Thermal and Thermodynamic Stability of Nanomaterials [1 ed.] 9783038133315, 9780878492572

Citation preview

Thermal and Thermodynamic Stability of Nanomaterials

Edited by Suresh Chandra Parida

Thermal and Thermodynamic Stability of Nanomaterials

Special topic volume with invited peer reviewed papers only.

Edited by:

Suresh Chandra Parida Bhabha Atomic Research Centre, Mumbai, India

TRANS TECH PUBLICATIONS LTD Switzerland • UK • USA

Copyright © 2010 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of the contents of this publication may be reproduced or transmitted in any form or by any means without the written permission of the publisher. Trans Tech Publications Ltd Laubisrutistr. 24 CH-8712 Stafa-Zurich Switzerland http://www.ttp.net

Volume 653 of Materials Science Forum ISSN 0255-5476 Full text available online at http://www.scientific.net

Distributed worldwide by

and in the Americas by

Trans Tech Publications Ltd Laubisrutistr. 24 CH-8712 Stafa-Zurich Switzerland

Trans Tech Publications Inc. PO Box 699, May Street Enfield, NH 03748 USA

Fax: +41 (44) 922 10 33 e-mail: [email protected]

Phone: +1 (603) 632-7377 Fax: +1 (603) 632-5611 e-mail: [email protected]

Preface The study of nanomaterials is an active area of research in physics, chemistry, and materials engineering as well as biomedical engineering in the 21st Century. Nanomaterials which are categorized as substances that are in the shape of spherical dot, rod, thin plate, or void of any irregular shape smaller than 100 nm, find wide application in materials science and technology due to their very distinctive properties compared to their bulk counterparts. Depending on the size of the building blocks of their constituent structural elements, they can be classified as: zero- (0D), one- (1D), two- (2D) and three-dimensional (3D). Nanomaterials can be in the form of composites, alloys, compounds or pure elemental solids and sometimes referred to as nanostructured materials, nanosolids, nanoclusters, nanocrystallites, nanograins, etc.,. and the term nanotechnology refers to the methods used for the construction of nanomaterials and nanodevices. The key difference in properties of nanomaterials compared to their bulk counterparts arise due to the difference in interatomic interactions which arise due to high surface-to-volume ratio and a high portion of undercoordinated surface atoms when the particle size approaches nanometer range. The size dependent properties of solids are very challenging to study both theoretically and experimentally. This special volume is focused on two fundamental issues related to the stability of nanomaterials. The thermal stability of nanomaterials is a very important issue for controlling the size during synthesis as well as in high temperature application environments where as, the thermodynamic stability of nanomaterial is very important in order to understand the underlying principle behind its formation either from atomic or molecular constituents through the bottom-up approach (where nanomaterials are formed from atoms or molecules as starting materials and the starting species are enlarged to nanometer size) or from disintegration of larger particles through the top-down approach (where nanometer size materials are obtained by disintegration of larger particles). Large variation in thermo-physical properties like melting points, enthalpy of formation etc. have been observed for nanomaterials compared to their bulk counterparts. The underlying principles behind these anomalous properties have been addressed in some of the articles in this volume. We hope, the articles published in this special volume will provide many important inputs to researchers to address fundamental and technical issues in the field of nanomaterials.

Suresh C. Parida Guest Editor

Table of Contents Preface Thermal Stability of Nanostructured Coatings A. Fabrizi, M. Cabibbo, R. Cecchini, S. Spigarelli, C. Paternoster, M. Haidopoulo and P.V. Kiryukhantsev-Korneev Anomaly in Thermal Stability of Nanostructured Materials K.K. Nanda Thermodynamic Phase Transitions in Nanometer-Sized Metallic Systems F. Delogu Prediction of Phase Diagrams in Nano-Sized Binary Alloys T. Tanaka Au-Si and Au-Ge Phases Diagrams for Nanosytems D. Hourlier and P. Perrot Grain Growth Behavior of Al2O3 Nanomaterials: A Review A. Gupta, S. Sharma, M.R. Joshi, P. Agarwal and K. Balani Phase Stability of Rare-Earth Based Mixed Oxides in Nano-Regime: Role of Synthesis R. Shukla and A.K. Tyagi

1 23 31 55 77 87 131

Materials Science Forum Vol. 653 (2010) pp 1-22 © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.653.1

Thermal Stability of Nanostructured Coatings A. Fabrizi1,a, M. Cabibbo*1,b, R. Cecchini1,c, S. Spigarelli1,d, C. Paternoster2,e, M. Haidopoulo3,f and Ph.V. Kiryukhantsev-Korneev4 1

Department of Mechanical Engineering, Marche Polytechnic University, Via Brecce Bianche, 60131-Ancona, Italy 2 Chemicals and Materials Department, Université Libre de Bruxelles, Av. F.D. Roosevelt 50, 1050 Brussels, Belgium 3 VINF/Arcelor Mittal, Research Liege, Bld. De Colonster B57, B4000-Liege, Belgium 4 VINF/ Scientific-Educational Center of SHS, Moscow State Institute of Steel and Alloys, Leninsky pr. 4, Moscow 119049, Russia a [email protected]; b [email protected]; c [email protected] d [email protected]; e [email protected]; [email protected] *: M.Cabibbo (Marcello Cabibbo) corresponding author. Keywords: Hard coatings; CrN-based coatings; BN-based coatings; thermal treatments; nanoindentation; GIXRD; TEM

Abstract. This paper is a review of the thermal stability of nanostructured nitride coatings synthesised by reactive magnetron sputtering technique. In the last three decade, nitride based coatings have been widely applied as hard wear-protective coatings in mechanical components. More recently, a larger interest has been addressed to evaluate the thermal stability of such coatings, as their mechanical and tribological properties are deteriorated at high working temperatures. This study describes the microstructural, mechanical and compositional stability of nanocrystalline Cr-N and nano-composited Ti-N based coatings (Ti-Al-Si-B-N and Ti-Cr-B-N) after air and vacuum annealing. For Cr-N coatings annealing in vacuum induces phase transformation from CrN to Cr2N, while after annealing in air only Cr2O3 phase is present. For Ti-N based coatings, a well-definite multilayered structure was shown after air annealing. Degradation of mechanical properties was observed for all the nitride coatings after thermal annealing in air. 1. Introduction Corrosion resistance is usually one of the major requirements in the selection of a particular grade of stainless steel for a given application. Chemical composition, surface treatment, heat treatment, and fabrication, generally influence the response of a given stainless steel grade in a specific environment. Among all the stainless steels [1], AISI 304 grade is one of the most commonly used. It has good corrosion resistance in most environments and also in saturated oxidizing acid solutions. Nevertheless, it has not satisfactory corrosion resistance in chloride or non-oxidizing acid solutions, which constitutes the major drawback of this stainless steel grade [2]. One effective means to overcome this disadvantage is the surface coating by physical vapour deposition (PVD) [3,4]. It is known that mostly nitrides or carbides, produced by PVD, are able to show a rather good corrosion resistance of the austenitic stainless steels in different reactive environments [3,4]. PVD generally refers to three generic coating methods that involve evaporation, ion-implating, and sputtering. The application of one of these three coating processes can be used for depositing virtually any solid film to the surface of any metallic material. This versatility makes PVD especially useful for depositing hard coatings for corrosion and wear-applications [5]. With this respect, the chromium-based nitrides, Cr2N and CrN, deposited by PVD, have been reported to have high hardness, enhanced wear and corrosion resistance, and can be utilized as anti-wear and anti-corrosion coatings [6,7]. The processing conditions during sputtering clearly influence the resulting tribological, mechanical and chemical properties of the films. For example, Pakala and Ray found microhardness rises with increasing nitrogen content in the sputtering gas

2

Thermal and Thermodynamic Stability of Nanomaterials

corresponding to the formation of the Cr2N phase [8]. N2 partial pressure plays a very important role in depositing Cr-N and its influence on the structure and properties of thin films has been widely studied [9-11]. On the other hand, friction properties are a consequence of structure and orientation of crystals in the film [12]. The corrosion properties also depend on the porosity and density of the coatings [13]. Cr-N coatings have also been used for bending and stamping tools [14,15]. For these reasons, chromium nitrides (Cr-N) are nowadays considered very popular as coating material for tools and similar products. Tribological behavior at room and elevated temperatures were reported to be quite satisfactory. Yet, only few studies dealt with properties at high temperatures. For instance, Sue et al. compared TiN, ZrN and CrN coatings on steel at temperatures of 770 and 830 K using a in ring-on-disc test machine. The CrN coating showed wear rates about one and two orders lower than that of ZrN and TiN, respectively [16]. Superhardness can be achieved in a variety of ordinary hard coatings either by energetic ion bombardment during their deposition (which results in a variety of effect including a high compressive stress) or by the formation of an appropriate nanostructure, such as superlattices and nanocomposites (see [17,18] and references therein). Cr-N coatings have been reported to have high surface hardness, low coefficient of friction, and high toughness compared with the more conventional TiN [19]. Thus, Cr-N thin films have proven their capability of enhancing the wear protection of a coated piece. In addition to its superior wear resistant property, Cr-N is thought to be chemically inert in various environments. Some studies have been performed in acidic solutions (HCl, H2S04) or chloride solutions (NaCl) on deposits often made of mixtures of chromium nitrides [20-22]. On the other hand, the hardness rise, due to the energetic ion bombardment, is easy to achieve in a variety of coatings including the so-called ‘nanocomposites’ M(1)nNyM(2). Here M(1) is a hard and stable transition metal nitride, such as ZrN, CrN, TiN, etc., and M(2) is another metal which does not form any thermodynamically stable nitride, such as Ni, Cu, etc. However, the superhardness is lost when the high stress and other effects induced by the energetic ion bombardment relax upon annealing to 670 – 870 K [17,18] or upon a long term storage in air. The Ti–B–N system represents another class of super-hard coatings which are prepared by a variety of PVD methods, such as vacuum arc evaporation (e.g. [23]) and sputtering [24]. The use of conventional sputtering at a low pressure results either in the formation of a homogeneous phase TiB2Nx [24,25], or a TiNxBy phase consisting of TiN lattice in which the nitrogen sites are occupied by 33% of boron, 49% of nitrogen and 18% of vacancies, or amorphous Ti–B–N coatings [26]. At a lower boron content, nanocrystalline TiN and quasi-amorphous TiB2 phase are formed whereas a higher boron content leads to a structure consisting of quasi-amorphous TiN and nanocrystalline TiB2 [27]. The BN matrix can be hexagonal, amorphous or cubic [28], or even a mixture of f.c.c. TiN, orthorhombic TiB, c-BN and hexagonal Ti–B–N [29]. Hardness of 40– 70 GPa was reported in many papers [24-29]. Generally, hardness change with composition does not follow the rule of mixture but displays a maximum at a given composition where the microstructure of the films is very uniform (no columnar growth) and the crystallite size is of few nanometers. Another very important property of protective films required for industrial application is the thermal stability of their mechanical characteristics at elevated temperatures. For instance, due to the age hardening effect the Ti–B–N films showed the hardness values up to 43 GPa for annealing temperature below 1170 K [30]. The best Ti–Si–N [31] and Ti–Al–Si–N [32] nanocomposite films were reported to be stable up to 1370 K. The oxidation of nitride coatings is an important mechanism leading to the degradation of the mechanical properties and performances at elevated temperatures. The differences in mechanical properties can be attributed to the stress and structure of the CrN coating at 720–870 K [33]. CrN coating would form a dense and stable Cr2O3 film as a protective scale for thermal oxidation at 1070 K, and a great mechanical integrity with high thermal stability was observed [34]. In many applications, coated tools are exposed to aggressive environments including corrosive

Materials Science Forum Vol. 653

3

media, stresses, elevated temperatures or combinations of them. In order to extend the high temperature applications of TiN coatings, ternary Ti–Me–N coating systems (where Me can be B, Al, Si, Cr, and others) have been actively explored and studied [35-37]. Among these, Ti–Al–N coating layer showed, in several studies, improved oxidation resistance compared to that of TiN coating layers due to the formation of a stable Al2O3 surface film by migration of aluminium atoms of the coating itself to the surface region [37,38]. On the other hand, Ti–Si–N coatings are generally reported to have nano-composite microstructure with nano-sized TiN crystallites distributed in amorphous Si3N4 matrix and to show superhardness above 40 GPa due to its nano-composite microstructure [38]. Ti–Si–N also exhibits significantly improved oxidation resistance compared to that of TiN coating layer. In this ternary system, the amorphous SiO2 formation plays a major role as oxidation barrier [39]. Thus, as a general rule, silicon containing films also showed significantly better oxidation resistance compared to that of TiN. This is due to either the formation of a Si-rich diffusion barrier oxide layer [40] or to the formation of a strong and dense Si3N4 interface in nc-TiN/a-Si3N4 nanocomposite that hinders oxygen diffusion along the grain boundaries [41]. Recently, Zhang et al. [42] showed that the oxidation of nc-TiN/a-Si3N4 takes place by a progressive replacement of nitrogen in both TiN and Si3N4 phases with diffused oxygen. Ti–B–N films are attracting much attention due to the combination of high hardness, wear and corrosion resistance. However, the oxidation resistance of Ti–B–N films was shown to be much lower than that of Ti–Si–N nanocomposite films due to the low oxidation stability of the BN phase [43]. Otani and Hofmann [36] proposed the main rate controlling mechanism of oxidation of TiCrN coating being a combined action of oxygen inward and Cr outward diffusion. This oxidation mechanism is based upon the fact that oxidation of pure TiN is mainly controlled by the inward diffusion of oxygen through the oxide layer, whereas, for pure CrN, outward diffusion of chromium is the rate determining mechanism. Lee [44] showed that the oxidation phenomena on TiCrN coatings, deposited on steel substrate, proceeded by not only the inward diffusion of oxygen but also the outward diffusion of Cr and Ti to form Cr2O3 and TiO2, respectively. At the same time, Fe from the substrate was found to transport outwardly toward the oxide layer. Lee suggested that the TiCrN oxidation is mainly controlled by Ti and O diffusion through the dense Cr-oxide layer. In terms of anti-oxidation, silicon seems to be more efficient than Al and Cr. With films containing Si [45], a significant oxidation commences at about 1120 K. A comparable result was reached with 26 wt.% of Al [46]. At 870 K, a minimum oxidation rate was observed with a 32.7 wt.% of Cr [36]. Despite a relatively large volume of data pertaining to the high temperature oxidation properties of Cr-N coatings, few studies have been performed to assess the thermal stability of the coating microstructure. This study presents microstructure and mechanical insights in Cr-N and Ti-Al-Si-B-N, TiCr-B-N nanostructured coatings on AISI 304. The behavior of 110 to 210 nm thick Cr-N coatings, deposited by reactive magnetron sputtering and then subjected to thermal annealing both in air and vacuum, was investigated. Transmission Electron Microscopy (TEM) and Grazing Incident X-Ray Diffractometry (GIXRD) were used to study crystal structure, Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM) for surface morphology evolution and nanoindentation for hardness measurements. Microstructure and mechanical properties evolution of Ti-Cr-B-N and Ti-Al-Si-B-N, produced by ion implantation assisted magnetron sputtering, were studied by TEM, X-Ray Diffractometry (XRD) and nanoindentation. Oxidation phenomena and thermal stability of the Ti-Al-Si-B-N and Ti-Cr-B-N were investigated. Air annealing aimed at studying the performance of the coating in an oxidizing environment, while vacuum annealing experiments allowed to determine the mechanisms of diffusion and grain growth of the thin-film constituting phases.

