Electronic Properties of Nanoclusters in Amorphous Materials [1 ed.] 9781527540095, 9781527537552

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Electronic Properties of Nanoclusters in Amorphous Materials



Electronic Properties of Nanoclusters in Amorphous Materials By

Mikio Fukuhara

Electronic Properties of Nanoclusters in Amorphous Materials By Mikio Fukuhara This book first published 2019 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2019 by Mikio Fukuhara All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-5275-3755-2 ISBN (13): 978-1-5275-3755-2



&217(176    3UHIDFHYLL  &KDSWHU ,QWURGXFWLRQ  &KDSWHU (OHFWURQLFUXOHVDQGH[FHVVHOHFWURQVIRUWKHIRUPDWLRQRIDPRUSKRXVDOOR\V 2.1 Electronic rules for the formation of amorphous alloys 2.2 Ab initio molecular orbital calculations of excess electrons  &KDSWHU /RFDODWRPLFVWUXFWXUHVRI1L1E=UFOXVWHUVLQ1L1E=U+DPRUSKRXVDOOR\V 3.1 X-ray absorption fine structure (XAFS) analysis 3.2 Structures of the icosahedral clusters by first-principles molecular dynamics calculation and XAFS measurements 3.3 Structures and electronic properties of Ni5Nb3Zr5 clusters in Ni-Nb-Zr amorphous alloys 3.4 Local structures and structural phase change in Ni-Zr-Nb amorphous alloys composed of Ni5Nb3Zr5 icosahedral clusters 3.5 Distorted icosahedral Ni5Nb3Zr5 clusters in the as-quenched and hydrogenated amorphous (Ni0.6Nb0.24)0.65Zr0.35 alloys 3.6 Vacancy analysis in Ni-Nb-Zr-H amorphous alloys by positron annihilation spectroscopy 3.7 Proton NMR studies of hydrogen diffusion and electron tunneling in Ni-Nb-Zr-H amorphous alloys  &KDSWHU 5RRPWHPSHUDWXUH&RXORPERVFLOODWLRQDQG DPRUSKRXVDOOR\ILHOGHIIHFWWUDQVLVWRU$$)(7  LQ1L1E=U+DPRUSKRXVDOOR\V 4.1 Coulomb oscillation in a Ni-Nb-Zr-H amorphous alloy with multiple junctions 4.2 Room temperature Coulomb oscillation in Ni-Nb-Zr-H amorphous alloys with nanofarad capacitance 4.3Effect of current on Coulomb oscillation 4.4 Magnetic field induced Coulomb oscillation in Ni-Nb-Zr-H amorphous alloys 4.5 Fano Effect on AAFET in Ni-Nb-Zr-H amorphous alloys 4.6 Room temperature Fabry-Perot (FP) effect on AAFET with particle and wave natures &KDSWHU %DOOLVWLFWUDQVSRUWLQ1L1E=U+DPRUSKRXVDOOR\V 5-1 Electronic transport behaviours of Ni-Nb-Zr-H amorphous alloys 5-2 The effect of degree of amorphousness on electronic transport behaviours 5-3 Rotating speed effects on electronic transport behaviours 5-4 Effect of hydrogen content on ballistic transport behaviours 5-5 Chaotic properties of quantum transport 





vi

Contents

Chapter 6 ...................................................................................................................................89 Superconductivity, resistivity under pressure, and thermoelectricity 6-1 Superconductivity of Ni-Nb-Zr-H amorphous alloys under magnetic field 6-2 Pressure-induced positive electrical resistivity coefficient in Ni-Nb-Zr-H amorphous alloys 6-3 Electric resistivity and thermoelectricity in Ni-Nb-Zr-H amorphous alloys Chapter 7 ...................................................................................................................................99 Electric Storage and supercapacitors in amorphous materials 7-1 AC impedance analysis of a Ni-Nb-Zr-H amorphous alloy with femtofarad capacitance tunnels 7-2 Electric storage in de-alloyed Si-Al alloy ribbons 7-3 Super electric storage in de-alloyed and anodic oxidised Ti-Ni-Si amorphous alloy ribbons 7-4 Supercapacitors in amorphous titania 7-5 Superior electric storage on amorphous perfluorinated polymer surface 7-6 Amorphous alumina supercapacitor Chapter 8 .................................................................................................................................130 Electronic transport behaviours due to charge density waves Chapter 9 .................................................................................................................................136 Conclusion References ...............................................................................................................................138





PREFACE

I had a vivid impression that most amorphous alloys glisten notably rather than having a general metallic luster, when I came across metallic amorphous containing metallic glasses at the Institute for Materials Research, Tohoku University, in 2005. I lost no time in elucidating the reason. Since amorphous alloys are generally synthesised from molten alloys using free jet melt spinning at a cooling rate of 101–106 K/s, they are pseudo liquids. From Ab initio molecular orbital calculations of excess electrons, we found that many free electrons containing d or f electrons, in addition to s and p ones, play a definitive role in the formation of amorphous alloys. Therefore, we established a valence electron rule for amorphous formation based on the analysis results, which stated that the resonance bonding of the amorphous alloys could be caused by spd or spf hybridisation. The establishment of the rule enabled a person to form new kinds of amorphous alloys. When I unexpectedly measured the electrical resistivity of amorphous Ni42Nb28Zr30 –H alloys developed as a membrane for hydrogen permeability from 373 to 6 K in He of ambient pressure, I observed an abnormal variation in cooling and heating runs at specific hydrogen concentrations and within a certain temperature range. This was the Coulomb oscillation based on lowtemperature electric current-induced voltage oscillation. Further investigations into the effects of Zr and H contents in amorphous{(Ni0.6Nb0.4)100-xZrx}100-yHy (x = 30, 35, 40, 45 and 50, 5.2 ӌ y ӌ 22) alloys revealed about five kinds of electrical and electronical transport behaviours, such as room temperature Coulomb oscillation, ballistic transport, electron avalanche, superconducting, semi-conducting, and electric storage. The realisation of room-temperature macroscopic aluminium-oxide amorphous alloy field effect transistor (AAFET) exhibited a one-electron Coulomb oscillation, a Fabry-Periot interface under nonmagnetic conditions, and a Fano effect under a magnetic field. Ballistic transport, which is generally observed in one-dimensional nanometre sized channel at a very low temperature, reached 230 K for amorphous (Ni0.39Nb0.25Zr0.35)78.8H21.2 alloys. However, we found a superior electric storage effect on a nanometre-sized uneven surface with an insulating resistance for amorphous titanium and aluminum oxides, and perfluorinated polymer, resulting from both the quantum-size effect and an offset effect from positive charges at oxygenvacancy sites and C=O and N-H radicals with permanent dipoles, respectively. A common requirement for electric storage is an amorphous structure. To elucidate on the various electronic properties, we analysed cluster-vacancy structures composing amorphous alloys, using XAFS, XANES, and positron annihilation spectroscopy and proton NMR analyses. In our results, we found that the distorted icosahedral Ni5Nb3Zr5 clusters with tetrahedral H sites and tetrahedral vacancy sites play important roles in various electron transport phenomena. The cluster was recognised as a “perovskite-like cluster” in amorphous compounds. These behaviours could be explained by the macroscopic CDW properties of amorphous alloys. These new findings are expected to give rise to a new era of amorphous materials. 



CHAPTER 1 INTRODUCTION

The amorphous alloys, which are the last frontier of metals and metallic alloys, are peculiar metallic alloys in that they lack, on the nanoscale, the long-range translational order of crystalline alloys, as they have grain boundaries and lattice imperfections [1, 2]. Since 1960, when Klement et al. [3] discovered amorphous alloys in the Au-Si system, work has been carried out on the preparation and properties of various amorphous alloys [4–7]. Amorphous alloys have characteristic physical and chemical properties, such as high strength, high corrosion resistance, and superior electronic properties, which are significantly different from the corresponding crystalline alloys. Much attention has been devoted to the amorphous forming ability of elements of different types in amorphous alloys [6]: i.e., their cluster structures [8] and potential applications. Special interest focuses on glass-forming ability associated with formation of metastable polyhedra [8], and glass transition by a free volume related kinetic phenomenon [9]. However, in addition to these characteristics, it is also important to examine their cluster characteristics in order to understand electronic properties of amorphous materials. We have reported electronic properties such as Coulomb oscillation, ballistic transport, superconductivity, and electric storage in terms of atomic morphology of subnanometre-sized clusters composing the amorphous alloys and titanium and aluminium-oxides, and perfluorinated polymer. These phenomena are reasonably similar to those appearing in many different types of crystalline charge-density-wave (CDW) conductors with energy gaps at the Fermi surface. We report that low-dimensional CDW phenomena are characterised by five types of nonlinear, anisotropic behaviours involving their electronic characteristics. In contrast to crystalline perovskite compounds with various electronic properties, we especially focused on analysis of sub-nanometre-sized Ni5Nb5Zr5 icosahedral cluster in Ni-Nb-Zr-H amorphous alloys. In our results, we found that the cluster has perovskite-like properties in amorphous compounds. These findings provide new insights into electron transport devices in this century, which are based on cluster science and technology. However, to the best of our knowledge, no work has been carried out previously on electronic studies of amorphous materials, especially amorphous alloys with various properties.

CHAPTER 2 ELECTRONIC RULE AND EXCESS ELECTRONS FOR FORMATION OF AMORPHOUS ALLOYS

2.1 Electronic rule for formation of amorphous alloys [10, 11] Pauling has derived the concept of “valence electron” for elements when they are bonded in the crystalline metallic state [12]. Pauling defined that the valence number of metals cannot be greater than six in the valence-bond theory of metals. Figure 1 is a representative example, which presents values of metallic valence for the transition elements of the first long period [13]. However, the valence electron theory for intermetallic compounds has not been as fully developed during the past century as for other compounds, such as organic and inorganic ones, because of their undefined composition [14]. Only the Hume-Rothery interpretation of the valence electron concentration rule for intermetallic compounds has been vigorously investigated [15]. The valence electrons are defined as outer freely moving s and p or d electrons that are not bound to any particular cations. The decrease in both the potential and the kinetic energies of the valence electrons due to the unsynchronised resonance of electron-pair bonds is responsible for crystalline metallic bonding. Therefore, the resonance energy of the metallic orbital is very sensitive to the form of the cyclic potential energy that is associated with the crystal system. On the other hand, the distinguishing feature of amorphous alloys without a crystal structure is the randomness of their potential energy [6]. The potential energy minimum among atoms in the multi-component amorphous alloys is not as rigid as that of crystal alloys, so that the wave functions of these electrons are irregularly spread out much more than those of the crystalline metallic valence electrons. Therefore, we cannot expect the unsynchronised resonance effect by the cyclic potential energy to form the amorphous phases. Furthermore, the amorphous alloys have two bonding types, metal/metal and metal/metalloid [16], and the atomic configurations of the amorphous alloys differ between them. The amorphous structure of the former is composed of icosahedral clusters, while the structural feature of the alloy of the latter is the construction of a network of atomic configurations consisting of trigonal prisms [17] and transformed tetragonal

Electronic rule and excess electrons for formation of amorphous alloys

3

dodecahedrons [8]. Our interest lies in studying thermal stability of amorphous alloys as the function of their valence electron concentration (VEC) in terms of amorphous metallic bonding, using 121 types of amorphous alloys. We consider that the electron contribution provides useful information when interpreting the bonding mechanism of the amorphous alloys. Indeed, the electronic structure of Pd- and Zr-based bulk amorphous alloys has been examined by X-ray photoelectron spectroscopy (XPS) [18]. Additionally, the relationship between stability and electronic structure for Zr-based ternary amorphous alloys has been investigated by band calculation using LMTO-ASA method [19]. However, as far as we know, no research has been previously carried out on the statistic valence electron contribution to bonding nature responsible for the thermal stability of a large number of amorphous alloys. Inoue et al. proposed the three empirical rules for an amorphous alloy-forming ability [20]. However, the use of crystal element radii puts constraints on these rules. Indeed, there are some examples that violate these rules. In general, the thermal stability of metallic alloys can be evaluated by adjusting the height of the Fermi level to the VEC proposed by Bilz [21]. The VEC in the amorphous alloys (IIA, IIIB, IVC, VD, VIE, VIIF, VIIIG) and (IIA, IIIB, IVC, VD, VIE, VIIF, VIIIG) (Mx)w (M= B, C, Si, P, Ge, Sn, Sb, Bi), respectively, of group II to VIII elements has been defined as follows [22, 23]: VEC =IIA+IIIB+IVC+VD+VIE+VIIF+VIIIG for metal/metal type,

(1)

VEC =IIA+IIIB+IVC+VD+VIE+VIIF+VIIIGȈ0iXW for metal/metalloid type,

(2)

where A, B, C, D, E, F, and G are atomic fractions, A+B+C+D+E+F+G =1 and ȈMiX=1. The VEC for 2 kinds of binary, 89 kinds of ternary, 16 kinds of quaternary, and quintuple of 6 kinds Pd-, Zr-, Fe-, Ni-, Co-, Cu-, Mg-, Ti-, Hf-, Au-, Al-,Pt-, La-, Ca-, and Be- based amorphous alloys have been calculated using electron valences from 42 of their constituent elements. As an intrinsic parameter for thermal stability of the amorphous alloys, we selected a glass transition temperature of Tg. The data (see Table 1) used in this study has been taken from literature [24] on 121 amorphous alloys with Tg compositions. After we assigned the electron valence from 1 to 15 for s, p, d, and f orbits in all elements, taking multiple orbital electron hybridisation into consideration and based on the standard method of the least squares, we repeatedly calculated until we obtained the best linearity for the correlation between Tg and VEC. The best result is shown in Fig. 2, for metal/metal and metal/metalloid bonding types. Both type alloy groups show fairly good linearity: r =0.887 and 0.866, respectively. The metallic valence for all elements used in this section is shown in Table 2 using a periodic table format with four kinds of s-, p-, d-, and f- electron blocks. Cooper [25] has classified all elements in the periodic table into four kinds of s-, p-, d-, and felectron blocks: the s- block includes the Ia and IIa group elements; the p- includes the IIIb, IVb, Vb, VIb, VIIb and 0 group elements, the d- includes the IIIa, IVa, Va, VIa, VIIa, VIIIa, Ib and IIb group elements; and the f- includes the lanthanide and actinide group elements. We used his proposal for the classification of the elements in Table 1. Although Al and Pb belong to the pelectron block, they were treated as 100 % metallic/metallic and 50% metallic/50% metalloid

4

Chapter 2

elements, respectively. The valence values for other elements, Ca, Sc, Zn, Ga, In, Er, and Tl were 2.4, 3.0, 2.0, 3.0, 3.0, 3.0, and 3.0, respectively.

As can be seen from Fig. 2, Tg (K) can be expressed as Tg = 131VEC +65 (r =0.887) for metal/metal bonding type

(3)

Tg = -240VEC +2408 (r=0.866) for meta/metalloid bonding type.

(4)

For metal/metal type amorphous alloys, a positive slope means that their thermal stability increases when the valence also increases. In crystalline metals, an increase in the valence electron correlates to a reduction of atomic distance due to the unsynchronised resonance of electron-pair bonds, leading to higher strength and melting points [12]. Therefore, metal/metal type amorphous alloys also follow the valence electron rule, which is predicted using crystalline metallic valence bond theory. However, for metal/metalloid type-metallic amorphous alloys, an increase in VEC––i.e., an increase in the amount of metalloid elements––indicates deterioration in the thermal stability of the amorphous. 1000 metalloid metal

Tg (K)

800 600 400 200 0 0

5 VEC

10

Fig. 2 The relationship between Tg and VEC for 112 types of amorphous alloys: open and solid circles present metal/metal and metal/metalloid bonding types, respectively.

Electronic rule and excess electrons for formation of amorphous alloys

5

Thus, the stable region for formation of the amorphous phase would be 2.3 < VEC < 5.2 and 6.6 < VEC < 9.1 for metallic and metalloid-type metallic amorphous, respectively. The most optimum condition for the formation of amorphous alloys with the highest Tg would be VEC Ҹ 6. This means that transition metal elements with higher valence (e.g., group VIII and Ib elements) are the most desirable ones for the formation of amorphous alloys with higher Tg. In addition, it is empirically confirmed that the inorganic compound of transition metals is stable when VEC ” 8.8 [22]. To certificate the application of VEC for the electronic rule associated with thermodynamic stability of amorphous alloys (i.e., the reliability of metallic valences in Table 1), we here calculated the stability for anionic clusters by an excess amount of electrons transferring from inner orbital d or f electrons, in comparison with the stability for neutral ones [26]. Since it is very difficult to precisely calculate the stability of polyhedral clusters constituting of amorphous alloys at the present time, we chose magnesium based amorphous alloys as a representative amorphous alloy. In Mg-Ni-Nd, Mg-Cu-Sn, and Mg-Cu-Y systems from Table 2, it is anticipated that anionic magnesium clusters [27] will be formed by an electron transfer from the Ni, Nd, Sn, and Y elements (Fig. 2) using the Ab initio molecular orbital calculations described in 1.2. Table 2. Values of Tg and VEC for 121 kinds of amorphous alloys used in this section. metal/metal type㻌 Zr40Nb20Al10Ni10Cu20 Zr41Be23Ti14Cu12Ni10 Zr41.2Tl13.8Ni10Cu12.5Be22.5 Zr50Nb10Al10Ni10Cu20 Zr50Cu40Al10 Zr55Cu30Al10Ni5 Zr60Ni20Cu20㻌 Zr65Al7.5Ni10Cu17.5㻌 Zr65Ni10Cu5Al7.5Pd12.5㻌 Ti41.5Cu47.5Hf5Zr2.5Ni7.5Sn1 Ti45Cu40Ni7.5Zr5Sn7.5 Ti50Ni25Cu25㻌 Ti50Cu25Ni25㻌 Ti60Cu30Ni10㻌 Ti61Cu23Ni16㻌 Mg65Cu15Ag5Pd5Gd10 Mg65Ni20Nd15㻌 Mg70Ni15Nd15㻌 Mg75Ni15Nd10㻌 Mg75Ni20Nd5㻌 Mg77Ni18Nd5㻌 Mg80Cu15Sn5㻌 Mg80Ni10Nd10㻌 Mg80Cu10Y10㻌 Mg85Cu5Y10㻌 Mg75Cu15Y10㻌 Mg75Cu10Y15㻌 Mg70Cu10Y20㻌 Cu42Zr42Al8Ag8 Cu46Zr45Al7Y5 Cu45Zr45Ag10㻌 Cu45Zr20Hf25Ag10㻌 Cu55Zr30Ti10Pd5 Al25La55Cu20㻌 Al25La55Ni20㻌 Al20Zr55Ni25㻌 Al15Zr60Cu25㻌 Al87Ni10Zr3㻌 Al85Ni10Zr5㻌 Hf60Ni20Cu20㻌

VEC㻌 4.96 4.27 4.15 4.87 4.87 4.83 4.96㻌 4.55㻌 4.70㻌 5.24 4.91 5.05㻌 5.05㻌 4.78㻌 4.80㻌 3.29 3.29㻌 3.09㻌 3.06㻌 3.23㻌 3.15㻌 2.99㻌 2.86㻌 2.80㻌 2.63㻌 2.97㻌 2.83㻌 2.86㻌 7.15 5.05 5.10㻌 5.20㻌 5.07 3.56㻌 3.79㻌 4.51㻌 4.42㻌 3.38㻌 3.40㻌 4.96㻌

Tg(K)㻌 728 693 613 691 703 690 655㻌 622 674㻌 680 690 707㻌 707㻌 621㻌 715㻌 430 467㻌 473㻌 450㻌 450㻌 456㻌 383㻌 453㻌 427㻌 420㻌 416㻌 445㻌 464㻌 715 672 682㻌 696㻌 735 470㻌 473㻌 743㻌 694㻌 452㻌 515㻌 739㻌

