap. 4. Lu et al. (2019) detected the slip lines and cracks caused by electrochemical charging of the superalloy 718. This superalloy is widely used for structural components in the aerospace and nuclear industries and in other high-temperature applications. Except for carbonitrides, all the phases are completely dissolved at 1050 °C, as shown by Rezende et al. (2015). In the course of subsequent cooling, precipitation of γ and γ phases occurs at temperatures from 900 °C down to 600 °C, which causes hydrogen embrittlement. The occurrence of γ , γ and δ phases retards hydrogen diffusion and permeation. The hydrogen embrittlement of alloy 718 is found to occur with both transgranular and intragranular cracking, depending on the heat treatment and, consequently, the microstructure, see e.g. Galliano et al. (2014) and Lu et al. (2020). After hightemperature solution and recrystallisation treatment at 1080 °C, the primary carbides NbC and nitrocarbides (Nb, Ti)CN are preferentially located at the grain boundaries, which leads to the predominant intergranular brittle fracture. Typical heat treatment including ageing at ~ 700 °C followed by slow cooling with intermediate holding for the precipitation of γ /γ phases at ~ 600 °C results in both intergranular and

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transgranular cleavage fracture. The same kinds of fracture featuring clear precipitate/matrix decohesion were observed due to platelets of the δ phase obtained during holding at 960 °C for 48 h and located at grain boundaries as well as in the grain interior. Free of Al, enriched in Mo and having decreased Fe and Nb contents, alloy 725 is embrittled by hydrogen predominantly through intergranular fracture and reveals lower HE resistance in comparison with alloy 718 (Lu et al. 2020). The mechanisms of embrittlement are shown to be related to hydrogen-dislocation interaction regardless of variation in chemical composition. For example, the decisive role of the strain rate in HE was shown by Fournier et al. (1999) for alloy 718 and by Lecoester et al. (1999) for alloy 600, the latter being less alloyed with Ti and Al and containing more carbon. Hydrogen transport by moving dislocations controls the brittleness of both alloys. It is the highest at strain rates allowing hydrogen atoms to follow dislocations during tensile tests and disappears if the strain rate is sufficient for breaking moving dislocations away from hydrogen atmospheres. As shown above, see Sect. 5.1.8.2, such a response to the change in strain rate is quite consistent with the HELP phenomenon. The occurrence of the hydrogendislocation mechanism is supported by TEM observations of planar slip bands along the (111) atomic planes, the evidence of nanoscale voids nucleated at slip bands, particularly at the intersection of non-parallel slip bands, and crack propagation along slip bands, see Zhang et al. (2016). The hydrogen-induced superabundant vacancies in the hydrogen atmospheres accompanying dislocations are clearly responsible for the formation of nanovoids and their coalescence promoting crack propagation along slip bands. These observations were confirmed by Tarzimoghadam et al. (2017) who used in situ hydrogen charging during mechanical tests. Transgranular cracking occurred in solution-treated as well as aged states, whereas the occurrence of intergranular cracking was promoted by the δ phase alone. Michler et al. (2014) studied the mechanical properties of high Ni solution-treated superalloys including Incoloy DS, Incoloy 925, Inconel 600 and Chromel A, at ambient temperature under the hydrogen pressure of 1 MPa. No remarkable degradation of plasticity was obtained in all them, except for the severe embrittlement of Chromel A where planar dislocation slip was detected and, according to Miyata (2003), short-range atomic ordering should occur during ageing resulting in the superstructure Ni2 Cr. It is also worth noting that the 2.3% of silicon in Incoloy DS did not impair its resistance to hydrogen embrittlement. Of course, the hydrogen pressure of 1 MPa is far below that in the Gaskey diagram. At the same time, more important for discussing this positive Ni effect is the comparison of solution-treated superalloys subjected to thermal treatment for the precipitation of hardening phases. Their practical application occurs even at higher temperatures, where a short-range atomic order occurs along with the precipitation process. In their thermally treated state, all the Ni superalloys are prone to embrittlement under high gaseous hydrogen pressure, see e.g. Louthan and Caskey (1976), Lecoester et al. (1999), Rezende et al. (2015), Zhang et al. (2016), Balitskii and Ivaskevich (2019), Lu et al. (2020) etc.

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Atomic distribution in the Fe–Cr–Ni system is generally characterized by a tendency to short-range decomposition. As shown in Sect. 4.1.4, Chap. 4, the Fe–Fe and Ni–Ni nearest neighborhoods prevail in the fcc Fe–Ni system, see Table 4.2. Because of their higher bonding energy with iron atoms, hydrogen atoms in the Fe– Ni solid solution prefer to occupy interstitial sites in regions rich with Fe, see Table 4.3. It is also relevant to mention that both components of SRO, ordering and decomposition, are found in binary Fe–Cr alloys, see Philipova et al. (2000) and Shabashov et al. (2001). Short-range atomic ordering occurs at Cr concentrations of up to 10 at.%, whereas short-range decomposition is observed within the Cr concentration range of 10.8–48.1 at.%. Therefore, one can suppose that, at its contents close to 18% and more, chromium assists short-range decomposition in Ni–Cr–Fe superalloys. Similar concentration fluctuations were found in Fe–Cr–Ni solid solutions after their irradiation within the temperature range of 450–700 °C. Periodic alternation of regions enriched in Ni and those rich with Fe and Cr atoms with their spatial extent of ~ 600 nm was observed by Garner and McCarthy (1989) in the Fe-35Ni-7.0Cr alloy after its irradiation by 5 meV Ni+ ions at 625 °C. The same results were obtained by Rotman (1990) who studied the Fe-45Ni-16.0Cr alloy after its 1 meV electron irradiation at 500 °C. It is important that the role of irradiation amounts merely to an increase in the concentration of vacancies, which accelerates the diffusion of metallic atoms in agreement with the experimental data presented in Sect. 3.5 of Chap. 3. The inherent thermodynamic nature of this process has been proven by Wiedenmann et al. (1989) in their measurements of small-angle neutron scattering in the Fe-34 at.% Ni alloy within the temperature range of 625–725 °C. The authors detected oscillating fluctuations of Ni concentration between 28.5 and 36.5 at.% of Ni. The spatial extent of these fluctuations exceeded 200 nm. The heat treatment of nickel superalloys occurs just within the temperature range of their short-range atomic decomposition. Therefore, its role in hydrogen embrittlement should be taken into account along with that of carbonitride precipitates.

