Precipitates and lamellar microstructures in NiTi films

Precipitates and lamellar microstructures in NiTi films

Materials Science and Engineering A 378 (2004) 437–442 Precipitates and lamellar microstructures in NiTi films Michael J. Vestel a,∗ , David S. Grumm...

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Materials Science and Engineering A 378 (2004) 437–442

Precipitates and lamellar microstructures in NiTi films Michael J. Vestel a,∗ , David S. Grummon b a

Laboratory for Ultra Small Technologies Engineering and Research (LUSTER), Engineering Division, One Cyclotron Road, MS71R0259 National Laboratory, Berkeley, CA, USA b Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI, USA Received 24 June 2003; received in revised form 24 August 2003

Abstract The crystallization process in thick sputtered amorphous films was examined using differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). Crystalline grains always nucleated first at the surface, rapidly grew laterally until impingement, and then grew inward to form columnar grains. Surface roughness delayed the onset of surface nucleation. For very smooth surfaces, crystallization of columnar grains nucleated quickly, but after lateral impingement, inward growth was more sluggish. Multiple DSC exotherms observed in these films suggested that additional nucleation events occurred, and TEM study of partially transformed films confirmed that secondary nucleation events resulted in distinct microstructual layers. These were perfectly stratified in the plane of the film, with single grain aspect ratios that were radically different from those of surface-nucleated columnar grains. After crystallization was largely complete, Ti-rich particles, Ti2 Ni, nucleated in high concentrations at the columnar/plate grain interface. These precipitates were mostly observed in the columnar grains with a maximum density at the columnar/plate grain interface. It is proposed that excess titanium was driven into the amorphous region ahead of the crystal/amorphous interface during crystallization, leading to a high concentration of titanium and, thus, precipitates at the columnar/plate grain interface. © 2004 Elsevier B.V. All rights reserved. Keywords: Transmission electron microscopy (TEM); Shape memory alloys (SMA); Thin films; Crystallization; Precipitates

1. Introduction The shape memory (SME) and superelastic effects (SE) involve a thermally- and/or mechanically-induced solid state, allotropic phase transformation between a ductile martensitic phase and a stiffer austenite phase, and have been thoroughly described [1–4]. Crystalline NiTi films made by sputtering are known to possess SE properties and display a robust SME [5–9] applicable where resilient mechanical response is essential, or where thermal actuation or sensing is desired. Photolithographically machined microelectromechanical systems (MEMS) may benefit from these effects for various reasons: very high work energy densities (25 MJ/m3 ) are possible [10] and outstanding fatigue resistance and high damping capacity can be delivered in a biocompatible alloy.

∗ Corresponding author. Tel.: +1-510-486-6596; fax: +1-510-486-6596. E-mail address: [email protected] (M.J. Vestel).

0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.338

An application in the biomedical field that motivates the present study is the fabrication of micro-needles [11] for transdermal or subdermal fluid transport [12], including the integration of micro-needles with silicon structures [13] in bio-MEMS assemblies. The direct deposition of crystalline NiTi alloys onto silicon is complicated by mismatched thermal expansion coefficients [14]. Large tensile stresses induced when NiTi films cool can cause catastrophic delamination in films thicker than 5–7 ␮m [7]. This obstacle can be overcome by using low temperature deposition to obtain an amorphous film that can then be lithographically etched, released from the substrate, and crystallized in an annealing step. Amorphous films have the additional advantage that HF etchants yield more precise etch profiles and smoother surfaces [15]. Crystallization is therefore preferably done after micromachining operations are largely complete. An additional advantage of deposition of the amorphous phase is that substantial titanium supersaturation can be achieved in the solid state. This allows post-deposition annealing to develop useful distributions of Ti-rich precipitates

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that strengthen the alloy against dislocational slip [8,9,16], permitting higher levels of recovery force and strain. Exploiting these advantages requires good understanding of the crystallization (devitrification) process in sputtered amorphous NiTi.