4

Thermal and Thermodynamic Stability of Nanomaterials

2. Experimental details and methods 2.1. The materials and deposition methods. Three different Cr-N nanostructured coatings were deposited on AISI 304 stainless steel substrate (in the following referred to as sample A, B, C). Ti-Cr-B-N and Ti-Al-Si-B-N coatings were deposited on single crystal Si100 and AISI 304 with a commercial 2B surface finish consisting of a pickling process after several stages of hot and cold rolling, and of a final skin pass. Ti-Cr-B-N and Ti-Al-Si-B-N coatings were also deposited on single crystal Si(100) by ion implantation assisted magnetron sputtering (IIAMS) in which magnetron sputtering is combined with a Ti ions source. The Cr-N coatings were deposited by Cockerill Sambre ARCELOR-MITTAL (Belgium) while the Ti-N based coatings were produced by Moscow State Institute of Steel and Alloy (MSISA) in Russia. Flat AISI 304 sheets of 1.5 m with and thickness of 0.6 mm were pre-treated by Ar-plasma etching and coated using Direct Current (DC) reactive sputtering in a Ar/N2 mixture atmosphere. Plasma composition was monitored by Optical Emission Spectroscopy (OES) during deposition. Deposition conditions were defined by the Cr/Ar ionic ratios in the plasma and N2 flow. Cr/Ar ratios were: 0.65, 0.65 and 0.85 for type A, B and C respectively. Three different N2 flow regimes were used: high for type A, medium for type B and low for type C. From each type of the Cr-N coated sheets, several samples of 1 x 2 cm2 were extracted using a water cooled diamond blade. Coatings thicknesses, measured by AFM, were (210 ± 20) nm, (140 ± 10) nm and (110 ± 10) nm for samples A, B and C respectively. For the for Ti-Cr-B-N and Ti-Al-Si-B-N coatings, the deposition process was performed by IIAMS apparatus [47] in a gaseous mixture of Ar + N2. Prior to deposition, the surface of substrates was ion etched by Ar beam with energy of 1.5 KeV for 10 minutes in order to remove oxides and impurity atoms on the surface. The total pressure in the chamber was maintained at 0.01 Pa and the partial pressure of N2 was of 15% of the total one. TiCrB and TiAlSiB composite targets were synthesized by combined force self-propagating high-temperature synthesis-pressing technology (SHS). Targets compositions are described in [48]. The diameter of the targets was 125 mm and the target to substrate distance was 100 mm. Discharge magnetic current during sputtering was 2.3 A and a bias voltage of -250V was applied to the substrate. Ti ion implantation source was used at 20kV of accelerating voltage and an ions flux of 1.5·1014 ions/(cm2 s). Energy dispersive spectrometry (EDS) measurement of the Ti-Cr-B-N coating gave a Ti/Cr=2.6, while, for Ti-Al-Si-B-N was Ti/Al = 2.8 and Ti/Si = 2.9. Coatings and samples characteristics are summarized in Table 1. Table 1. Cr-N and Ti-Al-Si-B-N, Ti-Cr-B-N coating characteristics. Coating

Substrate

Cr-N (A)

Deposition Parameters Cr/A r

Ti/Cr

Ti/Al

Ti/Si

Thicknes s [nm]

Total Pressure [Pa]

N2/(N2+Ar)

Discharge current [A]

AISI 304

0.65

—

—

—

210±20

—

—

—

Cr-N (B)

AISI 304

0.65

—

—

—

140±10

—

—

—

Cr-N (C)

AISI 304

0.85

—

—

—

110±10

—

—

—

Ti-Al-Si-B-N

AISI 304, Si

—

—

2.8

2.9

~ 2000

0.1

14 %

2.3

Ti-Cr-B-N

AISI 304, Si

—

2.6

—

—

~ 2000

0.1

14 %

2.3

2.2. Microstructure inspections. Morphological inspections were performed using a PHILIPS® XL20 SEM equipped with a EDS ( Energie Dispervise Spectroscopy) system and a BURLEIGH INSTRUMENTS® Metris2001 AFM in contact mode. TEM discs from Cr-N/steel and Ti-X-B-N/Si samples were prepared respectivily in-plane view and in cross-section configuration. The TEM discs were mechanically polished to 100 μm, thinned to ~20 μm by dimpling and then ion milled to electron transparency.

Materials Science Forum Vol. 653

5

XRD measurements were performed both in the -2 geometry (SIEMENS® D5000, Cu waveleght λ = 0.154 nm, 30 kV, 40 mA) and GIXRD (INEL® CPS120, Cu waveleght λ = 0.154 nm, 30 kV, 40 mA). 2.3. Thermal treatments. For the Cr-N coatings, thermal annealing was performed at 920 K both in air and vacuum (2.0·10-4 Pa) for 1, 2, 4 and 8 h. After annealing, samples were left to cool in air and vacuum respectively at room temperature. All thermal annealing treatments of Ti–Cr–B–N and Ti–Al–Si– B–N coatings were performed in air at 1170 K/4 h. After annealing, samples were left to cool in air at room temperature. Phases and microstructure were investigated by a X-ray diffractometer and a PHILIPS® CM 200 TEM operating at 200 kV, equipped with an EDS. Thermal cycling was performed in air by repeatedly moving the Cr-N/steel samples in and out of a furnace for a set number of cycles. During thermal cycling, the heating and cooling curves depended on the furnace temperature (Tsetup furnace) and on the time of permanence inside and outside the furnace. The furnace and sample temperatures were measured by two thermocouples, one connected to the furnace and the other to the sample. Number of cycles, time of permanence of the sample inside and outside the furnace and Tsetup furnace were controlled by a dedicated software. During each cycle, the samples were kept for 150 sec inside the furnace, rapidly moved outside the furnace, kept in this position for 150 sec, then rapidly moved back inside the furnace. Four different thermal cycling treatments were performed, at increasing Tsetup furnace: 725, 925, 1045 and 1175 K. The recorded Tmin and Tmax were respectively 425 and 585 K, 510 and 755 K, 530 and 910 K, 605 and 1075 K. The temperature rise and fall rate were 1.0, 1.5, 2.5 and 3.0 K/sec respectively. The number of cycles was fixed to 120 for all the tests, corresponding to a 6 hour-duration per test. 2.4. Mechanical properties. Indentation measurements were performed using a Hysitron© UBI® I Nanoindenter, equipped with a motorized stage. To estimate the Young’s modulus unload curves. A Berkovich diamond tip was used. Tip was calibrated with a fused quartz reference sample. Analyses were done according to the Oliver and Pharr method [49]. For the morphological analyses, the nanoindenter was operated in scanning probe mode (SPM). Identification of the different layers in the cross section samples was thus possible. Mechanical properties were inferred on the coating surfaces with indentation sequence of loading and unloading time of 5sec, holding at the maximum load being of 4sec. The applied load ranged 500 to 10000 μN in a multistep mode. The penetration depth was maintained within 10% of the film thickness to avoid indentation substrate effects. Cross section samples were prepared by gluing the samples on a thin silicon plate using twocomponent epoxy resin and then cutting to 500 μm tick cross-section slides. The slides were mechanically reduced to a thickness ~ 100 μm and then polished to mirror-like finishing. 3. Results 3.1. Cr-N coatings. Fig. 1 shows the TEM bright field images of sample A in plane view at different magnifications. At low magnification (Fig. 1(a)), the substrate grain boundaries and the slip bands formed in the rolling stage of the steel are visible. At higher magnification (Fig. 1(b)), the Cr-N crystal structure is visible, showing a very fine structure, with grain sizes ranging 15 to 35 nm. Cr-N grains appeared elongated. Zhao et al. [50] reported similar observations in Cr-N sputtered on Silicon mono-crystal. They explained the grain elongation with the geometrical orientation of the sample substrate with respect to the target during sputtering. Fig. 2 shows the GIXRD measurements performed on the as-deposited Cr-N/steel samples. The peaks at angles of 43.6°, 50.8° and 74.8° are due to substrate (111), (200) and (220) planes of austenitic steel, respectively. The 37.4° peak comes from the CrN (111) plane. Part of the 43.6° peak is likely to come from CrN (200).

6

Thermal and Thermodynamic Stability of Nanomaterials

20

Sub. CrN

CrN

Sub. Cr2O3 Cr2N

CrN Cr2N

Cr2O3 Cr2O3

Cr2O3

Rrelative Intensity

CrN

Sub.

Fig. 1. TEM in plane view of sample A showing: a) substrate grain boundaries and slip bands at low magnification, and b) coating microstructure at higher magnification.

C B A 30

40

50

60

70

80

2 (degree)

Fig. 2. GIXRD patterns of sample A, sample B and sample C in as-deposited conditions.

Fig. 3(a),(b) reports the GIXRD diffraction patterns for samples A and C, after thermal annealing in vacuum at 920 K for increasing annealing times. The diffraction pattern of the asdeposited samples is also reported. The intensity of all the peaks recorded on the as-deposited samples shrunk upon annealing. The clear peak at 42.6°, in the annealed conditions, is consistent with diffraction from Cr2N (111) plane. The evolution of samples A and C diffraction patterns with respect to Cr2N (111) peak seems to be different. In sample A, the intensity of Cr2N (111) peak increases progressively with annealing time. In sample C, the diffraction pattern changes with annealing time are rather modest and not significant. The diffraction patterns of samples A and C after 920 K air-annealing are reported in Fig. 3(c),(d). Peaks corresponding to the Cr2O3 phase appear on the diffraction patterns starting from 1h

Materials Science Forum Vol. 653

7

2h 1h as dep. 60

70

80

20

30

40

1h as dep. 50

60

2 (degree)

70

80

20

Cr2O3 Cr2O3

CrN

CrN

Sub.

Cr2N

70

80

Sub. CrN

CrN

2h

Cr2O3

Rrelative Intensity

4h

40

60

CrN

Sub. CrN

CrN

Sub.

d)

8h

30

50

2 (degree)

Cr2O3 Cr2N

Cr2N

CrN Cr2O3 Cr2O3

Cr2O3

Rrelative Intensity 20

CrN Sub.

2 (degree)

c)

Cr2O3 Cr2N

Cr2N

Cr2O3 Cr2O3

as dep.

Sub.

50

2h 1h

Cr2O3 Cr2N

40

8h 4h

CrN Sub.

30

Cr2O3

CrN

4h

20

CrN Sub.

Sub. CrN

CrN

Sub.

Rrelative Intensity

8h

b)

Cr2O3 Cr2N

Cr2N

Cr2O3 Cr2O3

Cr2O3

Rrelative Intensity

CrN

CrN Sub.

a)

Sub.

of annealing, with intensity increasing with annealing time. At the same time, CrN phase peaks intensity decreases and have almost completely disappeared after 8h of annealing, when only substrate and chromium oxide peaks are present in the diffraction patterns. Samples A and C show a similar diffraction patterns evolution on air-annealing. Sample C shows Cr2O3 peaks with higher intensity than sample A. In particular, the 4h and 8h annealing times, showed a considerable higher intensity at 33.6° and 54.9°, that correspond to the (104) and (116) Cr2O3 planes. As for vacuumannealing, sample B shows an intermediate behavior with respect to the diffraction spectrum of samples A and C.

8h 4h 2h 1h as dep. 30

40

50

60

70

80

2 (degree)

Fig. 3. GIXRD patterns of: a) sample A and b) sample C after annealing at 920 K in air for 1, 2, 4 and 8 h, and in vacuum for the same durations, c) sample A and d) sample C. The surface morphologies properties of the as-deposited and annealed samples were studied by AFM. In the as-deposited condition, samples A, B and C show similar Root Mean Square (RMS) surface roughness, whose average value was ~15 nm [51]. Air annealing, in sample B, led to a significant rise of the surface roughness, already at 1h annealing duration. The coating surface morphology changes revealing large host features, identified through GIXRD as Cr2O3 crystallites, generated by oxidation phenomena. Fig. 4 shows the GIXRD measurements performed on the Cr-N/steel samples before and after thermal cycling. All measurements were taken at a grazing angle of 0.8°. On the as-deposited samples, the three peaks recorded at angles of 38°, 43.5° and 63° are consistent with the contributions from CrN (111), (200) and (220) planes [52]. The intensity of these peaks decreases with increasing diffraction angle. Peaks due to the austenitic steel (substrate) are also visible on the as-deposited samples.

8

Thermal and Thermodynamic Stability of Nanomaterials

Fig. 4. GIXRD and XRD spectra of the as deposited Cr-N/steel samples after different thermal cycling treatments. CrN, Cr2N, Cr2O3 and substrate (AISI 304 stainless steel) diffraction angles positions are indicated.

In order to evaluate the morphological evolution induced by thermal cycling, SEM analyses on the Cr-N/steel samples were performed before and after thermal treatments. Fig. 5(a) shows a SEM micrograph taken on the as-deposited sample. Some of the substrate features are still clearly visible: steel grain boundaries and scratches are reproduced on the deposited film. Also the waviness present on the film (Fig. 5(a)) is due to the substrate. This explanation is consistent with the waviness change of orientation from grain to grain in the steel. This is due to the slip bands formed in the rolling stage of the steel. The surface morphology of the coating changes after thermal cycling. The change is more evident at the higher temperatures Tmax of the treatment. Fig. 5(b) refers to the sample after thermal cycling (Tmax = 1075 K), and it shows an increase of the film roughness, which makes the substrate features no longer visible. These morphological modifications are due to CrN oxidation to Cr2O3 [53,54], as suggested by the GIXRD analyses. Fig. 5(b) also shows that after cycling the film surface morphology is not longer homogeneous: large crystallites aligned in rows are present on the coating surface. These crystallites have a diameters ranging 0.2 to 1 m, and the rows formed are few tens of micrometers long.

Fig. 5. Representative SEM micrographs of Cr-N/steel samples: a) as-deposited and b) after thermal cycling with Tmax =1075 K. Rolling direction (RD) of steel is indicated. Sometimes such rows start from a single point and then separate apart. In general, they are oriented along a direction forming an angle of about 30° with respect to the steel rolling direction. These rows appear at Tmax ≥ 755 K and their surface density increases at higher cycling

Materials Science Forum Vol. 653

9

temperatures (910 and 1075 K). Surface morphology and roughness evolution of the Cr-N coatings before and after thermal cycling were investigated by AFM. AFM scans were taken in contact mode at different scan sizes. RMS surface roughness was determined from 22.7 x 22.7 μm2 scan areas. As it can be seen from Fig. 6(a), the film surface is characterized by parallel grooves, which are due to the slip bands produced on the steel during rolling. Fig. 6(b) shows the film surface after thermal cycling at Tmax = 1075 K. The increase of roughness is evident as well as the presence of larger crystallites (< 1 m in diameter).

Fig. 6. Representative AFM images of Cr-N coating surface: a) as-deposited and b) after thermal cycling with Tmax = 1075 K.

Nanoindentation was used to calculate the hardness of the Cr-N coatings, using indentation load-displacement data. Fig. 7 shows the hardness of samples A, B and C in as-deposited condition and after 8 h of annealing in vacuum as a function of penetration depth. It can be observed that hardness decreases with penetration depth for all the as-deposited and vacuum annealed samples. Hardness of samples A, B and C was measured with penetration depths starting from 15 nm. Largest penetration depths were kept below the film thickness. The hardness behavior as a function of penetration depth is typical of film with higher hardness than the substrate.

Fig. 7. Nanoindentation measured hardness of: a) as-deposited samples and b) after annealing in vacuum at 920 K/8h. Sample A ( ), sample B ( ), sample C ( ). For small penetration depth, the measured hardness approaches the hardness of the film, whereas, for high penetration depths the measured hardness approaches that of the substrate. For all samples the measured hardness tends to H  4.5 GPa for large penetration depths. This value is

10

Thermal and Thermodynamic Stability of Nanomaterials

consistent with the hardness measured on uncoated regions of substrate, and close to AISI 304 values referred in literature. For the smallest penetration depths of 30nm, which can be considered not affected by roughness and tip calibration, the hardness of as-deposited Cr-N approaches to 10 GPa (Fig. 7(a)). The true hardness of the as-deposited film should then be > 10 GPa. A hardness rise of all the samples is found after annealing in vacuum (Fig. 7(b)), with the highest rise on sample A. Due the large increase of roughness after annealing in air, it was not possible to obtain reliable nano-hardness measurements for these sample conditions. 3.2. Ti-Cr-B-N and Ti-Al-Si-B-N coatings. Fig. 8 shows the XRD θ-2θ pattern for as-deposited and thermally annealed Ti-Cr-B-N and Ti-Al-Si-B-N coatings. As-deposited Ti-Cr-B-N/Si samples show broad peaks consistent with the cubic NaCl-type structure of TiN. It can be noticed that the relative intensity of the peak TiN (220) peak is lower than expected for random orientation of the nano-crystals.