5.2.3 Ti Alloys Commercially pure titanium. Hydrogen effect on the stress–strain behaviour of titanium at H concentrations of 20–1070 wt ppm was studied by Lentz et al. (1983) using multiaxial loading. The authors observed hydrogen-decreased yield strength without strain hardening at strains ε ≥ 0.02. The conclusion was made that hydrogen embrittlement is not related to any features of plastic flow behaviour and, possibly, the operating mechanism reveals itself in the fracture process. Taking into account the findings of previous studies about good resistance to hydrogen embrittlement of fine-grained titanium and its decrease at low temperatures, high strain rates, large grain size and the occurrence of a notch, Gerhard and Koss

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(1985) studied the combined effect of grain size and stress state. They found that, in contrast to uniaxial tension tests, the hydrogen-caused loss of ductility under equibiaxial tension increases with increasing grain size. These data were interpreted in terms of the nucleation of voids enhanced by hydride fracture and their eased coalescence due to large grain size/biaxial stresses. It was also noted that, through the creation of paths for void link-up, void coalescence should be enhanced in coarse grains by the large and interconnected plate-like Ti hydrides. Hydrogen effect on the mechanical properties of titanium at higher H concentrations was studied by Briant et al. (2002). Significant immunity to hydrogen-induced cracking was observed in the tests performed in sodium chloride solutions. Even a thick hydride layer formed on the surface of tensile samples did not significantly affect their elongation to failure. Quite different was the effect of gaseous hydrogen charging where hydrides were nucleated throughout the material and, as a result, the relative elongation decreased from 40% in samples containing 32 H wt ppm down to several per cent due to hydrogen content of 3490 wt ppm. Alpha titanium is presumed to be embrittled by gaseous hydrogen via two mechanisms: the brittle fracture of stress-induced titanium hydride or hydrogen-enhanced plastic deformation (Shih et al. 1988). Plate hydrides are nucleated under applied stress preferentially in the region of a crack. Their fraction increases due to the autocatalytic discrete nucleation of new plate precipitates followed by their growth and coalescence. The increase in the volume caused by hydride nucleation creates a self stress field, which promotes the growth of hydride precipitates even in the absence of applied stress if the hydrogen supply continues. Generally, all this process is controlled by a decrease in the free energy. According to Numakura and Koiwa (1984), the accommodation of volume increase can be elastic or plastic depending on the hydride habit plane, while the emitted dislocations slip on the same atomic plane. If stress intensity at the crack tip is low, fracture occurs due to the abovementioned sequence of hydride precipitation and cleavage. At high stress intensity and consequent high rate of crack propagation, the hydrogen supply is not sufficient for sequential hydride precipitation and, in this case, the HELP mechanism of hydrogen embrittlement is at work. Alpha + beta titanium alloys are characterized by their two substantially different microstructures. The first microstructure amounts to a basic α phase containing fine dispersed almost uniformly distributed β-inclusions, whereas a continuous β phase network on α phase grain boundaries is typical of the second microstructure. The latter was found more severely embrittled by gaseous hydrogen. This different mechanical behaviour was interpreted in the early studies on hydrogen transport rates in the two phases, see Williams et al. (1960), Williams and Nelson (1970) and Nelson et al. (1972). While studying hydrogen embrittlement of a Ti-6Al-4V alloy subjected to two different heat treatments to obtain the aforementioned microstructures, Nelson (1973) has shown that, with increasing hydrogen gas pressure, the competition between

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the intergranular cracking along the α/β boundaries and the transgranular cracking through the α grains changes its sign. A “short-circuit” H diffusion path occurs in the continuous β phase network, which allows hydrogen to penetrate deeply into the titanium lattice. For this reason, at decreased hydrogen pressures its concentration in the β phase near the crack tip surface is rather small, the hydrogen diffusion controlled by the H concentration gradient decreases and less hydrogen migrates into the microstructure. As a result, embrittlement along the α/β boundaries decreases. With increasing hydrogen pressure, the high H concentration gradient assists hydrogen penetration into the sample and, consequently, brittle fracture. The “short-circuit” H diffusion is absent in the case of a continuous α phase microstructure, and hydrogen directly interacts with the α phase, thereby forming a hydride on the α surface which does not depend on the hydrogen pressure for growth. Therefore, at high hydrogen pressures, the continuum α matrix containing a disperse β phase in the bulk is more resistant to hydrogen embrittlement. Beta titanium alloys are rather resistant to hydrogen embrittlement because hydrides are not formed easily, see brief reviews presented by Tal-Gutelmacher and Eliezer (2004, 2005). For example, the brittle fracture in the metastable β-titanium alloy Timetal 21S (Ti–15Mo–2.7Nb–3Al–0.25Si–0.15O in mass%) can occur at rather high hydrogen concentrations exceeding the H/M ratio of 0.21, see Teter et al. (2001) and Sect. 5.1.4 for detail. This alloy was previously investigated by Young and Scully (1993) in an aged state where the α-phase is precipitated preferentially at β grain boundaries after holding at 538 °C for 1 h, whereas its homogeneous distribution in the alloy is achieved due to holding time of up to 8 h. With increasing hydrogen content from 50 100 to 1900– 3600 wt. ppm, the fracture mode was observed to change from tearing along the α-β interfaces to transgranular tearing through the β-grains containing α-precipitates and the final intergranular fracture, in contrast to the fracture of a non-aged alloy through void nucleation, growth and coalescence. It is remarkable that this embrittlement occurred at hydrogen concentrations significantly lower than those required for hydride formation. Ductility was sharply decreased at some critical hydrogen content of 1400 to 1800 wt. ppm, and the ductile-to-brittle temperature was increased by hydrogen to above room temperature. Hydrogen in the metastable β-Ti alloys can affect mechanical properties quite differently. Two mechanisms of hydrogen-caused change in the mechanical behavior of commercially pure TIMET Ti-10V-2Fe-3Al alloy were found by Costa et al. (1987), see Fig. 5.21. Having been stabilized by rapid quenching in water after solution treatment at 1123 K, this alloy reveals a “strain plateau” in the non-monotonous H-concentration dependence of critical stress initiating plastic deformation. This plateau is caused by the triggering effect of stress-induced α  -martensite and competitive hydrogencaused stabilization of the β-phase, see Duerig et al. (1982) and Sect. 4.3 in Chap. 4. As hydrogen stabilizes the β phase, no martensitic transformation occurs with increasing hydrogen content, and the critical stress flattens. Obtaining α  -martensite