2. Background Moberly et al. [5] confirmed that amorphous deposits crystallized to the ordered B2 (CsCl) phase and measured a crystallization enthalpy of 21.6 J/g at 490 ◦ C in differential scanning calorimetry (DSC) experiments. Gisser et al., [17] found that NiTi thin films deposited onto (1 0 0)-silicon substrates at elevated temperature (460 ◦ C) were crystalline and had (1 1 0) texture. This study showed that deposition temperatures could be lowered to 350 ◦ C after nucleation of the crystalline phase at >460 ◦ C. It was later shown by Hou and Grummon [6] that (1 1 0) texture disappeared at deposition temperatures above 425 ◦ C. Chang and Grummon [18] showed that the crystallization temperature, Tx , at 10 K/min decreased with increasing Ti content, from 490 ◦ C for Ni52.6 Ti47.4 at.% , to 475 ◦ C for Ni49 Ti51 , and observed a systematic increase of Tx with heating rate that allowed estimates for the activation energy for crystallization that ranged from 385 kJ/mol for Ni49 Ti51 to 501 kJ/mol for Ni52.6 Ti47.4 . It was further shown that crystallization was entirely polymorphic. Grummon and Zhang [19] showed that isothermal crystallization of NiTi on (1 0 0)-Si produces a transient increase in tensile film stress of approximately 180 MPa. The time for this stress to develop was analyzed as a function of the annealing temperature to give an activation energy for growth of the crystalline phase of 477 kJ/mol. Coherent plate precipitates 0.5–1 nm thick and 10–20 nm across, were observed by Ogawa, Kajiwara and co workers [9,20] in Ti-rich films crystallized from the amorphous state at temperatures below Tx . These precipitates were associated with strengthening of the austenite and thus brought about high levels of recovery force and recoverable strain. Magnetron sputtered Ti51 Ni49 films annealed by Luo et. al. [21] showed both Ti2 Ni and Ni3 Ti precipitates. Their size, distribution and morphology were shown to be a function of annealing condition and to affect the transformation temperatures. Ishida et. al. [22,23] also observed that the size and distribution of Ti2 Ni precipitates affected the martensitic transformation temperatures. In the latter case, both interand intra-granular precipitates were observed, depending on heat treatment conditions. The present work was undertaken to clarify details of the crystallization process in relatively thick, free-standing sputtered NiTi films, and to study precipitate formation during low temperature (390–450 ◦ C) crystallization of Ti-rich amorphous films. Such low temperature, post-processing crystallization anneals would be favorable for post-CMOS modular integration.

3. Experimental procedures Near-equiatomic NiTi films were deposited on stainless steel (SS) and silicon substrates by dc diode magnetron sputtering as described previously [1]. Films deposited on stainless steel were films 22 ␮m thick, brittle, with a dull metallic luster, and a pronounced surface roughness inherited from the substrate finish. Large pieces were easily peeled from the substrate. A 13 ␮m thick Ti-rich amorphous film was sputterdeposited on a 125 mm polished (1 0 0)-silicon substrate. This film was tough, very smooth, and had a bright metallic luster. The metallized wafer was diced and the films delaminated by repeated thermal shock cycles between liquid nitrogen and 100 ◦ C water. X-ray diffraction confirmed that both films were amorphous. Individual samples from these films were isothermally or isochronally annealed in a power-compensated DSC under a nitrogen atmosphere. For isothermal anneals, the furnace and reference pan were equilibrated at the desired temperature, the furnace lid removed, and the sample quickly placed into the furnace just prior to recording data. The heating rate prior to the isothermal hold was therefore quite high, and probably exceeded 1000 K/min. A thorough description of the DSC procedure and a complete treatment of the crystallization kinetics inferred from the DSC results are given in [1–4]. Transmission electron microscopy samples were prepared by the wedge method [24] followed by multiple ion milling steps. Fifty individual energy dispersive X-ray spectra were taken using a 1.4 nm nanoprobe along a line to produce a line-scan across a precipitate on a Philips CM 200/FEG. In addition, elemental mapping was used to show two-dimensional distributions of Ni and Ti. This was done by recording two images, one before and one after the electron energy loss spectroscopy (EELS) ionization edge and dividing the post-edge image by the pre-edge image. The resulting ‘jump ratio’ image yields contrast due to elemental distribution only, with thickness and diffraction contrast eliminated [25].