Fig. 8. XRD patterns of as-deposited (1a) and air annealed (1b) Ti-Cr-B-N/Si and as-deposited (2a) and annealed (2b) Ti-Al-Si-B-N/Si samples. TiN (), TiO2 () and Cr2O3 () peaks are indicated. On the bottom the relative intensity of stronger peaks from TiN powder diffraction (PDF: 00-0381420) is reported.

The average crystal size in the growth direction was estimated using Scherrer’s equation [55]: D  0.9 B cos   , D being the crystal size, B the corrected full-width at half maximum (FWHM) of the Bragg peak, λ the X-ray wavelength, and θ the Bragg angle. B is obtained from the measured XRD patterns after subtracting the instrumental broadening (assuming it is equal to the FWHM of a single-crystal silicon wafer). Using (111) and (200) peaks, the average grain size of TiN crystals in the as-deposited Ti-Cr-B-N/Si samples was found to be 1 to 2 nm. For Ti-Al-Si-B-N/Si as-deposited samples, only sharp peaks due to impurities in the film appear, indicating the presence a large fraction of amorphous phase compared to the Ti-Cr-B-N coating. Morphology and phase of the as-deposited coatings were further investigated by TEM. Cross sections of Ti-Cr-B-N/Si samples revealed the presence of columnar structure, as reported in Fig. 9. The relative selected area electron diffraction pattern (SAEDP) shows (111), (200) and (220) TiN rings. The lattice parameter calculated from the diffraction pattern was 0.42 nm. Intensity of the rings confirms (111) and (200) texture of the coatings. It can be noticed that

Materials Science Forum Vol. 653

11

(200) ring intensity is not homogeneous, with broad spots that indicate preferential orientation of the crystals parallel to the Si (200) forbidden reflection, i.e. along the growth direction and column length.

Fig. 9. Cross section TEM bright field image of as-deposited Ti-Cr-B-N/Si. In the insert SAEDP recorded Silicon substrate (a) and from the coating (b) are reported.

After thermal annealing in air at 1170 K/4h, XRD patterns of Ti-Cr-B-N/Si and Ti-Al-Si-BN/Si samples (Fig. 8), indicate the presence of rutile-TiO2 and Cr2O3, and TiO2 phases respectively. TiN phase is also still present on Ti-Cr-B-N/Si samples, and average grain size of TiN crystals increases to ~30 nm. A more detailed description of annealed coatings on Si was documented by TEM inspections of the cross section samples. It was seen that oxidation led to increase of average grain size and to formation of a multilayered structure in both coatings (Fig. 10). The main features of the air annealed Ti-Cr-B-N, Ti-Al-Si-B-N coatings on steel are shown in Fig. 11. Several similarities were revealed in both coatings: the formation of a superficial layer of well-crystallized oxide, the development of layers beneath the top oxidized layer and a diffuse failure of the coatings. The adhesion of Ti-Al-Si-B-N to the steel substrate after the exposition at 1170 K is generally better than that of Ti-Cr-B-N. However in both the films the adhesion to the substrate is severely compromised after the oxidation process. In Ti-Al-Si-B-N only limited portions of oxidized coating are present. Generally, the remaining fragments are composed by all the three layers discussed above. The largest amount of coating delamination occurred during the cooling stage of the sample outside the furnace. A residual part of the removed coating, in which Ti is mainly present, fills the valleys between the islands of the substrate and it is thus present on the surface of the coatings. The oxidized top layer, whose topography is quite different from that of the as-deposited sample, shows many regions in which phenomena of buckling are evident. As the thickness of the coated film (~ 2 μm) is negligible compared with that of AISI 304 substrate (~ 600 μm), the thermal response of the system coating-substrate is mainly controlled by the thermal expansion coefficient of the substrate (α = 17.8 · 10-6 m-1). The spallation mechanism is evident, in both the coatings (Fig. 11).

12

Thermal and Thermodynamic Stability of Nanomaterials

a)

b)

Fig. 10. Cross section TEM bright field image of annealed a) Ti-Cr-B-N/Si, and b) Ti-Al-Si-B-N/Si with indication of the different layers (L). SAEDPs recorded from the different layers (L) are also reported.

Fig. 11. SEM plan-view of air annealed a) Ti-Al-Si-B-N and b) Ti-Cr-B-N coatings deposited on AISI 304 stainless steel substrate. EDS analyses were carried out on in-plane and cross-section samples for the determination of the coating layers composition. (Due to the interaction volume of electrons in the EDS analysis, in-plane measurement of each layer includes the contribution of both the layers and of the substrate beneath). It was also possible to analyse the composition of the AISI 304 substrate after the air annealing by direct analyses through the surface craters. The chemical composition of coatings and substrate are reported in Table 2.

Materials Science Forum Vol. 653

13

Table 2. Chemical composition (at %) of Ti-Al-Si-B-N and Ti-Cr-B-N annealed coatings, and AISI 304 substrate. Sample

Layer

Element composition (at. %) Ti

Al

Si

Ar

Cr

Fe

Ni

39

26

5

1

29

—

— —

Ti-Cr-B-N

L1+ L2 L3 L1 L2

AISI 304 substrate

L3+ L4 as received annealed

Ti-Al-Si-B-N

56

12

11

4

17

—

65

—

—

—

35

40

—

—

—

60

— —

— —

74

—

—

3

23

—

—

—

—

—

—

19

73

8

—

—

—

—

11

80

9

Mechanical properties of the Ti-Cr-B-N and Ti-Al-Si-B-N coatings were inferred by nanoindentation. The mechanical properties, nano-hardness H and reduced Young’s modulus Er, are defined by the following formulas:

H

Pmax , AC

(1)

where Pmax is the maximum load applied during the indentation, AC is the projection of the contact area of the at the maximum depth.

1 1   i2 1   2 ,   Er Ei E

(2)

where Ei and E are the Young’s modulus of the indenter tip (1171 GPa for diamond) and the sample, and νi and ν are the Poisson coefficients of the indenter tip (0,04 for diamond) and of the sample, respectively. Load–displacement curves were recorded for in-plane and cross-section indentations. Fig. 12 shows such a comparison for a Ti-Cr-B-N sample, tested with 2000 µN of maximum load. The as-deposited Ti-Cr-B-N and Ti-Al-Si-B-N coatings show no differences between load-displacement curves.

Fig. 12. Nano-indentation load-displacement curves measured for Ti-Cr-B-N coating with 2000 µN of maximum load: ( ) in plane indentation and ( ) cross section indentation.

14

Thermal and Thermodynamic Stability of Nanomaterials

Fig. 13(a) reports the values of the reduced Young’s modulus, Er ≈ 270 GPa, and hardness, H ≈ 28 GPa, of the Ti-Cr-B-N/Si. Fig. 13(b) reports the values for Ti-Al-Si-B-N/Si: Er ≈ 210 GPa, and H ≈ 19 GPa. Furthermore, in Fig. 13, the hardness and Young’s modulus of each single layer formed after the thermal treatment, measured on the cross-section, are reported for both coatings.

a)

b)

Fig. 13. Hardness ( ) and reduced Young’s modulus ( ) measured by nanoindentation on cross section of a) annealed Ti-Cr-B-N/Si, and b) annealed Ti-Al-Si-B-N/Si, for the different layers. 4. Discussion 4.1. Cr-N coatings. In the present study, both CrN and Cr2N phases have been reported in reactively sputtered Cr-N films, depending on the Ar to N2 flow ratio during deposition. CrN (111) or (200) and Cr2N (002) or (111) texture components were reported for the as-deposited Cr-N films sputtered on Si(100) substrates, depending on the deposition parameters [56]. In particular the fraction of Cr2N versus CrN was found to increase as N2/Ar flow ratio decreased, and the presence of both phases was detected at very low N2/Ar flow ratios [56]. Although there was no clear evidence of Cr2N phase in the as-deposited samples, a contribution on the peak at 43.6° from Cr2N (111) plane is likely to exist. The relative reduction of CrN peaks and increase of contribution from Cr2N (111) peak measured from sample A to sample C (Fig. 1) is consistent with the progressive reduction of N2 flow during sputtering. No presence of chromium oxide phase is visible on the as-deposited samples. Phase transformation of Cr-N films upon thermal anneal in air, vacuum and controlled atmosphere was investigated by other authors [56-58]. In some of these works phase transformation from CrN to Cr2N, upon thermal annealing in vacuum has been observed [57,58]. In some other works Cr2N phase formation was observed under conditions for which it cannot be explained by thermodynamics considerations. It has been pointed out that phase transformation from CrN to Cr2N phase can involve both thermodynamic and non-thermodynamic factors, such as stress relaxation induced phase transformation. The more stable behavior of sample C with respect to vacuum thermal annealing can therefore be explained by the presence of a larger component of Cr2N phase on the as-deposited sample (Fig. 2). This is consistent with the lower N2 flow used in sample C, compared to sample A and B. The diffraction patterns reported in Fig. 3 also confirmed that, as expected, no chromium oxidation is occurred during vacuum annealing. Chromium oxidation in Cr-N films after thermal annealing in air was described by several other authors [58-60] and can be explained in terms of thermodynamics. The change in the Gibbs free energy associated with the oxidation reactions of respectively CrN and Cr2N can be written as follows:

Materials Science Forum Vol. 653

3 2CrN ( s )  O2( g )  Cr2 O3( s )  N 2( g ) 2 3 G  G 0  RT ln p N 2 / pO22     3   883.368  0.101 T   RT ln p N 2 / pO22    3 1 Cr2 N ( s )  O2( g )  Cr2 O3( s )  N 2( g ) 2 2 3 1 0 G  G  RT ln p N22 / pO22     3 1   1010.937  0.200  T   RT ln p N22 / pO22   

(kJ/mol)

(kJ/mol)

15

(3)

(4)

where G represents the change in the Gibbs free energy for this transformation; G o is the standard Gibbs free energy; R is the gas constant; T [K] is the absolute temperature, p N 2 is the partial pressure of nitrogen and pO2 is the partial pressure of oxygen. Using equation 3 and 4 to calculate Gibbs free energy change of both reactions for the present conditions (T= 932.16 K, air: p N 2 =0.79 atm and pO2 =0.21 atm) gives respectively G equal to -774 kJ/mol and -809 kJ/mol for CrN and Cr2N respectively. This implies that both phases tend to oxidize forming Cr2O3 layers and Cr2N having higher tendency to oxidize. As discussed above, sample C is expected to have a higher Cr2N content. This can explain the higher intensity of Cr2O3 peaks for a given annealing time on sample C compared to sample A (Fig. 1). In reactively sputtered Cr-N films, the formation of phases is strongly influenced by the deposition parameters: for instance, both CrN and Cr2N phases have been reported in reactively sputtered Cr-N films, depending on the Ar to N2 flow ratio during deposition [61]. No clear evidence of Cr2N phase presence in the as-deposited films was found in the recorded diffraction patterns, such as the one of Fig. 4. The peaks at 38° and 43.5° in the GIXRD mode are rather broad and the proximity of the austenitic steel and Cr2N peaks makes difficult their identification, while the weak peak at 63° is only consistent with CrN (220) planes [62]. The presence of the CrN phase for the as-deposited samples was confirmed by the XRD measurement in θ–2θ configuration, where the CrN (220) peak at 63° is clearly visible. Moreover, Cr-N and substrate GIXRD peaks intensity decreases with temperature. From Tmax = 910 K, peaks related to Cr2O3 phase appear on the diffraction pattern at angles of 24.5°, 33.6° and 36.2°, corresponding to Cr2O3 (012), (104) and (110) planes respectively [52,62]. Chromium oxidation in Cr-N films after thermal annealing in air was reported by several other authors [59,61]. For Tmax = 1075 K a peak at  = 43° developed. This peak indicates the presence of Cr2N phase. Phase transformation from CrN to Cr2N could be due to the stress relaxation occurring in the film during the oxidation at Tmax = 1075 K [63]. Furthermore, the diffraction patterns evolution with temperature reported in Fig. 4, shows the increase of the Cr2O3 (110) peak intensity relative to the Cr2O3 (012) and Cr2O3 (104) peaks. Conversely, the increase of roughness and the detected presence of larger crystallites (diameter of ~ 1 m) in the CrN coatings is likely to be attributed to Cr2O3 crystallites. These result from oxidation of the film, as indicated by the GIXRD analyses. Roughness increases and appearance of large crystallites occurs after thermal cycling at Tmax = 910 K and become more evident at Tmax = 1075 K, whereas thermal cycling at lower temperatures (585 K and 755 K) does not induce relevant morphological changes. As it can be seen, roughness is fairly stable up to Tmax =755 K, starts increasing with temperature at 910 K and increases more rapidly at Tmax = 1075 K. Moreover, as temperature increases, some portions of the Cr-N coating start detaching from the surface.

16

Thermal and Thermodynamic Stability of Nanomaterials

Hardness was found to reduce with penetration depth in the as-deposited and vacuum annealed conditions. This is attributed to the influence of the substrate on the measured hardness. A ‘rule of thumb’ requires that penetration depth is kept below one-tenth of the film thickness to contain the deformation within the film. On the other hand, relatively high penetration depths are required to achieve measurements not affected by the roughness of the system. Furthermore, for penetration depths near or lower than the indenter tip radius, the area function calibration is not reliable. For very thin films, these conditions are difficult to achieve, and measured hardness is often affected by the substrate [64,65]. AFM investigations showed that as-deposited and vacuum annealed samples have an RMS surface roughness of ~15 nm, which requires indentation depths above this value. Hardness changes in Cr-N coatings after vacuum annealing were also reported in other published works [56,66]. As for measurements on the as-deposited samples, the measured hardness depends on the penetration depth, and it can be concluded that the true hardness is >20 GPa for sample A, and >15 GPa for samples B and C. Nano-hardness of sputtered Cr-N films has been studied only for thicknesses greater than ~500 nm, whereas no data have been published in the thickness range considered in this study. The reported values of Cr-N hardness are quite scattered [67] and in the range of 10 to 30 GPa. The change in hardness upon anneal can be attributed to two different factors: microstructure, i.e. phase transformations, and stress relaxation. The Cr-N films studied in this work, as in other, are expected to have a compressive stress, due to the different thermal expansion coefficients of CrN (2.3·10-6 K-1) [58] and AISI 304 (~17.8·10-6 K-1). Relaxation of compressive stress of Cr-N coatings is expected to occur in the temperature range of 670 to 870 K and should be accompanied by a reduction of hardness. In this work, the hardness rise indicates changes in the microstructure able to compensate the stress relaxation effects. The higher hardness rise was recorded in sample A, i.e. the sample where the observed CrN to Cr2N phase transformation was larger. The hardness rises in samples B and C were lower compared to sample A, and in this latter cases minimal microstructure modifications were detected by GIXRD. 4.2. Ti-Cr-B-N and Ti-Al-Si-B-N coatings. Columnar growth has often been reported for TiN. Depending on deposition process and parameters, nano-crystalline TiN and Ti-Si-N coatings can also follow this morphology [68,69]. In previous studies of Ti-Cr-B-N coatings deposited by IIAMS on Si, similar texture and grain size to the present findings were reported, though no conclusive evidence of columnar growth was revealed [70,71]. In [71], TEM inspections of Ti–Cr–B–N films did not show a pronounced columnar structure, while AFM analyses showed a well-developed columnar structure. Ti-Cr-B-N/Si coating showed a multilayered structure after air annealing. The top layer (L1) consists of large TiO2 grains, while a lower layer (L2) consists of a mixture of rutile-TiO2 and Cr2O3 grains. These results are consistent with earlier observations [36,72]. Under this region, a layer of about 1000 nm in thickness (L3) shows fine crystallites with similar morphology to L3 in the Ti-Al-Si-B-N coating. In L3 SAEDP diffraction pattern indicates the presence of TiN and possibly of Cr2N. Rather large voids can be seen in L2 and at the interface L1/L2 and L2/L3. Beneath it, a 150 nm thick layer (L4) seemed to be constituted by a mixture of amorphous phase and nanometric crystallites with smaller size respect to L3. The resultant SAEDPs (Fig. 10) show a clear ring-like diffraction, consistent with Ti2N and TiB2 nano-crystallites. Finally, coarse grains with an average size of 500 nm constitute the layer directly in contact to the substrate (L5). EDS indicates a large content of Cr and some Ti, N and B [73-75]. The microstructure features involved in the air annealed samples are rather complex, since mechanisms of diffusion (both self-diffusion of elements in the coating and diffusion of oxygen from the atmosphere), of residual stresses release and differential thermal expansion are involved. During oxidation, Ti- and Cr-oxide crystallites are formed on the coating surface. Since the TiO2 formation is thermodynamically favoured compared to Cr2O3 formation, coarse Ti-oxide grains grow rapidly on the coating surface. Outward Ti diffusion causes a depletion of Ti below L1 and promotes the formation of Cr2O3 in L2 [76]. Also in this case, the presence of Ti- and Cr-oxide