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Fig. 5.21 Critical stress for plastic deformation of the H-charged alloy Ti-10V-2Fe-3Al as a function of hydrogen concentration. Costa et al. (1987), Springer

at higher hydrogen concentrations requires plastic deformation, which results in the increase of critical stress. Indicative in this alloy is the hydrogen effect on the ultimate strength and strain up to the fracture measured in the tensile tests, see Fig. 5.22. Hydrogen in this experiment was introduced into specimens using Siverts gaseous hydrogenation in the course of high temperature solution treatment, which excluded plastic deformation and consequent hydrogen hardening usually occurring due to electrochemical charging. The permanent decrease in the ultimate strength with increasing hydrogen content, Fig. 5.22a, is accompanied by increased relative reduction in area up to some critical hydrogen concentration, Fig. 5.22b, which initiates formation of α -martensite thereby decreasing plasticity.

Fig. 5.22 Ultimate strength and relative reduction in area in the tension tests of the H-charged alloy Ti-10V-2Fe-3Al as a function of hydrogen concentration. Costa et al. (1987), Springer

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Fig. 5.23 Stress–strain curves of β-alloys Ti-10V-2Fe-3Al (a) and Ti-35V-15Cr (b). Christ et al. (2003), Springer

It is reasonable to link this hydrogen-induced softening with the hydrogenincreased density of electron states at the Fermi level, see Fig. 1.29 in Chap. 1, and a corresponding increase in the concentration of free electrons. Such interpretation is supported by comparing the mechanical behaviour of two β-titanium alloys: “the near β alloy” Ti-10V-2Fe-3Al and the “stable beta alloy C” Ti-35V-15Cr, as studied by Christ et al. (2003). A feature of the latter alloy is significantly lower hydrogen solubility and a propensity for hydride formation at hydrogen contents less than 10 at.%. Consequently, the tensile properties of these alloys are different, see Fig. 5.23. Christ et al. (2003) discussed their data in terms of “extrinsic” and “intrinsic” hydrogen effects, respectively. An intrinsic hydrogen effect in alloy C was interpreted based on the classic decohesion theory as a hydrogen-induced break of interatomic bonds leading to brittle fracture without any plastic deformation, see Sect. 5.1.4, although the increase in strength, see Fig. 5.23b, conflicts with the decohesion mechanism. Some change in microstructure due to α phase precipitates was stated to be responsible for the unusual extrinsic hydrogen effect in the “near beta alloy”, see Fig. 5.23a. In contrast, we are inclined to interpret the above experimental data as hydrogencaused weakening of interatomic bonds in the first alloy and hydride formation in the second alloy. The increased content of dissolved hydrogen in the alloy Ti-10V2Fe-3Al leads to a decrease in yield strength, disappearing cold work hardening and increased relative elongation. Such softening points to a decrease in the stress for start of dislocation sources and the enhanced mobility of dislocations, as is expected for the enhanced metallic character of interatomic bonds due to hydrogen-increased concentration of free electrons. As commented by the authors in relation to the mechanical behaviour of the alloy C Ti-35V-15Cr, the stress-induced hydride formation may contribute to its hydrogen embritlement. For example, Alvarez (1999) found hydrides in the needles of the α phase ahead of a crack in β-Ti alloys C. The low hydrogen solubility suggests that a stress-induced titanium hydride could be precipitated and the propensity for hydride formation suggests the prevailing covalent character of interatomic bonds.

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Impact tests are rather sensitive to the character of interatomic bonds, and the studies of the ductile-to-brittle transition, as performed by Christ et al. (2003), provided clear evidence for the opposite hydrogen effect on atomic interactions in these two alloys. In contrast to mechanical behaviour of alloy Ti-35V-15Cr, with increasing hydrogen content in the Ti-10V-2Fe-3Al alloy, the ductile-to-brittle-transition temperature, DTBT, decreases consistently with a decrease in yield strength and relative reduction in area measured in the tensile tests. This result is in conflict with the widespread statements about hydrogen-increased DBTT in metastable β-Ti alloys based on the tensile tests. For example, Hardwick and Ulmer (1996) studied the Ti-15Mo-3Nb-3Al-0.2Si, Timetal β 21S, subjected to gaseous H charging at temperatures of 482, 538 and 732 °C after preliminary ageing at 538 °C in vacuum. Acicular precipitates of the α-phase in the β-matrix were observed in the initial aged state. Hydrogen charging at elevated temperatures stabilized the β-phase, and the athermal ω phase was found to precipitate on cooling, although hydrogen suppressed the ω start temperature. No hydride precipitation was observed at ambient temperature. However, the needle-like hydride phase was detected after holding in liquid nitrogen. Tensile tests at ambient temperature revealed a decrease in yield strength and an increase in relative elongation with increasing hydrogen concentration, which was attributed to hydrogen-caused stabilization of the β phase. However, carrying out tensile tests at different temperatures, the authors observed that, with increasing hydrogen content, the temperature of brittle fracture increases from − 80 to 20 °C and denoted it as DBTT. Testing the same Timetal β 21S alloy, quite a similar result was obtained by Nelson (1996). It seems the essential difference between tensile and impact tests amounts to different times of stress relaxation by moving dislocations before the act of brittle fracture. For this reason, impact tests represent more accurately the role of atomic bonds in the fracture process and the corresponding hydrogen effect. Summary This chapter presents a detailed analysis of the available hypotheses on hydrogen embrittlement of metals, HE, which shows hydrogen-enhanced localised plasticity, HELP, to be predominantly responsible for this phenomenon. Among the available HE hypotheses, the most accepted is the HELP theory developed within the framework of continuum mechanics, according to which hydrogen shields stresses created by neighbouring dislocations, thereby increasing dislocation mobility. Recent attempts to describe hydrogen embrittlement as a product of synergy between HELP and hydrogen-enhanced decohesion, HEDE, as well as HELPmediated HEDE, are critically reviewed and characterized as not sufficiently substantiated. Notwithstanding its successful interpretation of many experimental data, the HELP theory’s main omission is that it represents hydrogen merely as a point defect causing distortions in the crystal lattice and ignores its nature as a chemical element. This flaw in the HELP theory is confirmed by comparative experiments