4. Results 4.1. Differential scanning calorimetry (DSC) Amorphous NiTi films released from both stainless steel (rough-surface films) and silicon substrates (smooth) were isothermally crystallized in the calorimeter at temperatures between 450 and 390 ◦ C for times as long as 600 min. The lowest crystallization temperature at which an exothermic peak could be easily discerned was 420 ◦ C for the films release from both substrates. TEM examination, however, indicated that films released from silicon and annealed at 400 ◦ C for 400 min were fully crystalline, but that those crystallized at 390 ◦ C for 600 min did not fully crystallize, and contained surface-nucleated columnar grains impinging

Heat Flow

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Table 1 Activation energies (Q) for rough (SS) and smooth (Si) surfaced films

τ τ 0

439

SS, 430˚C 20 mW/g 25

Silicon, 425˚C 50

Substrate (film surface)

Q (kJ/mol)

Q (kcal/mol)

Stainless steel (rough) Silicon (smooth)

347 430

83 103

75

Crystallization Time (min) Fig. 1. Typical DSC curves for isothermal anneals. The film released from the rough surfaced stainless steel (SS) substrate was annealed at 430 ◦ C and showed only one peak. The smooth surfaced film released from silicon and crystallized at 425 ◦ C clearly shows two distinct peaks.

on a remnant amorphous stratum in the center of the film. As the annealing temperature was lowered from 440 to 420 ◦ C, the incubation time, τ, required to establish a population of critical nuclei of the crystalline phase, increased, and the devitrification exotherm broadened as diffusion became progressively more sluggish [26]. A single exothermic crystallization peak was observed for films released from SS. In contrast, all the films released from silicon displayed double exothermic peaks suggestive of separate nucleation regimes. An example of each is shown in Fig. 1. Note that the incubation times are markedly shorter for the smooth-surface compared to the rough-surface condition. The tendency for crystallites to surface-nucleate more quickly on smooth-surface specimens has been attributed to enhanced surface diffusion [2] in the former case. The activation energy (Q) based on simple Arrhenius law analysis of times for 50% crystallization at various temperatures, have been determined [1] and are summarized in Table 1. The results for Q were within the range of previously reported values for NiTi, as well as other metallic glass systems [5,18,19,27]. This may be explained by temperature dependent activation energies.

4.2. Transmission electron microscopy (TEM) For rough-surface materials giving a single DSC crystallization peak, previous work illustrated that the crystalline phase had simultaneously nucleated at both free surfaces [1–4]. Lateral (in-plane) grain impingement occurred quickly and was followed by growth of columnar grains in the direction of the film-plane normal with a nominally planar interface. The columnar grains, typically ∼1 ␮m in diameter, were equiaxed in the film-plane. Partially crystallized specimens contained two outer zones of surface-nucleated columnar grains, and an inner zone of remnant, perfectly homogenous amorphous metal. For free-standing films from polished silicon, double peaks in the DSC spectra suggested that multiple nucleation and growth regimes operated, each having distinct kinetic parameters. This is born out by TEM observation that revealed inhomogenous microstructures containing both surface-nucleated columnar grains and much wider plate shaped grains that had clearly nucleated in the interior, Figs. 2 and 3. These bulk-nucleated plate shaped grains probably account for the second of the two crystallization peaks. The contrast difference between the two grain types is illustrated in Fig. 2, which shows only the tops of three plate shaped grains, while in Fig. 4, the bright/dark field contrast shows a 3.4 ␮m wide plate grain at least 3 ␮m thick. Other TEM observations showed the plate grains could be as wide as 5 ␮m. The central 1/3 of these films was plate shaped grains.

Fig. 2. Transverse TEM foil of a film annealed at 420 ◦ C for 200 min illustrates difference in morphology between columnar grains and plate shaped grains. Close-up is shown in Fig. 3.

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Fig. 3. Close-up from Fig. 2. Note the high density of precipitates in the columnar grains and the penetration of precipitates into only the first 100 nm of the plate shaped grains.