Hf65Cu25Al10㻌 Hf65Ni25Al10㻌 Y56Al24Co20 La55Al25Ni20㻌 La55Al25Cu20㻌 Be20Nb15Zr65㻌 Be25Nb15Zr60㻌 Be30Nb20Zr50㻌 Be35Nb10Zr55㻌 Be35Nb5Zr60㻌 Be35Nb2.5Zr62.5㻌 Ca65Mg15Zn20 Ca57Mg19Cu24 Ca60Mg20Ag20 㼅㻟㻢㻿㼏㻞㻜㻭㼘㻞㻠㻯㼛㻞㻜㻌 metalloid/metal type㻌 Pd40Ni40P20㻌 Pd30Ni50P20㻌 Pd50Ni28P22㻌 Pd40Cu40P20㻌 Pd50Cu30P20㻌 Pd60Cu20P20㻌 Pd20Cu40Ni20P20㻌 Pd25Cu30Ni25P20㻌 Pd30Cu30Ni20P20㻌 Pd40Cu30Ni10P20㻌 Pd50Cu20Ni10P20㻌 Pd60Cu10Ni10P20㻌 Pd40Ni25Fe15P20㻌 Pd40Ni20Fe20P20㻌 Pd15Ni65P20㻌 Pd27Ni53P20㻌 Pd74Cu10Si16㻌 Pd77Cu6Si17㻌 Pd78Cu6Si16㻌 Pd79Ag4.5Si16.5㻌 Pd77Cu5Si18㻌 Pd75Cu8.5Si16.5㻌 Pd79Au4Si17㻌 Pd73Au7Si20㻌 Pd80Cu3.5Si16.5㻌

4.53㻌 4.63㻌 3.62 3.56㻌 3.60㻌 3.98㻌 3.89㻌 3.84㻌 3.66㻌 3.62㻌 3.59㻌 2.32 3.22 3.12 㻟㻚㻢㻞㻌 VEC㻌 7.70㻌 7.69㻌 7.87㻌 7.50㻌 7.49㻌 7.58㻌 7.38㻌 7.46㻌 7.46㻌 7.48㻌 7.56㻌 7.65㻌 7.64㻌 7.63㻌 7.67㻌 7.68㻌 7.18㻌 7.27㻌 7.21㻌 7.27㻌 7.26㻌 7.22㻌 7.35㻌 7.55㻌 7.26㻌

762㻌 778㻌 636 487㻌 449㻌 640㻌 630㻌 670㻌 642㻌 620㻌 635㻌 379 404 401 㻢㻠㻡㻌 Tg(K)㻌 576㻌 583㻌 584㻌 548㻌 562㻌 596㻌 551㻌 572㻌 569㻌 571㻌 597㻌 604㻌 603㻌 598㻌 642㻌 620㻌 639㻌 636㻌 620㻌 640㻌 655㻌 645㻌 646㻌 670㻌 640㻌

Pd73.5Cu10Si16.5㻌 Pd69Cu14.5Si16.5㻌 Pd77.5Cu6Si16.5㻌 Pd73.8Cu5.7Si20.5㻌 Pd84Si14Ge2㻌 Pd83Si10Ge7㻌 Pd48Ni32P20㻌 Pd37.5Ni37.5P25㻌 㻼㼠㻠㻞㻚㻡㻯㼡㻞㻣㻺㼕㻥㻚㻡㻼㻞㻝㻌 Pt60Ni15P25㻌 Pt64Ni16P20㻌 Ni40Fe40P20㻌 Ni40Fe30Pd10P20㻌 Ni40Fe20Pd20P20㻌 㻺㼕㻠㻡㻼㼐㻟㻡㻼㻞㻜㻌 Ni75Si8B17㻌 Fe48Cr15Mo14Er2C15B6 Fe80P20㻌 Fe82B18㻌 Fe70Nb10B20㻌 Fe70Zr10B20㻌 Fe70W10B20㻌 Fe70Hf10B20㻌 Fe40Ni40P14B6㻌 Fe41.5Ni41.5B17㻌 Fe79Si10B11㻌 Fe80P13C7㻌 Fe77Mn4B19㻌 Fe80P17Al3㻌 Fe83P15B2㻌 Fe80Pd2B18㻌 Fe80B17Si3㻌 Fe40Ni40P20㻌 Fe83P14Si3㻌 Au53.2Pb27.5Sb19.2㻌 Au50Pb22.5Sb22.5㻌 Au63.5Pb11.5Ge14Si9㻌 Au78Ge14Si8㻌 Au77Ge14Si9㻌 Co75Si15B10㻌 㻯㼛㻠㻤㻯㼞㻝㻡㻹㼛㻝㻠㻯㻝㻡㻮㻢㼀㼙㻞㻌

7.21㻌 7.16㻌 7.24㻌 7.48㻌 7.26㻌 7.32㻌 7.71㻌 7.67㻌 㻣㻚㻢㻝㻌 8.23㻌 7.81㻌 7.50㻌 7.55㻌 7.60㻌 㻣㻚㻡㻤㻌 7.51㻌 6.99 7.35㻌 6.76㻌 6.74㻌 6.61㻌 6.86㻌 6.61㻌 7.35㻌 6.87㻌 7.02㻌 7.26㻌 6.80㻌 7.01㻌 7.08㻌 6.77㻌 6.85㻌 7.50㻌 7.09㻌 8.92㻌 9.08㻌 7.99㻌 8.23㻌 8.30㻌 7.40㻌 㻢㻚㻥㻥㻌

652㻌 657㻌 635㻌 660㻌 634㻌 624㻌 582㻌 619㻌 㻡㻝㻡㻌 500㻌 483㻌 650㻌 600㻌 600㻌 㻡㻤㻤㻌 782㻌 843 650㻌 760㻌 833㻌 860㻌 819㻌 871㻌 670㻌 720㻌 818㻌 720㻌 750㻌 710㻌 660㻌 693㻌 750㻌 612㻌 660㻌 314㻌 318㻌 320㻌 294㻌 295㻌 785㻌 㻤㻡㻟㻌

In Table 2, our definitive valence for Mg is 2.4. This value means the magnesium atom is partially charged. We then calculated the monoanion Mg3- (average valence is 2.33) and Mg4- clusters (average valence is 2.25) taking the electron transfer from other constituent elements into consideration. The initial structure for optimisation is a part of crystalline magnesium. Mg3- has a

6

Chapter 2

three-membered ring structure (D3h), while, for Mg4-, two types of structure are possible: a four-membered ring and a tetrahedron. Full optimisation of Mg4- gives tetrahedron (C3v) an equilibrium structure. Comparing the optimised structures between the neutral cluster and the monoanion, the magnesium bond lengths of the monoanion are shortened: 0.3475 (0.3475) nm at the CBS-QB3 (G3B3) level for neutral Mg3 and 0.3140 (0.3145) nm for the monoanion Mg3; 0.3165 (0.3178) nm for neutral Mg4 and 0.3127 (0.3140) nm for the monoanion Mg4-. The energy difference between the neutral cluster and the monoanion indicates that the monoanion is more stable than the neutral clusters by 264 (283) m eV/atom for Mg3 and 286 (233) meV/atom for Mg4 at the CBS-QB3 (G3B3) level, respectively. We can, therefore, conclude that the increase in the valence of magnesium stabilises the cluster structures and positively affirms the application of VEC for the electronic rule associated with the stability of amorphous alloys. In Table 1, the valences are somewhat larger than those based on crystalline metallic valence bond theory [13]. This suggests that many free electrons containing d or f electrons, in addition to s and p ones, play a definitive role in the formation of amorphous alloys. Therefore, the resonance bonding of the amorphous alloys could be caused by spd or spf hybridisation. As corroborating evidence, X-ray photoelectron spectroscopy analysis [28] of amorphous alloy Zr55Al10Cu30Ni5 suggested that stabilisation in the amorphous phase is derived from the formation of a pseudo gap below the Fermi energy EF due to spd hybridisation. When periodicity in transition metal elements increases, it is expected that the wide of d- band will also increase and consequently promote spd hybridisation. Furthermore, since the amorphous alloys are pseudo-liquid, the liquid would be formed by multiple orbital electron hybridisation. Lastly, we applied the new rule to metallic typeCu45Zr(45-x)HfxAg10 alloys on trial. According to the rule, VEC of Cu45Zr20Hf25 Ag10 amorphous alloy is 5.26, which is closed to the stable limit, 5.3. Since VEC in Hf is slightly larger than Zr due to the difference in the width of d-band, we can estimate that it is difficult to form stable amorphous alloys with Hf content over 25%. Indeed, the experimental result coincided perfectly with the estimation [29]. This study makes the electronic contribution for thermal stability of most of all the amorphous alloys clear. The primary study in this paper will lead to an amorphous alloy bonding theory that Pauling has not considered. It also provides some guidelines for the selection of amorphous forming compositions that prevent the formation of crystalline phases and alloy design of promising amorphous alloys with functional properties, such as electronics, optics, and catalysis. 2.2 Ab initio molecular orbital calculations of excess electrons [30] Since the formation mechanism of amorphous alloys has not been clearly elucidated, we will investigate the effect of excess electrons accommodated in hcp Mg and various Mg clusters as a representative example, using density functional theory-based calculations in order to reveal the role of conduction electron concentration in the amorphous-forming ability and thermal stabilities of Mg-based amorphous alloy. The role of conduction electron concentration is one of the key roles to reveal the mechanism.

Electronic rule and excess electrons for formation of amorphous alloys

7

The search for the equilibrium structures of the clusters was performed using density functional theory (DFT) with the Becke3-Lee-Yang-Parr (B3LYP) functional and the 6-311+G (d) basis set as implemented in the GAUSSIAN-03 package [31]. The important feature of the density functional method is characterised by many electron correlations via the phenomenological exchange-correlation potential. From the point of the electronic structure, the density of states (DOS) revealed the effect of excess electrons. The DOS of the neutral hcp Mg exhibits a “free-electron-gas” parabolic behaviour until –1.5 Fig. 3 Formation of the multiple charge anion Mg formed by an electron transfer from Ni, eV below the Fermi level, due to weak s-p Nd,nCu, Sn, and Y elements. hybridisation and the strong contribution of the p bands to the total DOS [32, 33]. However, the DOS of the expanded lattice showed a high concentration of bands with small dispersions and the appearance of a spiky structure, which is reported for quasicrystalline materials [34]. The spiky peaks are a state signature, which is preferentially localised around the structural cluster [34, 35]. Since our aim is to understand the formation mechanism of Mg-based amorphous alloys, we then investigated the effects of excess electrons on hexagonal close-packed (hcp) Mg and the model clusters, which can be explained by an inflation process. For the clusters (Mg7, Mg10, and Mg17) and hcp Mg, the c/a ratio increases proportionally with the concentration of excess electrons and the cell volume also expands. This suggests that the increase in the conduction electron concentration of Mg in amorphous alloys possibly stabilises the cluster structures. The higher c/a ratio accompanied by distortion suggests that the melting point would be lowered in the charge state. The pseudogap by s-p mixing at the Fermi level is weakened in the expanded cell with a distorted c/a ratio and the spiky structure is mainly created by p-bands. This means it has preferential localisation around the structural cluster. In other words, the expanded volume and the distorted c/a ratio by the charge transfer from additives suppress the crystallisation of super-cooled liquid. Figure 3 summarises that the formation of multiply charge anion Mgn is stabilised by electron transfer from Ni, Nd, Cu, Sn, and Y elements with many free electrons.

CHAPTER 3 LOCAL ATOMIC STRUCTURES OF NI5NB3ZR5 CLUSTERS IN NI-NB-ZR-H AMORPHOUS ALLOYS

We recently found that melt-spun flexible amorphous [(Ni0.6Nb0.4)1-xZrx] 100-yHy ” x ” 0.50, 0 ” y ” 20) alloys show semi-conductivity, superior conductivity (ballistic) and super-conductivity; current-controlled electron avalanches; and Coulomb oscillation as a function of hydrogen content [36]. In particular, the amorphous alloy (Ni0.36Nb0.24Zr0.40)90H10 exhibited Coulomb dot oscillation at room temperature [37] and magnetic-field-induced Coulomb oscillation at 200 K [38]. Furthermore, a Nyquist diagram of a semitrue circle of the alloy with a total capacitance of 17.8 PF [39] showed that the material could be regarded as a dc/ac converter. From these electronic behaviours, we infer that Zr-Ni-Nb clusters, coupled with H, play a decisive role in the promising electronic properties observed in these amorphous alloys, as well as in the familiar Perovskite crystal phase. 3.1 X-ray absorption fine structure (XAFS) analysis [40] To elucidate the hydrogen effect on the metallic bonding configuration, we measured the X-ray Absorption Fine Structure (XAFS) spectra of the Ni-Nb-Zr amorphous alloy films with two different chemical compositions––i.e. Ni42Nb28Zr30 (hereafter referred to as Zr30-H0)––and Ni36Nb24Zr40 (Zr40-H0), and their hydrogen-charged compositions––i.e. (Ni42Nb28Zr30)0.91H0.09 (Zr30-H9) and (Ni36Nb24Zr40)0.89H0.11 (Zr40-H11). Although both Zr30-H0 and Zr40-H0 are amorphous [42], the hydrogen permeation characteristic of the latter is higher than that of the former [43]. XAFS as one category of X-ray absorption spectroscopy is a powerful tool for the structural analysis of amorphous materials because the useful information of the local structure around an element of interest can be obtained by tuning the photon energy to the absorption edge of the specific element [44]. By analysing the XAFS oscillation in the X-ray absorption spectra of the Ni-Nb-Zr (-H) alloys measured at the Ni, Nb, and Zr K-edges, we obtained the local structure around these three elements. The results revealed that there are significant differences in the behaviour of the structural change between the Zr-30at% and Zr-40at% samples when hydrogen is charged. The XAFS spectra were measured at the bending-magnet beamline BL14B2 [45] of the Large-Scale Synchrotron Radiation Facility (SPring-8) in Hyogo, Japan. The incident X-rays were monochromatised by a silicon double crystal monochromator. The net planes used were (311) for the Nb and Zr K-absorption edges, and (111) for the Ni K-absorption edge. The higher harmonics of the incident X-rays were reduced by two Rh-coated mirrors. The spectra were taken in a normal transmittance mode. To obtain the appropriate X-ray absorption intensity, the two sheets of ribbon

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

9

had to be stacked in the Nb K- and Zr K-edge measurements, while one sheet of ribbon was the optimum thickness for the Ni K-edge. The samples were cooled down to ~20 K in order to avoid thermal disturbance. The extraction of the XAFS oscillation from the spectra, normalisation by edge-jump, and Fourier transformation were performed by the Athena code [46]. The curve-fitting analysis was carried out in R-space by a code Artemis. The XAFS oscillation function F(k) is written as 2

F k

S 0 N i Fi k kri

2

§ 2ri · 2 ¸ sin 2kri  Ii k exp¨¨  2k 2V i  Oi k ¸¹ © ,

(5)

where the electron wave vector k is defined as

k

>2mE  E

0



h2

1

@

2

,

(6)

and S02 is the amplitude reduction factor; Ni the number of atoms in the ith shell; Fi(k) the backscattering amplitude of the ith neighbour atom; ri the mean distance between the absorbing atom and the ith shell; Vi2 the mean squared relative disorder (MSRD) between the absorbing atom and an atom in the ith shell; IL(k) the phase shift; and OL(k) the mean-free path of the photoelectron. In the code Artemis, Fi(k), IL(k), and OL(k) were theoretically calculated by the code, FEFF6L. The other parameters, Ni, ri, Vi2, and E0, are treated as fitting the parameters in the curve-fitting analysis. In this analysis, S02 is assumed to be unity.

Fig. 4 XAFS oscillations extracted from the X-ray absorption spectra of Zr30-H0, Zr30-H9, Zr40-H0, and Zr40-H11 amorphous alloys measured at the (a) Ni, (b) Nb, and (c) Zr K-edges. Note that the oscillations shown here are weighted by k3.

Figures 4(a), (b), and (c) show the k3-weighted XAFS oscillations extracted from the absorption spectra of the Zr30-H0, Zr30-H9, Zr40-H0, and Zr40-H11 amorphous alloys measured at the Ni, Nb, and Zr K-edges, respectively. All the oscillation patterns show simple curves, as typically seen

10

Chapter 3

for amorphous materials. The Zr K-edge XAFS oscillations of Zr30-H0 resemble that of the Ni-Nb-Zr alloys with the same chemical composition reported by Sakurai et al [47]. The XAFS oscillations for all the K-edges in Zr30-H0 are almost identical with those of Zr30-H9. However, the oscillations of Zr40-H11 are significantly different from those of Zr40-H0, indicating distinct structural change caused by hydrogenation. The absolute values of Fourier transforms (FTs) of the k3-weighted XAFS oscillations (|F(r)|) are depicted in Figs. 5(a), (b), and (c) for the Ni-, Nb-, and Zr K-edge oscillations, respectively. The analysed FT ranges are 2.7 – 13.3 Å-1, 3.0 – 12.0 Å-1, and 2.9 – 13.5 Å-1 for the Ni, Nb, and Zr K-edges, respectively. Each FT spectrum gives basically similar information to the partial radial-distribution-function (RDF) around the core-excited atoms. Note, however, that the apparent inter-atomic distances in the spectra shift on the shorter side by several tenth of Ångström from the average values of the atomic distances obtainable in a diffraction method, since the phase shift correction has not been carried out. At r > 4 Å, there is no clear structure in the FT spectra for all the samples at the three absorption edges, indicating that there is mostly no longer-range ordering in the amorphous alloys. The electron scattering from the atoms locating at longer position than 4 Å in these amorphous alloys only piles up a little in the background of the FT spectra. The closest neighbour peaks of the FT spectra from the Ni K-edge for all the samples are asymmetrical (Fig. 5[a]), suggesting that each of these peaks consists of two or more components. Firstly, there should be two components which come from the Ni-Zr and Ni-Nb coordination, because the feature of the Ni coordination can be evaluated from the first nearest neighbour peaks at both the Nb and Zr K-edges, as discussed below. Secondly, the contribution of Ni-Ni to the peak cannot be ignored when taking the realistic structures of Ni-Zr and Ni-Nb bimetallic crystal alloys into consideration [48–53]. Therefore, the first nearest neighbour peaks of the FT spectra on the Ni K-edge probably consist of at least three components (Ni-Zr, Ni-Nb, and Ni-Ni). The first nearest neighbour peak at r ~ 2 Å of the FT spectra for the Nb K-edge is symmetrical in the shape, indicating that it consists of a single component (Fig. 5[b]). Judging from the reported atomic structures of NiNb crystal alloys [48, 49], it is reasonable to assign this peak to the Nb-Ni coordination. As can be seen in Fig. 5, there is a close resemblance between the FT spectra of Zr30-H0 and Zr30-H9 for each absorption edge. However, the FT spectra of Zr40-H0 are clearly different from those of Zr40-H11. The height of first nearest neighbour peak of the Zr40 alloy decreases significantly for all the three K-edges after hydrogen charging. There is also a significant difference between Zr40-H0 and Zr40-H9 in the shape of the FTs from the Nb and Zr K-edges around r = 2.6 – 3.5 Å. These results clearly indicate that essentially hydrogen doping does not alter the framework of the Zr30 alloy, but reasonably modifies that of the Zr40 alloy.

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

11

Fig. 5 The absolute values of Fourier transforms (FTs) the k3-weighted XAFS oscillations (|F(r)|) of Zr30-H0 (upper solid lines), Zr30-H11 (upper dotted lines), Zr40-H0 (lower solid lines), and Zr40-H11 (lower dotted lines) at the (a) Ni, (b) Nb, and (c) Zr K-edges. The FT ranges analysed are 2.7 -13.3 Å-1, 3.0 - 12.0 Å-1, and 2.9 -13.5 Å-1, for Ni, Nb, and Zr K-edges, respectively.

In order to obtain the more quantitative structural parameters (N, r, V2) around the core-excited atoms, fine analysis using curve-fitting techniques was carried out. The curve-fitting results for the Nb K-edge are summarised in Table 4. Only the closest neighbour peaks are treated in the ranges of R = 1.7 – 2.8 Å for the Zr40-H11 alloy and R = 1.7 – 2.5 Å for the other amorphous alloys in the curve fitting analysis. Here, we assume that each peak consists of one structural component (one-shell model), i.e. Nb-Ni alone, in the analysis [54]. The inter-atomic distances obtained are close to the Nb-Ni inter-atomic distance for the reported atomic structures of NiNb crystal alloys [48, 49]. For the Zr30 alloy, there are no differences in the inter-atomic distance (r), the coordination number (N), and the MSRD (V2) between alloys with and without hydrogen within the analytical limits. However, the inter-atomic distance in the Zr40 alloys becomes longer, and the coordination number and MSRD become larger after hydrogenation. The peak corresponding to the closest neighbour has an asymmetrical form after the hydrogenation (see Fig. 5 (a)). This suggests that the two structural factors are contained in the closest neighbour peak of the Zr40-H11 alloy. Therefore, the “one-shell model” seems to be not appropriate for the Zr40-H11 alloy peak. The results of the curve-fitting analysis for the Zr K-edge are summarised in Table 5. The first and second nearest neighbour peaks are treated in the fitting analysis (R = 1.75 – 3.3 Å). In the analysis, we assumed that these peaks consist of two components: i.e., a “two-shell model”. The closest neighbour peak is more likely to only consist of Zr-Ni coordination. The second nearest neighbour peak probably consists of two major components: i.e., Zr-Zr and Zr-Nb. However, we collected the two components in one shell. The functions Fi(k), IL(k), and OL(k) used in this shell are calculated by the Zr-Zr single scattering path. This treatment is valid because Nb and Zr adjoin in the atomic

12

Chapter 3

number, resulting in a very small difference in the functions Fi(k), IL(k), and OL(k) between the Zr-Nb and Zr-Zr scattering paths.