5.2 Hydrogen Embrittlement of Fe-, Ni- and Ti-Based Alloys

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on nitrogen and carbon, which are compatible with their induced distortions in fcc iron-based alloys, but produce opposite effects on the electron structure and eliminated by the electron concept of the HELP phenomenon based on ab initio calculations of hydrogen effect on the electron structure, namely the density of electron states at the Fermi level in iron, nickel and titanium, and experimental data on the hydrogen-increased concentration of free electrons. Localization of plastic deformation is shown to be not an inherent part of the HELP phenomenon, but a phenomenon inherent in the hydrogen-free metallic solid solutions. The role of hydrogen merely amounts to its enhancement because of the non-homogenous distribution of hydrogen atoms and consequent local decrease in the start stress of dislocation sources and the increase in dislocation emission rate and dislocation velocity. Available experimental data are analysed concerning the hydrogen effect on the mechanical properties of iron-, nickel- and titanium-based alloys, which confirm a correlation between hydrogen embrittlement and the a priori existing short-range ordering or decomposition of solid solutions.

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Weber S, Martin M, Theisen W (2011) Lean-alloyed austenitic stainless steels with high resistance against hydrogen environment embrittlement. Mat Sci Eng A 528(25–26):7688–7695. https:// doi.org/10.1016/j.msea.2011.06.049 Wen M, Xu X-J, Fukuyama S, Yokogawa K (2001) Embedded-atom-method functions for the bodycentered-cubic iron and hydrogen. J Mater Res 16(12):3496–3502. https://doi.org/10.1557/jmr. 2001.0480 West AJ, Louthan MR (1982) Hydrogen effects on the tensile properties of 21-6-9 stainless steel. Metall Trans A 13(11):2049–2058. https://doi.org/10.1007/bf02645950 Wiedenmann A, Wagner W, Wollenberger H (1989) Thermal decomposition of Fe-34at.% Ni between 625°C and 725°C. Scripta Metall 23(4):603–605. https://doi.org/10.1016/0036-974 8(89)90459-6 Williams DN, Schwartzberg FR, Jaffee RI (1960) Trans ASM 52:183–190 Williams DP, Nelson HC (1970) Embrittlement of 4130 steel by low-pressure gaseoud hydrogen. Metal Trans 1(1):63–68. https://doi.org/10.1007/BF02819243 Wilsdorf HGF (1982) The role of glide and twinning in the final separation of ruptured gold crystals. Acta Metall 30(6):1247–1258. https://doi.org/10.1016/0001-6160(82)90021-9 Wu R, Freeman AJ, Olson GB (1993) Effects of P and B adsorbates on the Fe(111) surface. Phys Rev B 47(11):6855–6858. https://doi.org/10.1103/physrevb.47.6855 Wu R, Freeman AJ, Olson GB (1996) Effects of carbon on Fe-grain-boundary cohesion: firstprinciples determination. Phys Rev B 53(11):7504–7509. https://doi.org/10.1103/physrevb.53. 7504 Yokobori AT, Chinda Y, Nemoto T, Satoh K, Yamada T (2002) The characteristics of hydrogen diffusion and concentration around a crack tip concerned with hydrogen embrittlement. Corros Sci 44(3):407–424. https://doi.org/10.1016/s0010-938x(01)00095-6 Yuasa M, Hakamada M, Chino Y, Mabuchi M (2015) First-principles study of hydrogen-induced embrittlement in Fe grain boundary with Cr segregation. ISIJ Intern 55(5):1131–1134. https:// doi.org/10.2355/isijinternational.55.1131 Zapfe C (1947) Discussion of metal arc welding of sttels by S.A. Herres. Trans ASM 39:191–192 Zhang Z, Obasi G, Morana R, Preuss M (2016) Hydrogen assisted crack initiation and propagation in a nickel-based superalloy. Acta Materi 113:272–283. https://doi.org/10.1016/j.actamat.2016. 05.003 Zhong L, Wu R, Freeman AJ, Olson GB (2000) Charge transfer mechanism of hydrogen-induced intergranular embrittlement of iron. Phys Rev B 62(21):13938–13941. https://doi.org/10.1103/ physrevb.62.13938 Zmudzinski C, Bretin L, Toitot M (1977) Hydrogen in metals (Paris), vol 3, paper 6A-2, Pergamon Press, New York

Chapter 6

Hydrogen as Alloying Element

As mentioned in Sect. 1.5, Chap. 1, hydrogen in iron, nickel, titanium increases the density of electron states at the Fermi level and, consequently, the concentration of free electrons, thereby enhancing the metallic component of interatomic bonds. The latter was confirmed by the measurements free electron concentration performed in hydrogen-charged austenitic steels, see Fig. 1.25 in Chap. 1. The hydrogen-caused softening of interatomic bonds decreases the specific energy, i.e. line tension, of dislocations, see Sect. 2.2 in Chap. 2, which increases their mobility and should result in the increased ductility of hydrogen-charged metals. As follows from Sect. 2.3 in Chap. 2, a similar effect is expected for the hydrogen-enhanced mobility of grain boundaries during recrystalization treatment. However, realization of this favourable hydrogen effect in practice is prevented by localized plastic deformation which is the inherent property of most metallic alloys and is further enhanced by hydrogen. Described below are some positive hydrogen effects in titanium and iron-based alloys which are interpreted as being caused by increased free electron concentration and the consequent metallic character of interatomic bonds.