Materials Science Forum Vol. 653

17

layers on the coating surface prevents the further inward oxygen diffusion; thus, the presence of Ti in L3 can be related to the formation of TiN phase, as XRD measurements have revealed. For the same reason, a Cr2N phase, also detected by XRD, is present in L3. Ti-Al-Si-B-N/Si showed a similar multilayered structure after air annealing. The first layer (L1) was characterized by the presence of Al and O (as detected by EDS). This suggested that Al2O3 crystallites formed as a consequence of the outward Al diffusion to the free surface [75,76]. Preferential oxidation of Al with respect to Ti at high temperature was reported by A. Joshi et al. in [81]. Next oxide layer (L2) is formed by Ti and Al oxide grains with diameter of ~100 nm. The formation of Al2O3/mixed rutile-TiO2 + Al2O3 structure in the high temperature range differs from the results reported in [37] for Ti-Al-N coatings. In [37] at T ≥ 1070 K, Joshi and Hu reported oxidation associated with the growth of well separated Al2O3 and TiO2 regions, with a layered structure becoming more evident with increasing oxidation time. Beneath L2 lies a layer (L3) with thickness of about 600 nm, characterized by equiaxed crystals with a diameter ranging 10 to 45 nm and some elongated crystallites with length < 80 nm and a length-to-width ratio up to 4:1. This phase was identified by SAEDP as TiN. The last layer (L4), directly in contact to the substrate, was 200 nm thick and characterized by very small crystallites. In the Ti-Al-Si-B-N film on steel, the oxidized coating fragments, constituted by two layers (L1+L2), are not separated by a well-defined interface. An uncoated L2 layer has not been observed, thus, it was not possible to perform an EDS analysis on this layer. EDS data reports a higher content of Al in L1+L2 than in L3 and it suggests that the crystallites on the coating surface are likely to be constituted by Al2O3. These results are in agreement with Joshi and Hu [43], suggesting that a layered oxide structure Al2O3/TiO2 forms on the Ti-Al-nitride coating surface at temperatures above 1070 K. Moreover, in L1 a high amount of Cr was detected. Since this element is not present in the as-deposited coating, it is believed that Cr atoms are made to diffuse from AISI 304 substrate toward the surface of the coating during thermal treatment, forming a Cr-rich oxide region. Cr presence in this layer is consistent with a reduction of concentration of ~ 7 % of atomic composition in the substrate after air annealing. Thus, L1 is constituted by a mixture of Al- and Crrich oxides and a certain amount of rutile-TiO2, as detected by XRD measurements. L3 shows a relative higher Ti and Si concentration and a consequent depletion of Cr and Al due to the outwards diffusion of these elements during oxidation. TiN phase could be present in L3, as XRD data revealed the presence of this phase after air annealing. It has been reported that Al 2O3 can form a protective barrier which limit the inward oxygen diffusion in the Ti-nitride coating [76]. During the heating stage of the thermal treatment, release of the residual stresses occurs while the diffusion processes starts: oxygen diffuses inward into the coating, while other elements, such as Ti, from the coating, and Cr, from the coating/substrate interface, diffuse outward, thus forming oxidized sub-layers. As the oxides and the new phases formed at high temperature are created on the dilated substrate, they are subjected to a compression stress during the cooling phase of the thermal treatment. These mechanisms are responsible for a strong mechanical local stress on the oxidized coating, and the result is a spallation diffused all over the surface of the system [77]. The spallation mechanism revealed in the present study, was also described by Tolpygo and Clarke [78,79] in relation to Al films deposited on a metallic substrate. In Ti-Al-Si-B-N the independence of mechanical properties with respect to the indentation direction is consistent with the amorphous-like structure of the coating. XRD and TEM observation of Ti-Cr-B-N did show columnar growth formed by smaller crystals with preferential (200) orientation. Morphology and texture can influence mechanical properties of coatings [80]. If column sliding is the operating mechanism of plastic deformation, our result indicates that its effect on measured hardness and Young’s modulus is the same for a stress parallel and perpendicular to the columns growth direction. Nanoindentation measurement on annealed Ti-Al-Si-B-N/Si cross-section showed that the hardness of the layer L1 is consistent with values found in literature for films which a similar composition [81,82]: the hardness of Al2O3 changes with the microstructure, and can assume values up to 20 GPa for a complete developed corundum structure. In this case, the values of 15 GPa for

18

Thermal and Thermodynamic Stability of Nanomaterials

the hardness and 120 GPa for the reduced Young’s modulus are typical for an α-Al2O3 corundum phase. Hardness and reduced Young’s modulus for the L2 zone of the coating could not be measured due to its small thickness. Hardness of layers L3 and L4 were ~8 and ~15 GPa, respectively. The hardness profile of the Ti-Cr-B-N/Si after annealing is much more complex. The hardness of L1 and L2 is respectively 17 and 12 GPa. The composition of L1, which is mainly a fully crystallized TiO2-rich layer, is consistent with the hardness value of rutile single crystal (18.5 GPa), as reported in [83,84]. Depending on the amount of the crystallized phase, the hardness of TiO2 can vary from few GPa, for a total amorphous and anatase-like structure, to 19 GPa, for a fully crystallized rutile crystal; in this case the hardness achieved is very close to the latter. The hardness of the zone L2 is due to the presence of two components, TiO2 and Cr2O3, whose hardness is respectively 18.5 and 18 GPa [36,85,86] and to the microstructural presence of nanometre-size voids of Ti-Cr-B-N. Due to their thicknesses, just an average value for the hardness of layers L3 and L4 was measured. The hardness of L3/L4, 8 GPa, is similar to the value of the correspondent layer L3 for the Ti-Al-Si-B-N coated. L3/L4 of Ti-Cr-B-N and L3 of Ti-Al-Si-B-N also show similar morphology, but different phase composition, as seen by TEM observations. The hardest layer of Ti-Cr-B-N was L5, with an hardness value of ~17.5 GPa. This bottom layer was characterized by large crystallites between the film and the substrate. The mechanical characteristics of the tested samples are consistent to previously published results [87]. Mechanical response did not change significantly in both the coatings as Pmax increases, while after vacuum annealing, some modifications appear in the mechanical properties of both coatings. For the Ti-Al-Si-B-N coating, Er does not change, compared to the as deposited condition but the value of hardness decreases to ~ 5 GPa. The vacuum annealed Ti-Cr-B-N showed a different behavior. H stayed at the same value (~30 GPa), while Er increased significantly, reaching the value of ~ 325 GPa. One of the main factors affecting the Young’s modulus is the nature of the atomic bonding, which is related to the atomic configuration of each component of the material. Interfaces and grain boundaries play an important role in the definition of the mechanical properties, since these zones are rich of lattice defects, voids, and lattice parameter mismatch [88]. Elastic modulus is also affected by material porosity [89], which is likely dependent on the preparation method of the film. The effect of the atomic bonding, such as covalent, metallic and ionic, and the influence of the residual stresses have been studied by Karlsson et al. [90]. In Ti-Al-Si-B-N, compressive stress, due to the deposition, is responsible for the high values of hardness found in the as-deposited material. Different mechanisms are involved in decreasing of hardness for Ti-Al-Si-B-N (~15 GPa) after vacuum annealing, such as the stress relaxation and the crystallization of the film in coarser grains or in new phases. The release of embedded Ar is another cause reduction of hardness. The presence of Cr, diffused from the substrate, is responsible for the formation of crystalline Cr2N phase, which contributes to the change of the Er value, also described by He et al. [88]. Conversely, in Ti-Cr-B-N, porosity level due to Ar incorporation, during deposition, seemed to be lower. On the other hand, Cr content was found to be higher in Ti-Cr-B-N than in Ti-Al-Si-BN: these two combined effects are believed to be responsible for the unchanged hardness upon annealing. 5. Conclusions Crystal structure, surface morphology and hardness of thin Cr-N coatings, deposited by reactive sputtering on AISI 304 stainless steel sheets, were investigated after deposition and after thermal annealing in air and vacuum. - Transmission electron microscopy inspections showed that the as-deposited coatings have a very fine grain structure. - CrN phase was found on all the samples, with a predominant (111) texture.

Materials Science Forum Vol. 653

19

- Annealing in vacuum induced formation of Cr2N phase with (111) texture from CrN phase. - Anneal in air induced formation of Cr2O3 phase, with higher oxidation speed for Cr2N phase. - Surface roughness increased for all the samples after annealing in air and large features appeared on the surface, as a consequence of Cr2O3 phase formation. Cr-N coatings with higher Cr2N phase content showed a modest roughness rise. Annealing in vacuum did not modify significantly surface roughness and morphology of the Cr-N coatings for all the samples. - Film hardness was above 10 GPa for as-deposited Cr-N. Annealing in vacuum was found to increase hardness for all the samples, as a consequence of microstructure changes overcoming stress relaxation phenomena. Thermal cycling tests were used to simulate the working conditions of nanometric Cr-N coating deposited on AISI 304. Morphological and structural changes were characterized by XRD, GIXRD, SEM and AFM analyses. It was found that: - Thermal cycling induces CrN oxidation to Cr2O3. - Coating morphology changes gradually with temperature, due to Cr2O3 crystallites growth. For temperatures up to Tmax = 755 K crystallites size and roughness are quite stable. For temperature starting from Tmax = 910 K, Cr2O3 crystallites size and the coating roughness starts increasing. - Thermally induced stress generates cracks on the coatings, parallel to the substrate rolling direction, where Cr2O3 crystallites growth is favored. After cycling at Tmax = 1075 K, the coating is highly oxidized, while large and numerous areas are detached from the substrate. Ti-Al-Si-B-N and Ti-Cr-B-N deposited on AISI 304 stainless steel with a 2B superficial finishing have been investigated in the as-deposited condition and after air and vacuum annealing. - The presence of layers with a different composition in the air annealed coatings is due to the affinity of Ti, Cr and Al for oxygen at elevated temperature. - The mechanical properties of the formed layers are different, and as a consequence, buckling of the coating in the cooling phase is reported. - Cr diffuses from the substrate/coating interface to the surface of the film. - The changes in the mechanical properties of the vacuum annealed films has been attributed to antagonist effects, such as the presence of Ar in the as-deposited coatings, the formation of new phases and modifications in the phases already present in the coating. The microstructure and mechanical properties evolution of Ti-Cr-B-N and Ti-Al-Si-B-N coatings subjected to thermal oxidation were studied. - As-deposited Ti-Cr-B-N showed columnar growth with TiN grains of 1-2 nm in diameter, whereas as deposited Ti-Al-Si-B-N was found to be amorphous. Identical values were found when measuring hardness and Young’s modulus along directions parallel and perpendicular to column growth. - After annealing, both coatings formed several oxidation layers, with several phases including fccTiN phase. Top layers are mainly constituted by TiO2 and Cr2O3 for Ti-Cr-B-N and by TiO2 and Al2O3 for Ti-Al-Si-B-N. In lower layers fcc-TiN phase is present. Mechanical properties of all layers are degraded compared with as-deposited coatings. Acknowledgements The authors gratefully acknowledge to Mr. D. Ciccarelli and Mr. M. Pieralisi for their help in the specimen preparations. This research has been financially supported by European FP6 framework program-EXCELL Project NoE 5157032 (website: www.noe-excell.net) and by V.I.N.F (Virtual Institute of NanoFilms, web site: www.vinf.eu). References [1] A.I.M. Bernstin: Handbook of Stainless Steels, (McGraw-Hill, New York 1977). [2] T.M. Angeliu and P.L. Andresen: Corrosion Vol. 52 (1) (1996), p.28. [3] H.G. Prengel, P.C. Jindal, K.H. Wendt, A.T. Santhanam, P.L. Hegde and R.M. Renich: Surf. Coat. Technol. Vol 139 (2001), p. 25.

20

Thermal and Thermodynamic Stability of Nanomaterials

[4] H.P. Feng, S.C. Lee, C.H. Hsu and J.M. Ho: Materials Chemistry and Physics Vol. 59 (1999), p. 154. [5] R.F. Bunshah: Handbook of Hard Coatings, (Noyes Publications, New York 2001). [6] P. Engel, G. Schwarz and G.K. Wolf: Surf. Coat. Technol. Vol. 98 (1998), p. 1002. [7] J.F. Lin, M.H. Liu and J.Du. Wu, Wear Vol. 194 (1996), p. 1. [8] M. Pakala and R.Y. Lin: Surf. Coat. Technol. Vol. 81 (1996), p. 233. [9] C. Meunier, S. Vives and G. Bertrand: Surf. Coat. Technol. Vol.107 (1998), p. 158. [10] C. Rebholz, H. Ziegele, A. Leyland and A. Matthews: Surf. Coat. Technol. 115 (1999), p. 222. [11] P. Hones, R. Sanjines and F. Levy: Surf. Coat. Technol. Vol. 94-95 (1997), p. 398. [12] J.P. Terrat, A. Gaucher and H. Hadj-Rabah: Surf. Coat. Technol. Vol. 45 (1991), p. 59. [13] L. Cunha, M. Andritschky, L. Rebouta and K. Pischow: Surf. Coat. Technol. Vol. 116-119 (1999), p. 1152. [14] K. Tfnshoff, A. Mohlfeld, T. Teyendecker, H.G. Fug, G. Erkens, R. Wenke, T. Cselle and M. Schwenk: Surf. Coat. Technol. Vol. 94–95 (1997), p. 603. [15] S. Ortsmann, A. Savan, Y. Gerbig and H. Haefke: Wear Vol. 254 (2003), p. 1099. [16] J.A. Sue and T.P. Chang: Surf. Coat. Technol. Vol. 76–77 (1995), p. 61. [17] P. Karvankova, H. Männling and S. Veprek: Surf. Coat. Technol. Vol. 146–147 (2001), p. 280. [18] S. Veprek and A.S. Argon: J. Vac. Sci. Technol. B Vol. 20 (2002), p. 650. [19] A. Kawana, H. Ichimura, Y. Iwata and S. Ono: Surf. Coat. Technol. 86-87 (1996), p. 212. [20] J. Creus, H. Idrissi, H. Mazille, F. Sanchette and P. Jacquot: Surf. Coat. Technol. Vol. 107 (1998), p. 183. [21] I. Milosev and B. Navinsek: Surf. Coat. Technol. Vol. 60 (1993), p. 545. [22] L. Cunha and M. Andritschky: Surf. Coat. Technol. Vol. 111 (1999), p. 162. [23] R.A. Andrievski: J. Mater. Sci. Vol. 32 (1997), p. 4463. [24] W. Gissler, M.A. Baker, J. Haupt, P.N. Gibson, R. Gilmore and T.P. Mollart: Diamond Film Technol. Vol. 7 (1997), p. 165. [25] T.P. Mollart, J. Haupt, R. Gilmore and W. Gissler: Surf. Coat. Technol. Vol. 86–87 (1996), p. 231. [26] R. Wiedemann, V. Weihnacht and H. Oettel: Surf. Coat. Technol. Vol. 116–119 (1999), p. 302. [27] P.H. Mayrhofer and C. Mitterer: Surf. Coat. Technol. Vol. 133–134 (2000), p. 131. [28] P. Holubar, M. Jılek and M. Sıma: Surf. Coat. Technol. Vol. 120–121 (1999), p. 184. [29] Q.Q. Yang, L.H. Zhao, H.Q. Du and L.S. Wen: Surf. Coat. Technol. Vol. 81 (1996), p. 287. [30] P.H. Mayrhofer, M. Stoiber and C. Mitterer: Scr. Mater. Vol. 53 (2005), p. 241. [31] A. Niederhofer, P. Nesládek, H.-D. Männling, K. Moto, S. Veprek and M. Jílek: Surf. Coat. Technol. Vol. 120–121 (1999), p. 173. [32] H.-D. Männling, D.S. Patil, K. Moto, M. Jílek and S. Veprek: Surf. Coat. Technol. Vol. 146– 147 (2001), p. 263. [33] W. Herr and E. Broszeit: Surf. Coat. Technol. Vol. 97 (1997), p. 335. [34] D.Y. Wang, J.H. Lin and W.Y. Ho: Thin Solid Films Vol. 332 (1998), p. 246.