Table 4 Results of the curve-fitting analysis for the Nb K-edge. The interatomic distances (r), the coordination numbers (N), 'E0 = E - E0, and the MSRDs (V 2) for all four amorphous alloys obtained by the analysis are shown. The values of R-factor are also given at the bottom of the table. bond

Nb-Ni

Zr30-H0

Zr30-H9

Zr40-H0

Zr40-H11

r /Å

2.55

2.54

2.54

2.59

N

1.5

1.5

0.90

1.6

'E0 /eV

-5.3

-7.0

-6.3

-3.7

V2 /Å2

0.0086

0.0088

0.0069

0.013

0.0022

0.0031

0.0093

0.051

R-factor

As can be seen in Table 5, the Zr-Ni bond lengths for the Zr30 and Zr40 alloys are almost identical (2.63 - 2.64 Å) independent of their hydrogen contents. The coordination numbers of the Zr30 alloys are significantly larger than those of the Zr40 alloys, thereby reflecting the difference in Zr-concentration between them. The Zr-Zr/Zr-Nb distances between the Zr30-H0 and the Zr30-H9 alloys are same within experimental accuracy. However, the Zr-Zr/Zr-Nb distance of the Zr40-H11 alloy is reasonably longer than that of the Zr40-H0 alloy by 0.08 Å. The hydrogen-induced expansion of the Zr-Zr distance have been also reported by Sakurai et al. [47] on (Ni0.6Nb0.4)100-xZrx (x = 30, 50) amorphous alloys by the Zr K-edge XAFS and X-ray diffraction [55]. They have also been reported by Liu et al. [56] on NiZr2 by the Zr K-edge XAFS. Furthermore, the Nb-Ni distance of the Zr40-H11 alloy also expands when compared with the Zr40-H0 one, although there is no report on this. Table 5 Results of the curve-fitting analysis for the Zr K-edge. For details, see the caption for Table 5. bond

Zr-Ni

Zr-Zr or Zr-Nb

Zr30-H0

Zr30-H9

Zr40-H0

Zr40-H11

r /Å

2.63

2.64

2.63

2.64

N

3.3

3.6

2.6

2.2

'E0 /eV

-7.0

-6.3

-7.5

-10.3

V2 /Å2

0.011

0.012

0.011

0.013

r /Å

3.24

3.25

3.25

3.33

N

5.4

4.8

5.1

5.0a)

'E0 /eV

2.3

2.9

1.8

-0.1

V2 /Å2

0.025

0.025

0.022

0.024

The difference in the structural response between Zr30 and Zr40 alloys probably comes from the difference in the site where the hydrogen atoms are located. In the Zr30 alloy, hydrogen atoms

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

13

plunge somewhere outside the clusters, since no significant changes in bond length was observed. The elongation of Zr-Zr/Zr-Nb and Nb-Ni distances in the Zr40-H11 alloy is associated with an occupation of hydrogen in tetrahedral sites surrounded by Zr and Nb, or Zr, Nb, and Ni atoms. For the Ni K-edge, the closest neighbour peak is probably derived from at least three contributions (Ni-Ni, Ni-Nb, and Ni-Zr), as discussed above. Consequently, the number of the fitting parameters becomes so large that we could not obtain reliable fitting results, even if the inter-atomic distances and MSRDs of Ni-Nb and Ni-Zr are constrained to those obtained in the fitting analysis of the Nb and Zr K-edges. To enhance the performance of the curve-fitting analysis on the data of the Ni K-edges, we must increase restriction condition for the fitting parameters. This will allow us to construct concrete atomic cluster models. It is known that icosahedron-like polyhedra play an important role in stabilising the structure of metal-metal type amorphous alloys [57]. With this fact in mind, we will discuss possible structural models for the Ni-Nb-Zr amorphous alloy studied here. Firstly, we will examine the model reported by Fukunaga et al [57]. Their results of the analysis of Voronoi polyhedra in the reverse Monte-Carlo (RMC) simulation based on the data of neutron and X-ray diffraction indicate that all the Zr atoms in the Ni25Zr60Al15 amorphous alloy are mostly surrounded by icosahedra or icosahedron-like polyhedra. This means the average coordination number for Zr atom is ca. 12. However, the coordination numbers estimated from our XAFS results are 7.2–8.7. Therefore, Fukunaga’s model is inconsistent with our results of the XAFS analysis. We will also discuss a model in which the icosahedral or icosahedron-like clusters are randomly packed. In this model, the contribution from the atoms in neighbouring clusters to the FT spectra of XAFS will be negligibly small, because it is evident that the positional correlation between the atoms in one cluster and in another will be weak in an amorphous state. The coordination numbers observed using XAFS account for the configuration of the atoms within a cluster. In the analysis of the Zr K-edge XAFS spectra of the Ni-Nb-Zr amorphous alloys, Sakurai et al. [47] presumed that the second closest neighbour peak in FT spectra is mostly comes from the Zr-Zr bonds, and the contribution from Zr-Nb is negligible. This means that the Zr and Nb atoms are not directly bonded. The icosahedral cluster model satisfying this condition (hereafter referred to as model-(a)) is depicted in Fig. 6(a). The average coordination numbers calculated for the model-(a) are listed in Table 6, together with the coordination numbers estimated by the XAFS analysis for the Zr30-H0 and Zr40-H0 alloys. As given in Table 6, the average coordination number of 6 for Nb-Ni estimated from the model-(a) is apparently large in comparison with the values obtained by XAFS analysis. Furthermore, the content ratio of Nb to the other atoms (Zr and Ni) in the cluster is too small when taking the actual chemical compositions of the Zr30 and Zr40 alloys into consideration. Therefore, it is more likely that the second neighbour peak of the Zr K-edge also includes the inevitable component of Zr-Nb as well as that of Zr-Zr. As the previous models described above do not explain the analysis results of the XAFS spectra, we propose two probable cluster models for the Zr-Nb-Ni ternary amorphous alloys as depicted in Figs. 6(b) and (c) (hereafter referred to as models-(b) and (c), respectively). In fact, the average coordination numbers calculated for both the cluster models (Table 6) fairly agree with the coordination

14

Chapter 3

numbers estimated by XAFS. It should be noted that the shape of the icosahedron should be distorted, since the bond-lengths of Zr-Ni, Nb-Ni, Zr-Zr, and Zr-Nb are different among them, as shown in Fig. 6. In both models, the maximum numbers of hydrogen atoms that can be stored in the clusters are different. From the XAFS analysis, it is difficult to determine which model is more preferable, since the difference between the coordination numbers calculated for models-(b) and (c) is so small when obtained by XAFS analysis. The distorted icosahedral cluster(s) of models (b) and (c), or a combination of them will be the main constituent of the amorphous alloys. The addition of hydrogen atoms has no significant effect on the atomic configuration in Zr30 alloy, but dies on the Zr40 one. This suggests that hydrogen atoms occupy only the sites outside the Ni-Nb-Zr clusters in Zr30 alloys, but both inside and outside the clusters in Zr40 alloys. This difference in the location of hydrogen atoms possibly comes from a certain structural difference between Zr30 and Zr40 alloys. Although we have not had a clear picture yet, there may be a structural difference in the cluster itself and/or in the interstitial space outside the cluster defined by the manner in which clusters are arranged in the alloys. Table 6 Average coordination numbers calculated for three cluster models. The structures of model clusters are illustrated in Fig. 5. The coordination numbers estimated by XAFS analysis are also shown. Edge

Bond Nb-Ni

Nb K

Model

XAFS

(a)

(b)

(c)

Zr30-H0

Zr40-H0

6

1.67

2.33

1.5

0.90

0

4.33

3.67

--

--

2.6

2.2

2.6

3.3

2.6

3.4

5

4.6

5.4

5.1

Nb-Nb or Nb-Zr Zr-Ni

Zr K

Zr-Zr or Zr-Nb

From the structural change of the hydrogenated alloys observed by XAFS analysis, we can decide the occupation sites of hydrogen, as indicated by small gray solid circles in Fig. 6. In the upper part of the clusters, hydrogen atoms are settled into the tetrahedron sites that are surrounded by three Zr atoms and one Nb atom, since the Zr-Zr and Zr-Nb bonds expand after hydrogenation. The Nb-Ni bond also lengthens by hydrogenation. Thus, the hydrogen atoms are plunged into a near Nb atom in tetrahedral sites in the lower part of the clusters. More hydrogen atoms occupy the upper side. Considering the stoichiometry, these sites will be partially occupied by the hydrogen atoms in the Zr40-H11 alloy. The atomic radii of Ni, Nb, and Zr in the crystalline form are 1.24, 1.45, and 1.60 Å, respectively [58]. Therefore, the atomic distances of Nb-Ni and Zr-Ni in the Ni-Nb-Zr amorphous alloys obtained in the present study (2.54 - 2.55 and 2.63 Å, respectively) are considerably shorter than those calculated from the crystalline atomic radii (2.69 and 2.84 Å, respectively). This is an important point for application of amorphous alloys, such as

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

15

super-conductivity and ballistic transport. Furthermore, dropping a hydrogen atom into the designated tetrahedral site induces shrinkage of the atomic distances in the neighbour sites, as a high pressure effect. This also provides another important effect for atomic structural elucidation of the various electronic transport behaviours [36] in the Ni-Nb-Zr glassy alloys of interest. (a)

(b)

Fig. 6 Cluster models with an icosahedral structure and the chemical compositions of Ni5Nb3Zr5 (a, b). The sites that can be occupied by hydrogen atoms are also indicated by small gray circles. The bond-lengths obtained by the XAFS analysis are indicated in the bottom part.

3.2 Structures of the icosahedral clusters by first-principles molecular dynamics calculation and XAFS measurements [59] In the previous section, we considered that hydrogen atoms in the Zr30at.% alloy plunge into a space somewhere outside the clusters, based on the fact that there is no change in the bond length, while the elongation of the Zr–Zr/Zr–Nb and Nb–Ni distances in the (Ni36Nb24Zr40)0.89H0.11 (Zr40-H11) alloy are associated with the occupation of the tetrahedral sites surrounded by Zr and Nb or Zr, Nb, and Ni atoms by hydrogen in the clusters [46, 41]. In fact, the Zr40at. % alloy showed room temperature Coulomb oscillation when it was hydrogenated, while the Zr30at. % alloy did not [37]. Therefore, the origin of the difference in the electronic properties of these alloys lies in the structural difference between them. Especially, the spectra of the pre-edge region reflect the electronic structure of the relevant ion and its surroundings, as is well known. We found that the hydrogen atoms occupy highly symmetric sites in Zr40-H11 to prevent the d-p mixing, and that hydrogen atoms principally surround the Zr and Nb atoms [60]. In the section, we will discuss in detail a possible cluster model for the amorphous alloys. First, we will examine the XAFS data again and we will focus on the X-ray absorption Near Edge Structure (XANES) spectra, in order to extract further structural information, especially related to the possible position of the hydrogen atoms inside the cluster. Also, the results of the cluster simulation of the Zr40at. % alloy using first-principles calculations are presented. This gives a more probable hydrogen position than the model proposed based on the analysis of the extended X-ray absorption fine structure (EXAFS) and XANES spectra. The stable hydrogen sites are discussed based on the results of the XAFS and theoretical simulation.

16

Chapter 3

The optimised atomic configurations of the icosahedral clusters that consisted of Ni, Nb, Zr and H atoms were determined by VASP: a plane-wave-based first-principles molecular dynamics calculation package [61]. We employed the ultrasoft pseudopotential for the core orbitals [62] (1s-3p for Ni and 1s-4p for Zr and Nb) under the generalised gradient approximation (PW91 [57]). The cutoff energy for the plane wave basis was 241.622 eV (NORMAL precision in VASP). The isolated cluster system was realised in a supercell with the ī-point approximation. A length of more than 10Å was adopted for the cell dimension. A quasi-Newtonian algorithm was used to relax the ions until the change in the total energy reached below 10-3 eV between the two ionic steps. The results of the simulation were compared with those of the XAFS analysis to construct the optimum cluster model. The electronic states around the outmost shell of the absorbing atom should be reflected in the pre-edge energy region, where transitions from a 1s orbital to an nd, an (n+1)d and an (n+1)p state can be observed in the transition metals. The former two transitions are essentially forbidden, while the last one is allowed for the electric dipole moment. Therefore, the absorption intensities of the former two transitions are weak, but very sensitive to the alignment symmetry of the surroundings. A few pre-edge peaks were often observed in the XAFS spectra of transition metal compounds. Weak but explicit pre-peaks were sometimes found, and were assigned to the transition to the nd states. Figure 7 shows the absorption spectra around the K-edge of Ni, Nb, and Zr, respectively, for the Ni-Nb-Zr-H amorphous alloys. A shoulder accompanies the rising of each absorption edge, except in the case of the Zr40-H11 alloy. The energy position of the shoulder is in the range of 1~5 eV below the edge is determined as having half the intensity of the edge jump. Therefore, it is reasonable to assign the shoulder peaks to the parity forbidden transition to the 3d orbital (Ni) and the 4d orbital (Nb and Zr). The transition moment to the orbitals generally does not reach zero, due to the crystal (ligand) field with odd parity or the lattice vibration (phonon) of odd parity modes in solids. As can be seen in Fig. 7, the intensity of the shoulder for the Zr30at. % alloy remains unchanged in hydrogenation at all three absorption edges. However, the Zr40at. % alloy is substantially weakened by hydrogenation at the Nb and Zr K-edges, although less affected at the Ni K-edge. Turning our attention to the post-edge energy region in the XANES spectrum, a difference between Zr30% and Zr40% was similar to that in the pre-edge region on the hydrogenation of the alloys. The difference in the post-edge region for the XANES spectrum would include structural information on the cluster backbone, which is complementary to the information given by the EXAFS spectra. Moreover, the scattering caused by light elements such as H, He, and Li diminished at a low wavenumber, because the back-scattering amplitudes rapidly decreased with the wavenumber of the photoelectrons. Since the kinetic energy of the photoelectrons in the XANES region was much lower than that in the EXAFS region, the spectra ware directly and considerably affected even by these light elements. For these reasons, the XANES part of the XAFS spectra was more sensitive to the coordination of the H atoms than the EXAFS part. Therefore, we were also able to inspect the effects of hydrogenation on the structure from the post-edge XANES spectra.

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

17

Fig. 7 Close-ups of the pre-edge peaks in the XANES spectra of the amorphous alloys at the (a) Ni, (b) Nb, and (c) Zr K-edges.

As shown in Fig. 8, the post-edge spectrum of the Zr40at. % alloy for the Ni K-edge was less affected by hydrogenation. However, those for the Nb and Zr K-edges were rather strongly modified by the hydrogenation. In the case of the Zr30 at.% alloy, almost no change was observed upon hydrogen doping. Here, it should be noted that the modification of the spectrum by the charged hydrogen showed a similar tendency for both Nb and Zr K-post-edges. This finding implies that the multi-scattering paths of the hydrogen atoms surrounding these metal atoms were analogical: that is, the hydrogen atoms coordinated around these metal atoms in a similar electronic configuration in both cases. The results shown in Fig. 8 are consistent with the structural configurations yielded by the XANES analysis, shown in Fig. 7. The results of the XANES analysis described above strongly suggest the following several points: i) in Zr30at. % amorphous alloys, the hydrogen atoms do not localise inside, but outside the clusters; ii) the hydrogen atoms rarely localise the position around Ni atoms; iii) the hydrogen atoms occupy suitable sites in the clusters in the Zr40at. % alloy, and localise around the Nb and Zr atoms but not around the Ni atoms; iv) the sites occupied by the hydrogen atoms are positions which prevent p – d hybridisation.

18

Chapter 3

Fig. 8 XANES spectra of the amorphous alloys at (a) Ni, (b)Nb and (c)Zr K-edges, including pre- and post-edge regions.

To clarify the mechanism of the room-temperature Coulomb oscillation observed in (Ni0.36Nb0.24Zr0.40)90H10 amorphous alloy, we will focus on the Zr40 % sample with hydrogen in this section. Applying the coordination numbers obtained from the XAFS analysis results to the cluster model simulation by first-principles calculations, we reconstructed the atomic cluster model. It is well known that the atomic clusters of metal/metal-typed amorphous alloys are characterised by a Zr-centred icosahedral structure [36]. So, we will focus on isolated icosahedral Zr-centred Ni5Nb3Zr5 clusters, whose composition is close to that of the Ni36Nb24Zr40 alloy [40]; this is assuming that the energy of the hydrogen on the surface of the cluster is not significantly changed by the presence of neighbouring clusters [41]. Real clusters are combined with small amounts of other Voronoi-like polyhedra: i.e., they are not isolated [36]. The four possible structural models are presented in Table 7, along with the total binding energies, which are given for each structural model in the order of stability. The four kinds of models are shown in Fig. 9 through a side and top view. The relationships between the coordination numbers of the Zr-Zr (or Zr-Nb) and Nb-Ni bondings, on the one hand, and the coordination numbers of the Zr-Ni bonding, on the other, are shown in Fig. 10. When applying the calculated coordination numbers for the four kinds of clusters to the experimental ones, the coordination numbers of Ih553z and Ih553i agree well with those determined by the XAFS analysis. Therefore, the Ih553z and Ih553i cluster are candidates for the main intrinsic cluster. From the energetic point of view, the Ih553i cluster is more feasible, as seen in the total energies listed in Table 8. However, as seen in Fig. 9, the shape of Ih553i and Ih553z is distorted relative to the ideal icosahedron shape. In comparison with two models, the Ih553z cluster is slightly more stable than the Ih553i one. Therefore, we currently believe that the Ih533z cluster is the most probable cluster.

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

19

Fig. 9 Side and top views of the four stable kinds of simulated Ni5Zr5Nb3 clusters. The solid circles represent Zr atoms (black), Nb atoms (gray), and Ni atoms (white). Table 7 Comparison between the calculated and the experimental coordination numbers for the Zr-Ni, Zr-Zr or Zr-Nb and Nb-Ni bindings in four kinds of simulated clusters.

Cluster type Cluster type

Coordination numbers

Centered element

Total

binding㻌

Zr-Ni

energy (eV)

Zr-Zr

Nb-Ni

or Zr-Nb

1. Ih553i

-79.8289

Zr

2.40

4.80

1.00

2. Ih553z

-79.157

Zr

2.60

4.60

1.67

3. Ih553b

-78.8349

Zr

1.40

4.60

2.00

4. Ih553e㻌

-77.2815

Zr

2.00

5.20

3.33

Fig. 10 Comparison between the calculated and the experimental coordination numbers for the Zr-Zr or Zr-Nb and Nb-Ni bindings in four stable types of simulated clusters.

20

Chapter 3

Fig. 11 The side and top views of 20 kinds of simulated Ni5Zr5Nb3 clusters with H atom. The clusters are in the order of stability. The distance from the facet surface of the cage is also shown. The plus sign of the distance denotes running away from the centre of the grey tetrahedral cage, while larger negative values mean stable localisation of hydrogen in the one.

