On glass formation thermodynamics: Enthalpy vs. Entropy

Wang Li-Min; Liu Ri-Ping; Tian Yong-Jun

doi:10.7498/aps.69.20200707

Abstract

Glass formation thermodynamics usually concerns the liquid-crystal Gibbs free energy difference. But, in practice, its efficiency in predicting the occurrence of the glass transition of materials and guiding the composition design is quite quantitative. In particular, it remains to be clarified to understand the relationship between and the contributions to the two fundamental quantities of enthalpy and entropy involved herein. In this paper, we study the relation between the enthalpy and the entropy involved in glass formation of various materials, and find that they are strongly correlated with each other. Theoretical and experimental analyses indicate the intrinsic correlation of the entropy of fusion with other key parameters associated with glass formation like melting viscosity and enthalpy of mixing, which confirms the close relation between the entropy of fusion and glass formation. Close inspection finds that the low entropy of fusion benefits the glass formation. Owing to the fact that the two glass-formation key variables of viscosity and enthalpy can be addressed by the entropy of fusion, we propose that the entropy of fusion be able to serve as a representative thermodynamic quantity to understand the glass formation in materials. The reliability in understanding the glass formation in terms of entropy of fusion is further verified. The studies provide a new reference for developing the glass formation thermodynamics.

Keywords:

Authors and contacts

State Key Laboratory of Metastable Materials Science and Technology, College of Materials Science and Engineering, Yanshan University, Qinhuangdao 066004, China

Corresponding author: Wang Li-Min, limin_wang@ysu.edu.cn ; Liu Ri-Ping, riping@ysu.edu.cn ; Tian Yong-Jun, fhcl@ysu.edu.cn

Funds: Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51421091), the National Key R&D Program of China (Grant No. 2018YFA0703602), the National Natural Science Foundation of China (Grant No. 51801174), and the High-level Talents Funded Projects of Hebei Province, China (Grant No. BJ2018021)