6.1 Temporary Alloying of Titanium Alloys with Hydrogen for Improving their Technological Plasticity Titanium alloys are suitable material for temporary alloying with hydrogen thanks to the absence of visible signs of localized plastic deformation. Nevertheless, their hydrogen embrittlement was detected already during the first attempts at practical usage and different measures were undertaken to minimize hydrogen content, e.g. vacuum melting, vacuum annealing etc.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. G. Gavriljuk et al., Hydrogen in Engineering Metallic Materials, https://doi.org/10.1007/978-3-030-98550-9_6

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High-temperature hydrogen plasticizing. Among the scientists researching ways to avoid hydrogen-caused brittleness in titanium alloys, Zwicker and Schleicher (1959) were the first to discover, by chance, that hydrogen improves the hot deformability of cast titanium alloys when introduced in the ingot, not in the semi-finished product. For example, a Ti-8%Al ingot containing 0.061% H has been successfully deformed at 950 °C using 65% of single deformation, whereas a hydrogen-free billet was completely destroyed by this deformation. After that, there were no publications on this topic for quite a long time. Perhaps one of the first published studies belongs to Kolachev et al. (1972) who deformed Ti–Al alloys hydrogen-charged using hot compression after melting. At hydrogen content of 0.1%, the critical deformation not leading to cracking was equal to 25 and 38% at temperatures 950 and 1000 °C, respectively. Moreover, this excellent deformability was accompanied by a significant decrease in the stress needed for deformation. For example, in comparison with the hydrogen-free ingot, the stress needed for 25% deformation at 950 °C decreased from 30 kg/mm2 down to 6 kg/mm2 . A further increase of deformation temperature up to 1100 °C led to superplastic mechanical behaviour. The critical hydrogen content above which brittleness started to appear again was indentified as ~ 0.2%. To avoid many harmful hydrogen effects in titanium products for industrial use, hydrogen should be finally removed by means of vacuum annealing. The authors denoted this favourable effect as “hydrogen plasticizing”. Four possible mechanisms were proposed for its realisation in Ti–Al alloys (Lyvanov et al. 1977; Kolachev and Nosov 1984). First, hydrogen stabilises the soft bcc β phase at lower temperatures. Second, it suppresses precipitation of the brittle intermetallic α2 -phase Ti3 Al. Third, the enhanced diffusion of substitutional and host metallic atoms in the β phase in comparison with that in the α phase is supposed to contribute to increased plasticity. Fourth, new systems of dislocation slip are supposed to be realised due to hydrogen. Thus, despite the initially obtained results demonstrating a clear hint to the enhanced metallic character of interatomic bonds, the hydrogen-caused plasticizing of titanium alloys during hot deformation was interpreted as the intensification of previously known technological processes like isothermal deformation or superplasticity related to a change in the phase composition and correlated with phase equilibrium diagrams. Two hydrogen effects were particularly underlined: a reduction in the temperature for the appearance of superplasticity and an increase in the strain rate. The optimum superplastic state was reached at critical temperature T0 , where the α and β phases have the same strength. At temperatures below T0 , plastic deformation is controlled by the α-Ti phase, whereas properties of the β-Ti phase become dominant above T0 . At the same time, high-temperature hydrogen plasticizing was found to be definitely different from superplasticity. Namely, the strain rates for superplasticity are one or two orders of magnitude slower in comparison with hydrogen plasticizing. Beside this, hydrogen plasticizing occurs at temperatures by 100–150 °C lower than superplasticity.

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Successful industrial use of high-temperature hydrogen plasticizing was illustrated by the hot upsetting of titanium bolts produced from alloy VT-16 (Ti-2.7Al4.73Mo-4.2V) at a temperature reduced from 850 down to 600 °C, see Kolachev et al. (1991b). A similar result was obtained by Anisimova et al. (1992) who obtained a reduction in the temperature of the hot upsetting of alloy VT6 (Ti-6Al-4V) from 950 down to 750 °C with unchanged applied stress. The latter authors also demonstrated a significant hydrogen-caused decrease in the yield strength, namely from 30 kg/mm2 down to 6 kg/mm2 . Necessary conditions for high-temperature hydrogen plasticizing were analyzed by Belova et al. (1987) using the α-alloy VT5-1 (Ti-5.4Al-2.6Sn). The authors attributed the increase in the plasticity of this alloy at temperatures above 400 °C to the β phase appearing in its structure and found a decrease in the temperature of hot deformation by more than 100 °C due to 0.3–0.4 %H with the deforming force unchanged. It was also shown that, at temperatures approaching RT, hydrogen strengthens this alloy and decreases plasticity because of the increased fraction of the α phase and the appearance of hydrides. The high-temperature plasticity and strength of the pseudo-alpha alloy VT20 (Ti6Al-2Zr-1.5V-1Mo) doped with hydrogen within its concentrations of up to 1.07 wt.% was studied by Ponyatowsky et al. (1989) at temperatures up to 740 °C. Using differential thermal analysis, the authors detected a hydrogen-caused decrease in the temperature of β → α + β transition and observed a difference in the hydrogen effect on plasticity depending on its concentration. Alloying with hydrogen below 0.15 wt.% decreased plasticity, whereas hydrogenation with more than 0.3 wt.% led to its increase already at temperatures above 400 °C. In this temperature range, the hydrogen concentration dependence of the yield strength revealed a minimum at ~ 0.6 wt.%H slightly shifting to lower hydrogen contents with the increasing temperature of mechanical tests. The hydrogen-caused decrease in the yield strength of the α phase was attributed to a decrease of its shear modulus, which should increase dislocation mobility and induce softening, see Senkov et al. (1996b). The hydrogen-induced softening of α + β alloys was attributed to the increased fraction of the softer β phase, whereas their strain-induced softening was interpreted in terms of the lamellar structure transforming into a globular one, see Senkov and Jonas (1996). According to Nosov and Kolachev (1986) and Kolachev (1993), high-temperature hydrogen plasticizing mostly appears in pseudo α-Ti alloys with a high Al content, Fig. 6.1. To a lesser degree, it occurs in α + β alloys, see Fig. 6.2, and was practically not found in β-Ti alloys, where a soft bcc structure is already achieved due to alloying with β-modificators. Along with this, the hydrogen-enhanced diffusion of metallic atoms in the bcc β phase due to hydrogen-induced superabundant vacancies should be taken into account, see Sect. 2.1 in Chap. 2. These vacancies can be also responsible for the hydrogen-enhanced adhesion found in experiments on the comparative annealing of titanium alloy samples in vacuum and in the hydrogen atmosphere. These findings were proposed for the improvement of welding technologies, as well as for compacting powder materials, see Kolachev et al. (1993).