Materials Science Forum Vol. 653

21

[35] M. Wittmer, J. Noser and H. Melchior: J. Appl. Phys. Vol 52 (1981), p. 6659. [36] Y. Otani and S. Hofmann: Thin Solid Films Vol. 287 (1996), p. 188. [37] A. Joshi and H.S. Hu: Surf. Coat. Technol. Vol. 76–77 (1995), p. 499. [38] F. Vaz, L. Rebouta, S. Ramos, M.F. da Silva and J.C. Soares: Surf. Coat. Technol. Vol 108– 109 (1998), p. 236. [39] G. Llauro, F. Gourbilleau and R. Hillel: Thin Solid Films Vol. 315 (1998), p. 336. [40] J.B. Choi, K. Cho, M.-H. Lee and K.-H. Kim: Thin Solid Films Vol. 447–448 (2004), p. 365. [41] S. Veprek, M.G.J. Veprek-Heijman, P. Karvankova and J. Prochazka: Thin Solid Films Vol. 476 (2005), p. 1. [42] S. Zhang, D. Sun and X. Zeng: J. Mater. Res. Vol. 20 (2005), p. 2754. [43] P. Karvankova, M.G.J. Veprek-Heijman, M. Zawrah and S. Veprek: Thin Solid Films Vol. 467 (2004), p. 133. [44] K.H. Lee, S.J. Jung, J.J. Lee and C.H. Park: J. Mater. Sci. Lett. Vol. 21 (2002), p. 423. [45] S. Veprek, S. Reiprich and L. Shizhi: Appl. Phys. Lett. Vol. 66 (1995), p. 2640. [46] D. McIntyre, J.E. Greene, G. Hakansson, J.E. Sundgren and W.D. Munz: J. Appl. Phys. Vol. 67 (1990), p. 1542. [47] I.G. Brown: Rev. Sci. Instrum.Vol. 65 (1994), p. 3061. [48] D.V. Shtansky, A.N. Sheveiko, M.I. Petrzhika, F.V. Kiryukhantsev-Korneeva, E.A. Levashov, A. Leyland, A.L. Yerokhin and A. Matthews: Surf. Coat. Technol. Vol. 200 (2005), p. 208. [49] W.C. Oliver and G.M. Pharr: J. Mater. Res. Vol. 7 (1992), p. 1564. [50] Z.B. Zhao, Z.U. Rek, S.M. Yalisove and J.C. Bilello: Thin Solid Films Vol. 472 (2005), p. 96. [51] C. Paternoster, A. Fabrizi, R. Cecchini, M. El Mehtedi and P. Choquet: J. Mater. Sci. Vol. 43 (2008), p. 3377. [52]. Powder Diffraction File, JCPDS International Center for Diffraction Data, Swarthmore, PA, (1992). [53] F.-H. Lu and H.-Y. Chen: Thin Solid Films Vol. 398–399 (2001), p. 368. [54] H.-Y. Chen and F.-H. Lu: Thin Solid Films Vol. 515 (2006), p. 2179. [55] P. Scherrer: Gftt. Nachr Vol. 2 (1918), p. 98. [56] A. Aubert, R. Gillet, A. Gaucher and J.P. Terrat: Thin Solid Films Vol. 108 (1983), p.165. [57] P.H. Mayrhofer, G. Tischler and C. Mitterer: Surf. Coat. Technol. Vol. 142–144 (2001), p. 78. [58] M. Odén, J. Almer, G. Håkansson and M. Olsson: Thin Solid Films Vol. 377–378 (2000), p. 407. [59] P.H. Mayrhofer, H. Willmann and C. Mitterer: Surf. Coat. Technol. Vol. 146 (2001), p. 222. [60] D.Y. Wang, J.H. Lin and W.Y. Ho: Thin Solid Films Vol. 332 (1998), p. 295. [61] A. Barata, L. Cunha and C. Moura: Thin Solid Films Vol. 398 (2001), p. 501. [62] C. Paternoster, A. Fabrizi, R. Cecchini and P.Choquet: High Temperature Materials and Processes Vol. 26 (2007), p. 349. [63] K.-L. Chang, S.-C. Chung, S.-H. Lai and H.-C. Shih: Applied Surface Science Vol. 236 (2004), p. 406.

22

Thermal and Thermodynamic Stability of Nanomaterials

[64] A. M. Korsunsky, M.R. McGurk, S.J. Bull and T.F. Page: Surf. Coat. Technol. Vol. 99 (1998), p. 171. [65] H. Ichimura and I. Ando: Surf. Coat. Technol. Vol. 145 (2001), p. 88. [66] J.N. Tu, J.G. Duh and S.Y. Tsai: Surf. Coat. Technol. Vol. 133–134 (2000), p. 181. [67] W. Herr W and E. Broszeit : Surf. Coat. Technol. 97 (1997), p. 669. [68] J.H. Huang, C.H. Lin, C.H. Ma and H. Chen: Script. Mater. Vol. 42 (2000), p. 573. [69] F. Kauffmann, G. Dehm, V. Schier, A. Schattke, T. Beck, S. Lang and E. Arzt: Thin Solid Films Vol. 473 (2005), p. 114. [70] D.V. Shtansky, Ph.V. Kiryukhantsev-Korneev, A.N. Sheveyko, A.E. Kutyrev and E.A. Levashov: Surf. Coat. Technol. Vol. 202 (2007), p. 861. [71] D.V. Shtansky, S.A. Kulinich, E.A. Levashov, A.N. Sheveiko, F.V. Kiriuhancev and J.J. Moore: Thin Solid Films Vol. 420–421 (2002), p. 330. [72] D.B. Lee: Surf. Coat. Technol. Vol. 173 (2003), p. 81. [73] C. Paternoster, A. Fabrizi, R. Cecchini, S. Spigarelli, Ph.V. Kiryukhantsev-Korneev and A. Sheveyko: Surf. Coat. Technol. Vol. 203(2008), p. 736. [74] A. Fabrizi, C. Paternoster, R. Cecchini, Ph.V. Kiryukhantsev-Korneev, A. Sheveyko, M. Cabibbo, M. Haidöpoulo and S. Spigarelli: Materials Science Forum Vol. 604-605 (2009), p. 19. [75] P.V. Kiryukhantsev-Korneev, C. Paternoster, A. Fabrizi, A. N. Sheveyko, E.A. Levashov, E. Evangelista and D.V. Shtansky: Proceedings of EUROMAT-2007, Nurnberg (2007). [76] S. Inoue, H. Uchida, Y. Yoshinaga and K. Koterazawa: Thin Solid Films Vol. 300 (1997), p. 171. [77] V. K Tolpygo, J. R. Dryden, D. R. Clarke: Acta Mater. Vol. 46 (1998), p. 927. [78] V.K. Tolpygo and D.R. Clarke: Mat. Sci. and Eng. Vol. A278 (2000), p. 142. [79] V.K. Tolpygo and D.R.Clarke: Mat. Sci. and Eng. Vol. A278 (2000), p. 151. [80] C.H. Ma, J.H. Huang, Haydn Chen: Surf. Coat. Technol. Vol. 200 (2006), p. 3868. [81] O. Zywitzki and G. Hoetzsch: Surf. Coat. Technol. Vol. 94–95 (1997), p. 303. [82] M. Birkholz, U. Albers and T. Jung: Surf. Coat. Technol. Vol. 179 (2004), p. 279. [83] A. Bendavid, P.J. Martin, A. Jamting and H. Takikawa: Thin Solid Films Vol. 355–356 (1999), p. 6. [84] A.O. Olofinjana, J.M. Bell and A.K. Jåmting: Wear Vol. 241 (2000), p. 174. [85] D.B. Lee, M.H. Kim, Y.C. Lee and S.C. Kwon: Surf. Coat. Technol. Vol. 141 (2001), p. 232. [86] F. Luo, K. Gao, X. Pang, H. Yang, L. Qiao, Y.Wang and A.A. Volinsky: Surf. Coat. Technol. 202 (2008), p. 3354. [87] Ph.V. Kiryukhantsev-Korneev, D.V. Shtansky, M.I. Petrzhik, E.A. Levashov and B.N. Mavrin: Surf. and Coat. Technol. Vol. 201 (2007), p. 6143. [88] G. He, J. Eckert, W. Loser and M. Hagiwara: Solid State Comm. Vol. 129 (2004), p. 711. [89] M. Asmani, C. Kermel, A. Leriche and M. Ourak: J. Of Europ. Cer. Soc. Vol. 21 (2001), p. 1081. [90] L. Karlsson, L. Hultman and J.-E.Sundgren: Thin Solid Films Vol. 371 (2000), p. 167.

Materials Science Forum Vol. 653 (2010) pp 23-30 © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.653.23

Anomaly in Thermal Stability of Nanostructured Materials Karuna Kar Nanda1,* 1

Materials Research Centre, Indian Institute of Science, Bangalore – 560012, India *Email: [email protected]

Abstract. Understanding of the melting temperature of nanostructures is beneficial to exploit phase transitions and their applications at elevated temperatures. The melting temperature of nanostructured materials depends on particle size, shape and dimensionality and has been well established both experimentally and theoretically. The large surface-to-volume ratio is the key for the low melting temperature of nanostructured materials. The melting temperature of almost free nanoparticles decreases with decreasing size although there are anomalies for some cases. Superheating has been reported for some embedded nanoparticles. Local maxima and minima in the melting temperature have been reported for particles with fewer atoms. Another quantity that is influenced by large surface-to-volume ratio and related to the thermal stability, is the vapour pressure. The vapour pressure of nanoparticles is shown to be enhanced for smaller particles. In this article, we have discussed the anomaly in thermal stability of nanostructured materials. I. Introduction The melting temperature (Tm) of a material is crucial for many applications. In bulk systems, the surface-to-volume ratio is small and the surface effects on Tm can be disregarded. However, nanoparticles have a much greater surface to volume ratio than bulk materials. As a consequence, Tm is size dependent in nanoscale materials which melt at temperatures hundreds of degrees lower than bulk materials.The increased surface to volume ratio means surface atoms have a much greater effect on chemical and physical properties of a nanoparticle. Surface atoms have fewer neighboring atoms in close proximity compared to atoms in the interior and bind in the solid phase with less cohesive energy. The average cohesive energy per atom of a nanoparticle has been theoretically predicted as a function of particle size agiven by [1-16]:

  E np  Eb 1    D

(1)

where D is the particle size, is a material dependent constant and Eb is the cohesive energy of bulk. This behavior can be understood from the surface-to-volume ratio. Similar variation has been obaserved experimentally [17,18]. The melting temperature of a material is proportional to it’s cohesive energy [2]. Since atoms near the surface have fewer bonds and reduced cohesive energy, they require less energy to free from the solid phase. Melting point depression of high surface to volume ratio materials results from this effect. It has been well established that the melting point depression occurs for almost free nanoparticles [19-49]. The melting temperature higher than that of bulk-a phenomenon called superheating has also been reported for nanoparticles embedded in another host material [50–64] such as Pb nanoparticles in Al host, In nanoparticles in Al host, Ge in SiO2 host, etc. The results are not straight forward from the size-dependency of the cohesive energy. Though there are lots of reports on the melting point depression of nanoparticles, there exists anomaly in the melting behavior. In this article, we have summarized the anomaly observed in the size effect on the melting temperature of nanoparticles.

24

Thermal and Thermodynamic Stability of Nanomaterials

II. Different variations of the melting temperature Linear and nonlinear variation of the melting temperature has been reported even for the same materials. This can be realized when the melting temperature of the same material reported by different researchers are compared. We have provided a comparison of the melting temperature of Sn as reported by several groups [19-21] in Fig. 1(a). It is evident from the comparison that different researchers have observed different variations of the melting temperature. Generally, three melting models such as homogenous melting model (HMM), liquid skin melting (LSM) and liquid nucleation and growth (LNG) are being considered. According to HMM, the entire solid is in equilibrium with entire melted particles and there is no surface melting. LSM considers the formation of a liquid layer over the solid core at a low temperature that remains unchanged till the particle transforms completely to liquid at the melting temperature. According to LNG model, a liquid layer nucleates and grows with temperature and corresponds to surface melting. Based on the thermodynamic model, the melting temperature of nanoparticles can be represented by

1

Tm z  TM D  2 (2)

2V  sv   lv  , z=3 for HMM & LSM and z=2 for LNG and TM is the bulk melting H f temperature. The  value is positive only for LSM and zero for other two cases. Fig. 1(b) shows a comparison of the three different models. It may be noted that the different models predict different variations of the melting temperature. The difference in the variation of melting behavior is due to the difference in surface melting. Experimental results [35,64] reveal surface melting before the complete melting and the surface melting temperature decreases with size. The driving force for the surface melting is thought to be a reduction in the total surface energy  [65,66]: where,  

 hk l   svhk l   slhk l   lv

(3)

 ‘s are surface energies of solid-vapor, solid-liquid and liquid-vapor interfaces of the material and the superscript hkl represents the crystal faces. For most cubic metals, the ‘‘average’’ driving force for surface melting is close to zero ~i.e.,  and subtle changes of surface conditions can have marked effects on surface melting as it occurs for   0 . The orientation dependence of sv and sl leads to a strong orientation dependence of surface melting [67]. It is known from experiments that the macroscopic Au (110) surface melts at 770 K [68], (100) surface disorders at 970 K [69], while (111) surface is stable up to, and even above, the bulk melting point [70]. Similar melting phenomena have been reported for Au nanoplates [71]. Based on the average value of the surface energies, it can be realized that Ag does not exhibit surface melting [66]. However, MD simulations predict surface melting for Ag (110) surface at a temperature very close to the melting point [72]. Equivalently, TSM of Ag (110) surface is much higher as compared to that of Au (110) though the temperature of complete melting for Ag is lower with respect to Au. The surface melting not only influences the melting but also the evaporation of nanoparticles [73].