Smooth-surface films that were only partially crystallized contained two columnar-grain strata, each nucleated at a free surface, together with a central region containing plate shaped, bulk-nucleated grains. Residual untransformed amorphous material remained between these crystalline layers, situated on either side of the plate grain zone. Fig. 5 shows an example in which columnar grains (top, right) are

Fig. 5. Three of five strata illustrating plate shaped grains nucleated in the film interior, separately from the columnar grains. The lack of precipitates is clearly evident; film was crystallized at 440 ◦ C for 12 min.

separated from plate shaped grains (lower left) by a 1 ␮m thick amorphous layer. The plate shaped strata generally contained wide, flat grains, indicating that crystallite growth rate was substantially higher in the lateral rather than the through-thickness direction. These complex stratified microstructures were observed in samples annealed at other temperatures as well. An example appears in the sample annealed at 425 ◦ C for 120 min, shown in Fig. 5. The two DSC exotherms observed for this film, thus, likely correspond to the separate nucleation and growth of the two crystalline microstructural zones. 4.3. Precipitates

Fig. 4. Columnar grains in the top left corner have long thin single grain morphology while the strata on the right bottom of the image are wide, flat grains crystallized at 425 ◦ C for 120 min.

Figs. 2–4 all show a 250 nm thick zone on both sides of the interface between surface-nucleated columnar grains and bulk-nucleated plate grains that contains large numbers of equiaxed precipitates, approximately 10–60 nm in diameter. The interiors of the plate shaped grains were generally free of these precipitates, but the presence of the particles is seen to extend, with decreasing frequency, some 1–2 ␮m into the columnar region. In the columnar region little tendency for precipitation at grain boundaries was observed. The precipitate density reaches an apparent maximum at the interface proper. X-ray fluorescence microanalysis experiments clearly indicated that these precipitates were enriched in titanium, leading to the tentative conclusion that they are incoherent particles of the Ti2 Ni phase. Results from a line-scan for Ti and Ni, taken along the path indicated in Fig. 3, is shown in Fig. 6. Jump ratio images resulting from electron energy loss measurements for a sample crystallized at 420 ◦ C for 200 min (Fig. 7) additionally indicate a very large increment in titanium content in a narrow zone, no more than 50 nm

Atomic Percent Ti ( ) or Ni ( )

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Plate Shaped Grain

60 58 56 52

60nm Particle

Columnar Grain

Ni Kα1

54 50 48 46 44 42 40

Ti Kα1

0

20

40

60

80

100

120

140

160

180

Line Scan Position (nm)

Fig. 6. Line-scan shown in Fig. 3 across a 60 nm particle. A significant X-ray signal is from the matrix, which is equiatomic and accounts for the signal not rising to 66% Ti for the Ti2 Ni.

Fig. 7. Jump ratio images show elemental distributions: bright contrast in (a) indicates a high concentration of Ti at the interface and in the surround particles while dark contrast in (b) indicates a depletion of Ni.

wide, directly on the interface. These jump ratio images also reveal the precipitates are Ti-rich likely Ti2 Ni. Although the precipitates near the interface almost certainly formed after crystallization was complete (none were found in partially crystallized films) the distribution of the particles within the columnar grains indicates that, although excess titanium was rejected ahead of the columnar grain crystallization front, crystallization could still proceed in the presence of excess titanium. A continuous gradient in titanium concentration was apparently created in the columnar grain region, with titanium content increasing with depth below the free surface. It is likely then, that the columnar crystallization reaction pushed a transient spike of substantial titanium enrichment ahead of the moving phase-boundary. It is not clear, however, that the phase-front velocity was limited by the rate of titanium diffusion in the glassy phase (as would be the case for solute partition during solidification of liquid alloys), since it has been shown in several studies [28] that excess titanium actually encourages crystallization1 Ti-rejection may simply result from a difference, between nickel and titanium, in the jump-rate across the crystal-amorphous interface. A higher interfacial jump-rate for Ni would produce Ti-enrichment ahead of the interface. The interface is not at 1 The crystallization temperature has been found to decrease with increasing Ti-content [28] and apparently reaches a minimum near the composition Ti2 Ni.