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References

[1]	Anderson P W 1995 Science 267 1615 Google Scholar
[2]	Angell C A, Ngai K L, McKenna G B, McMillan P F, Martin S 2000 J. Appl. Phys. 88 3113 Google Scholar
[3]	汪卫华 2013 物理学进展 33 177 Wang W H 2013 Prog. Phys. 33 177
[4]	Turnbull D 1969 Contemp. Phys. 10 473 Google Scholar
[5]	Turnbull D, Cohen M H 1960 Modern Aspects of the Vitreous State (London: Butterworth)
[6]	Uhlmann D R 1977 J. Non-Cryst. Solids 25 42 Google Scholar
[7]	Schmentzer J 2005 Nucleation Theory and Applications (New York: Wiley-VCH)
[8]	Kalikmanov V I 2013 Nucleation Theory (Netherlands: Springer)
[9]	Klement W, Willens R H, Duwez P O L 1960 Nature 187 869
[10]	Jiang Z, Hu X, Zhao X 1982 J. Non-Cryst. Solids 52 235 Google Scholar
[11]	Peker A, Johnson W L 1993 Appl. Phys. Lett. 63 2342 Google Scholar
[12]	Highmore R J, Greer A L 1989 Nature 339 363 Google Scholar
[13]	Ottou Abe M T, Viciosa M T, Correia N T, Affouard F 2018 Phys. Chem. Chem. Phys. 20 29528 Google Scholar
[14]	Atawa B, Correia N T, Couvrat N, Affouard F, Coquerel G, Dargent E, Saiter A 2019 Phys. Chem. Chem. Phys. 21 702
[15]	Kauzmann W 1949 Chem. Rev. 43 219
[16]	Angell C A 1995 Science 267 1924 Google Scholar
[17]	Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200 Google Scholar
[18]	Mukherjee S, Schroers J, Johnson W L, Rhim W K, 2005 Phys. Rev. Lett. 94 245501 Google Scholar
[19]	Lu Z P, Ma D, Liu C T, Chang Y A 2007 Intermetallics 15 253 Google Scholar
[20]	Yang B, Du Y, Liu Y 2009 Trans. Nonferrous Met. Soc. China 19 78 Google Scholar
[21]	Chattopadhyay C, Satish Idury K S N, Bhatt J, Mondal K, Murty B S 2016 Mater. Sci. Technol. 32 380 Google Scholar
[22]	Mondal K, Chatterjee U K, Murty B S 2003 Appl. Phys. Lett. 83 671 Google Scholar
[23]	Chen H S 1980 Rep. Prog. Phys. 43 353 Google Scholar
[24]	Kim D, Lee B J, Kim N J 2004 Intermetallics 12 1103 Google Scholar
[25]	Sun K H 1947 J. Am. Ceram. Soc. 30 277 Google Scholar
[26]	Rawson H 1956 Proc. IV Intern. Congress on Glass (Paris: Impremenic Chaix) p62
[27]	Xia L, Li W H, Fang S S, Wei B C, Dong Y D 2006 J. Appl. Phys. 99 026103 Google Scholar
[28]	Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817 Google Scholar
[29]	Takeuchi A, Inoue A 2000 Mater. Trans., JIM 41 1372 Google Scholar
[30]	Busch R, Liu W, Johnson W L 1998 J. Appl. Phys. 83 4134 Google Scholar
[31]	Singh P K, Dubey K S 2010 J. Therm. Anal. Calorim. 100 347 Google Scholar
[32]	Adam G, Gibbs J H 1965 J. Chem. Phys. 43 139 Google Scholar
[33]	Perepezko J H 2004 Prog. Mater. Sci. 49 263 Google Scholar
[34]	Fecht H J, Johnson W L 2004 Mater. Sci. Eng. A 375 2
[35]	Battezzati L 1994 Mater. Sci. Eng. A 178 43 Google Scholar
[36]	Battezzati L, Castellero A, Rizzi P 2007 J. Non-Cryst. Solids 353 3318 Google Scholar
[37]	Gallington L C, Bongiorno A 2010 J. Chem. Phys. 132 174707 Google Scholar
[38]	Gutzow I, Schmelzer J W P, Petroff B 2008 J. Non-Cryst. Solids 354 311 Google Scholar
[39]	Ji X, Pan Y 2007 J. Non-Cryst. Solids 353 2443 Google Scholar
[40]	Fultz B 2010 Prog. Mater. Sci. 55 247 Google Scholar
[41]	van de Walle A, Ceder G 2002 Rev. Mod. Phys. 74 11 Google Scholar
[42]	Manzoor A, Pandey S, Chakraborty D, Phillpot S R, Aidhy D S 2018 NPJ Comput. Mater. 4 47 Google Scholar
[43]	Ohsaka K, Trinh E H 1995 Appl. Phys. Lett. 66 3123 Google Scholar
[44]	Goldstein M, 1969 J. Chem. Phys. 51 3728 Google Scholar
[45]	Stillinger F H 1995 Science 267 1935 Google Scholar