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Fig. 6.1 Yield strength and relative elongation of a high aluminum Ti alloy CT5 doped with hydrogen in mass%. Redrawn from Kolachev (1993), Springer

Fig. 6.2 Hydrogen effect, in mass%, on the yield strength of alloy VT-6 (Ti-6Al-4V). Redrawn from Kolachev (1993), Springer

A number of experimental data on high-temperature hydrogen plasticizing were reviewed in detail by Froes et al. (2003, 2004), see e.g. Senkov and Jonas (1996), Senkov et al. (1996a, b), Senkov and Froes (1999), Eliezer et al. (2000) etc. The corresponding technology is denoted as thermohydrogen processing, THP, and its nature is interpreted mainly as a result of hydrogen-caused α phase softening due to a decrease in its shear modulus, which reduces the internal strain field and

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Fig. 6.3 Hydrogen effect on yield strength σ0.2 and critical upsetting deformation degree εcr of quenched alloy VT30 at RT before the appearance of the first crack. Redrawn from Kolachev (1993), Springer

increases dislocation mobility. To substantiate the last two statements, the authors referred to studies carried out by Birnbaum and his colleagues, namely by Birnbaum and Sofronis (1994) on austenitic steels, Ni, Al etc., and by Teter et al. (2001) on a βTi alloy. It is worth noting that, as mentioned in Sect. 5.1.8, Chap. 5, the above authors attributed hydrogen-caused softening only to the shielding of repulsive interactions between dislocations. Finally, based on the ab initio calculated hydrogen effect on the electron structure of titanium, see Chap. 1, and the experimental data on hydrogen-increased dislocation mobility presented in Chap. 2, it seems natural to characterise the high-temperature hydrogen plasticizing in terms of an increase in the concentration of free electrons in both α and β phases and a consequent increase in dislocation mobility. Low-temperature hydrogen plasticizing. Kolachev et al. (1974) were also the first to discover that a favourable hydrogen effect on the plasticity of β-alloy VT15 (Ti11Cr-7Mo) and transition alloy VT30 (Ti-11Mo-6Zr-4.5Sn) occurs even at ambient temperatures, see Fig. 6.3. At hydrogen content higher than 1 mass%, cylindric samples of 10 mm in diameter and 15 mm in length were deformed close to 100% during upsetting tests. Later, Nosov et al. (1995, 2008) demonstrated the high deformability at ambient temperature of β-alloys VT22 (Ti-5Al-5Mo-1Cr-1Fe), VT22I (Ti-3Al-5Mo-1Cr1Fe) and alloy Ti-10V-2Fe-3Al, see Fig. 6.4. The increased allowable deformation degree was attributed to hydrogen-caused mechanical stability of β phase with respect to β → α transformation. These results demonstrated the difference between high-temperature and lowtemperature hydrogen plasticizing. The former occurs at temperatures of 500– 1100 °C depending on the phase composition. It is manifested in the decreased flow stress of metals and increased maximum allowable degree of deformation. The latter occurs at ambient temperature or close to that and is manifested in the increased degree of deformation, whereas the flow stress may increase because of cold work hardening. At the same time, hydrogen decreases its intensity, see Fig. 6.5.

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Fig. 6.4 Hydrogen effect on the ultimate plasticity of alloys VT 221 (1) and Ti-10V-2Fe-3Al (2) during cold deformation. Redrawn from Nosov et al. (2008), Springer

Fig. 6.5 Specific force q of deformation by upsetting as function of strain ϕ = ln(H0 /Hi ) for alloys Ti-10V-2Fe-3Al (a) and VT221 (b). Hydrogen content in wt.% is presented at the curves. Redrawn from Nosov et al. (2008), Springer

The strengthening of β-Ti phase by hydrogen is claimed by Froes et al. (2004) based on the data of hydrogen-increased shear modulus obtained in the measurements performed at 960 °C. The authors supposed the hydrogen-caused transformation induced plasticity, TRIP, to be responsible for such a huge plastic deformation of β-Ti alloys at ambient temperatures. However, this interpretation is at variance with the available experimental data. For example, Ilyin et al. (1995a) observed hydrogen-facilitated β → α transformation accompanied by the shape memory effect in commercial alloy VT23 (Ti-6Al4.6V-1.7Mo-1.2Cr-0.7Fe), whereas Li et al. (2019) studied stress-induced martensitic transformation in the Ti-50.8Ni shape memory alloy. The recovered strain in alloy VT23 did not exceed 3%, and the total strain of the Ti-Ni alloy including the TRIP effect amounted only to ~ 3%.

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Therefore, it is extremely doubtful that a huge hydrogen-induced plasticity at RT can be related with the TRIP effect. The hydrogen-assisted slip of dislocations, their more intensive multiplication and activation of additional slip systems were mentioned as a reason for low-temperature hydrogen plasticizing already at the early stage of its studies, see e.g. Kolachev et al. (1974). It is remarkable that all the listed phenomena are consistent with hydrogen effect on the electron structure and properties of dislocations, as described in Chaps. 1 and 2.

6.2 Hydrogen-Induced Grain Refinement This Section describes the use of hydrogen-induced phase instability in metastable Fe- and Ti-based alloys for grain refinement and corresponding improvement of mechanical properties.