441

chemical equilibrium and a steady state condition would not be achieved. Thus, the depth of the Ti-enriched zone would depend on the relationship between the interface velocity and the nickel diffusion rate. In this case the interface velocity (presumably controlled by the slower titanium interfacial jump-rate) controls the level of Ti-enrichment, rather than the amorphous-phase Ti diffusion rate directly controlling the interface velocity. In the case of the plate shaped grains it is not clear whether significant Ti-rejection ahead of the phase-front has occurred since the precipitates seen at the interface in these grains may have originated from titanium rejected ahead of the columnar grains. The morphology of these grains, whose aspect ratio (relatively shallow, wide plates) differs sharply from that of the columnar grains, is consistent with a relatively high lateral growth rate (in the plane of the film), combined with a lower crystallite nucleation rate. The high lateral crystallite growth velocity is relatively easy to rationalize for surface-nucleated grains, since the negative volume dilatation associated with crystallization is more easily accommodated at the free surfaces. This, however, cannot explain the apparently high lateral growth rates for plate grains nucleated in the interior. It may be that internally equilibrated stresses play a role: densification during crystallization of the columnar surface-nucleated regions would tend to place the amorphous central zone in balanced biaxial compression, storing strain energy that could subsequently be released most effectively by lateral growth of internally nucleated crystalline grains. Titanium segregation has also been observed in Ti-rich films by Kajiwara et al. [8,9], producing a small number of equiaxed Ti2 Ni particles, and additionally, large numbers of extremely thin Ti-rich Guinier–Preston zone-like structures. Two differences between this work and the present study merit mention. First, in the Kajiwara study, TEM foils were made in the plane of the film rather than in the transverse direction, so the phase-fronts observed represent crystal/amorphous interfaces only in the lateral growth direction. Secondly, the Kajiwara study used a 20 K/min heating rate to approach the isothermal annealing temperature, whereas the specimens in the present study were brought very rapidly to the annealing temperature to allow for precise control of the degree of crystallization. It may be that the lower heating rate in the Kajiwara study encourages GP-zone formation that effectively tied up excess titanium and delayed the formation of the equilibrium Ti2 Ni phase.

5. Conclusions Low temperature, post-deposition anneals successfully crystallized thick free-standing NiTi films, but under certain circumstances resulted in substantial microstructural inhomogeneity. From this initial study of crystallization of films released from both rough stainless steel and smooth

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(1 0 0)-silicon substrates, we additionally conclude the following: (1) Crystallization of thick, free-standing amorphous NiTi films in a reasonable time requires annealing temperatures of at least 400 ◦ C. (2) Crystallization nucleates simultaneously at both free surfaces. Incubation time increases with decreasing temperature, and transformation rates display activation energies between 346 and 430 kJ/mol. Roughened surfaces appear to retard nucleation. (3) Initial rapid lateral growth of surface-nucleated crystallites leads to early impingement of the grains within the plane of the film, after which continued growth normal to the surface proceeded at a substantially slower rate. The final crystalline grain size shows little dependence on annealing temperature. (4) In Ti-rich alloys, Ti is rejected ahead of the crystalamorphous interface, but excess titanium in the amorphous phase does not prevent crystallization. (5) Additional bulk nucleation events may produce stratified regions with relatively shallow, plate shaped grains. The lateral growth rate for these grains was also faster than the through-thickness rate. The resultant inhomogenous laminar microstructure may account for the occasional observation of multiple martensitic transformation events.

Acknowledgements The films used in this study were prepared by Thomas LaGrange and Wangyang Ni at Michigan State University. The authors also wish to thank Professor Nitash P. Balsara and Hany Eitouni, Department of Chemistry, UC Berkeley, for use of the DSC, and Dr. Eric Stach, Dr. Tamara Radetic and Chris Nelson, Lawrence Berkeley National Laboratory, for assistance with TEM.

References [1] M.J. Vestel, D.S. Grummon, R. Gronsky, A.P. Pisano, Acta Mater. 51 (2003) 5309–5318. [2] M.J. Vestel, D.S. Grummon, Microstructures observed in crystallized NiTi films, in: S.M. Russel, A. Pelton (Eds.), SMST-2003: Proceedings of the International Conference on Shape Memory and Superelastic Technologies, Asilomar, CA, USA, 4–8 May 2003, in press.