Materials Science Forum Vol. 653

540

25

1.0

(a)

(b)

480 0.8

360 300 240 0.0

Tm/TM

Tm (K)

420 [6] [6] [17] [18] equation (2) 0.2

0.4

0.6

-1

-1

D (nm )

0.8

1.0

0.6

0.4 0.0

LNG HMM LSM

0.1

0.2 -1

0.3

0.4

0.5

-1

D (nm )

Fig.1. (a) Size-dependent melting of Sn nanoparticles as reported by different researchers. (b) Comparison of melting temperature according to HMM, LNG and LSM. III. On the extrapolation of the bulk melting temperature It has been noted by different researchers that the bulk melting temperature cannot be extrapolated from the nanoscale results [74-80]. Molecular dynamic (MD) simulations of Ti nanowires and Ni clusters also predict similar results [78,79]. The extrapolated bulk melting temperature for nanowires or clusters is lower than the experimental values. In case of Zn nanowires also, the extrapolated value is lower than the bulk melting temperature [44,75]. Similarly, the bulk melting temperature cannot be extrapolated from the data on prism-shaped indium nanoparticles [43,74]. The extrapolated value will always be lower than the bulk melting temperature as long as the height of the prism is finite. Overall, the bulk melting temperature can not be extrapolated from the nanoscale results of non-spherical particles and short nanowires. In some cases, the higher value of bulk melting temperature is realized when extrapolated from the nanoscale results [36,37] and is thought to be due to structural difference [36]. IV. Melting of nanowires Like the case of nanoparticles, melting point depression has also been evaluated for nanowires and thin films. The melting temperature is linear with the inverse of the diameter of the nanowires. The ratio of slopes evaluated by MD simulations for Pb nanoparticles and nanowiress is ~2:1 [81], while the ratio for Pd is ~3:2 [82]. Thermodynamic model predicts the ratio to be 3:2 or 2:1 for LNG and HMM, respectively [76], suggesting that the ratio depends on the melting process. The author is not aware of any report that deals with the experimental determination of the melting temperature of nanoparticles as well as of nanowires for the same material. IV. Superheating of nanoparticles Superheating has been reported for nanoparticles embedded in some matrices while the same nanoparticles embedded in some other matrices, the melting temperature will be lower. Superheating has been reported for Pb in Al, In in Al, Bi in Zn and Ge in SiO2, inert-gas nanocrystals in Cu, Al and Ni matrices [50-64]. Experimental results of Sheng et al. [55,56] reveal that the enhancement or depression of the melting temperature of the embedded nanoparticles depends on the epitaxy between the nanoparticles and the embedding matrix. This is attributed to the suppression of vibrational motion of the surface atoms by the interface epitaxy and increases the melting temperature. In other words, superheating occurs when the melting starts from the centre

26

Thermal and Thermodynamic Stability of Nanomaterials

and proceed towards the surface, while melting point depression occurs when the melting starts from the surface and proceeds towards the centre. The superheating observed for Ge in SiO2 indicates that the epitaxial relation between the material and the matrix is not the essential criteria of superheating [62]. Superheating has also been reported for free nanoparticles and is thought to be due to the different phases of the materials when reduced to nano-dimension. Materials like Sn with 10–30 atoms remain solid at ~50 K above the melting point of bulk tin [83]. Similar superheating has been observed for Ga with few atoms [84]. This is thought to be due to the structural difference or the difference in bonding [85,86]. Melting of TiO2 nanotubes [87] with different crystal structures have been discussed and a phase transition associated with size has been predicted. V. Irregular variation of melting temperature of clusters As discussed earlier, the melting of small particles reveals a melting point depression that scales as approximately 1/D. The 1/D dependence breaks down for particles with less than around 500 atoms. Local maxima and minima in the melting temperature have been reported for Na, Al and Ar clusters and are expected to be due to structural effect [88-91]. The observed pattern of maxima and minima in Tm cannot be fully explained by electronic or geometric shell closings. The geometry of nanoparticles decides the melting temperature of the clusters. VI. Extremely low melting temperature of nanorods Recently, it has been shown that ZnO nanorods melts at a temperature of 750 0C [92], while the bulk melting temperature is 1975 0C. As the size of the nanorods is of the order of ~100 nm, the melting temperature was expected to be close to the bulk melting temperature [93]. Though the cause of the low melting temperature is not yet known, it is believed to be due to non-stoichiometric ZnO. Shape transformation of gold nanorods has been observed at a temperature of 523 K which is much lower than the bulk melting temperature [94] and is initiated by the surface melting. VII. Melting of semiconducting nanoparticles Almost all theoretical models predict a linear relation between the melting temperature and inverse of the particle size. However, recent work indicates the melting point of semiconductor and covalently bonded nanoparticles may have a different dependence on particle size [95,96]. The covalent character of the bonds changes the melting physics of these materials. Researchers have demonstrated that melting point depression in covalently bonded materials can be accurately modeled as [95,96]

T  Tnp T

D   0   D

2

(4)

where D0 is the average diameter of a particle with one atom (n=1). This has also been verified [96] by comparing the experimental data for CdS with Eq. (4). Similar variation has been predicted for Si, Ge, Sn. VII. Vapor pressure of nanoparticles It is well known that the vapor pressure increases as the particle size is reduced and is governed by the Kelvin equation (KE) as

 4M  ps ,  exp    RTD  ps0  p 

(5)

Materials Science Forum Vol. 653

27

where  is the surface tension, M is the molecular weight,  p is the particle density, R is the gas constant, T is the temperature. As noted from KE, the vapor pressure of a curved surface is higher than that of a flat surface and has been verified by measuring the time taken for the complete evaporation or by monitoring the size change of nanoparticles [97-99]. Recently, it has been  reported [100] that the vapor pressure of Na 139 cluster is comparable to that of bulk Na which is in 

contrast with the prediction of KE. This may be due to the higher stability of Na 139 as evident from the abundance mass spectrum [88]. VIII. Summary We have discussed few anomalies in the thermal stability of nanostructured materials. Different variation of the melting temperature even for the same materials is thought to be due to the difference in the surface melting of different facets. The bulk melting temperature cannot be extrapolated from the nanoscale results. Irregular variation of the melting temperature is observed for particles with less than around 500 atoms. Superheating is observed for nanoparticles embedded in a matrix or that undergoes a phase transition. One of the interesting anomalies is that the variation of the melting temperature is quadratic with the inverse of the particle size for covalently bonded nanoparticles. Acknowledgement The author acknowledges Prof. S. B. Krupanidhi, Prof. K. B. R. Varma, Prof. S. A. Shivshankar, Prof. A. M. Umarji, Dr S. Raghavan, Dr N. Ravishankar, Prof. S. N. Behera and Prof. S. N. Sahu for their constant encouragement. The author also acknowledges the support of Dr. S. C. Vanithakumari, L. T. Singh, Amitha Shetty, Gopal K. Goswami, R. P. Sugavaneswara, L. Shinde, D. K. Sar, Sanjaya Brahma, Dr. P. Mahanandia, all students and staff members of our Materials Research Centre. References [1] W. H. Qi and M. P. Wang J. Mat. Sci. Lett. Vol. 21 (2002), p. 1743. [2] K. K. Nanda, S. N. Sahu and S. N. Behera Phys. Rev. A Vol. 66 (2002), p. 013208. [3] K. K. Nanda, Appl. Phys. Lett. Vol. 87, (2005), p. 021909. [4] K. K. Nanda, Chem. Phys. Lett. Vol. 419 (2006), p. 195. [5] S. C. Vanithakumari and K. K. Nanda, J. Phys. Chem. B Vol. 110 (2006), p. 1033. [6] S. C. Vanithakumari and K. K. Nanda, Phys. Lett. A Vol. 372 (2008), p.6930. [7] W.H. Qi, M.P. Wang, G.Y. Xu, Chem. Phys. Lett. Vol. 372 (2004), p. 632. [8] D. Xie, M.P. Wang, W.H. Qi, J. Phys.: Condens. Matter Vol. 16 (2004), p. L401. [9] W.H. Qi, M.P. Wang, Mater. Chem. Phys. Vol. 88 (2004), p. 280. [10] W.H. Qi, M.P. Wang, J. Mater. Sci. Lett. Vol. 21 (2002), p. 1743. [11] W.H. Qi, M.P. Wang, W.Y. Hu, J. Phys. D: Appl. Phys. Vol. 38 (2005), p. 1429. [12] Q. Jiang, J.C. Li, B.Q. Chi, Chem. Phys. Lett. Vol. 366 (2002), p. 551. [13] C.Q. Sun, Y. Wang, B.K. Tay, S. Li, H. Huang, Y.B. Zhang, J. Phys. Chem. B Vo. 106 (2002), p. 10701. [14] C.Q. Sun, C.M. Li, H.L. Bai, E.Y. Jiang, Nanotechnology Vol. 16 (2005), p. 1290. [15] C.Q. Sun, Y. Shi, C.M. Li, S. Li, T.C. Au Yeung, Phys. Rev. B Vol. 73 (2006), p. 075408. [16] D. Tomanek, S. Mukherjee, K.H. Bennemann, Phys. Rev. B Vol. 28 (1983), p. 665. [17] C. Bre´chignac, H. Busch, Ph. Cahuzac, and J. Leygnier, J. Chem. Phys. Vol. 101 (1994), p. 6992. [18] H. K. Kim, S. H. Huh, J. W. Park, J. W. Jeong, and G. H. Lee, Chem. Phys. Lett. Vol. 354 (2002), p. 165.

28

Thermal and Thermodynamic Stability of Nanomaterials

[19] C. R. M. Wronski, Br. J. Appl. Phys. Vol. 18 (1967), p. 1731. [20] S. L. Lai, J. Y. Guo, V. Petrova, G. Ramanath, and L. H. Allen, Phys. Rev. Lett. Vol. 77 (1996), p. 99. [21] Y. Oshima and K. Takayanagi, Z. Phys. D Vol. 27 (1993), p. 287. [22] T. Bachels, H.-J. Gunterodt and R. Schafer, Phys. Rev. Lett. Vol. 85 (2000), p. 1250. [23] M. Takagi, J. Phys. Soc. Jap. Vol. 9 (1954), p. 359. [24] L. S. Palatnik and Yu. F. Konnik, Phys. Metals Metal. Vol. 9 (1960), p.48. [25] J. F. Pocza, A. Barna and P. B. Barna, J. Vacuum. Sci. & Technol. Vol. 6 (1969), p.472. [26] R. P. Berman and A. E. Curzon, Can. J. Phys. Vol. 52 (1974), p. 923. [27] B. T. Boiko, A. T. Pugachev and V. M. Bratsykhin, Sov. Phys. Solid State Vol. 10 (1969), p. 2832. [28] J. R. Sambles, Proc. R. Soc. Lond. A Vol. 324 (1971), p. 339. [29] T. Ben-David, Y. Lereah, G. Deutscher, R. Kofman and P. Cheyssac, Phil. Mag. A Vol. 71 (1995), p. 1135. [30] A. N. Goldstein, C. M. Echer, and A. P. Alivisatos, Science Vol. 256 (1992), p. 1425. [31] A. N. Goldstein, Appl. Phys. A Vol. 62 (1996), p. 33. [32] T. Castro, R. Reifenberger, E. Choi, and R. P. Andres, Phys. Rev. B Vol. 42 (1990), p. 8548. [33] Ph. Buffat and J-P. Borel, Phys. Rev. A Vol. 13 (1976), p. 2287. [34] K. Dick, T. Dhanasekaran, Z. Zhang and D. Meisel, J. Am. Chem. Soc. Vol. 124 (2002), p. 2312. [35] T. P. Martin, U. Naher, H. Schaber, and U. Zimmermann, J. Chem. Phys. Vol. 100 (1994), p. 2322. [36] E. A. Olson, M. Yu. Efremov, M. Zhang, Z. Zhang, and L. H. Allen, J. Appl. Phys. Vol. 97 (2005), p. 034304. [37] V. P. Skripov, V. P. Koverda and V. N. Skokov, Phys. Stat. Sol. A Vol. 66 (1981), p. 109. [38] Y. Lereah, G. Deutscher, P. Cheyssac, R. Kofman, Europhys. Lett. Vol. 12 (1990), p. 709. [39] R. Kofman, P. Cheyssac, A. Aouaj, Y. Lereah, G. Deutscher, T. Ben-David, H. M. Penisson and A. Bourret, Surf. Sci. Vol. 303 (1994), p. 231. [40] E. Sondergard, R. Kofman, P. Cheyssac, F. Celestini, T. Ben-David and Y. Lereah, Surf. Sci. Vol. 388 (1997), p. L1115. [41] M. Zhang, M. Yu Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene and L. H. Allen, Phys. Rev. B Vol. 62 (2000), p. 10548. [42] R. Kofman, P. Cheyssac, R. Garrigos, Y. Lereah and G. Deutscher, Z. Phys. D Vol. 20 (1991), p. 267. [43] M. Dippel, A. Maier, V. Gimple, H. Wider, W.E. Evenson, R.L. Rasera, G. Schatz, Phys. Rev. Lett. Vol. 87 (2001), p. 095505. [44] X. W. Wang, G. T. Fei, K. Zheng, Z. Jin and L. D. Zhang, Appl. Phys. Lett. Vol. 88 (2006), p. 173114. [45] K. Morishige and K. Kawano, J. Phys. Chem. B Vol. 104 (2000), 2894. [46] E. Molz, A. P. Y. Wong, M. H. W. Chan and J. R. Beamish, Phys. Rev. B Vol. 48 (1993), p. 5741. [47] J. L. Tell and H. J. Maris, Phys. Rev. B Vol. 28 (1983), p. 5122. [48] F. Cellestini, R. J. -M. Pellenq, P. Bordarier and B. Rousseau, Z. Phys. D Vol. 37 (1996), p. 49. [49] A. Rytkonen, S.Valkealahti, and M. Manninen, J. Chem. Phys. Vol. 106 (1997), p. 1888. [50] H. Saka, Y. Nishikawa, and T. Imura, Philos. Mag. A Vol. 57 (1988), p. 895. [51] H. W. Sheng, K. Lu, and E. Ma, Nanostruct. Mater. Vol. 10 (1998), p. 865. [52] L. Grabaek, J. Bohr, E. Johnson, A. Johansen, L. Sarholt-Kristensen, and H. H. Andersen, Phys. Rev. Lett. Vol. 64 (1990), p.934. [53] K. Chattopadhyay and R. Goswami, Prog. Mater. Sci. Vol. 42 (1997), p. 287.

Materials Science Forum Vol. 653

29

[54] R. Goswami and K. Chattopadhyay, Acta Mater. Vol. 52 (2004), p. 5503. [55] H. W. Sheng, G. Ren, L. M. Peng, Z. Q. Hu, and K. Lu, Philos Mag. Lett. Vol. 73 (1996), p. 179 . [56] H. W. Sheng, G. Ren, L. M. Peng, Z. Q. Hu, and K. Lu, J. Mater. Res. Vol. 12 (1997), p. 119. [57] T. Ohashi, K. Kuroda, and H. Saka, Philos. Mag. B Vol. 65 (1992), p. 1041. [58] F. G. Shi, J. Mater. Res. Vol. 9 (1994), p. 1307. [59] Q. Jiang, Z. Zhang, and J. C. Li, Chem. Phys. Lett.Vol. 322 (2000), p. 549. [60] Z. Zhang, Z. C. Li, and Q. Jiang, J. Phys. D Vol. 33 (2000), p. 2653. [61] L. Zhang, Z. H. Jin, L. H. Zhang, M. L. Sui, and K. Lu, Phys. Rev. Lett. Vol. 85 (2000), p. 1484. [62] Q. Xu, I. D. Sharp, C. W. Yuan, D. O. Yi, C. Y. Liao, A. M. Glaeser, A. M. Minor, J. W. Beeman, M. C. Ridgway, P. Kluth, J. W. Ager III, D. C. Chrzan, and E. E. Haller, Phys. Rev. Lett. Vol. 97 (2006), p. 155701. [63] C. J. Rossouw and S. E. Donnelly, Phys. Rev. Lett. Vol. 55 (1985), p. 2960 [64] J. H. Evans and D. J. Mazey, J. Phys. F Vol. 15 (1985), p. L1. [65] K. F. Peters, Y. –W. Chung and J. B. Cohen, Appl. Phys. Lett. Vol. 71 (1997), p. 2391. [66] B. Pluis, D. Frenkel, J. F. Van der Veen, Surf. Sci. Vol. 239 (1990), p. 282. [67] B. Pluis, A. W. Denier van der Gon, J. W. M. Frenken and, J. F. van der Veen, Phys. Rev. Lett. Vol. 59 (1987), p. 2678. [68] A. Hoss, M. Nold, P. von Blackenhagen and O. Moyer, Phys. Rev. B Vol. 45 (1992), p. 8714. [69] S. G. J. Mochrie, D. M. Zehner, B. M. Ocko and D. Gibbs, Phys. Rev. Lett. Vol. 64 (1990), p. 2925. [70] P. Carnevali, F. Ercolessi and E. Tosatti, Phys. Rev. B Vol. 36 (1987), p. 6701. [71] C. Kan, G. Wang, X. Zhu, C. Li and B. Cao, Appl. Phys. Lett. Vol. 88 (2006), p. 071904. [72] T. S. Rahman, Z. Tian and J. E. Black, Surf. Sci. Vol. 374 (1997), p. 9. [73] K. K. Nanda, A. Maisels, F. E. Kruis and B. Rellinghaus, Europhys. Lett. Vol. 80 (2007), 56003. [74] D. K. Sar, P. Nayak and K. K. Nanda, Phys. Lett. A Vol. 372 (2008), p. 4627. [75] G. K. Goswami and K. K. Nanda, Appl. Phys. Lett. 91 (2007), p, 196101. [76] K. K. Nanda, Pramana: J. Phys. Vol. 72 (2009), p. 671 [77] Y.-H. Wen, Z.-Z. Zhu, R. Zhu and G.-F. Shao, Physica E Vol. 25 (2004, p. 47 [78] B. Wang, G. Wang, X. Chen and J. Zhao, Phys. Rev. B Vol. 67 (2003), p. 193403 [79] Y. Qi, T. Cagin, W. L. Johnson and W. A. Goddard III, J. Chem. Phys. Vol. 115 (2001), p. 385 (2001) [80] L. Hui, F. Pederiva, B. L. Wang, J. L. Wang and G. H. Wang, Appl. Phys. Lett. Vol. 86 (2005), p. 011913 [81] O. Gülseren, F. Ercolessi and E. Tosatti, Phys. Rev. B Vol. 51 (1995), p. 7377. [82] L. Miao, V. R. Bhethanabotla and B. Joseph, Phys. Rev. B Vol. 72 (2005), p. 134109 [83] G. A. Breaux, R. C. Benirschke, T. Sugai, B. S. Kinnear and M. F. Jarrold, Phys. Rev. Lett. Vol. 91 (2003), p. 215508 [84] A. A. Shvartsburg and M. F. Jarrold, Phys. Rev. Lett. Vol. 85 (2000), p. 2530. [85] K. Joshi, S. Krishnamurty and D. G. Kanhere, Phys. Rev. Lett. Vol. 96 (2006), p. 135703. [86] S. Chacko, K. Joshi, D. G. Kanhere and S. A. Blundell, Phys. Rev. Lett. Vol. 92 (2004), p. 133506 [87] G. Guisbiers, O. Van Overschelde and M. Wautelet, Appl. Phys. Lett. Vol. 92 (2008), p. 103121. [88] M. Schmidt, R. Kusche, B. V. Issendorff and H. Haberland, Nature (London) Vol. 393 (1998), p. 238