Next, we simulated the possible localisation site of hydrogen in the hypothetical Ih553z icosahedron. A hydrogen atom was placed at the centre of one of the 20 tetrahedron cages as its initial position (distance from the central Zr atom = 1.32 Å). Then, the position of the H atom was optimised relative to the fixed cages. When one hydrogen atom plunged into a tetrahedral site in the Ih553z icosahedron, the total energy of the Zr-Ni-Nb-H network changed depending on the combination of the three constituent elements of the for tetrahedron. The optimised positions of

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

21

the H atom in the 20 possible kinds of Ni5Zr5Nb3 (Ih553z) configurations are presented in Fig. 11, along with the distance from the facet surface of the cage. It should again be noted that the initial position of the H atom was set at the center of the purple tetrahedral cage. A plus sign on the distance denotes movement away from the tetrahedral cage, while larger negative values mean the stable localisation of the hydrogen atom in the cage. Actually, the hydrogen atom in Fig. 15(c) and (e) moves away from the tetrahedrons composed of two or three Ni elements ((a)-(i) and (k) in Fig. 11), and settles inside the tetrahedron with zero or one Ni atom ((j)). As a result, the order of stability of the hydrogen site in the tetrahedrons is as follows: two Zr-Zr-Nb-Nb Fig. 12(a) Hydrogen-occupied icosahedron cluster (Ih553z) model, and (b) the distances among two stable ((r) and (t)); four Zr-Zr-Zr-Nb ((l)-(n) and and four metastable H sites. (p)); two Zr-Zr-Nb-Ni ((q) and (s)); and two Zr-Zr-Zr-Ni ((j) and (o)) tetrahedrons. Since Ni has an anti-affinity for hydrogen, the sites of the last two Zr-Zr-Ni-Ni tetrahedra are metastable, while the sites of the two Zr-Ni-Ni-Ni and Zr-Nb-Ni-Ni tetrahedral afford negligibly small stability. These results for the optimum hydrogen site are summarised in Fig. 12, alongside the ten hydrogen atoms. For clarity, the model cluster is illustrated in the regular icosahedron shape in the figure, although it is distorted in reality. The distances of inter hydrogen atoms among the two stable and four metastable H sites are presented in Fig. 12(b). From the calculated adiabatic potential energy of the hydrogen atom for the distorted icosahedral Ni5Zr5Nb3 cluster with hydrogen, it was concluded that the potential energy of hydrogen was adsorbed by the outer surface of the cluster, which was lower than that of the bonding state between Zr (or Nb) and the H atoms settled in the cluster [41, 63]. In other words, the outer adsorbed hydrogen from the cluster is in a stable state, while the inner bonding hydrogen in the tetrahedron is in a metastable state. Indeed, the hydrogen atom localised to a site between the clusters in alloys with a hydrogen content of approximately 5%, and inside the clusters in alloys with a hydrogen content of between 7% and 12.5 % [41]. The above calculation results are in good agreement with the XANES results on the affinity elements for hydrogen.

22

Chapter 3

It is known that icosahedral clusters with a size of ~1 nm exist in metal/metal-type Zr-based amorphous alloys with a Zr-centred cluster [36]. Since our model, Ih553z, is a Zr-centred icosahedral Ni5Zr5Nb3 cluster with a maximum size of 0.55 nm, the atomic configuration agrees with the results of the XAFS analysis, as shown in Fig. 9. The amorphous alloy used in the present study consists of antinomic elements (i.e., Zr and Nb show affinity and Ni anti-affinity for hydrogen). Indeed, the enthalpies of the dissolved hydrogen atoms for Zr, Nb, and Ni are -63, -34, and +16 kJ/mol H, respectively [64]. Therefore, we must take the antinomy into consideration when we examine the structure of icosahedral clusters with hydrogen as well as conventional hydrogenated crystals. As can be seen from the sign of the distance from the facet surface of the cage in Fig. 11, the most stable localisation site for hydrogen is the tetrahedral site formed by two Zr and two Nb atoms, while the tetrahedron consisting of three Zr atoms and one Nb atom is of secondary stability. The hydrogen is less stable if it is at a tetrahedral site that includes at least one Ni atom. Therefore, the distorted Ni5Zr5Nb3 cluster of interest is characterised by five Ni atoms, which form half a pentahedron and an opposite pentahedral Zr-Nb assembly, because the theoretical simulations indicate that the gathering of Ni atoms in the icosahedra lowers the total energy. The nanometre-sized strangely shaped icosahedral clusters and their atomic configurations seem to be the source of functional properties, such as the Coulomb oscillation [36-38, 65–68] in Chapter 4, ballistic transport behaviours [41, 69] in Chapter 5, and super-conductivity [36, 70] in Chapter 6. 3.3 Structures and electronic properties of Ni5Nb5Zr5 clusters in Ni-Nb-Zr amorphous alloys [71, with kind permission of The European Physical Journal (EPJ)] In this section, we will calculate the electronic states of the icosahedral Ni5Nb5Zr5 clusters and optimise the structures by using the first principles calculation. To check and compare the supercell calculation with isolated cluster calculation, we will employ the ADF package with the LCAO-GGA scheme [72]. The ADF package is also used for DOS calculation and population analysis. The initial structure of the Ni5Nb3Zr5 is taken as an icosahedron with the interatomic distance of 2.50 Å between the center and the surrounding atoms (2.63 Å between surrounding atoms). Then the structures are fully optimised by the quasi-Newton algorithm until the change in the total energy is smaller than 10-4 eV between the two ionic steps. Figure 13 shows the total energies of twenty-¿YH optimised clusters as a function of Nb-Ni CN (number of Ni atoms surrounding a Nb atom): (a) for Ni-centred, (b) for Nb-centred, and (c) for Zr-centred clusters. The vertical lines indicate the CN, 0.9, obtained by XAFS method [40]. Comparing three types of the centre atom, the Ni-centred clusters are more stable in general. This is mainly due to a small atomic radius of Ni atoms, Û$ (cf. Û$ for Nb, Û$ for Zr). Figure 13 also shows, especially for the Ni-centred cluster in Fig. 13 (a), that a smaller CN in the Nb-Ni makes the cluster more stable. This tendency agrees with the remarkably small number of the experimental result, 0.9. For Nb-centred clusters, the CNs of Nb-Ni are obviously larger than in the experimental one, and never come close to that value. The optimised structure of the most stable Ni-centred cluster, as shown by the inset in Fig. 13(a), keeps its icosahedral shape whereas

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

23

the optimised structure of the Zr-centred cluster in Fig. 13(c) is distorted and some Ni-Ni bonds are lost. The distortion in the Zr-centred cluster seems to be a kind of crystallisation that is unsuitable for glass formation as discussed below. The symbols of triangle indicate the cluster, which contains a Nb-triangle. The aggregated triangle implies small CNs in the Nb-Ni, and the most stable clusters in Fig. 13 include the Nb-triangle. Based on the three results above––(a) the relatively low energy, (b) keeping the icosahedral shape (non- crystallisation), and (c) small coordination number of Nb-Ni––we select the Ni-centred Nb-triangle clusters as the candidates for the local structural unit of Ni-Nb-Zr amorphous alloy.

Fig. 13 Total energies of various Ni5Nb3Zr5 clusters as a function of Nb-Ni CN for (a) Ni-centred, (b) Nb-centred, and (c) Zr-centred clusters.

We then calculate the electronic states and optimise the structures of Ni-centred Nb-triangle Ni5Nb3Zr5 clusters with the twenty-six energetically inequivalent atomic FRQ¿JXUDWLRQV There exist twenty-six energetically nonequivalent atomic FRQ¿JXUDWLRQV among the 9C4 combinations for four Ni atoms placed on nine atomic sites. This eliminates the atomic FRQ¿JXUDWLRQV that connect with other configurations by symmetry operations (rotation, mirror, inversion). The atomic FRQ¿JXUDWLRQV are denoted by four integers. An example is shown in the inset of Fig. 14. The total energies of the twenty-six clusters in the function of Nb-Ni coordination number in Fig. 14 suggest, as well as the total energies in Fig. 13, that the smaller CN in the Nb-Ni makes the cluster more stable.

24

Chapter 3

Fig. 14 Total energies of twenty-six Ni-centred Nb-triangle clusters as a function of CN in Nb-Ni. Optimized structures of several clusters (distinguished by underlines on the notations) are also indicated.

In addition to the dependency on the CN of Nb-Ni, we obtain the following characteristics D íF by comparing the total energies with the optimised structures. (a) The most stable clusters are distorted, and the structures are far from icosahedral shape. See example structures 1458 and 1279. (b) Some icosahedron-like clusters in which Ni atoms are not aggregated and found among Zr atoms such as 1489 and 4789 have higher total energy. These clusters also have relatively large CNs of Nb-Ni. (c) Another type of icosahedron-like cluster, 1234 and 1247, in which Ni atoms are aggregated from the Nb-triangle is relatively more stable than those in (b). The clusters described in (a) have a typical atomic structure: an octahedron composed of a Zr-square plane and a Ni-dimer perpendicular to the plane. Then, the distortion in (a) seems to be a crystallisation, which stabilises the cluster, and suggests that these atomic FRQ¿JXUDWLRQV have a low activation energy against crystallisation. Therefore, the structure in (a) is not suitable for amorphous alloy because of how easily it crystallises, although the structure is the most stable. It is noted that the pair interaction energy of the Ni-Ni pair in the fcc Zr crystal obtained by the full-potential KKR method shows an oscillatory behaviour on pair distance, in which the pair interaction energy is positive (0.118 eV) for the ¿rst nearest neighbours and negative (-0.088 eV) for the second neighbours, so that Ni atoms prefer to separate each other in Zr [73]. This is one of the driving forces to crystallise the regular (ordered) Ni-Zr alloys. The clusters in (b) are not suitable candidates simply because of the high energies and of the large CNs that disagree with the

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

25

experimental value. The clusters in (c) seem to possess (free) energy comparable with those of the related crystals and enough activation energy against crystallisation, both of which are associated with the mechanism for stabilisation of amorphous alloys. Moreover, the characteristically small CN from the Nb-Ni appears in these clusters. Therefore, we select the clusters in (c), 1234, 1237, and 1,245 (although this is slightly distorted) as the candidates of the local structural unit of Ni-Nb-Zr amorphous alloys.

Fig. 15 Total and partial density of states of Ni5Nb5Zr5 cluster (1234).

Figure 15 shows the total and partial density of states (DOS) for Ni5Nb3Zr5 (1234) cluster. The total DOS has a pseudo gap around the Fermi level, which is designated by a vertical broken line. The pseudo gap is caused from the bonding between the d orbitals from the Ni and Zr atoms, and stabilises the electronic states, like in the Hume-Rothery phase [74]. It is noted, although not shown here, that hydrogen adsorption preferably occurs in Zr/Nb tetrahedral sites, but not in Ni sites; this also occurs with the Zr-centred cluster [59].

We constructed the probable local structures of a Ni36Nb24Zr40 amorphous alloy composed of the clusters 1234, 1237, and 1245, based on the CNs and a density of 7.79 g/cm3, which was obtained experimentally. The CNs by XAFS listed in the bottom row of Table 8 suggests that the clusters do not interpenetrate each other because this creates a large CN. The atomic FRQ¿JXUDWLRQ described above also suggests that Ni atoms, as well as Nb atoms, prefer to aggregate. Then, we connected the Fig. 16 Local structures of Ni36Nb24Zr40 Ni5Nb3Zr5 clusters along the 3-fold axes, so that the amorphous alloy composed of Ni (vacancy)-centred Ni5(4)Nb3Zr5 clusters. Ni- or Nb-triangles constituted the octahedrons of Ni or Nb at the connection shown in Fig. 16. If the cluster connects regularly with six clusters, then a rhombohedron of icosahedron is constructed in a similar way to the quasicrystals. To ¿t the stoichiometry with that of the amorphous alloy, Ni36Nb24Zr40, and to reduce the CN, the centre Ni atoms are removed for half of the clusters. It is noted that the optimised structures of a vacancy-centred cluster of 1234 has an icosahedral shape (not shown here). The density of 7.78 g/cm3 is obtained for the rhombohedron, Ni36Nb24Zr40, when the inter-cluster distance (the distance between centres of the clusters) is 6.28 ǖ. Table 8 compares the CNs by XAFS with those of the

26

Chapter 3

proposed local structures for the unit of clusters 1245, 1237, and 1234, respectively. The CNs for 1234 agrees with those by XAFS on average, although the total coordination number is slightly larger. Therefore, we conclude that the cluster 1234 typically connects along the 3-fold axes in the Ni36Nb24Zr40 amorphous alloys. However many types of the Ni5Nb3Zr5 clusters still exist, and randomly and loosely connect with each other. Table 8 Coordination numbers in Ni36Nb24Zr40 composed of clusters, 1245, 1237, and 1234. The corresponding experimental results in reference [71] are listed in the bottom row. cluster

Zr-Ni Zr-Zr/Nb

1245

4.9

4.6

1.83

9.5

1237

5.4

4.1

1.83

9.5

1234

6.0

3.5

0.83

9.5

XAFS

5.1

2.6

0.90

7.7

Nb-Ni

Zr-total

Figure 17 shows the optimised structures of the twins from the 1234 clusters, which are connected along the 3-fold axes on (a) Ni- triangles, (b) Nb-triangles, and (c) Zr/Nb- triangles. The optimised structures are obtained from the two optimised 1234 clusters with an initial inter-cluster distance of 6.5 ǖ. Among the three, the twin clusters (b) connected by Nb-octahedron has an icosahedral shape, whereas the twin clusters (a) connected by Ni-octahedron are distorted, and some Ni-Ni bonds are lost, like in the Zr-centred clusters described above. Therefore, (aggregated) Nb-atoms seem to have stabilised the Ni36Nb24Zr40 in both the cluster and inter-cluster region.

Fig. 17 Optimised structures of the twins in the Ni-centred Ni5Nb3Zr5 clusters, which connect along the three 3-fold axes. Binding energies/cluster [eV] are also shown below the structures.

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

27

3.4 Local structures and structural phase change in Ni-Zr-Nb amorphous alloys composed of Ni5 Nb3Zr5 icosahedral clusters [73] Although the above estimations provide useful suggestions with regard to constructing the local atomic model for the alloys, they are limited within the ¿rst atomic shell, and have a certain ambiguity or inconsistency. The local atomic structure in Ni-Zr-Nb amorphous alloys and hydrogenated ones have not yet been FRQ¿UPHG however, interesting phenomena will appear, especially around its composition. From a ¿rst principles calculation perspective, it is one of many challenging problems to determine local structures in amorphous alloys. The molecular dynamics (MD) calculation is employed as a common manoeuvre for nonequilibrium systems and a few hundred atoms in a supercell are moved by the ¿rst principles MD scheme under a controlled temperature. After several thousand MD-steps, some snapshots of the atomic structure are taken. The local structures are discussed by the Voronoi polyhedron (VP) analysis, and the radial distribution functions (RDFs) and so on are derived from the snapshots. For example, local structures in the amorphous alloy, Ni62.5Nb37.5 [74], and in the liquid metal, Ni36Zr64 [75], were recently simulated by the ¿rst principles MD. These ¿rst principles MDs have revealed that the icosahedral local structure is commonly found in Ni-Nb [74] and Cu-Zr [76] amorphous alloys, but rarely in Ni-Zr alloys [75]. One of the reasons that the icosahedral structure is unfavourable in Ni-Zr alloys is because of the strong bond between Ni and Zr atoms where Friedel’s band ¿lling rule is VDWLV¿HG for d-electrons [71]. The strong Ni-Zr bond easily transforms a segment with a typical structure in regular alloys into amorphous alloys. The standard MD scheme may provide feasible structures for actual non-crystalline alloys. Some proposed cluster-packing models based on the MD calculations exist [77, 78]. However, for such a complicated case as Ni-Zr or ternary alloys, the obtained results may be averaged and are often so obscure that they might veil the essential or key structures in the alloys. There are other cluster-packing models [79–81] for amorphous alloys based on the Hume- Rothery stabilisation rule and the related composition rules [82–84] with icosahedral or relevant clusters, which exist in their GHYLWUL¿FDWLRQ or crystalline phases as common clusters. These models may be powerful skills to construct an amorphous structure whose composition is the same or similar to those in the crystalline derivatives. Nevertheless, it is still necessary to ¿nd out another structure of the clusters that are different from those in their crystalline phases for the composition dealt with in this paper, Ni-5: Zr-5: Nb-3: three of which are comparable, and far from NiZr, NiZr2, Ni6Nb7, etc. In this section, we will try a bottom-up approach, instead of the standard MD approach. First, we will explore a series of Ni5Zr5Nb3 isolated clusters (isomers), whose stoichiometric compositions are similar to that of the amorphous alloy, Ni36Zr40Nb24. We will then select some clusters as candidates for the local units through the structural investigation. We will construct a continuous local structural model of the Ni-Zr-Nb ternary alloy from the icosahedra, Ni5Zr5Nb3, described in the previous section. Oji et al. have estimated a remarkably small CN from a Zr atom, 7.7-8.7 [38]. It is well known that a CN estimated from the XAFS spectrum is uncertain; however, it is possible that a Zr atom has a relatively small CN in the amorphous alloy in comparison with those in

28

Chapter 3

regular Ni-Zr alloys, Ң 15. This small CN suggests that the local structural units neither penetrate each other nor share a facet because a dense connection, such as a penetration, may create a large CN. We assume that an icosahedron connects with six adjacent icosahedra along their 3-fold rotation axes and that an octahedron bridges the adjacent icosahedra (two triangle facets make the octahedron without a glue atom). According to the angle between the second nearest 3-fold rotation axes of an icosahedron, a rhombohedron with the face angle Į of cosí1(1/3) "- 70.53ƕ can be constructed as a structural unit, where the icosahedra are located at the vertices (I-sites in Fig. 18) and connected along their edges. We take a double-sized rhombohedral cell to be optimised, which contains eight icosahedra and eight vacant sites (V-sites in Fig. 18) among the icosahedra. We locate additional eight atoms at the V-sites, so that 112 atoms are included in total. Fig. 18 (a) shows an example of the structural model of 112 atom-rhombohedral cell, as well as those around the I-site and the V-site in Figs. 18 (b) and (c). As shown in Fig. 18 (c), the structure around the V-site is fairly distorted but also icosahedral (Voronoi index (0, 0, 12, 0) at the V-site, where the Voronoi polyhedron (VP) consists of only twelve pentagons). Then sixteen icosahedra (0, 0, 12, 0) exist in total in a cell. A lattice parameter of the rhombohedral cell of 13.04 ǖ is estimated from the mass density: 7.79 [g/cm3], of an experimentally obtained sample Ni36Zr40Nb24 [85] and the total mass of 112 atoms in a cell, Ni40.3Zr44.8Nb26.9, whose ratio is the same as that of in the sample. It is noted that we have obtained an equilibrium lattice constant of around 13.05 ǖ for the optimised structure of Ni48Zr40Nb24. It is also noted that we kept vacancies at the V-sites and also removed centre atoms from the half of the I-sites (i.e., added four vacancies in the proposal model in the previous work [69]) to realise the small CN and the composition ratio, which corresponds to the experimental sample. However, MD calculations have revealed that these vacancies easily disappear and the icosahedral structures are broken.

Fig. 18 An example of the initial structure of a Ni48Zr40Nb24 cell viewed from the direction of a primitive vector. Eight regular and eight distorted icosahedral units shown in (b) and (c) are contained in a cell. A regular icosahedron is connected with six adjacent icosahedra bridged by Nb6, Ni6, or other octahedra.

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

29

Variations in the alignment of eight icosahedra in a cell are almost LQ¿QLWH even if we employ only one type of the icosahedron, because this is also the case for the combinations of the icosahedra’s orientations. We can take the or randomly choose the orientation of each icosahedron. We can also randomly set an atom at a V-site from the three elements. However, it is very difficult for randomly aligned structures to obtain converged results within a few thousand MD steps; therefore, we concentrated on the relatively highly oriented alignments of the icosahedra and located Ni atoms at the V-sites. We will now show the calculated results for the following six alignments with eight additional Ni atoms, Ni48Zr40Nb24, with a typical structure: (a)An icosahedron connects with six inversions; a Nb6 (or a Ni6) octahedron appears at one of the six bridges between icosahedra as shown in Fig. 18. (b)The same alignment (a) in a layer along two primitive vectors, and the layer is stacked homogenously along another primitive vector; an icosahedron connects with four inversions in a layer and with two icosahedra oriented to the same direction; a Nb6 (or a Ni6) octahedron appears at one of six bridges similarly to the alignment (a) but the other four bridges are different from those in the alignment (a). (c)An icosahedron connects with six icosahedra rotated uniformly; an Nb6 (or a Ni6) octahedron appears at one of six bridges; the other bridges are different from those in (a) and (b). (d)An icosahedron connects with six icosahedra, which are rotated uniformly but differently from (c); an Nb5 pyramid appears at one of the six bridges. (e)Icosahedra are aligned homogenously in a layer but inverted layer by layer. (f) All icosahedra are aligned homogenously. Figure 19 shows the total energy vs. lattice constant for the optimised structures of Ni48Zr40Nb24 with the alignment of an icosahedron (a). A similar equilibrium lattice constant of 13.09 ǖ has been obtained for the alignment of (f). Hence optimisations for other alignments and comparison between the optimised structures with different alignments are performed at the lattice constant of 13.1 ǖ. The initial structure of an icosahedron in each alignment is taken as the interatomic distance of 2.75 ǖ between the centre and surrounding atoms. Then the structures are fully optimised by the quasi-Newton algorithm until the change in total energy is smaller than 10í4 eV between the two Fig. 19 Total energy vs. lattice constant, ǻE [eV/atom], for the optimised structures of steps of ionic relaxation. Ni48Zr40Nb24 with the alignment (a).