[3] M.J. Vestel, D.S. Grummon, A. Pisano, Crystallisation of sputtered NiTi films, in: ASME International Mechanical Engineering Congress and Exposition on MEMS, Washington, DC, USA, 15–21 November 2003, in press. [4] M.J. Vestel, Effect of devitrification temperature on the microstructure of NiTi films, Ph.D. Thesis, Materials Science and Engineering, University of California, Berkeley, 2002. [5] W.J. Moberly, J.D. Busch, A.D. Johnson, M.H. Berkson, in: M. Chen, M.O. Thompson, R.B. Schwarz, M. Libera (Eds.), Phase Transformation Kinetics in Thin Films Symposium, vol. 230, Material Research Society, Anaheim, CA, USA, 1991, pp. 85–90. [6] L. Hou, D.S. Grummon, Scr. Metall. Mater. 33 (1995) 989–995. [7] D.S. Grummon, T. LaGrange, J. Zhang, in: S.M. Russel A. Pelton (Eds.), SMST-2000: Proceedings of the International Conference on Shape Memory and Superelastic Technologies, Asilomar, CA, USA, 30 April 2000, pp. 183–195. [8] S. Kajiwara, K. Ogawa, T. Kikuchi, T. Matsunaga, S. Miyazaki, Philos. Mag. Lett. 74 (1996) 395–404. [9] S. Kajiwara, T. Kikuchi, K. Ogawa, T. Matsunaga, S. Miyazaki, Philos. Mag. Lett. 74 (1996) 137–144. [10] P. Krulevitch, A.P. Lee, P.B. Ramsey, J.C. Trevino, J. Hamilton, M.A. Northrup, J. MEMS 5 (1996) 270–282. [11] L. Lin, A.P. Pisano, J. MEMS 8 (1999) 78–84. [12] S. Henry, D.V. McAllister, M.G. Allen, M.R. Prausnitz, in: Eleventh Annual International Workshop on MEMS, Heidelberg, Germany, IEEE, 1998, pp. 494–498. [13] A.E. Franke, Polycrystalline silicon–germanium films for integrated microsystems, Ph.D. Thesis, Electrical Engineering and Computer Sciences, University of California, Berkeley, 2000. [14] L. Haji, P. Joubert, M. Guendouz, N. Duhamel, B. Loisel, in: M. Chen, M.O. Thompson, R.B. Schwarz, M. Libera (Eds.), Phase Transformation Kinetics in Thin Films Symposium, vol. 230, Material Research Society, Anaheim, CA, USA, 1991, pp. 177–182. [15] E. Makino, T. Mitsuya, T. Shibata, Sens. Actuators, A 79 (2000) 251–259. [16] T. Kikuchi, K. Ogawa, S. Kajiwara, T. Matusnaga, S. Miyazaki, Y. Tomota, Philos. Mag. A 78 (1998) 467–489. [17] K.R.C. Gisser, J.D. Busch, A.D. Johnson, A.B. Ellis, App. Phys. Lett. 61 (1992) 1632–1634. [18] L. Chang, D.S. Grummon, Philos. Mag. A 76 (1997) 191–219. [19] D.S. Grummon, J. Zhang, Phys. Status Solidi A 186 (2001) 17–39. [20] K. Ogawa, T. Kikuchi, S. Kajiwara, T. Matsunaga, S. Miyazaki, Coherent subnanometric plate precipitates formed during crystallization of as-sputtered Ti–Ni films, J. Phys. IV 7 (1997) 221–226. [21] H. Luo, F. Shan, Y. Huo, Y. Wang, Thin Solid Films 339 (1999) 305–308. [22] A. Ishida, M. Sato, A. Takei, S. Miyazaki, Mater. Trans. JIM 36 (1995) 1349–1355. [23] A. Ishida, M. Sato, A. Takei, Y. Kase, S. Miyazaki, in: Icomat 95, vol. 5, Lausanne, Switzerland, Editions de Physique, 1995, pp. 701–705. [24] J.M. Phelps, Microsc. Microanal. 4 (1998) 128–132. [25] C.C. Ahn, O.L. Krivanek, R.P. Burgner, M.M. Disko, P.R. Swann, Eels Atlas (Gatan Inc.), 1983. [26] A.L. Greer, in: P. Haasen, R.I. Jaffee (Eds.), Acta Scr. Metall. Proceedings Series, vol. 3, Pergamon Press, New York, 1985, pp. 94–107. [27] J.Z. Chen, S.K. Wu, J. Non-Cryst. Solids 288 (2001) 159–165. [28] L. Chang, D.S. Grummon, Philos. Mag. A 76 (1997) 163–189.