30

Thermal and Thermodynamic Stability of Nanomaterials

[89] G. A. Breaux, C. M. Neal, B. Cao and M. F. Jarrold, Phys. Rev. Lett. Vol. 94 (2005), p. 173401 [90] D. J. Wales and R. S. Berry, J. Chem. Phys. Vol. 92 (1990), 4473 [91] A. Augado and J. M. Lopez, Phys. Rev. Lett. Vol. 94 (2005), p. 233401 [92] X. W. Wang, G. T. Fei, K. Zheng, Z. Jin and L. D. Zhang, Appl. Phys. Lett. Vol. 88 (2006), p. 173114. [93] G. Guisbiers, M. Wautelet, Nanotechnology Vol. 18 (2007), p. 435710 [94] H. Petrova, J. P. Juste, I. P. Santos, G. V. Hartland, L. M. L. Marzan and P. Mulvaney, Phys. Chem. Chem. Phys. Vol. 8 (2006), p. 814. [95] H. H. Farrell and C. D. Van Siclen, J. Vac. Sci. Technol. B Vol. 25 (2007), p. 1441. [96] H. H. Farrell, J. Vac. Sci. Technol. B Vol. 26 (2008), p. 1534. [97] M. Blackman, N. D. Lisgarten and L. M. Skinner, Nature Vol. 217 (1968), p. 1245. [98] K. K. Nanda, F. E. Kruis and H. Fissan, Phys. Rev. Lett. Vol. 89 (2002), p. 256103. [99] K. K. Nanda. A. Maisels, F. E. Kruis, H. Fissan and S. Stappert, Phys. Rev. Lett. Vol. 91 (2003), p. 106102. [100] M. Schmidt, T. Hippler, J. Donges, W. Kronmüller, B. von Issendorff, H. Haberland and P. Labastie, Phys. Rev. Lett. Vol. 87 (2001), p. 203402.

Materials Science Forum Vol. 653 (2010) pp 31-53 © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.653.31

Thermodynamic Phase Transitions in Nanometer-sized Metallic Systems Francesco Delogu Dipartimento di Ingegneria Chimica e Materiali, Università degli Studi di Cagliari, piazza d’Armi, 09123 Cagliari, Italy E-mail: [email protected] Keywords: Phase transition; Melting; Structure; Modeling.

Abstract. The present chapter deals with the characterization and description of phase transitions in metallic systems with characteristic size down to the nanometer range. In particular, the chapter focuses on the solid-to-liquid transition in nanometer-sized particles. After a short introduction to classical thermodynamics and to the way it copes with the general properties exhibited by nanometer-sized systems, a rapid overview of the state of the art in the field of the solid-to-liquid transition is given. The heterogeneous melting processes taking place in mesoscopic systems are discussed in terms of both classical thermodynamic and numerical simulation approaches. In the former case, attention is focused on the case of mesoscopic Sn particles, for which a relatively large amount of consistent experimental data exists as a consequence of previous calorimetric studies. In the latter case, the behavior of mesoscopic Cu particles is discussed. Introduction Classical equilibrium thermodynamics represents one of the greatest scientific achievements of mankind. Firmly based on the empiricism permeating its three fundamental principles, thermodynamics provides a sound conceptual framework to describe macroscopic systems independent of any hypothesis on their microscopic nature [1,2]. Its beautiful generality has been a considerable source of inspiration, even when the uncertain shadows of an unsuspected microscopic world began to unveil [3]. It suffices here to remember that precisely from thermodynamics made its first steps wave mechanics, with the quantization of energy exchanges in the blackbody cavity proposed by M. Planck and the formal analogy between a monochromatic electromagnetic radiation and a collection of independent undistinguishable particles that pushed A. Einstein to advance the light quantum hypothesis [4,5]. After about two centuries, scientists still look to classical thermodynamics as to a robust phenomenological description of nature of invaluable help in addressing fundamental research. It is possible to make a number of different examples, but this chapter must focus on the physical behavior of nanometer-sized portions of matter and it is to such systems that attention will be immediately turned. What makes nanometer-sized systems so much interesting to scientists is their intermediate position between massive aggregates of matter on the one hand and individual atoms and molecules on the other [6-8]. Nanometer-sized systems are neither wholly macroscopic nor microscopic. Rather, they are identified as mesoscopic systems [9,10]. At such scale, a plethora of novel qualitative physical and chemical behaviors emerge [6-12]. In most cases, the emergence of such behaviors can be essentially ascribed to the size constraint [6-12]. Indeed, whenever the characteristic length scale of a given physical process becomes comparable with the linear size of the physical system, the process considered can be significantly affected [6-12]. There exists a huge number of unequivocally proven evidences in such direction in areas of science as different as heat conduction, magnetism, plasticity and solution chemistry to name just a few [6-13]. Therefore, scientists are no longer surprised by the emergence of unusual physical and chemical phenomena on the nanometer scale, which are instead systematically sought. Yet, the nature of the emerging

32

Thermal and Thermodynamic Stability of Nanomaterials

behaviors is usually far beyond their experience and intuition [13]. For this reasons, the physics and chemistry of nanometer-sized systems are commonly regarded as a new subject of scientific investigation [6-13]. Classical thermodynamics must be included in the list of scientific fields to be somewhat rethought to satisfactorily account for the behavior of condensed matter with size on the nanometer scale [10,13]. The motivation is that classical thermodynamics is eminently macroscopic [1,2]. In fact, thermodynamic variables, functions and states can be only defined for systems in equilibrium containing a huge number of individual particles [1,2]. Borrowing the jargon of statistical thermodynamics, which attempts to bridge the gap between the microscopic features of any given system and its thermodynamic properties, a correct definition of thermodynamic variables, functions and states only exists in the thermodynamic limit [1,2,14]. In turn, such limit can be properly defined with reference to the condition that the number of particles in the system and the system volume tend to infinity while the number density remains finite [14]. It is evident that mesoscopic systems violate such constraint [6-13]. The number of particles in such systems is orders of magnitude below the Avogadro number. A spherical crystalline Cu particle with radius of about 1 nm only contains about 450 atoms. A droplet of water about 10 nm in radius includes only 1.4×105 H2O molecules. It is not surprising that the physical and chemical properties of such systems significantly differ from the ones of massive Cu and bulk water. Surface energy, fluctuations, critical phenomena, dissipative structures, self-assembly concur to affect the thermodynamic behavior of small aggregates of atoms and molecules to such an extent that it is not rare that completely unexpected processes or properties are observed [13]. Furthermore, fundamental concepts such as the thermodynamic idea of phase are seriously questioned [9,10,13]. It follows that the thermodynamics of mesoscopic systems must be different from classical one. Not in the sense that a completely new approach to the field is necessary, although it has been invoked by various researchers [15-18], but rather in the sense that mesoscopic thermodynamics must explicitly deal with the system finiteness [9,10]. To such aim, the functions of classical thermodynamics must be suitably modified to include the least number of new quantities needed to describe finite systems [9]. Far from the idea of providing an exhaustive presentation of all the implications carried by the fundamental physics and chemistry of nanometer-sized systems, the present chapter aims at elucidating a few specific features of the thermodynamic behavior on the nanometer scale. In particular, the chapter must be intended as a short description of a few theoretical and numerical findings in the field of the solid-to-liquid phase transition in small systems. The topic will be discussed from both the perspective of classical thermodynamics and numerical simulations. Rather than proceeding with a formal enunciation of the fundamentals of thermodynamics and their modification in the case of mesoscopic systems, the different cases will be discussed on a phenomenological basis. For clarity, classical thermodynamic and numerical approaches will be presented in separate sections. The solid-to-liquid phase transformation considered in the present chapter will be studied for model metallic systems in the mesoscopic scale regime. This can be defined as the size range in which the system properties scale according to so-called smooth size effects [7]. These consist of a relatively simple scaling of physical and chemical properties with the system size, typically according to equations involving a power-law dependence [6-8]. Such feature identifies the systems as different from clusters, which instead exhibit an irregular variation of properties according to socalled specific size effects somehow related to “magic numbers” [7]. In fact, the power-law dependence of physical and chemical properties can be explained by the high ratio between the surface and volume characterizing nanometer-sized particles [6-8]. More specifically, the observed deviations can be related to the number of surface atoms, which in turn determines the surface energy contribution to the Gibbs free energy of the system [6-8]. In the light of the above mentioned observations, attention will be focused on spherical particles in the size range roughly between 1 and 50 nm. Being concerned with the thermodynamic behavior

Materials Science Forum Vol. 653

33

of metals, such size range permits to avoid the undesired complications arising from the irregular change of thermodynamic properties in metallic clusters. The solid-to-liquid phase transition The phase transition from a solid to a liquid is a ubiquitous and familiar process that attracted a great deal of interest for centuries, representing one of the rare cases in which a phase transition is completely accessible by common experience [1,2]. Generally referred to as melting, it is a topological transition from an ordered phase to a disordered one [1,2,14,19]. As the temperature attains the melting point, the crystalline lattice defined by the average positions around which atoms oscillate undergoes a fast collapse driven by the action of inharmonic forces [1,2,14,19]. The atomic species acquire translational degrees of freedom and exhibit a regime of motion characterized by a localized vibrational behavior occasionally replaced by short displacements governed by caging effects [1,2,14,19]. Such particular regime of motion originates a dynamical structure showing a relatively high degree of order on the short range, but no order in the long range. The conceptual framework briefly sketched above is only apparently simple. Actually, it hides a complexity such that it is still challenging to modern scientists. Only the most fundamental thermodynamic features of equilibrium melting processes regarding massive systems can be considered as fully understood [1,2,14,19]. In fact, for such systems and conditions, the temperature at which the solid-to-liquid transition occurs is univocally identified by the equality of the Gibbs free energies of the solid and liquid phases [1,2,14,19]. Conversely, from a kinetic point of view the situation is much more confused. The mechanisms underlying the transformation of the anisotropic crystalline lattices into isotropic liquid systems are not yet satisfactorily understood and the identification of the transition temperature relies essentially upon phenomenological criteria [2038]. The overall situation is further complicated by the evidence that the melting behavior is affected by the system size. The depression of the melting point of small particles of metallic species probably represents the most striking example of deviation of thermodynamic behavior as a consequence of smooth size effects. The melting point depression was first theorized in 1909 [39] and attracted renewed attention in 1953 [40]. However, the first direct experimental investigations on the melting point of small metal particles were only carried out roughly a decade later [41,42]. The phenomenon is generally explained in terms of the size dependence of the chemical potential in finite systems [43-51]. This leads to several phenomenological models capable of successfully reproducing experimental observations either by predicting the existence of a quasi-liquid layer covering the particle surface below its equilibrium melting point or by allowing the nucleation and growth of a liquid layer at the particle surface [43-51]. However, experimental and theoretical studies restricted to melting point depression do not permit a comprehensive understanding of the thermodynamic features of the solid-to-liquid transition on the nanometer scale. In fact, an accurate analysis of heat exchange processes indicate that also the latent heat of fusion exhibits a size-dependent depression [52-55]. The rationale for the depression of both melting points and latent heats of melting can be reasonably ascribed to the properties of the particle surface. In particular, the decrease of the latent heat of melting with the particle size decrease suggests that not all the matter included into the particle has undergone the solid-to-liquid transition at the same time [52-55]. In turn, such behavior can be connected with the occurrence of pre-melting processes at temperatures lower than the melting point and with transition signatures different from the ones typical of melting, i.e. a secondorder character [20-38]. The idea that a liquid layer could form at the free planar surface of a crystalline solid at temperatures lower than the equilibrium melting point dates back to 1910 [56-58]. Although significant exceptions have been demonstrated [48], it is now generally accepted that the surface atoms can progressively move from a solid-like to a liquid-like dynamics at temperatures lower than

34

Thermal and Thermodynamic Stability of Nanomaterials

the ones required by bulk atoms [19,24,48,59-63]. The resulting pre-melting phenomena can be then ascribed to the higher potential energy of the atomic species lying at the surface, which can be approximately regarded as chemical species with unsaturated bonds [64,65]. The number of such unsaturated bonds, and then the potential energy of the surface atoms, depend on the surface topology [8,12]. In general terms, the lower the number of nearest neighbors, the higher the energy of the atom [8,12,66]. Along this line, the hypothesis that pre-melting phenomena could take place in mesoscopic particles automatically comes out. In fact, mesoscopic particles are portions of matter having a curved surface as limit boundary [8,12,66]. It follows that the coordination of surface atoms in nanometer-sized particles depends on the surface curvature [8,12,66]. In particular, the coordination decreases as the curvature increases, i.e. when the particle size decreases [8,12,66]. Therefore, a direct correlation can be established between the particle size and the number of atoms that can undergo pre-melting processes [48]. Pursuing the analysis further, it clearly appears that the capability of surface atoms of undergoing pre-melting provides a rationale for the depression of the latent heat of fusion with the decrease of the particle size [30,52-55,67]. A thermodynamic approach The qualitative observations above can be suitably formalized by carrying out a detailed analysis of the thermodynamics of melting processes for a mesoscopic particle. For simplicity, spherical model particles with radius r embedded in vacuum will be hereafter considered. Two different melting scenarios can be reasonably conceived, which are schematically depicted in Fig. 1.

Fig.1. The one-stage (top) and two-stage (bottom) solid-to-liquid transition of a mesoscopic metallic particle.

In the first case, it can be hypothesized that the metallic particle undergoes a one-stage melting process, which implies that the transition from the solid to the liquid phase contemporary involves all the particle volume. In the second case, the melting mechanism consists of two elementary steps involving first the melting of a thin layer at the surface of the metallic particle and then the solid-toliquid transition of the remaining solid phase in the particle interior. Both cases can be analyzed by resorting to a classical thermodynamic approach. Correspondingly, the temperature at which the solid-to-liquid phase transition occurs can be identified by equaling the Gibbs free energies of the different phases involved in the one- or twostage scenarios.