30

Chapter 3

Figure 20 shows optimised structures of six alignments (a)–(f) of Ni48Zr40Nb24 with a lattice constant of 13.1 ǖ. Table 9 indicates the results of the Voronoi polyhedron (VP) analysis for the optimised structures; the average CNs, nC; average compositions of atoms related tp VP, NilZrmNbn; and numbers of VPs with the index (0, 0, 12, 0): that is, numbers of icosahedra in a cell, Nicos, for 48-Ni, 40-Zr, and 24-Nb atoms, respectively. For comparison, the results of the VP analysis for the initial structures of alignments (a) in Figs. 20 (a) and 20 (f) are also indicated in the bottom as (a) and (f). The optimised structures in Fig. 22 show two characteristic phases: an amorphous phase in which the local icosahedral structure keeps well and an almost periodic phase in which the icosahedral structure changes to an fcc-like lattice. The former phase is typically shown in Fig. 20 (a), and the latter in Fig. 24 (f). Two cutouts of the optimised structure around a vertex (I-site in Fig. 18) of the rhombohedral cell are indicated in Figs. 21 (a) and 21 (f). A distorted icosahedron of Table 9 Voronoi polyhedron (VP) analysis for the three elements (Ni, Zr and Nb) in the optimised structures of Ni48Zr40Nb24 in the alignments (a)–(f) of the local icosahedral units: average CN at the centre of VP(nC), average composition of atoms related to a VP (Ni l ZrmNb n), number of (0, 0, 12, 0)-VP (Nicoss) in a cell, and total energy differences ¨E)[eV/atom]. These quantities for the initial structures of (a) and (f) are also indicated at the bottom rows (A) and (F).

Fig. 20 Optimized structures of Ni48Zr40Nb24 in rhombohedral cells with the lattice constant of 13.1 ǖ for the alignment of icosahedra (a–-(f). A prominent structural difference appears between (a)–(d) and (e), (f).

Table 9 Voronoi polyhedron (VP) analysis for the three elements (Ni, Zr and Nb) in the optimised structures of Ni48 Zr40 Nb24 in the alignments (a)–(f) of the local icosahedral units: average CN at the centre of VP(nC ), average composition of atoms related t o a VP (Ni l Zrm Nb n ), number of (0, 0, 12, 0)-VP (Nicos s) in a cell, and total energy differences ¨E)[eV/atom]. These quantities for the initial structures of (a) and (f) are also indicated at the bottom rows (A) and (F).

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

Ni-centre nC (a)

l

m

Zr-centre n

12.167 6.500 4.833 1.833

Nicos

nC

l

m

31

Nb-centre n

Nicos

nC

l

m

n

Nicos

¨E

12 13.800 5.800 6.200 2.800

0

13.000 3.667 4.667 5.667

0

+0.136

(b) 12.333 6.500 5.333 1.500

8

14.200 6.400 6.400 2.400

0

12.333 3.000 4.000 6.333

0

+0.032

(c) 11.688 6.500 4.917 1.271

4

14.100 5.900 6.200 3.000

0

12.542 2.542 5.000 6.000

0

+0.054

(d) 12.292 6.667 5.125 1.500

4

13.750 6.150 5.600 3.000

0

13.333 3.000 5.000 6.333

0

+0.070

(e) 12.167 5.833 4.500 2.833

0

14.200 5.400 6.400 3.400

0

13.333 5.667 5.667 3.000

0

+0.000

(f) 12.083 5.750 4.500 2.833

0

13.850 5.400 6.450 3.000

0

12.667 5.667 5.000 3.000

0

+0.032

(A) 11.333 6.333 4.500 1.500

16 11.000 5.400 4.200 2.400

0 11.000 3.000 4.000 5.000

0

í

(F) 11.333 5.667 4.333 2.333

16

0

0

í

11.000 5.200 4.200 2.600

11.000 4.667 4.333 3.000

Voronoi-index (0, 0, 12, 0) is seen for the alignment (a), while a distorted cuboctahedron of the Voronoi-index (0, 4, 4, 4) exists for the alignment (f). The icosahedron in Fig. 21 (a) is connected with adjacent icosahedra, which is bridged by octahedral, as well as the initial structure. The cuboctahedron in Fig. 21 (f) constitutes a fcc-like lattice. As shown along the edges of both sides in Fig. 20 (f), the cuboctahedra align stepwise with a step-height of half of the fcc-lattice constant. The number of icosahedra, Nicos, for the Ni-centre listed in the sixth column in Table 9 remains (Nicos = 12) in the alignment (a), while all the sixteen icosahedra vanish (Nicos = 0) in the alignments (e) and (f). No icosahedral structure appears at Zr-centre or Nb-centre sites for all the alignments, as shown in the 11th and 16th columns. Alignments from (a) to (d), which keep some icosahedral structure (Nicos = 4 - 12), have Nb-octahedra in (a)–(c) or Nb-pyramids in (d) as the bridge between the icosahedra. After the optimisation, they still have large average Nb-components in Nb-centred VPs, ݊ത = 5.67-6.33 in Nbn as shown on the 15th column in Table 9.

Fig. 21 Thirteen atom distorted icosahedrons and cuboctahedrons as cutouts of the optimized structures around a vertex of the rhombohedral cell in Figs. 20(a) and 20(f). Interatomic distances >ǖ@ between the centre and surrounding atoms are indicated beside the atoms. Interatomic distances between the centre Ni atom and surrounding Ni atoms are remarkably smaller in (a) (avg. 2.61 ǖ) than in (f) (avg. 2.89 ǖ)

32

Chapter 3

However, alignments (e) and (f) (Nicos = 0) have small numbers of Nb- components in Nb-centred VPs, ݊ത = 3.00; they are half of those for alignments (a)–(d). Therefore, taking account of the results on the isolated clusters, we conclude that Nb- clustering prevents the local structure from crystallisation and maintains the icosahedral structure. Differences in the total energy of the optimised structure between alignments are listed in the last column. It is evident that the total energies for the periodic phase, (e) and (f), are lower than the amorphous phase, (a)–(d). The lower energy for the periodic phase seems to correspond to stabilisation by crystallisation, which is similar to the situation for the isolated clusters. It is noted that we have found the amorphous phase similar to those in the alignment (a)–(d); this is also the case in the alignment (f) around the lattice constant of 13.05 ǖ. However, the energy of the amorphous phase in the alignment (f) is 0.05 [eV/atom] higher than that of the periodic phase. The average CNs nC increase via optimisation from those in the initial structure ݊തC Ң11; ݊തC Ң12 for Ni; Ң 14 for Zr; and Ң 13 for Nb. Differences among these values may correspond to differences among the atomic radii of Ni, Zr, and Nb atoms. Radial distribution functions (RDFs) of the Ni-Zr-Nb amorphous alloys, which have been estimated from XAFS data, have been reported and the local structures around the three elements have been discussed by the RDFs [38, 86]. In this subsection, RDFs obtained from the optimised structures are indicated and compared with the XAFS results. The RDFs are calculated by using Gaussian distribution functions with a standard deviation ı = 0.05 ǖ at an optimised position of an I atom, r, to broaden the spiky peaks due to the small number of atoms in the cell. Figs. 22 (a), (b) and (f) show the RDFs obtained from the optimised structures of Ni48Zr40Nb24 alloys. The RDFs around Ni atoms, gNi(r), around Zr atoms, gZr(r), and around Nb atoms, gNb(r) are shown from left to right in each row. The total RDFs, gI(r) (I = Ni, Zr, Nb) are indicated by black solid curves, and three components for the individual elements, gI(r) (I = Ni, Zr, Nb) are indicated by dashed, dotted and gray curves, respectively. The optimised structure of the alignment (a) has twelve distorted icosahedra, which may bring a certain non-periodicity to the atomic structure. Then, the signals further than the main peak are oscillated around ݃ூ௜ (r) = 1 in Fig. 22 (a), although the signals are spiky. In contrast, the RDFs for the alignment (f) in Fig. 22 (f) have four prominent peaks like a crystalline phase. The optimised structure for the alignment (f) indicates a distorted fcc-like structure with a certain periodicity in a unit cell. Thus, the four large peaks correspond to the interatomic distance between the neighbouring atoms in the fcc lattice. Four vertical arrows on each gI-curves in Fig. 22 (f) indicate distances of 2.9, 5.0, 6.5, and 7.7 ǖ. The ratio of these distances is 1: ξ3: ξ5:ξ7, which corresponds to the ratio for the 1st, 3rd, 5th, and 7th nearest neighbours in the fcc lattice. The signal from the ¿rst atomic shell in gNi(r) in Fig. 22 (a) has separated peaks at 2.60 and 2.80 ǖ. The ¿rst peak is mainly originated from Ni atoms and the second peak from Zr atoms, as shown by the dashed and dotted curves for Ni- and Zr-components,

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

33

ே௜ ே௕ ௓௥ ݃ே௜ (r) and ݃ே௜ (r). However, the contribution of the Nb-component, ݃ே௜ (r) to the peaks is ௜ remarkably small because of the small Nb-Ni CN. In contrast, three of ݃ே௜ (r) in Fig. 22 (f) have comparable components. In gZr(r) and gNb(r) in Fig. 22(a), the signal from the ¿rst atomic shell has

a single strong peak with small side peaks: one peak is at the near side (2.55–2.60 ǖ), two or three peaks are at the far side (3.25–3.35 and 3.55–3.60 ǖ). The main peak at 2.85 ǖ originated from the Ni and Nb atoms, while the far side peaks are from Zr atoms for gZr(r). For gNb(r), the main peak at 2.85 ǖ originated from Zr atoms, and the far side peaks are from Nb atoms. The outlines of the ¿rst shells in RDFs in alignment (f) are different from those in alignment (a). The two peaks gNi(r) in Fig. 22 (a) are close together and seem to an almost single peak in Fig. 22 (f). The main peak of gZr(r) or gNb(r) in Fig. 22 (a) separates into three and two peaks in Fig. 22(f). 3UR¿OHV of RDFs in alignment (b) in Fig. 22 (b) are basically between those in (a) and (f).

Fig. 22 Radial distribution function gNi (r), gZr (r), and gNb (r) in the optimised structures of Ni48 Nb24Zr40 for the alignments (a), (b), and (f). Four vertical arrows on each gI-curves in (f) indicate distances to the 1st (2.9 ǖ), 3 rd (5.0 ǖ), 5 th (6.5 ǖ), and 7th (7.7 ǖ) neighbouring atoms in the corresponding fcc lattice.

Matsuura et al. [88] have estimated the RDFs in the Ni39Nb26Zr35 amorphous alloys from the Fourier Transform of the XAFS spectra (FT-XAFS) and have reported the following RDF SUR¿OHV (i) FT-XAFS obtained from Ni K-edge has a doubly splitting main peak; (ii) FT- XAFS obtained from Zr K-edge and Nb K-edge has a single main peak with some near-side and far-side peaks; (iii) An atomic model largely distorted from the icosahedron ((0, 2, 8, 2)-VP similar to Ni-01457/Nb-abc) is well ¿tted with the FT-XAFS (Ni K-edge) and reproduces the spitting peak. The RDF SUR¿OHV (i) and (iii) seem to resemble those for the ¿rst atomic shell in the Ni-centred RDF in Figs. 22 (a). However, a RDF estimated by FT- XAFS cannot be compared directly with a RDF obtained from a real geometrical structure because the phase shift of the photoelectron wave in the FT-XAFS makes the estimated interatomic distance shorter than the real value and the phase shift depends on a combination of absorbing and scattering elements. Then we try to reproduce a RDF within the ¿rst atomic shell (r < 3.ǖ from their structural model ¿tted with their FT-XAFS

34

Chapter 3

data (Ni K-edge), and compare it with the RDF obtained from the optimised structure for some alignments. Figure 23 shows RDFs for Ni atom gNi(r) within the ¿rst atomic shell in the Ni48Zr40Nb24 for the alignments (a), (b), and (f) (portions of Fig. 22 [a], [b] and [f]), compared with those derived from the ¿tting model for XAFS [88] in the leftmost curve. Three peaks observed in the curve by the ¿tting model are reproduced in the curves (a) and (b), but not in the curve (f). The positions of peaks in curves (a) and (b) are shifted Fig. 23 The RDF of the 1 st shell (r < 3.5 ǖ) around Ni about 0.1 ǖ to the lower side from the atoms, and the gNi (r) for the optimized structures of the vertical lines, which represent the peaks Ni48Nb24Zr40 with the alignments (a), (b), and (f). The estimation from the XAFS spectrum is shown as the in the ¿tting model. However, they are leftmost curve. The vertical lines indicate the peak in agreement in the overall SUR¿OH positions and the relative heights of the experimental estimation. despite the fact they have been derived by completely independent manners. The curve by the model ¿tted with XAFS spectra is estimated from a single Ni atom surrounded by twelve atoms, whereas those in (a) and (b) are averagely obtained from Ni atoms on forty-eight inequivalent atomic sites in the optimised structures. Only from the comparison of gNi, the RDF for the alignment (b) agrees the best with that experimentally obtained. However SUR¿OHV of gZr and gNb for the alignment (b) do not agree as well as those for the alignment (a). In conclusion, we constructed a local structural model for Ni-Zr-Nb amorphous alloys based on an icosahedral unit, Ni5Nb3Zr5, and fully optimised the structures of a 112-atom rhombohedral cell using the ¿rst principles calculation. We have obtained two typical optimised structures: (1) an amorphous phase in which the icosahedra maintains its shape and (2) a crystalline phase, with a lower energy than that of the amorphous phase, in which the icosahedra change to fcc-like cuboctahedra. Clustering Nb atoms play an important role in preventing the amorphous structure from crystallisation and they are also important in maintaining the icosahedral structure. 3.5 Distorted icosahedral Ni5Nb3Zr5 clusters in as-quenched and hydrogenated amorphous (Ni0.6Nb0.24)0.65Zr0.35 alloys [88] To clarify a mechanism of ballistic transport behaviour in Chapter 5, we focus our attentions on the local structures around Ni atoms for the [(Ni0.6Nb0.4)1-xZrx ]1-yHy with the specific concentration of Zr ( x=0.35 ) and hydrogen ( y=0.078 ). We measured the Ni, Nb, and Zr K-edge XAFS for the as-quenched and hydrogenated (Ni0.6Nb0.4)0.65Zr0.35 amorphous alloys by using synchrotron radiation. The results of the Ni K-edge for the (Ni0.6Nb0.4)0.65Zr0.35 alloy was analysed with the

Local atomic structures of Ni5Nb3Zr5 clusters in Ni-Nb-Zr-H amorphous alloys

35

icosahedral cluster model, which was calculated using the first principle theory. Fine Structure (EXAFS) functions ȤN and the magnitude of Fourier transforms |F(r)| of the k3-ZHLJKWHGȤN were reduced from the raw data using a coded programme called Athena [89].

Fig. 24 Magnitude of the Fourier transform of the Ni (a), Nb (b), and Zr (c) K edges for the as-quenched (NiNbZr-H0) and hydrogenated (NiNbZr-H7.8) (Ni0.6Nb0.4)0.65Zr0.35 amorphous alloys.

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60

Chapter 4

tunnelling oscillation, the average frequency of the saw waves is assumed to be 1 GHz [130], provided that the tunnelling current is 0.16 nA and the barrier capacitance is less than 1 fF. If the oscillation is derived from the tunnelling of a proton, as seen in previous papers [37, 65–68], it is estimated as being 5.45 MHz, taking into consideration the proton mass (938.256 MeV), when the tunnelling current is 1.6 nA. This value is in accordance with the experimental values (1.2–4.0 MHz) (Figs. 55 (a), (b). Ono et al. [161] have reported that the magnetic field affects not only the amplitude of the Coulomb oscillations but also their phase in single electron transistor (SET). High resistance due to the off state in the gray scale plot of the zero-bias Fig. 55 Power spectra (a) and (b), and Nyquist resistance shows continuous and monotonic phase diagrams (c) and (d) showing the receiving voltage patterns for Ni32.4Nb21.6Zr36H10 shift of the Coulomb oscillations in the negative amorphous alloys at 100 K and 200 K, gate voltage direction upon application of the respectively, under a normally applied magnetic field of 15 T. magnetic field. To determine the modulation of voltage variation under magnetic field in Figs. 54 (a) and (b), we constructed a Nyquist diagram for receiving voltage waves. The Nyquist diagram was plotted in the complex plane of the open-loop transfer (propagation) wave function for all the complex frequencies in the counter-clockwise direction, using a vector locus phase [164, 165]. The Nyquist diagrams of the magnetic field application are shown in Figs. 57 (c) and (d). As magnetic field increases, the loop area, especially the third and fourth quadrants, also increases and corresponds to phase shift of Coulomb oscillation. Such an increment of the imaginary parts in the complex waves suggests a delay advancement in phase [166]: i.e., a facilitation of conductance to capacitance. Here, it should be noted that the chemical potential of the conduction electrons in the ferromagnetic island is affected by the magnetic field. This is similar to variation in electrostatic potential caused by gate voltage in field electrostatic transistor (FET) [167]. By analogy, we can infer that the application of magnetic field induces Coulomb oscillation, which is derived from a noticeable variation in the chemical potential of an isolated ferromagnet (island) in ferromagnetic fields. In this study, the ferromagnetic metal responsible for the magneto-Coulomb oscillation is Ni alone, because Zr and Nb are nonmagnetic elements. In the atomic configuration of a Ni5Nb3Zr5 cluster, five Ni atoms are separately coordinated against Zr and Nb atoms (Fig. 56, inset [59]), according to the atomic bonding data in the XAFS measurement using strong radiation photos by SPring-8 [40, 59]. It can be assumed from the superconductivity in Fig. 53, the assembly of the five Ni atoms is not ferromagnetic. Next, we will consider a field-induced magnetic transition for the assembly, which is composed of a half-pentagonal bipyramid [168]. As an

Room-temperature Coulomb oscillation and amorphous alloy field-effect transistor (AAFET)

61

example, YxNi1-x amorphous alloys are similar to the magnetic properties of (Ni36Nb24Zr40)90.1H9.9 amorphous alloys. The Pauli paramagnetic Y9.5Ni90.5 shows field induced weak itinerant ferromagnetism in a temperature region above 177.5 K [169, 170]. Therefore, if we regard the Zr and Nb atoms in the clusters as nonmagnetic lead, we can visualise the three-terminal ferromagnetic single electron transistor, using the single electron repopulation by a magnetic field at a fixed gate voltage. The magnet-Coulomb oscillation of the junction array consists of ferromagnetic island and nonmagnetic lead; it occurs with the oscillation period of the magnetic field ǻ+, which is given as 2

1 2

2Ec =

PgP%ǻ+ =

e C

6

D D P = D D , 







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(15)

where Ec, P, g, P%, C6and D+ (D-) are single electrons charging the island’s energy, electron spin polarisation, g factor, Bohr magneton, total capacitance of the island, and the density of states at the Fermi energy for majority (minority) spins, respectively [161]. The mean electron number of the island increases with an increasing H for a positive P [134], leading to an increase in voltage, as shown in Fig. 58. For e2/ C6= 100.1 PeV [37], H= 6 T from Fig. 56 and g=2 [167], Eq. (14) gives PNi = 11.7%. However, (P%'H)-1 is proportional to (2Ec) -1 as expected from Eq. (14), we

Fig. 56 The linear relationship between the magneto-Coulomb oscillation ǻ+ and the charging energy Ec. Inset: icosahedral Zr5Ni5Nb3 cluster.

plot (P%'H)-1 against (2Ec) -1 in Fig. 56, where (P%'H)-1 presents the period of the magneto-Coulomb oscillation. The period from 1.85 to 2.75 (1/meV) is almost the same as that of a Ni/Co/Ni single electron transistor from 1 to 4 (1/meV) [132]. The ratio of the two quantity is |PNi|= 20.9%. These two PNi values are in fairly good agreement with the value (P = 23 % [171]), which was determined by a spin polarised tunnelling technique. Finding the precise measurement of P is so difficult that the method in this study provides a sensitive tool to evaluate spin polarisation in ferromagnetic elements. Furthermore, lower-temperature data in Ref. 168 estimates the enhancement of the magnetic field-induced Coulomb oscillation in temperatures below 100 K. The magnetic field-induced Coulomb oscillation is derived from spin polarisation of Ni atoms in Ni5Nb3Zr5 clusters.