6.2.1 Austenitic Steels Phase transformations in metastable austenitic steels were used for recrystallization regardless of their hydrogenation. For example, Tomimura et al. (1991) obtained an ultrafine-grained structure in metastable Fe–Cr–Ni fcc alloys through the reversion of strain-induced martensite by annealing at 873 K. Three main compositional conditions were recommended for this purpose. First, up to 90% of metastable austenite should be transformed into α -martensite, which can be achieved, e.g., in steel having the Ni equivalent of less than 16 mass% due to cold rolling at room temperature. Second, to prevent grain coarsening, strain-induced α -martensite must be reversed into the original γ-phase to a large degree at quite low temperatures. And third, the reversed austenite should be stable at room temperature. The starting temperature for the reversion of martensite in 304-type stainless steels was determined to be above 673 K by Singh (1985) using hardness measurements, and above 823 K by Tavares et al. (2000) and Herrera et al. (2007) based on their studies of magnetization. Shyvaniuk et al. (2012) were the first to find that a combination of deformation and hydrogen charging can produce an ultrafine-grained structure in austenitic steels at the extremely low temperature of 543 K. The effect of hydrogen on the reversion of martensite in a metastable austenitic steel was subjected to preliminary investigation using the ab initio atomic calculations of hydrogen effect on the free energies of fcc and bcc iron. The lattice dynamics and corresponding thermodynamics functions were calculated within the framework of harmonic approximation using the PHONON software, see Parlinski (2010). Under the condition of constant volume, the total free energy of a crystal can be expressed as the Helmholtz free energy that includes the following components:

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F(T, V ) = E tot (V ) + F ph (V, T ),

(6.1)

where E tot (V ) stands for the ground state energy accounting for the electron and nuclear interactions and F ph (V, T ) is the phonon free energy at a given unit cell volume which represents the vibrational contribution to F(T, V ). To include phonon-related effects, a dynamical matrix has to be determined. The elements of this matrix are constructed based on the Hellmann–Feynman forces exerted on all the atoms in the cell, which could be obtained from ab initio calculations according to a direct method proposed by Kunc and Martin (1982), Yin and Cohen (1982) and modified by Parlinski et al. (1997). Diagonalisation of the dynamic matrix D(k) produces the phonon frequencies ω(k, j): ω2 (k, j)e(k, j) = D(k)e(k, j)

(6.2)

where e(k, j) is a polarization vector. Afterwards by constructing the phonon density of state dependences, the vibrational component of the free energy function is determined as ∝ F ph = r k B T

   ω dω g(ω) ln 2 sinh 2k B T

(6.3)

0

where r is the number of degrees of freedom in the primitive unit cell, k B is the Boltzmann constant, T is the temperature, g(ω) is the density of phonon states. The obtained results are presented in Fig. 6.6. One can see from Fig. 6.6 that the bcc phase is more stable at low temperatures and the intersection of curves occurs at a phase equilibrium temperature near 430 K. This temperature is much lower in comparison with that of hydrogen-free iron, 1183 K, and close to 1000 K in CrNi austenitic steels. The obtained result characterises a general trend in the hydrogen effect on the γ-α thermodynamic equilibrium. The effect of cold work on the balance between the γ and α phases in 304 type steel is presented in Fig. 6.7. Plastic deformation by 15% induces the α-phase, whereas subsequent hydrogenation at 543 K for 200 h under the hydrogen gas pressure of 100 MPa substantially removes it (Fig. 6.7a). The increase of the deformation degree up to 45% intensified the γ → α transformation, therefore subsequent annealing in vacuum at 573 K for 12 h did not restore the austenitic state. However, a full austenitic structure

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Fig. 6.6 Temperature dependence of the Helmholtz free energy for a Fe–H system with fcc or bcc crystal lattices

Fig. 6.7 X-ray diffraction patterns of 304 type steel containing, in mass %, 18.06 Cr, 9.09 Ni, 1.05 Mn and 0.02 C: a deformed by 15% of tension at RT: non-charged and charged with gaseous hydrogen at 543 K for 200 h after tension; b deformed by 45% of tension at RT: non-charged, aged at 573 K in vacuum after tension, charged with gaseous hydrogen at 543 K after tension. All intensities are normalised to that of the (111)γ peak

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was obtained by hydrogen charging at 543 K for 200 h under hydrogen pressure of 100 MPa (Fig. 6.7b). Hydrogenation in these conditions produced uniform hydrogen distribution in the wire of 1 mm in diameter. The hydrogen content was measured as 100 mass ppm using thermal desorption analysis. The microstructure and phase map of 45% pre-strained type 304 steel before hydrogen charging are presented in Fig. 6.8a, b respectively. The fraction of strain-induced bcc phase estimated from the EBSD phase map was equal to be about 25%. Hydrogenation led to a remarkable decrease in the grain size (Fig. 6.8c). The distribution of grain size, as presented in Fig. 6.9, indicates a striking hydrogen-caused reduction by one order of magnitude. The grain structure is remarkable in its uniformity. Saturation with hydrogen allowed a striking decrease in the recrystallization temperature of metastable austenitic steels and ultrafine grain microsructure. For comparison, according to Herrera et al. (2007), the recrystallization temperature in prestrained type 304 austenitic steel is about 150 K higher than that of α -martensite reversion and constitutes about 950 K. Thus, hydrogen treatment decreases the recrystallization temperature by more than 400 K. As follows from the calculations of free energies of the competing α and γ phases, this effect is a result of hydrogen-changed atomic interactions in both phases. Hydrogen destabilises the α phase in comparison with the β phase.

Fig. 6.8 EBSD orientation maps of 45%-prestrained 304 steel before (a) and after (c) hydrogenation; b EBSD phase map of a

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Fig. 6.9 Grain size distribution in 304 type steel after plastic deformation and subsequent gaseous hydrogenation under pressure of 100 MPa

The obtained unique grain refinement is obviously related to the hydrogendecreased γ-α equilibrium temperature, which should increase the driving force for nucleation of new grains retarding simultaneously their growth, and to the hydrogen-increased mobility of high-angle grain boundaries, see Sect. 2.3 in Chap. 2.