Materials Science Forum Vol. 653

35

Under the hypothesis that melting takes place contemporarily in all the particle volume at a temperature Tm , the condition of equality of the Gibbs free energies of the solid and liquid phases leads to the following equation: 4 3 4 π r ρ s ∆Gs (Tm ) + 4π r 2 γ sv (Tm ) = π r 3 ρ l ∆Gl (Tm ) + 4π r 2 γ lv (Tm ) . 3 3

(1)

The quantities ∆Gs (Tm ) and ∆Gl (Tm ) represent the Gibbs free energies respectively of the solid and liquid phases at the melting point Tm , whereas γ sv (Tm ) and γ lv (Tm ) are the free energies associated with the solid- and liquid-vapor interfaces. Instead, ρ s and ρ l represent the molar densities of the solid and liquid phases. A simple algebraic manipulation of Eq. 1 brings to the expression 1 r [ρ l ∆Gl (Tm ) − ρ s ∆Gs (Tm )] = γ sv (Tm ) − γ lv (Tm ) , 3

(2)

which emphasizes the direct relationship between the particle radius, the bulk Gibbs free energies and the interface free energies at the melting point. According to the second melting scenario, the complete melting of the metallic particle is preceded by the solid-to-liquid transition of a surface layer, the thickness of which is indicated by δ . The temperature Tpm at which surface pre-melting phenomena take place can be suitably identified by equaling the Gibbs free energies of the completely solid particle and of the one exhibiting a liquid layer of thickness δ at its surface. The resulting equation is

4 3 4 π r ρ s ∆Gs (Tpm ) + 4π r 2 γ sv (Tpm ) = π (r − δ )3 ρ s ∆Gs (Tpm ) + 3 3 4 2 3 4π (r − δ ) γ sl (Tpm ) + π r 3 − (r − δ ) ρ l ∆Gl (Tpm ) + 4π r 2 γ lv (Tpm ), 3

[

]

(3)

where γ sl (Tpm ) represents the free energy contribution of the solid-liquid interface at the pre-melting point Tpm . Eq. 3 can be further manipulated to yield

[

] [

]

r δ ρ l ∆Gl (Tpm ) − ρ s ∆Gs (Tpm ) = r γ sv (Tpm ) − γ sl (Tpm ) − γ lv (Tpm ) + 2 δ γ sl (Tpm ) .

(4)

The pre-melting stage is followed by the transition of the solid phase in the particle interior to the liquid phase. The condition of equality of the Gibbs free energies for the second stage of the twostage melting process is expressed by the following equation:

[

]

4 4 π (r − δ )3 ρ s ∆Gs (Tm ) + 4π (r − δ )2 γ sl (Tm ) + π r 3 − (r − δ )3 ρ l ∆Gl (Tm ) 3 3 4 + 4π r 2 γ lv (Tm ) = π r 3 ρ l ∆Gl (Tm ) + 4π r 2 γ lv (Tm ). 3

(5)

Simple algebraic manipulations permit to re-write Eq. 5 as 1 (r − δ )[ρ l ∆Gl (Tm ) − ρ s ∆Gs (Tm )] = γ sl (Tm ) , 3

(6)

36

Thermal and Thermodynamic Stability of Nanomaterials

which closely resembles Eq. 2. Eqs. 1-6 express the thermodynamic conditions under which the one-stage and the two-stage melting scenarios can actually occur. Therefore, they provide a reference framework to indirectly ascertain the nature of the melting process taking place in mesoscopic particles. However, it is worth noting that such conceptual framework is not completely satisfactory. In fact, the incomplete characterization of the temperature and size dependence of the thermodynamic quantities involved limits any direct applicability independent of experimental data. For example, no detailed description of the variation of the average free energies of solid-liquid, solid-vapor and liquid-vapor interfaces is available. In addition, no independent quantification of the thickness of the surface layer affected by pre-melting is possible. In spite of this, a few important conclusions can be still drawn when Eqs. 1-6 are properly utilized in connection with suitable experimental data. Before doing this, a further thermodynamic evidence can be obtained. Under the hypothesis that melting takes place according to a two-stage mechanism, the formation of a liquid layer of thickness δ at the particle surface has immediate consequences on the change of enthalpy at melting, i.e. on the latent heat of transition ∆H m (Tm ) . For a bulk system, this quantity corresponds to the enthalpy difference ∆H l (Tm ) − ∆H s (Tm ) between the liquid and the solid phase at the melting point Tm . It is now worth noting that the latent heat of melting predicted by the onestage scenario is different from the one predicted by the two-stage mechanism. In the former case, the latent heat of transition is 4 3 4 π r ρ s ∆H m (Tm ) = π r 3 ρ s [∆H l (Tm ) − ∆H s (Tm )] . 3 3

(7)

Instead, in the latter case the surface layer that has undergone pre-melting at a temperature Tpm does not contribute to the total latent heat of melting at the melting point Tm . It follows that the apparent latent heat of melting ∆H m (Tm ) , i.e. the total change of enthalpy referred to the total amount of matter included into the initial solid particle, is 4 3 4 π r ρ s ∆H m (Tm ) = π (r − δ )3 ρ s [∆H l (Tm ) − ∆H s (Tm )] . 3 3

(8)

Correspondingly, the apparent heat of melting can be also expressed as ∆H m (Tm ) =

(r − δ )3 [∆H (T ) − ∆H (T )] ≈ 1 − 3δ  [∆H (T ) − ∆H (T )] .   l m s m l m s m 3 r



r 

(9)

Therefore, the apparent heat of melting ∆H m (Tm ) is expected to decrease as the particle radius r decreases, with the rate of decrease mediated by the thickness δ of the pre-molten surface layer. The difference between the values of the latent heat of melting expected in case of one-stage or twostage melting processes is Γ = ∆H mone (Tm ) − ∆H mtwo (Tm ) =

3δ [∆H l (Tm ) − ∆H s (Tm )] . r

(10)

Such quantity can be also regarded as a measure of the depression undergone by the latent heat of melting with respect to the value expected in case of transition of a corresponding amount of bulk matter. Then, when observed, the depression of the latent heat of melting can be regarded as a

Materials Science Forum Vol. 653

37

signature of a pre-melting process at the surface of the particle. Furthermore, it can be utilized to roughly evaluate the thickness δ of the surface layer involved in pre-melting phenomena.

An example of thermodynamic calculations with experimental data Obtaining accurate experimental information on the thermodynamics of mesoscopic metallic particles is not an easy task [52-55]. In fact, it necessarily involves the accurate characterization of heat transfer processes taking place at the nanometer scale [52-55]. In turn, this requires the capability of evaluating very small heat fluxes, which can be done only with a suitably manufactured calorimeter [52-55]. As a consequence, the amount of systematic experimental data available to apply Eqs. 1-10 to a practical case is quite limited. One of the most complete experimental data sets concerns the thermodynamics of mesoscopic Sn particles having the average radius r approximately in the range between 5 and 50 nm [52]. The data set includes the experimental values of the melting point Tm and the latent heat of transition ∆H mexp (Tm ) pertaining to fifteen particles [52]. Such values are shown in Fig. 2 as a function of the average particle radius r.

Fig. 2. The experimental latent heats of melting, ∆H mexp (Tm ) , (a) and melting points, Tm , (b) for the mesoscopic Sn particles as a function of the average particle radius r [52]. It can be seen that both ∆H mexp (Tm ) and Tm decrease as the average particle radius r decreases. Correspondingly, not only the solid-to-liquid transition occurs at temperatures Tm lower than the equilibrium melting point for bulk systems, but also the thermal effects associated with the latent heat of transition are significantly reduced [30,52,67]. The knowledge of both experimental melting points Tm and latent heats of melting ∆H mexp (Tm ) allows a systematic comparison between the latter quantity and the theoretically expected latent heat of melting ∆H mth (Tm ) = ∆H l (Tm ) − ∆H s (Tm ) for bulk systems. The corresponding pairs of ∆H mexp (Tm ) and ∆H mth (Tm ) values are shown in Fig. 3 as a function of the transition temperature Tm . The variation of the latent heat of melting ∆H mth (Tm ) theoretically expected for bulk Sn is quite small. It definitely contrasts with the pronounced depression undergone by the experimental ∆H mexp (Tm ) values. The difference between ∆H mth (Tm ) and ∆H mexp (Tm ) can be directly connected with

38

Thermal and Thermodynamic Stability of Nanomaterials

the occurrence of pre-melting phenomena and exploited to estimate the thickness δ of the surface layer involved in such processes.

Fig. 3. The experimentally observed and theoretically expected latent heats of melting, respectively ∆H mexp (Tm ) and ∆H mth (Tm ) , as a function of the experimental melting points, Tm , for the mesoscopic Sn particles. To such aim, it must be first noted that the ratio ∆H mexp (Tm ) ∆H mth (Tm ) between the experimental, ∆H mexp (Tm ) , and theoretical, ∆H mth (Tm ) , values represents a measure of the molar fraction xb (Tm ) of Sn atoms undergoing the solid-to-liquid transition at a temperature Tm . The physical meaning of xb (Tm ) can be further clarified by defining it as the number of moles of Sn atoms not involved in pre-melting processes per mole of Sn atoms in the form of mesoscopic particles. Therefore, the quantity xb (Tm ) can be exploited to estimate the number χ b (Tm ) of moles of Sn atoms not involved in pre-melting processes per particle. Under the assumption that the Sn particles have spherical shape with radius r, the total number np of mesoscopic Sn particles per mole of Sn can be roughly calculated by the expression 3 M 4 π ρ r 3 , where M is the molar mass of Sn and ρ the mass density of solid Sn. Of course, the quantity χ b (Tm ) will be equal to the ratio xb (Tm ) np between the number xb (Tm ) of moles of Sn atoms not involved in pre-melting processes per mole of Sn atoms and the total number np of Sn particles per mole of Sn. Both quantities xb (Tm ) and χ b (Tm ) can be evaluated starting from tabulated data [68]. The obtained estimates are shown in Fig. 4 as a function of the average particle radius r. The molar fraction xb (Tm ) of Sn atoms not involved in pre-melting processes at the particle surface undergoes a marked decrease as the average radius r of the Sn particles decreases. The number np of particles per mole of solid Sn undergoes a hyperbolic increase as the particle average volume decreases. Then, the xb (Tm ) variation corresponds to a considerable decrease of the number χ b (Tm ) of moles of Sn atoms not involved in pre-melting phenomena at the particle surface as the particle radius r decreases. Accordingly, the thermal behavior of Sn particles is increasingly affected by the premelting of surface layers of thickness δ as the particle size becomes smaller.

Materials Science Forum Vol. 653

39

Precisely the correlation between the volume occupied by Sn atoms in solid phase after premelting has occurred and the number χ b (Tm ) of Sn moles undergoing a solid-to-liquid transition at a temperature Tm can be exploited to gain information on the extent of surface pre-melting. In fact, 4 3

4 3

χ b (Tm ) = π (r − δ )3 ρ s ≈ π (r 3 − 3 r 2 δ ) ρ s .

(11)

Fig. 4. (a) The molar fraction xb (Tm ) of Sn atoms not involved in pre-melting phenomena at the particle surface and (b) the number χ b (Tm ) of moles of Sn atoms not involved in pre-melting processes per particle as a function of the average particle radius r.

Thus, the thickness of the surface layer affected by pre-melting processes can be expressed as

3 χ b (Tm ) . (12) 4π r 2 ρs The δ estimates obtained are shown in Fig. 5 as a function of the average particle radius r. The plot obtained clearly indicates that pre-melting phenomena involve a surface layer the thickness δ of which on the average increases with a roughly sigmoidal trend as the particle radius r decreases. Although no definite conclusion can be drawn, this suggests that the curvature of the particle surface can play an important role in the physics of pre-melting processes. In particular, it seems that the higher the surface curvature, the thicker the surface layer prone to pre-melting. In the light of the relationship between the surface curvature and the average coordination number of surface species [64,65], it is tempting to connect the capability of a given surface to undergo pre-melting with the degree of chemical unsaturation of the surface atoms.

δ ≈r−

40

Thermal and Thermodynamic Stability of Nanomaterials

Fig.5. The average thickness δ of the surface layer that undergoes pre-melting processes as a function of the average particle radius r. However, it must be noted that the different δ values obtained have been worked out at different temperatures Tm . The relationship between these two quantities is pointed out in Fig. 6, where the thickness of the pre-molten surface layer is shown as a function of the melting point Tm .

Fig.6. The average thickness δ of the surface layer that undergoes pre-melting processes as a function of the particle melting point Tm . The points in the plot arrange according to a smooth curved trend, with the δ values decreasing as the temperature Tm increases. In general terms, such trend is quite counterintuitive. In fact, it could be reasonably expected that the thickness δ of the pre-molten surface layer increases as the temperature Tm increases. The data set in Fig. 6 indicates instead exactly the opposite. Therefore, it can be surmised that curvature effects prevail over thermal ones. Accordingly, it can be conjectured in first approximation that the increase of the particle curvature determines an increase of the thickness of the surface layer involved in pre-melting phenomena. However, more refined experimental data are necessary to pursue the research further along such direction. Severe limitations in the thermodynamic approach sketched above are also met when it is applied to roughly estimate the temperature at which pre-melting processes take place. In principle, the knowledge of approximate δ values permits the utilization of Eqs. 3 and 4 to indirectly evaluate the

Materials Science Forum Vol. 653

41

pre-melting points Tpm for the different particles considered. Nevertheless, the obtained estimates will be necessarily quite rough. In fact, Eqs. 3 and 4 include the free energies γ sl (Tm ) , γ sv (Tm ) and

γ lv (Tm ) of the solid-liquid, solid-vapor and liquid-vapor interfaces. Also in this case, these quantities will be affected by both surface curvature of particles and thermal effects, intimately superimposed and intertwined [69]. Unfortunately, no information is available suggesting how such free energies change with temperature and particle size. The pre-melting point estimates Tpm worked out by using Eqs. 3 and 4 as well as the tabulated values of the quantities there included are shown in Fig. 7 as a function of the average particle radius r. Such results have been obtained from calculations carried out with constant tabulated γ sl (Tm ) , γ sv (Tm ) and γ lv (Tm ) values, equal to about 0.055, 0.68 and 0.55 J m-2 respectively [70].

Fig.7. The estimated pre-melting point Tpm as a function of the average particle radius r. Data arrange according to a decreasing trend. Correspondingly, the pre-melting point Tpm decreases as the particle radius r increases, which represents a counterintuitive behavior. In fact, the plot in Fig. 7 suggests that pre-melting processes are facilitated in larger particles, which contrasts with the generally accepted evidence that pre-melting processes become increasingly favored as the system size decreases and the curvature of the particle surface increases [8,10,12,52-55]. Even most important, the pre-melting points Tpm for the smallest particles are higher than their melting points

Tm , which is of course unacceptable. This suggests that the γ sl (Tm ) , γ sv (Tm ) and γ lv (Tm ) values change with the particle size, although no clue is available to work out such variation. In particular, a decrease of pre-melting points Tpm is obtained when the difference

γ sv (Tpm ) − γ sl (Tpm )(1 − 2 δ r ) − γ lv (Tpm ) increases. Therefore, it can be reasonably expected that the quantities γ sl (Tm ) , γ sv (Tm ) and γ lv (Tm ) exhibit a dependence on the particle radius r such that they increase as it decreases. Furthermore, it is worth noting that the above mentioned difference increases only if the rate of increase of γ sv (Tm ) is higher than the rates of increase of γ sl (Tm ) and

γ lv (Tm ) . According to all of these observations, the most reliable pre-melting point Tpm estimates are the ones for the largest Sn particles. These indicate that a particle in the size range between 40 and 50 nm undergoes pre-melting processes at about 170 K, whereas melting takes place around 501 K. Taking into account that the melting point Tm for bulk Sn systems is equal to 505 K [68], the premelting point Tpm of about 170 K obtained for the largest mesoscopic particles can be also

42

Thermal and Thermodynamic Stability of Nanomaterials

considered as a good estimate for the pre-melting point of a massive Sn crystal with planar solidvapor interfaces [69]. In the light of these considerations, Eqs. 3 and 4 can be more usefully exploited to gain indirect information on the γ sl (Tpm ) , γ sv (Tpm ) and γ lv (Tpm ) quantities for the Sn particles with radius r in the range between 40 and 50 nm. A suitable algebraic manipulation of Eq. 4 leads to the expression  

γ sv (Tpm ) − γ sl (Tpm )1 −

2δ   − γ lv (Tpm ) = δ ρ l ∆Gl (Tpm ) − ρ s ∆Gs (Tpm ) . r 

[

]

(13)

As far as δ