62

Chapter 4

4.5 The Fano Effect on the transistor behaviour of Ni-Nb-Zr-H amorphous alloys [172, with kind permission of The European Physical Journal (EPJ)] The electronic properties of amorphous alloys are a particularly active area of research for transition metals, while the lack of a long-range order has an important role in the electronic properties of macroscopic scale materials. This has an influence on the efficacy of quantum dot tunnelling, which is one topic currently attracting a great deal of interest in the field of physics. A number of studies have reported on achieved room temperature Coulomb dot oscillation [141, 149, 172–176]. Among these studies, conductance tuning of the Fano effect on the phase and coherence of electrons through a quantum dot in an Aharonov-Bohm (AB) interferometer with an AlGaAs/GaAs heterostructure was reported by Kobayashi et al. [177]. These experiments were conducted at a temperature of 30 mK using magnetic fields in the range of 0.9140–0.9164 T. In the previous section, 4-2, we reported electric current-induced voltage oscillation in ((Ni0.6Nb0.4)1_xZrx)1_y Hy (0.30 ” x ” 0.50, 0 ” y ” 20) amorphous alloys with multiple junctions in the 6-373 K temperature range [37, 65]. These systems can be regarded as dc/ac-converting electronic devices with a large capacitance (in the order of several femtofarads) between Zr-centred icosahedral Ni5Nb3Zr5 clusters [59]. In this section, we report on the effect of hydrogen and cluster morphology on the transistor behaviours of (Ni0.36Nb0.24Zr0.40)100_xHx (0 < x < 20) amorphous alloys containing subnanometre- sized icosahedral Ni5Nb3Zr5 clusters. An aluminium-oxide amorphous alloy field-effect transistor (AAFET) was produced on the (Ni0.36Nb0.24Zr0.40)90H10 amorphous alloy using two gold wire electrodes by means of Ar arc sputtering of alumina under a pressure of 0.22 Pa. A schematic of a cross section of the resultant AAFET device is shown in Fig. 57 (a). The thickness of the alumina film was 10 nm. Before sputtering, and to avoid the interfacial impedance effect of the semiconducting oxygen-rich layer, two gold wires of diameter 100 ȝP were welded to the amorphous alloy to act as the source and drain electrodes. The distance between the two electrodes was 2 mm. The Id-Vg curves of the AAFET for Vd from 0 to 60 PV were measured using a dc battery (Xitron 2000) from -5.0 to +5.0 mV at a sweep rate of 6.3 mV/s for Vg. The Fano effect for the AAFET was detected from -10 to +10 mV in He at an ambient pressure under a magnetic field 0-2 T at the High Field Laboratory (IMR, Tohoku University, Japan).

Fig. 57 (a) Schematic diagram of the AAFET device; (b) calculated potential energy curve for the interaction of the H atom with the icosahedral Zr5Ni5Nb3 cluster as a function of H atom position relative to the cluster. The models comprise Zr5Ni5Nb3 clusters with hydrogen exterior to the cluster and bonded to

Room-temperature Coulomb oscillation and amorphous alloy field-effect transistor (AAFET)

63

The atomic configuration and adiabatic potential energy curve of the icosahedral cluster consisting of Ni-Nb-Zr-H were calculated by first-principles density-functional calculations using the Vienna Ab Initio Simulation Package [60]. The nuclei and core electrons were described by the projector augmented plane-wave method [126] and the wave functions were expanded using a plane-wave basis set with a cutoff energy of 293.2 eV. We calculated the adiabatic potential energy for motion of the hydrogen atom in the distorted Zr-centred icosahedral Ni5Nb3Zr5 cluster, which possesses a composition close to Ni36Nb24Zr40 alloys. For this calculation, we assumed that the energy of the hydrogen on the cluster surface was not significantly affected by the presence of the neighbouring cluster. As can be seen from Fig. 57 (b), the structure where the hydrogen is adsorbed at the outer surface of the cluster (A) has a lower energy than when the H atom is at the interior of the cluster and bonded to Zr or Nb (B). This, therefore, helps to explain why it has been found that the hydrogen atom localises to a site between the clusters at a hydrogen content below 7 % [36]. Indeed, 1H NMR studies (Section 3-7) of hydrogen diffusion in Ni-Nb-Zr-H amorphous alloys have shown that there is movement of hydrogen atoms between clusters at temperatures in the range 150–300 K. The activation energy for this hydrogen movement was estimated to be 8.7 kJ/mol [126], which is lower than the dissolution enthalpies of hydrogen in Zr and Nb. This means that hydrogen atoms are trapped on the outer surfaces of the cluster. A recent neutron scattering experiment [112] showed an elongation in the Ni-Ni atomic distance that results from the addition of deuterium to a Ni-Nb-Zr-D amorphous alloy, suggesting that most deuterium atoms prefer to reside in inter-polyhedral sites or exterior to the polyhedra. Vacancy analysis, using positron annihilation spectroscopy, also suggested the existence of hydrogen atoms between Ni atoms that belong to different clusters [94]. These results show that hydrogen atoms exist between Ni atoms of neighbouring distorted icosahedral Ni5Nb3Zr5 clusters (Fig. 58 (a)). Therefore, among such clusters, hydrogen occupation provides a distinct model of quantum dot tunnelling along Ni-H-Ni atomic bond arrays (Fig. 58 (b), leading to Coulomb oscillations [37, 59]. In contrast, the vacancies that surround the Zr and Nb atoms become sources of Fig. 58 (a) Configuration pattern of four subnanometre-sized capacitors in the femtofarad icosahedral clusters and (b) Coulomb dot range [39]. The capacitance acts on the discrete tunneling model. variation in oscillation [115] and on the electric

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charge [179]. Due to the fact that the clusters are combined with a small amount of Voronoi-like polyhedra, precise calculations are required to detailed information on the atomic configuration. When the hydrogen contents is greater than 7 %, because of the high-pressure effect of the hydrogen in electrolysis [36], the hydrogen atom begins to plunge into the tetrahedral sites of the clusters, thereby enlarging the space between clusters, and constructing zigzag tunnels with an average width of 0.26 nm [39]. Thus, the doping of hydrogen in amorphous alloys has an important role in various electron transport phenomena. To re-evaluate the atomic configuration of the clusters that constitute the amorphous alloys under study, we measured the Id-Vg-B characteristics of the AAFET in a magnetic field (B) from 0 to 2 T at room temperature. The resulting three-dimensional Coulomb oscillation, as a function of Vg and B at room temperature, is shown in Fig. 59. The diagram represents a cyclic dip structure with conductance valleys, similar to previous results obtained by Kobayashi et al. [177]. The Id-Vg

Fig. 59 (a) A three-dimensional Id-Vg-B diagram for the AAFET device at room temperature; (b) conductance of three Fano peaks at room temperature in the selected magnetic fields. The direction of the asymmetric tail changes between B=1.2 and 1.6 T. (c) Id-B curve at gate voltages of -10, -5, 0, 5, and 10 mV.

Fig. 60 Estimated configuration pattern of a nanometer-sized amorphous alloy that exhibits the Fano effect.

curves (Fig. 59 (b)) show asymmetric lines with periods of 5 mV for Vg, and the Id-B curves (Fig. 59 (c)) vary with periods of 0.6 T. This is a clear indication of the Fano effect that arises from interference of electrons as they travel through two different cluster configurations: a localised discrete state inside the quantum dot and a continuum in the arm. Since the AB effect mainly affects the phase difference between the two paths through the resonant state and the continuum, we can assume that there exists a quantum dot-AB-ring hybrid structure in the amorphous alloys. Therefore, we can visualise these amorphous structures, such as those illustrated in Fig. 60. From the results described above, it is clear that the amorphous alloy of interest is constructed by a variation of structures with icosahedral Ni5Nb3Zr5 clusters.

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4.6 Room-temperature Fabry-Perot (FP) effect on AAFET with particle and wave natures [180] The challenge of realising FET at room temperature has been taken on by various research groups, and there have been few reports on the room-temperature operation of single electron transistors (SETs) composed of carbon nanotube [141, 149, 173–176]. However, no research work on room temperature millivoltage-biased SETs, without carbon materials, has achieved success, as far as we know. However, when the size of a device becomes comparable to electron coherence length, quantum coherence occurs between propagating electron waves, as a Fabry-Perot (FP) electron resonator [181]. Liang et al. [182] have reported a FP quantum interference of single-walled carbon nanotube (SWNT) devices at 4 K. Since the amorphous alloy consists of the assembly of a large number of clusters of subnanometre size, there is a possibility to observe similar behaviour in those of the SWNT. Furthermore, the conductance tuning of the Fano effect on the phase and coherence of electrons through a quantum dot in an Aharonov-Bohm (AB) interferometer with an AlGaAs/GaAs heterostructure has been reported by Kobayashi et al. [177] at a temperature of 30 mK and a magnetic field between 0.9140 and 0.9164 T. These phenomena are due to the combined quantum effects of particle and wave natures. Here, we will report on the quantum electronic transport effects of the millimetre-sized aluminium-oxide amorphous alloy (Ni0.36Nb0.24Zr0.40)90H10 field-effect transistor (AAFET) with particle and wave natures at room temperature. In a previous section (6-2), the dc current-induced Coulomb oscillation was observed at room temperature in (Ni0.36Nb0.24Zr0.40)90.1H9.9 amorphous alloy ribbons. We postulated the existence of millimetre-sized zigzag paths of the atomic bond arrays among clusters, and suggested the existence of macroscopic proton quantum dot tunnelling along the arrays [65, 67]. We found that the frequency in the dc/ac circuit decreased remarkably with increasing capacitance (C) and resistance (R) at room temperature. AC impedance analysis showed the alloy has a high number of insulating zigzag tunnels between the electric conducting distorted Zr-centred icosahedral Ni5Nb3Zr5 clusters [65, 66]. However, the discrete variation of oscillation could be elucidated by quantisation of electric conductance associated with subnanometre-sized RC circuits in the alloy [115]. The hydrogenised amorphous alloy showed room temperature ballistic transport and superconducting behaviours, in addition to Coulomb oscillation [36]. Furthermore, we observed a one-electron quantum dot tunnelling effect in a prototype AAFET device as a preliminary experiment for this study [172]. In this section, we analysed the Coulomb blockade and FP interference effects for dc voltage applied to the AAFET device, in terms of one-electron tunnelling. The Id-Vg curves of the fabricated AAFET (Fig. 57 (a)) for several values of dc gate voltages at sweep rate of ȝ9V were measured from -5 to +5 mV for Vd. We observed cyclic peaks in three-dimensional Id-Vd-Vg diagram (Fig. 61 (a)) with diamond hollow rows. The Coulomb staircase step width in Vd is one order smaller than that in Ref. 39. The reason for this is not clear at the present time. The representative Id-Vg curve (Fig. 61 (b)) for Vd = 49.5 ȝ9 has a series of peaks, where the current oscillates periodically in voltage of 0.28 mV as a function of the gate voltage at room temperature. The regularity (Figs. 61 (a), (b)) in the diamond patterns suggests the

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existence of a single electron channel. However, we could not measure whether there was exactly a single one-dimensional channel in each and every one of the transistors, because the amorphous alloy consisted of large numbers of cluster arrays and the precise cluster morphology has not yet been found [59, 75].

Fig. 61 (a) Schematic diagram of the AAFET device; (b) three-dimensional Id-Vd-Vg diagram of a AAFET device at room temperature; (c) two-dimensional Vd-Vg section, and periodic oscillation of the drain current vs. the gate voltage; (d) theoretical Coulomb energy and Coulomb temperature curves as a function of island distance. The black solid circle presents data of 0.56-nm sized cluster dots used in this study.

In general, the smaller the metallic island size becomes, the more the electrostatic energy, e2/2C, increases: i.e., the transition temperature of the Coulomb oscillation shifts to a higher temperature [67]. Since a barrier distance Gbetween the cluster island with the maximum size d of 0.548 nm

Room-temperature Coulomb oscillation and amorphous alloy field-effect transistor (AAFET)

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[59] is 0.225 nm [39], we obtain the gap energy between discrete energy level E= e2G/(2Hd2) =(1.60·10-19)2*(2.25·10-10)/2/(8.85•10-12) /(5.48•10-10)2 = 6.78 eV (Coulomb Temperature of 78,678 K, see Fig. 61(c)). This value is 265 times larger than thermal energy kBT (25.6 meV) at room temperature. Therefore, this intriguing phenomenon does not violate an essential principle. However, this value is six orders larger than ǻV (5.9 ȝ9 in Vd. With regard to the reason and mechanism, because there are many possibilities, e.g., accumulation of large numbers of electrons between the junctions, huge capacitance by the picometer size junction surface, and the formation of charge “solitons” [183] in one dimensional array of tunnel junctions, we cannot make any concrete assessment at the present time and further investigation is needed. Because the average frequency for Coulomb oscillation can be represented by f =I/e [184], where I is quantum current, we get f = 1.3 GHz when I = 200 pA in Fig. 61 (b), suggesting an occurrence of single electron tunnelling, which is in sharp contrast to proton tunnelling with 543 kHz [65]. Fig. 61 (b) is a two-dimensional Vd-Vg section of Fig. 61 (a) and is a shade scale plot of the current that shows the corresponding Coulomb diamond raw. The period of the peak (W = 0.28 mV) is about one thousand three hundred fortieth of that of Si devices (W = 0.38 V) at 4.2 K [149]. This could be due to the discreteness in the energy level resulting from the quantum confinement effect in the self-assembled 0.56-nm-sized cluster dots [184]. Next, we measured the contour plots of the second-order differential conductance d2Id/dVd2 and the first-order quantised 䌖 Id/ 䌖 Vd (e2/h) as a function of gate voltage at room temperature. These results are illustrated in Figs. 62 (a) and (b). We can see the Fabry-Perot (FP) interference patterns in both figures, which is similar to the quantum interference effect in SWNTs [182]. The plot shows a quasi-periodic pattern of crisscrossing lines for variation of Vd and Vg. The differential conductance (䌖Id/䌖Vd) of the AAFET against gate voltage is shown in Fig. 61 (c) with a drain voltage of 52 ȝ9 along with the dotted curve of a sinusoidal function with the same average period (2.35 ȝ9 as the measured data. Since the electrical behaviour of AAFET in Fig. 62 is distinct from Coulomb-blockade behaviour in Fig. 61, we can see the FP interference effect in the figure, which is similar to the quantum interference in SWNTs [182]. The average values of 䌖I/䌖V were around 900–1200 e2/h, irrespective of Vd and Vg. These values are 300–400 larger than that

Fig. 62 (a) illustration of contour plot of the second-order differential conductance ˜d2Id/˜Vd2 plot for a AAFET device; (b) differential conductance ˜Id/˜Vd) of the AAFET device plotted against gate voltage; and (c) ˜Id/˜Vd) plot at drain voltage of 52.5 ȝV as a function of Vg at room temperature.

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(around 3 e2/h) of Liang et al. [182]. This could be derived from larger conductivity in the amorphous alloy, as described above. Here, we note that Kamimura et al. [185] have reported on the transition between a resonant-tunnelling transistor (RTT) and a single-hole transistor (SHT) by modulating a coupling strength between an electrode and a quantum island using gate voltage change at 7.3 K. By analogy, from Fig. 61 and Fig. 62, we can infer that the amorphous alloy showed a similar behaviour––Coulomb oscillation and FP interference––by the gate voltage change at room temperature. Then, we measured G-Vg-B characteristics in magnetic field (B) from 0 to 3 T at room temperature, where G is conductance for drain current. We observed the peaks in three-dimensional G-Vg-B diagram (Fig. 63 (a)) at room temperature. The detailed result is shown in Fig. 63 (b), as a function of Vg and B. The diagram represents cyclic diamond structure with conductance valleys between the resonant peaks, similar to previous result by Kobayashi et al [177], showing the existence of macroscopic quantum dot channel, which has been previously reported in Refs. 65, 67, and 186. However, positron Fig. 63. The three dimensional Id-Vg-B diagram for the AAFET device at room temperature; (b) annihilation spectroscopy revealed the existence cyclic diamond structure indicating the Fano of vacancies that were the origin for the Coulomb effect at room temperature. The G-Vg (c) and G-B (d) curves changing periodically at blockade, and provided a model of one-electron magnetic field of 2.6, 2.7 and 3.0 T, and gate quantum dot tunnelling along Ni-H-Ni atomic voltage of 9.81, 9.83, and 9.84 mV, respectively. bond arrays among the clusters [94]. The G-Vg (Fig. 63 (c)) and G-B (Fig. 63 (d)) curves change periodically with the period of 0.26 mV and 0.2 T, respectively. This is a clear Fano effect, which arises from an interference of travelling electrons through two different configurations: a localised discrete state inside the quantum dot and a continuum in the arm [172, 177]. Due to the fact that the Fano effect mainly affects the phase difference between the two paths through the resonant state and the continuum, we can assume some parts of the quantum dot-AB-ring hybrid structure in the amorphous alloys [94]. Indeed, the amorphous alloy is composed of a high number of a subnanometre-sized RC circuit, which is constructed by a pair of pointed Ni5Nb3Z5 channels and perpendicularly connects the cluster array reservoirs that contain subnanometre-sized capacitors [115].

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As to the reason why the AAFET device can be modulated by gate voltage in the order of 100 PV, we noted that Meirav et al. [187] reported that the equipotential of narrow channels in the two-dimensional electron gas island on a GaAs layer showed a change in electron density (high mobility) with decreasing Vg, on the basis of Fermi-Dirac statistics, analogous to the Thomas-Fermi approximation. Hence, by analogy, we can infer that the effective gate voltage is controlled by the conductivity of the Fig. 64 The relation between tunnel resistance and electron gap: Au-Au[192] (R = 100 Nȍ ȟ = conducting material connected to the source and 0.5 nm), Au-Au [193] (R = 1 0ȍ ȟ = 1 nm), drain electrodes. In FET, the more conductive Co-Co [194] (R = 17 0ȍ ȟ = 1.5 nm), AuPd-AuPd [195] (R = 5 *ȍ ȟ = 5 nm), Co-Co the island material becomes, the less gate voltage [196] (R = 1 7ȍ ȟ = 9 nm), and Ni-Ni [197] (R is required for modulation operation. Therefore, =10 7ȍ ȟ = 50 nm). The red circle represents the specimen data used this study. the gate modulation can be as low as 20 ȝ9 when the conductivities of the amorphous alloy -3 and Si are 50 [65] and 10 S/m [177], respectively. We have yet to research this promising aspect for the islands. To evaluate the atomic structure, we will finally consider the quantum tunnel resistance R of the subnanometre-sized gaps between two metallic electrodes as a function of their spacing Ȝ. The relation between R and Ȝ in earlier paper [188–193] is presented logarithmically in Fig. 64. Unfortunately, very little that has been written on this subject proved usable. As can be seen from Fig. 64, R can be expressed as log R = 4.783log Ȝ-2.564. This means that the more the gap wide decreases, the more the resistance also decreases. Therefore, it is expected that the amorphous alloy will be a vacancy excess alloy (subnanometre porous alloy) with Ȝ = 0.14 nm.