6.2.2 Titanium Alloys Temporary doping of Ti–Al alloys with hydrogen for grain refinement was first proposed by Kerr et al. (1980) and denoted as “hydrovac”. Hydrogen-charging up to 0.4% of alloy Ti-6Al-4V at temperatures above 800 °C to obtain the single β phase, followed by its decomposition at lower temperatures through the eutectoid reaction with subsequent quenching in water and final dehydrogenating annealing resulted in a fine nearly equiaxed microstructure. Related phase transformations were studied by Kerr (1985). For example, the Ti-6Al-4V alloy charged with 0.73 wt.%H at 870 °C and cooled to 590 °C for eutectoid transformation contained the orthorhombic α martensite plus the β(H) phase saturated with hydrogen. A further increase in hydrogen content led to additional primary hydride platelets in the microstructure.

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Subsequent dehydrogenation at 650 °C resulted in partial reverse eutectoid transformation with the precipitation of the acicular α phase. However, the α particles were finer in comparison with the nonhydrogenated samples quenched from the single β phase. If the temperature of dehydrogenation was increased, coarse plates of the primary α phase appeared in the microstructure. The finest microstructure consisting of small β particles in the nearly equiaxed α matrix was obtained in the case of doping up to 1 wt.% with hydrogen and dehydrogenation at the lowest possible temperature. Vanadium and aluminium partitioning during dehydrogenation treatment stabilized the β phase with vanadium and enriched the α phase with aluminium, whereas the hydride was transformed into α. Such a change in the microstructure points to a combination of phase transformation and recrystallization. A significant increase in yield strength from 900 to 1200 MPA in combination with improved relative elongation from 5 to 15% results from the small size of β particles and the essentially equiaxed α phase. A number of other treatments proposed for grain refinement are based on a change in hydrogenation temperature, different hydrogen content and varied phase transformation reactions, e.g.: – solution treatment in the β temperature field followed by water quenching and hydrogenation-dehydrogenation below the eutectoid temperature, denoted as βQHDH (Levin et al. 1984); – constitutional solution treatment denoted as CST and amounting to hydrogenation at temperatures of a stable β phase with subsequent eutectoid reaction and final dehydrogenation (Smickley and Dardi 1985); – thermocyclic α ↔ β transformation at temperatures deeply below the start of a β → α reaction with a change in temperature or hydrogen concentration (Kolachev et al. 1991a); – hydrogenation and hot work in the β field followed by dehydrogenation below the β(H) field (Senkov et al. 1994); – repeated martensitic transformation of the β phase including hydrogenation in the β field, subsequent quenching into α martensite by cooling to RT, subsequent thermocycling for its decomposition and dehydrogenation (Ilyin et al. 1995b); – hydrogenation below the β(H) transus temperature followed by air cooling to RT and dehydrogenation at lower temperatures, denoted as BTH, (Niinomi et al. 1995). – (a) eutectoid decomposition of the beta (H) phase to alpha phase and hydride phase and (b) isothermal decomposition of alpha” martensite phase, obtained by quenching of hydrogenated samples (Guitar 2008); – recrystallization of Beta-C alloy at 920 °C → hydrogenation at 700 °C to shift phase equilibria to the β/β + λ phase boundary beyond the eutectoid temperature → annealing at 650 °C for 2 h for hydride formation and nucleation of α phase → dehydrogenation at 780 °C → aging for 20 h at 500 °C (Schmidt et al. 2014); – solution treatment of Ti-10V-2Fe-3Al alloy → (α + β) hydrogenation → solution treatment far above Tβ(H) → dehydrogenation and technical ageing (Macin et al. 2014);

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– blended elemental powder metallurgy (BEPM) of Ti-based alloys using TiH2 powder (Ivasishin et al. 2000; Ivasishin and Moxson 2015); – hydrogen sintering phase transformation (HSPT) → solid state additive manufacturing (AM), namely, fused filament fabrication, FFF (Dunstan et al. 2020); – vacuum sintering at 1100 °C → repeated hydrogenation-dehydrogenationhydrogenation at 850 °C ↔ 1100 °C → final cooling in furnace (Wang et al. 2021). The production technology of the fine-grained and dense Ti-6Al-4V alloy including the press-and-sinter blended elemental power metallurgy (BEPM) using titanium hydride powder, see Ivasishin et al. (2000), Ivasishin and Moxson (2015), was updated by thermocycling around the α↔β transus temperature and hydrogenation-dehydrogenation of powder compacts at 850 ºC, see Wang et al. (2021). The related change in the volume enhanced diffusion of metallic atoms and retarded grain growth. Summary Finally, one can state that, in no so far published studies on the hydrogen-increased workability of β-Ti alloys, the hydrogen-induced change in the atomic interactions has been mentioned. Nevertheless, the aforementioned data about hydrogen effect on the electron structure of β-titanium, see Chap. 1, and consequent change of dislocation properties in hydrogen-charged β-Ti alloys, see Chap. 2, as well as the analysis of the electron concept of hydrogen brittleness, see Sects. 5.1.8.4 and 5.2.3 in Chap. 5, represent sufficient evidence of the decisive role of the hydrogen-increased concentration of free electrons in the mechanical behaviour of metals. The consequent decreased stress for activation of dislocation sources, the intensified emission of dislocations under applied stress and their reduced specific energy resulting in the increased dislocation velocity make it possible to use hydrogen as interim element in technological processing of titanium alloys in the absence of localized plastic deformation. It follows from the ab initio calculations of free energy for γ and α phases in iron, as presented in this chapter, that temperature of their thermodynamic equilibrium is strikingly decreased by hydrogen. Similar calculations for hydrogen in titanium are now in progress and will be published elsewhere. It is also shown, see Chap. 2, that hydrogen increases mobility of high angle grain boundaries, which can play a definite role in the grain nucleation and growth. The successful hydrogen-caused grain refinement in the austenitic steels and titanium alloys results from the hydrogen-caused decrease in the temperature of thermodynamic equilibrium between the high-temperature and low-temperature phases. Fundamentally, the free energy of metallic solid solutions is controlled by the interactions between the constituting atoms, namely by the density of electron states at the Fermi level that determines thermodynamic stability of phases in metals.

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