CHAPTER 5 BALLISTIC TRANSPORT IN NI-NB-ZR-H AMORPHOUS ALLOYS

The electronic properties of amorphous alloys are the most active research area in transition metals. The lack of long-range order plays an important role for electronic properties of macroscopic materials. A number of studies have been carried out for the preparation and electronic characteristics of various amorphous alloys [192–194]. In this chapter, we will report the effect of hydrogen content on ballistic transport behaviours in Ni-Nb-Zr-H amorphous alloys with subnanometre-scale sized clusters. This superior conducting behaviour resembles the ballistic transport observed in one-dimensional, nanometre-scale channels, such as quantum wires [195], carbon nanotubes [196, 197] and GaAs-AlGaAs [198] at a low temperature, in the form of quantum interference associated with coherence. The ballistic electron transport effect is promising for future electron devices and electric power applications, such as lower supply voltages, which will lead to lower power consumption. However, no research work has been carried out on this subject for amorphous alloys with hydrogen, as far as we know. 5-1 Electronic transport behaviours of Ni-Nb-Zr-H amorphous alloys [36] In this section, we will report on various electronic transport behaviours, in addition to Coulombic oscillation, of individual Ni-Nb-Zr-H amorphous alloys. We have chosen a melt-spun flexible amorphous alloy ((Ni0.6Nb0.4)1-xZrx)1-yHy (x = 0.30, 0.32, 0.34, 0.35, 0.36, 0.38, 0.40, 0.45, and 0.50, 0 ” y ” 0.20) with excellent hydrogen permeability [55], as the matrix specimen. The alloy is a typical metal/metal-type alloy that consists of familiar transition elements. Our interest lies in investigating the hydrogen-dependent electronic transport behaviours of the (Ni0.36Nb0.24Zr0.40)100-yHy (0 ” y ” 20) amorphous alloys in terms of the localisation effect of hydrogen. However, these are no previous reports on this subject for amorphous alloys with hydrogen. The temperature dependencies for the resistivities of (Ni0.36Nb0.24Zr0.40) 100-yHy (0 ” y ” 20) amorphous alloys with different hydrogen contents are shown in Fig. 65. The resistivities showed large differences with increasing hydrogen content (Figs. 65 (a–d)). The resistivity of Ni36Nb24Zr40, which lacks hydrogen, increased almost linearly with a decreasing temperature that dropped to 6 K (Fig. 65 (a)). The negative temperature coefficient of resistivity (TCR) value of -12.18㽢10-5/K indicates a semiconducting character. The resistivity of the (Ni0.36Nb0.24Zr0.40) 96.1H3.9 alloy initially showed negative TCR behaviour similar to the alloy without hydrogen in the cooling run. However, in the heating run, the resistivity decreased up to 123 K, according to the same curve as the cooling run, but suddenly decreased to the 3rd order (Fig. 65 (b)) at 124 K, and then descended with TCR of -7.55㽢10-3/K up to 350 K. The resistivity (0.07 ȝȍFP at 300K was one-twentieth

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that of silver (1.62 ȝȍcm) at room temperature. Similar behaviours were also intensively observed for the (Ni0.39Nb0.26Zr0.35) 100-yH y (y = 5.6, 6.3, 7, 7.5) and (Ni0.396Nb0.264Zr0.34) 100-yH y (y = 6.2, 7.9) alloys. This superior conductivity resembles the ballistic transport described above. However, it is not clear at the present time whether the mean free path of the electron is much greater than the size of the medium or not. With regard to cause for the drop in resistivity at 124 K, although the topologic change (pseudo-transition) associated with the accumulation of strain is a possibility [199], we cannot confirm this without further investigation. The resistivity of the (Ni0.36Nb0.24Zr0.40) 94.3H 5.7 alloy increased with TCR of -7.05 㽢 10-5/K down to 9.5 K and then plunged to 4.2 K (Fig. Fig. 65 The temperature dependence for the 65 (c)). However, the resistivity continued resistivities of (Ni0.36Nb0.24Zr0.40)100-y H y alloys without decreasing to 4.2 K, under magnetic with different hydrogen contents: a (y =0), semiconducting; b (y =3.9), superior conducting; c fields of 5 T and 10 T. Indeed, the application (y =5.7), superconducting transports; and d (y of a magnetic field > 4.7 T arrested the drop of =9.3), Coulombic oscillation. resistivity (see insert in Fig. 65 (c)). Therefore, the drop from 9.5 K suggests the existence of type II superconductivity. The detailed results for diamagnetic effect will be described in Chapter 6. Hydrogen from the distorted icosahedral Zr-Nb-Ni cluster expands the Zr (Nb) tetrahedral sites [40, 41], leading to a decrement in the atomic distances of the neighbouring sites due to the high-pressure effect of hydrogen. Since the cluster can be regarded as a nanoscopic (~1 nm) metallic island that is isolated from other islands by potential barriers in the subnanometre range, the tunnelling of electron pairs to allow transport among the clusters is feasible. Figure 65 (d) shows the temperature-dependent electric resistivity of a (Ni0.36Nb0.24Zr0.40)90.7 H9.3 alloy. The abnormal resistivity continued from 148 K down to 127 K in the cooling run and from 27 K to up to 245 K in the heating run. This is the electric current-induced voltage amplification based on Coulombic oscillation. However, when the amorphous alloy absorbed hydrogen over a threshold content and the hydrogen atoms fully occupied the tetrahedral sites that are surrounded by four Zr (Nb) atoms, the hydrogen was forced to penetrate into the vacancies and, consequently, the tunnelling phenomenon disappeared.

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We observed similar resistivity variations for restricted contents of hydrogen and Zr. The effects of Zr and H content on these variations for ((Ni0.6Nb0.4)1-xZrx)1-y Hy amorphous alloys are collectively presented in Fig. 66. In the figure, the gray, dark, and twilight solids represent the alloys that were observed to have semi and superior conducting properties and Coulombic dot tunnelling, respectively, and the cross denotes alloys that showed onset superconductivity above 5.5 K. The electronic transport behaviours can be classified into Fig. 66 The effects of Zr and H contents on four groups. Since superior electric transport semiconducting, superior conducting, and superconducting transport and Coulombic occurs at limited region of 34–35 at %Zr and oscillation properties of ((Ni0.6Nb0.4)1-xZrx)1-yHy 5–7.5 at %H, the representative example for (30”x ” 50, 0 ”y ” 0.2) amorphous alloys. the alloy with 35 at% Zr is presented in Fig. 67. The drop in resistivity at 124 K in the heating run shown in Fig. 65 (b) and at 240 K in the cooling run shown in Fig. 67 is due to the topologic change (pseudo-transition) of clusters, as well as a cause of internal friction peaks in low temperature regions [199]. The morphology change is associated with two kinds of cluster ordering [200]. The one is due to the special short range ordering, so-called topological short ordering (TSRO), and another is the chemical short range ordering, which is known as compositional short range ordering (CSRO). The intrinsic cause of the drop in resistivity requires precise atomic configuration analysis. Furthermore, it is difficult to elucidate the cause of valleys at 63 and 51 K in cooling and heating runs shown in Fig. 67, respectively, at the present time.

Fig. 67 The superior conducting behaviour of the (Ni0.39Nb0.26Zr0.35) 93.7H 6.3 alloy.

Fig. 68 The I-V characteristic of the (Ni0.36Nb0.24Zr0.40)90.1H9.9 amorphous alloy at room temperature.

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In reference [37], the frequency of Coulombic oscillation decreased remarkably with increasing capacitance and resistance at room temperature. This behaviour is analogous to block oscillation with charge-discharge in a discharge tube. The oscillation in the discharge tube replaces a semiconductor with negative resistance [201]. Negative resistance is a property of electrical circuit elements that are composed of certain materials for which, over certain voltage ranges, current is a decreasing function of voltage. There are two forms of negative resistance: type N and type S. The former, which shows voltage-controlled behaviour, is used in devices, such as the tunnel diode and Gunn diode, while the latter current-controlled type is found in devices such as the unijunction transistor, neon lamps, thyristors, resonant tunnelling transistors, and old carbon arc oscillators. We measured the current-controlled I-V characteristics of the (Ni36Nb24Zr40)90.1H9.9 alloy in the current region from 0 mA to 100 mA (Fig. 68). The current did not flow up to 2.24 V, irrespective of voltage, and then increased linearly up to 19.99 V under the Ohmic rule. Subsequently, the current jumped to 100 mA, reflecting an electron avalanche. Strictly speaking, the voltage was reduced slightly at a high current (inset in Fig. 69). Therefore, it is clear that the amorphous alloy is transformed suddenly from an insulator into an extremely good conductor. This behaviour resembles that of a current-controlled S type negative resistor. Although it is known that there are high and low-current density regions in the region of negative resistance, we could not measure the electrical characteristics of the high-current density region owing to the high-density limitation of our device. As can be seen from above results, the doping of hydrogen in the amorphous alloys plays an important role in various electron transport phenomena. We will consider the reason the calculated adiabatic potential energy of the hydrogen atom for the distorted icosahedral Ni5Nb3Zr5 cluster, with composition close to that of the Ni36Nb24Zr40 alloy, provided that the energy of the hydrogen on the surface of cluster is not significantly changed by the presence of the nearly cluster. The potential energy (A in Fig. 69) of hydrogen adsorbed by the outer surface of the cluster was lower than that (B in Fig. 69) of the bonding state between Zr (or Nb) and H atoms settled in the cluster. In other words, the outer adsorbed hydrogen of the cluster is in a stable state and the inner bonding hydrogen in the tetrahedral is in a metastable state. This result provides the following assumptions. The hydrogen Fig. 69 The calculated potential energy curve atom localises to a space site between the clusters for the interaction of the H atom with the and then enlarges the space and lastly construct icosahedral Ni5Nb3Zr5 cluster as a function of the position of the H atom relative to the cluster. The zigzag tunnels with an average width of 0.26 nm models comprise Ni5Nb3Zr5 clusters with due to the high pressure effect of hydrogen in hydrogen adsorbed to the outer front of the cluster and combined with Zr (Nb) atoms in the electroanalysis, as the hydrogen content increases. cluster.

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When the hydrogen content reaches around 7 %, the hydrogen will begin to plunge into the clusters’ tetrahedral sites. The localisation of hydrogen also induces atomic distance shrinkage, in addition to construction of tunnels, as reported in previous papers [40, 41]. Thus, the existence of the outer hydrogen appears to be related to the occurrence of superior electric transport. In this case, the superior conductance would be derived from electron tunnelling along the cluster arrays, because the mean free path of the electron is larger than that (~0.26 nm [39]) of the tunnel width between the clusters. Indeed, the electrical transport in multi-walled carbon nanotubes is shown to be ballistic at room temperature with mean free paths in the order of tens of microns [197]. Since the amorphous alloy can be considered as a self-organised assembly of low-capacitance, multiple-junction configurations–– i.e., a huge assembly of 1-nm-sized quantum dots––using AC impedance analyses [39], it means we can see the existence of macroscopic quantum electron tunnelling passes along the arrays in the amorphous alloys, even if there are poor conduction cluster passes combined with small amounts of other Voronoi-like polyhedra with relatively long atomic distances [39, 79]. The superior conductance effect is promising for future electron devices and electric power applications, such as lower supply voltage, and could lead to low power consumption. 5-2 The effect of degree of amorphousness on electronic transport behaviours [87] In this section, we will study the effect of degree of amorphousness (as a function of hydrogen content) on electronic transport behaviour in ballistic conductivity and Coulomb oscillation in ((Ni0.6Nb0.4)1-xZrx)1-y Hy (x= 0.35 and 0.40, 0 ” y ” 20) amorphous alloys with subnanometre-scale size clusters. Although the degree of amorphousness has previously been described on the basis of amorphous-crystal transition, in this study, we define it as the degree of disorder in the amorphous phase. However, these are no previous reports on this subject for amorphous alloys with hydrogen, as far as we know. The rotating wheel method under an argon atmosphere was used to prepare amorphous Ni39Nb25Zr35 and Ni36Nb24Zr40 alloy ribbons with a 1-mm width. Three different rotation speeds were used: 1,000 rpm (10.5-m/s), 3,000-rpm (31.4-m/s), and 10,000-rpm (104.7-m/s). All specimens were around 20 Pm thick. The specimens that passed one week after charging were used to prevent the inhomogeneous distribution of hydrogen. The specimen density was measured using Archimedes’s principle by weighing specimens in tetrabromoethane (density: 2.962 Mg/m3) and air. The phase transformations upon heating were studied by differential scanning calorimetry (DSC) at a heating rate of 0.67 K/s using 20-mg specimens. Using a diagnosis and analysis apparatus (USH-B, Toshiba Tungaloy, Japan) fitted with a transmitter/receiver set, the ultrasonic horizontally-shear (SH) wave pattern was analysed in the pulse-diffraction mode with direct contact between the transducer and specimen [202]. The frequency was set to 1.6 MHz and naphthenic hydrogen oil with a viscosity of 400 Pa-s was used as the couplant [203]. The specimens’ surfaces were examined using a scanning electron microscopy (SEM) (Hitachi S800). The sample was provided with a low-temperature-proof polymer-coated Cu plate holder, which

Ballistic transport in Ni-Nb-Zr-H amorphous alloys

Fig. 70 SEM images of the roller-attached and free surfaces for specimens produced by rotating speed of 1,000-rpm (10.5-m/s), 3,000-rpm (31.4-m/s) and 10,000-rpm (104.7-m/s). Inset: enlarged images of perforated voids.

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Fig. 71 Density change of Ni36Nb24Zr40 amorphous alloys with and without hydrogen, produced by rotating wheel speed of 1,000, -(10.5-), 3,000, -(31.4-) and 10,000-rpm (104.7-m/s).

was inserted by a thermocuple using double faced-sticky insulating tape. In order to avoid short circuit trouble from water or ice contents between the two electrodes, we first removed air from the vessel of the cryostat and then substituted He gas. The distance between the two voltage electrodes was 20 mm. Two golf wires, each with a diameter of 100 Pm, were welded to the amorphous alloy, using a spot welder 1 mm in diameter, in order to eliminate contact trouble. Voltage oscillation was measured using a Spectrum Analyzer N9320B (Agilent Technologies Inc.). SEM images of roller-attached and free surfaces for specimens produced by rotating speeds of 1,000-rpm (10.5-m/s), 3,000-rpm (31.4-m/s), and 10,000-rpm (104.7-m/s) are presented in Fig. 70. The surface roughness of both surfaces decreases as the rotating speed increases. Strictly speaking, perforated voids made by rolling-up Ar gasses can be seen on the roller-attached surface, but the size and amount of the voids diminish with increasing speed. To study the effect of rotating speed for hydrogenation, the densities of Ni36Nb24Zr40 amorphous alloys with and without hydrogen are measured as a function of rotating speed. These results are shown in Fig. 71. The density of amorphous alloys without hydrogen increases

Fig. 72 X-ray diffraction patterns (a), DSC traces (b), and power spectra of receiving waves (c) of Ni36Nb24Zr40 amorphous alloys for 1,000, -(10.5-), 3,000, -(31.4-), and 10,000-rpm (104.7-m/s) specimens. The degree of amorphousness for 10.5-, 31.4-, and 104.7-m/s are 48.4, 56.1, and 91.9 %, respectively.

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somewhat with an increasing rotating speed, suggesting a decrease in porosity. The density of the hydrogenated alloys performed under the same condition (30 A/m2 for 86.4 ks) decreased with an increase in the rotating speed. This indicates that hydrogen absorption increases with an increasing rotating speed. In a preliminary experiment [204], we found that hydrogen penetrates preferentially into a roller-attached surface with a higher degree of amorphousness, compared to a free surface with a lower degree of amorphousness. Therefore, a stable cluster configuration favours hydrogen absorption. The X-ray diffraction pattern, as well as DSC and SH wave analyses of Ni36Nb24Zr40 amorphous alloys prepared at all three speeds are presented in Fig. 72 Fig. 73 The temperature dependences for the (a), (b), and (c), respectively. The X-ray pattern of resistivity of (Ni Nb Zr ) H and 0.36 0.24 0.40 95.7 4.3 the 1,000-rpm (10.5-m/s) specimen reveals (Ni0.36Nb0.24Zr0.40)94.6H5.4 amorphous alloys, produced at rotating speeds of 31.4 and 104.7 crystalline Zr2Ni7, but the 3,000-rpm (31.4-m/s) and m/s, respectively, followed by electrolytically 10,000-rpm (104.7-m/s) specimens were completely charging for 50.4 ks. The degree of amorphousness is 56.1 and 91.9 %, amorphous. The DSC curves indicated respectively. Panel (c) shows the superior crystallisation temperatures (Tx) of 828, 807, and (ballistic) conducting behaviour of (Ni0.39Nb0.26Zr0.35)98.8 H1.2 amorphous alloy 809 K for the 10.5-, 31.4-, and 104.7-m/s specimens, (degree of amorphousness: 98.4 %) for the respectively, thereby indicating that the 104.7-m/s 10,000-rpm (104.7 m/s). specimen is somewhat more stable than the 31.4-m/s specimen. The SH wave patterns revealed that the 10.5-, 31.4-, and 104.7-m/s specimens contained 3, 2, and 1 types of structural colonies, respectively. A “colony” in the amorphous phase is defined as group of organised aggregations having the same composition [202]. The structural colony size was calculated using the formula Vs = f O, where Vs, f, and O are shear wave velocity (2121 m/s), frequency, and wavelength, respectively. The wavelength O of the shear waves corresponds to colony size. Figure 72 (c) shows an increase in the colony size from 1.2 to 10.6 mm with increasing rotating speed. Since three specimens contain an amorphous phase with colony size of 10.6 mm, the power spectrum percentage for the colony size of 10.6 mm serves conveniently as a measure of degree of amorphousnessD, according as the following equation Dൌ

ࡵଵ଴Ǥ଺ ࡵଵ଴Ǥ଺ାࡵଵǤ଼ାࡵଵǤଶ

,

(18)

where I is intensity for the power spectrum. An increase in the rotating speed increases the degree of amorphousness: that is, homogeneity of the cluster assembly.

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The temperature dependences of the resistivity of (Ni0.36Nb0.24Zr0.40)95.7H4.3 and (Ni0.36Nb0.24Zr0.40)94.6H5.4 amorphous alloys, produced at rotating speeds of 31.4 and 104.7 m/s, respectively, followed by electrolytically charging for 50.4 ks, were investigated by measuring the degree of amorphousness. For a cooling run, the resistivity for the 31.4 -m/s specimen with a 56.1% degree of amorphousness (Fig. 73 (a)) shows a sluggish increase from 300 K down to 9 K (similar to a semiconducting material) and then an abrupt drop to 6 K. The same trend is also shown for a heating run. Since all the amorphous alloys that show the same trend were superconductors with an onset temperature below 12 K [195, 205], 9 K may be considered as the onset temperature of superconductivity of type II [63]. However, the resistivity for the 104.7-m/s specimen with a 91.9% degree of amorphousness of (Fig. 73 (b)) decreases almost linearly down to 15 K and then suddenly reduces by six orders of magnitude at 6 K to finally fluctuate between 0.1 and 1 n:cm. In the heating run, the fluctuation continues up to 190 K and then remarkably increases between 198 and 204 K by six orders of magnitude to match the resistivity values of the cooling run between 190 and 200 K, finally following the same trend as the cooling run. The resistivity at 200 K (0.1 n:cm), which is 0.01% of silver (1.62 P:cm) at room temperature, is the same as the minimum resistivity achieved for the 31.4-m/s specimen (degree of amorphousness: 58.8%) of (Ni0.39Nb0.26Zr0.35)93.7H6.3 at 51 K [36]. However, there is an unresolved reason why this remarkable recovery occurs in temperature interval of 6 K between 198 and 204 K. Figure 73 (c) shows another example for superior conductivity in the 104.7-m/s specimen (degree of amorphousness: 98.4%) from the (Ni0.39Nb0.26Zr0.35)97.6H2.4 amorphous alloy. To make absolutely sure, we measured the resistivity for the 10-Pm-thick (Ni0.39Nb0.26Zr0.35)98.3H1.7 amorphous alloy specimen with an electrode distance of 5 mm, produced by 104.7-m/s (degree of amorphousness: 98.4%), after polishing on both sides by 5 ȝm. The result showed similar resistance behaviour in a temperature region between 130 and 254 K during the heating run, as shown in Fig. 74. This indicates that the abnormal resistance behaviour is caused from the inhomogeneous distribution effect of hydrogen. Therefore, we can assume that the supercooling of the molten alloy gives rise to morphology changes associated with two types of cluster ordering: topological ordering and compositional short-range orderings [206].

Fig. 74

The temperature dependences of the resistivity of (Ni0.36Nb0.24Zr0.40)94.6H5.4 amorphous alloy, produced at rotating speeds of 104.7 m/s, respectively, followed by electrolytically charging for 50.4 ks, and then polished on both sides by 5 ȝm.

As can be seen from above results, the higher degree of amorphousness for hydrogenated amorphous alloys plays an important role in various electron transport phenomena, because the pronounced results are attributed to electronic structure and transitions related to local cluster structures. We will consider the effect of degree of amorphousness for ballistic transport

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Fig. 75

The transport mechanism for icosahedral cluster arrays of Ni- centred Zr5Ni5Nb3 (the Voronoi-type polyhedral portion is not shown).

behaviours in terms of cluster morphology, although the precise atomic structure of the hydrogenated amorphous alloys is perfectly resolved at present time, because of its subnanometre-sized structure. By applying the X-ray absorption results of a fine structure analysis [59] to a first-principles simulation, we can select an icosahedral cluster of Ni5Nb3Zr5 as

the atomic cluster model for Ni39Nb25Zr35 and Ni36Nb24Zr40 alloys which ballistic conductivity occur, respectively. Figure 75 illustrates the atomic configuration array of the Ni-centred icosahedral Ni5Nb3Zr5 clusters [88] separated by 0.23-nm-wide insulating zigzag tunnels [43], along with the electron tunnelling model. Due to the fact that it is assumed that the mean free path of electrons in an amorphous alloy is much larger than the width of the tunnels (0.23 nm) between the clusters, we can imagine the existence of macroscopic quantum electron tunnels passing along the arrays, even if there is poor condensation clustering combined with small amounts of other Voronoi-type polyhedral with relatively long atomic distances. This can be called a “two-fluid model” [207]. In addition, optimum hydrogen compositions (1.2 %) which showed superior ballistic transport (Fig. 73 (c)) for Ni0.39Nb0.26Zr0.35 amorphous alloys in 104.7 m/s-specimens are smaller than those (6.3 a% [36]) in 31.4 m/s-specimens, which showed the same behaviours. This means that there are higher-speed cooling accelerates hydrogen effects for electronic transport behaviours of the amorphous alloys. It also specifies that a uniform cluster configuration favours hydrogen absorption, as described in the previous section for Fig. 71. Lastly, we will consider the possibility of the short circuit problem for ballistic transport behaviours in Fig. 73 (b) and (c) and Fig. 74. Even if the short circuit formed between the electrodes, we cannot explain the following questions, as well as previous papers [36, 69, and 205]: 1. Why does the behaviour begin to occur from temperature region below 273 K in cooling runs, and stop before 273 K in heating runs? 2. Why is the increase of resistivity moderately up to the normal resistivity during heating runs? 3. Why is the occurrence of the behaviour limited to some Zr and H content regions? 4. Why is a great deal of water contained in cryostat, which then forms an ice bridge of 20 mm in length between electrodes? The ballistic transport behaviour is not caused by the short circuit problem. In addition, magnetic measurements by superconducting quantum interference device (SQUID) for the amorphous alloys showed Pauli paramagnetism in a temperature region above the onset of superconductivity [63].

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5-3 Rotating speed effects on electronic transport behaviours [208] For ballistic conductivity, the values obtained at 300 and 51 K were 5 and 0.01 % of silver (1.62P:cm), respectively. Therefore, supercooling molten alloys is expected to produce stable ballistic transport by increment of degree of amorphousness. In this section, we study the effect of rotating (or quenching) speed on electronic transport behaviour in ballistic conductivity and Coulomb oscillation for ((Ni0.6Nb0.4)0.65Zr0.35)100-yHy (0 ” y ” 15) amorphous alloys with nanometre-scale sized clusters. The rotating wheel method under an argon atmosphere was used for preparing amorphous Ni39Nb25Zr35 and Ni36Nb24Zr40 alloy ribbons of 1-mm width, using rotation speeds of 3,000 and 10,000 rpm. The resistivity was compared with silver, which has the highest electrical conductivity in all elements. The distance between the two voltage electrodes was 20 mm.

Fig. 76 The temperature dependence for the resistivities of (Ni0.39Nb0.26Zr0.35)100-yH y alloys, which was produced by rotating speed of 3,000 rpm, with different hydrogen contents (a ) (y =0), semiconducting; (b) (y =5.3), ballistic conducting; and (c) (y =7.1), superconducting transports; (d) (y =8.9), using Coulombic oscillation.

Fig. 77 The temperature dependence got the resistivities of (Ni0.39Nb0.26Zr0.35)100-yH y alloys, which was produced by a rotating speed of 10,000 rpm, with different hydrogen contents (a ) (y =0), semiconducting; (b) (y =2.2), ballistic conducting; and (c) (y =3.2), superconducting transports; (d) (y =4.8), using Coulombic oscillation.

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The temperature dependencies for the resistivities of (Ni0.39Nb0.25Zr0.35) 100-yHy (0 ” y ” 15) amorphous alloys, which was produced by a rotating speed of 3,000 rpm (31.4 m/s), with different hydrogen contents are shown in Fig. 76. The resistivities showed large differences with increasing hydrogen content (Fig. 76 (a–d)). The resistivity of Ni39Nb25Zr35, which lacks hydrogen, increased almost linearly with decreasing temperature down to 6 K (Fig. 76 (a)). The negative temperature coefficient of resistivity (TCR) of -1.3x10-4/K indicates a semiconducting character. The resistivity (Fig. 76 (b)) of the (Ni0.39Nb0.26Zr0.35) 94.7H5.3 initially showed similar negative TCR behaviour as the alloy without hydrogen, but suddenly fell to an order of 0.01 ȝȍcm at 240 K, and then continued down to around 100 K in the cooling run. Subsequently, the resistance showed one valley at 62 K, and lastly recovered to an order of 0.01 ȝȍcm as the temperature decreased. In the heating run, the resistivity varied according to the similar curve as the cooling run, except for minimum value at 50 K, and then ascended once again as the temperature increased to 340 K. The resistivity (0.063 ȝȍcm) at 300K was one twenty-fifth than that of silver (1.62 ȝȍcm) at room temperature. Similar behaviours were also observed for the (Ni0.39Nb0.26Zr0.35) 100-yH y (y = 5.6, 6.3, 7, 7.5) and (Ni0.396Nb0.264Zr0.34) 100-yH y (y = 6.2, 7.9) alloys. This superior conductivity resembles the ballistic transport observed in one-dimensional, nanometre-scale channels, such as quantum wires [195] and carbon nanotubes [196, 197] at a low temperature, in the form of quantum interference associated with coherence. Ballistic conductivity can be explained by the existence of a macroscopic quantum tunnel passing along Ni-centred ideal icosahedral Ni5Nb3Zr5 cluster arrays. However, it is not clear at present time whether the mean free path of the electron is much greater than the size of the medium or not. With regard to the drop in resistivity at 240 K, although the topologic change (pseudo-transition) associated with the accumulation of strain is a possibility [199], we cannot confirm this without further investigation. The resistivity of the (Ni0.39Nb0.25Zr0.35) 92.9H7.1 alloy (Fig. 76 (c)) initially showed negative TCR behaviour, similar to the alloy without hydrogen, but suddenly started to decrease at 10.4 K, and then gradually continued down to 5.4 K in the cooling run. Type II-superconductivity already knows this behaviour at 2.1 K [203]. Similar behaviour was observed in heating run. Figure 76 (d) shows the temperature-dependent electric resistivity of a (Ni0.39Nb0.25Zr0.35)91.1H8.9 alloy. The abnormal resistivity continued from 42 K down to 7 K in the cooling run and from 8 K up to 365 K in the heating run. This is electric current-induced voltage amplification based on the Coulomb oscillation, as described above. However, when the amorphous alloy absorbed hydrogen crosses over the threshold content, the point at which hydrogen atoms fully occupy the tetrahedral sites, which are surrounded in a tetrahedral arrangement by four Zr (Nb) atoms [59], the tunnelling phenomenon disappeared.

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We next investigated temperature dependent resistivity for (Ni0.39Nb0.25Zr0.35) 100-yHy (0 ” y ” 15) alloys, which are produced by a rotating speed of 10,000 rpm (104.7 m/s). These results are presented in Fig. 77. The resistivity (Fig. 77 (a)) of Ni39Nb25Zr35 without hydrogen is almost similar to that of Fig. 76 (a). However, the resistivity (Fig. 77 (b)) for the (Ni0.39Nb0.25Zr0.35)97.8H2.2 alloy displays gentle decreases in the cooling run. However, in the heating run, it suddenly reduced by six orders of magnitude at 40 K and fluctuated between 0.1 and 1 n:cm up to 252 K, and then remarkably increased by six orders of magnitude to match the resistivity values of the cooling run, finally following the same trend as the cooling run. The resistivity at 200 K (0.1 n:cm), which is 0.01 % of silver (1.62 P:cm) at room temperature, is the same as the minimum resistivity achieved for the 3,000 rpm-specimen of (Ni0.39Nb0.26Zr0.35)93.7H6.3 at 51 K [36]. The resistivity (Fig. 77 (c)) of the (Ni0.39Nb0.25Zr0.35)96.8H3.2 alloy is almost the same as the resistivity of Fig. 76 (c) except for the small drop from the onset temperature To = 8.2 K. The Coulomb oscillation (Fig. 77 (d)) in the cooling and heating runs of the (Ni0.39Nb0.25Zr0.35)95.2H4.8 alloy is about 4-times larger than that of heating run in Fig. 76 (d). The degree of amorphousness for the Ni39Nb25Zr35 alloy increases from 62.7 to 82.3 % as the rotating speed increases from 3,000 to 10,000 rpm (Fig. 78). Therefore, we can assume that the increase in rotating speed facilitates uniformity in the cluster morphology, resulting in the enhancement of superior ballistic transport. Supercooling of the molten alloy induces a superior ballistic conductor and a room temperature Coulomb oscillation at lower and higher hydrogen contents, respectively.

Fig. 78 The power spectra of receiving waves from Ni39Nb26Zr35 amorphous alloys for 3,000 -(31.4-) and 10,000-rpm (104.7-m/s) specimens.

Fig. 79 The effects of Zr and H contents on semiconducting, ballistic conducting, and superconducting transport and Coulombic oscillation properties for ((Ni0.6Nb0.4)1-xZrx)100-y Hy (x =35 and 40, 0 ” y ” 15) amorphous alloys.

We observed similar resistivity variations for restricted contents of hydrogen and Zr, although we could not observe changes in microstructure for all specimens used in this study. The detailed result after polishing on both sides by 5 ȣm was described in a previous section [69]. The effects of Zr and H content on these variations for ((Ni0.6Nb0.4)1-xZrx)1-y Hy (x=35 and 40, 0 ” y ” 15)

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amorphous alloys produced with speeds of 10,000 rpm are collectively presented in Fig. 79. In the figure, the black and gray solids and the circle represent the alloys that were observed to have ballistic conduction and Coulomb oscillation, and semiconducting property, respectively, and the cross denotes alloys that showed onset superconductivity above 5.5 K. The ballistic transport for the 10,000 rpm-Ni39Nb25Zr35 alloy occurs in the lower limited hydrogen region of 2.2–2.5 %, which is half hydrogen contents, compared with those of the alloy produced by 3,000 rpm. As can be seen from above results, the supercooling of the molten alloy plays an important role in various electron transport phenomena, because the pronounced results are attributed to the electronic structure and transitions related to local cluster structures. The localisation effect of hydrogen at outside and inside spaces of clusters particularly plays a decisive part in various electron transport phenomena. This article makes the effect of quenching speed for electronic characteristics of amorphous alloys clear. 5-4 The effect of hydrogen content on ballistic transport behaviours [69] In the previous section, supercooling (104.7-m/s) the molten alloy produces a ballistic conductor with electrical conductivity of about 0.1 nȍ·cm (0.01% of silver (1.62 ȝȍ·cm)) for (Ni0.39Nb0.26Zr0.35)97.8H2.2 amorphous alloy [205]. The increase in degree of amorphousness by supercooling induces uniformity in the cluster morphology, leading to superior conductivity. We postulated the existence of macroscopic quantum electron tunnels passing along the millimetre-sized zigzag paths of atomic bond arrays with a large capacitance (of the order of several femtofarad) among Ni-centred ideal Ni5Nb3Zr5 clusters for ballistic transport [88], although the amorphous structure in amorphous alloys is composed of a large number of low symmetry-clusters located around the main icosahedral ones. In this section, we will report the effect of hydrogen content on ballistic transport behaviours in Ni39Nb25Zr35 amorphous alloys with subnanometre-scale sized clusters, as a representative composition for ballistic behaviour. To make the hydrogen inhomogeneous effect clear, we also measured resistivity after polishing on both sides by 5 ȝm. Visibly, all the ribbons prepared by rotating wheel method were mirror-like and showed good levels of toughness. The change from argon to helium Fig. 80 The temperature dependence of the atmosphere gasses makes the surface smooth due to resistivity of polished (Ni Nb Zr ) H 0.39 0.26 0.35 85 15 one-order higher thermal conductivity of helium (Ar: amorphous alloys in cooling and heating runs. 0.1772 W/(m K), He: 0.152 W/(m K) [209]). This material showed three kinds of transport behaviours: semi-conducting, Coulomb oscillation, and ballistic transport.

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When the hydrogen content increases over 13.5 %, ballistic transport behaviour occurs. Fig. 80 is a representative example for polished (Ni0.39Nb0.26Zr0.35)85H15 amorphous alloys. In the cooling run, the resistivity decreases almost linearly down to 170 K and then suddenly reduces by three orders of magnitude at 165 K and falls down again to an order of 0.001 ȝȍ·cm at 88 K. Subsequently the resistivity recovers abruptly on the extended line of the cooling curve between 330 and 170 K, and then ascends once again as temperature decreases. In the heating run, the resistivity decreased according to the same curve as the cooling run, except for a drop down to order of 0.001 ȝȍ·cm between 130 and 172 K. The resistivity (0.1 nȍ·cm) at 130 K in heating run is around 0.006 % of silver (1.62 ȝȍ·cm) at room temperature.

Fig. 81 The temperature dependence for the resistivity of polished (Ni0.39Nb0.26Zr0.35)78.8H21.2 amorphous alloy in the 1st cooling and heating runs (a); the 2nd runs (b); the 3rd runs (c); and the 4th runs (d).

To ensure the reproducibility of these changes of the resistance and the domain of existence of the ballistic transport effect, we repeated the cooling and heating runs four times by measuring the ballistic transport behaviour in a temperature region of between 300 and 6 K using the polished (Ni0.39Nb0.26Zr0.35)78.8H21.2 amorphous alloy. The 2nd and 4th runs followed the 1st and 3rd runs, respectively, but the 3rd runs were carried out after 5 days of the 2nd runs (Fig. 81). The ballistic transport occurs in both cooling and heating runs for the 1st and 2nd runs, but in the heating run alone for the 3rd and 4th runs. Since a metal/ballistic transition occurs within narrow temperature region, the transition was derived from the morphology changes associated with two types of cluster ordering: topological and compositional short-range [206]. As can be seen from Figs. 80 and 81, the ballistic transport occurs in a temperature region of between 65 and 230 K, but there is no regular rule for holding the temperature region. Therefore, the increase in degree of amorphousness––i.e., supercooling the molten alloy––will help the uniformity of cluster morphology [205], leading to ballistic transport up to 272 K. Since it is assumed that the mean free path of electrons in the amorphous alloy is much larger than the width of the tunnels (0.23 nm

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[59]) between the clusters, we can imagine the existence of macroscopic quantum electron tunnels passing along the arrays. We summarise electronic transport behaviours for the cooling and heating runs of the hydrogenated (Ni0.39Nb0.25Zr0.35)100-xHx (0 ” x < 23.5) amorphous alloys before and after polishing (Fig. 82). The amorphous alloys display three types of electronic transport behaviours: semiconducting, ballistic transports, and Coulomb oscillation. Coulomb oscillation occurs below a hydrogen content of 13.5 %, except for 21.2 a% H-specimen under repeated cooling and heating runs, and the ballistic transport appears at hydrogen content region of between 13.5 and 21.2 %. This trend is similar to previous result of hydrogenated (Ni0.39Nb0.25Zr0.35)100íxHx (0 < x < 20) amorphous alloys obtained by a rotating speed of 3000 rpm (31.4 m/s) [36]. In addition, we observed the stability of the resistance with a constant temperature in the region characterised by these Coulomb oscillation and ballistic transport phenomena. Furthermore, we observed similar behaviours on ribbons prepared from different batches. From these results, we assume that, for ballistic transport, full hydrogen absorption into the clusters in hydrogen content between 13.5 and 21.2 % assists the regular array formation of clusters. The ballistic transport prefers to occur in the heating run rather than in the cooling run. This suggests that the occurrence of the phenomena needs a higher degree of amorphousness: i.e., the uniformity of cluster morphology. Furthermore, we found a similar Fig. 82 The effect of H content on the occurrence of resistance result for electronic transport semiconducting, ballistic transport, and Coulomb behaviours of the hydrogenated amorphous oscillation properties of (Ni0.39Nb0.25Zr0.35)100íxHx (0 ” x < 23.5) amorphous alloys. alloys before and after polishing. This indicates that there is no inhomogeneous distribution effect of hydrogen. 5-5 Chaotic properties of quantum transport [210] The dynamic evolution of an ensemble of electrons performing macroscopic resonant tunnelling is of great importance. Because of the linearity of the Schrödinger equation, the quantum system does not generally exhibit chaos characterised by the standard diagnostics of Kolmogorov-Sinai entropy or positive Lyapunov exponents. However, in addition to the continuous chaotic model that Jona-Lasinio and Presilla [211] have reported, we observed a quantum analogue of chaos: i.e., quantum chaology, rather than the genuine quantum chaos. Therefore, one of the questions foremost on the researcher’s mind is whether there us a chaotic dynamic system acting on transmissibility. In order to gain a deeper insight into the electron transport mechanism among icosahedral Ni5Nb3Zr5 cluster islands in Ni-Nb-Zr-H amorphous alloys, we will present the room temperature chaotic properties of quantum transport in terms of cluster morphology.

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A theoretical explanation for mesoscopic-quantised conductance was first proposed by Landauer and has since been successfully applied to a great variety of problems [212]. Following his idea, Jauslin [213] has studied the chaotic properties involved in a quantum scattering problem for a Kronig-Penny model under a constant electric field. Jona-Lasinio et al. have investigated a quantum many-body system undergoing multiple resonant tunnelling, which exhibits chaotic behaviour without a classical counterpart. Although the quantum system generally displays no chaos characterised by the standard diagnosis of Kolmogorov-Siani entropy and positive Lyapunov exponents, Jona-Lasinio and Presilla [214] have pointed out that the dynamical chaoticity of the quantum system is continuous up to the limit of an infinite degree of freedom. Nakamura et al. [215] have reported weak chaotic quantum transport in a static electric field, using the one-dimensional Kronig-Penny model. The chaotic nature of the scattering manifests in its dependence on the incoming energy of the transmission for a fixed number of barriers [213]. Although the electron transmission behaviour, such as ballistic transport, is based on a three-dimensional dynamic charge traveling mechanism, it also mimics chaotic quantum phenomena. So, we noted the existence of quantum many-body multiple resonant tunnelling in terms of chaotic properties for quantum scattering. Our interest lies in studying the complex superlattice pattern in electron tunnelling passing through zigzag cluster arrays for electric fields in ballistic transport. The goal of this study was to confirm the macroscopic quantum tunnelling of electrons in mesoscopic system. The approach that we have developed could lead to important similar studies in the field. We analysed the quantum transport of ballistic transport in Ni-Nb-Zr-H amorphous alloys in terms of weak chaos, by utilising tunnel resonance analysis as reported by Nakamura et al [215]. We considered a finite periodic structure––i.e., a strictly regular superlattice to examine the quantum transport among Ni5Nb3Zr5 clusters under a constant external electric field, as shown in Fig. 83––using the Kronig-Penny model with a stepwise potential

Fig. 83 The Kronig-Penny model for a onedimensional superlattice composed of large numbers of Ni5Nb3Zr5 clusters under a high electric field.

excluding the G-function due to the probability of electrons. The superlattice is composed of a large number of periodic unit cell elements in a matrix, M, with an alternating sequence of potential barriers and cluster wells. Since the Coulomb oscillation in Ni-Nb-Zr-H amorphous alloys is characterised by a non-scattering tunnelling process, we did not take the hierarchical (e.g., the Fibonacci-type) and random potential into consideration. Budiyono and Nakamura [216] have studied smoothed Coulomb blockade peak height fluctuations in a chaotic quantum cavity based on the semi-classical approach. If we present