[46]	Angell C A 2005 Phil. Trans. R. Soc. A 363 415 Google Scholar
[47]	Sastry S, Debenedetti P G, Stillinger F H 1998 Nature 393 554 Google Scholar
[48]	Bhatt J, Wu J, Xia J H, Wang Q, Dong C, Murty B S 2007 Intermetallics 15 716 Google Scholar
[49]	Ramakrishna Rao B, Gandhi A S, Vincent S, Bhatt J, Murty B S 2012 Trans. Indian Inst. Met. 65 559 Google Scholar
[50]	Zachariasen W H 1932 J. Am. Chem. Soc. 54 3841 Google Scholar
[51]	Johnson W L, Na J H, Demetriou M D 2016 Nat. Commun. 7 1
[52]	Jiusti J, Zanotto E D, Cassar D R, Andreeta M R B 2020 J. Am. Ceram. Soc. 103 921 Google Scholar
[53]	Minaev V S 1978 Amorphous Semiconductors-78 (Prague: AS ChSSR) p71
[54]	de Oliveira M F, Pereira F S, Bolfarini C, Kiminami C S, Botta W J 2009 Intermetallics 17 183 Google Scholar
[55]	Benson S W 1947 J. Chem. Phys. 15 367 Google Scholar
[56]	Myers R T 1979 J. Phys. Chem. 83 294 Google Scholar
[57]	Wessel M D, Jurs P C 1995 J. Chem. Inf. Comput. Sci. 35 841 Google Scholar
[58]	Wang L M, Richert R 2007 J. Phys. Chem. B. 111 3201 Google Scholar
[59]	Turnbull D, Cohen M H 1958 J. Chem. Phys. 29 1049 Google Scholar
[60]	郑兆勃 1979 金属学报 15 155 Zheng Z B 1979 Acta. Metall. Sin. 15 155
[61]	Hrubý A 1972 J. Phys. B 22 1187
[62]	Inoue A 2000 Acta Mater. 48 279 Google Scholar
[63]	Song W X, Zhao S J 2015 J. Chem. Phys. 142 144504 Google Scholar
[64]	Miedema A R, de Châtel P F, de Boer F R 1980 Phys. B+C 100 1 Google Scholar
[65]	Basu J, Murty B S, Ranganathan S 2008 J. Alloys Compd. 465 163 Google Scholar
[66]	Das N, Kulkarni U D, Pabi S K, Murty B S, Dey G K 2008 Defect Diffus. Forum 279 147 Google Scholar
[67]	Bhatt J, Dey G K, Murty B S 2008 Metall. Mater. Trans. A 39 1543 Google Scholar
[68]	Ray P K, Akinc M, Kramer M J 2008 22 nd Annu. Conf. Foss. Energy Mater (Pittsburgh) 2008 p474
[69]	Weeber A W 1987 J. Phys. F: Met. Phys. 17 809 Google Scholar
[70]	Pan Y, Zeng Y, Jing L, Zhang L, Pi J 2014 Mater. Des. 55 773 Google Scholar
[71]	Miracle D B 2006 Acta Mater. 54 4317 Google Scholar
[72]	Egami T, Waseda Y 1984 J. Non-Cryst. Solids 64 113 Google Scholar
[73]	Gargarella P, de Oliveira M F, Kiminami S, Pauly S, Kühn U, Bolfarini C, Botta W J, Eckert J 2011 J. Alloys Compd. 50 9
[74]	Hu Y C, Schroers J, Shattuck M D, O’Hern C S 2019 Phys. Rev. Mater. 3 085602 Google Scholar
[75]	Greer A L 1993 Nature 366 30
[76]	Zhang W, Liaw P K, Zhang Y 2018 Sci. China Mater. 61 2 Google Scholar
[77]	Lei Z, Liu X, Wu Y, Wang H, Jiang S, Wang S, Hui X, Wu Y, Gault B, Kontis P, Raabe D, Gu L, Zhang Q, Chen H, Wang H, Liu J, An K, Zeng Q, Nieh T G, Lu Z 2018 Nature 563 546 Google Scholar
[78]	Zhao L R, Li Z J, Gao Y Q, Bo H, Liu Y D, Wang L M 2016 Intermetallics 71 18 Google Scholar
[79]	Gibbs J H, DiMarzio E A 1958 J. Chem. Phys. 28 373 Google Scholar
[80]	Mansoori G A, Carnahan N F, Starling K E, Leland Jr T W 1971 J. Chem. Phys. 54 1523 Google Scholar
[81]	Takeuchi A, Amiya K, Wada T, Yubuta K, Zhang W, Makino A 2013 Entropy 15 3810 Google Scholar
[82]	Guo J, Bian X, Li X, Zhang C 2010 Intermetallics 18 933 Google Scholar
[83]	Li X, Song K, Wu Y, Ji H, Wang L 2013 Mater. Lett. 107 17 Google Scholar
[84]	Vincent S, Peshwe D R, Murty B S, Bhatt J 2011 J. Non-Cryst. Solids 357 3495 Google Scholar
[85]	Wang L M, Richert R 2007 Phys. Rev. Lett. 99 185701 Google Scholar
[86]	Wang W H 2012 Prog. Mater. Sci. 57 487 Google Scholar
[87]	Stillinger F H, Debenedetti P G 1999 J. Phys. Chem. B 103 4052 Google Scholar
[88]	Bendert J C, Gangopadhyay A K, Mauro N A, Kelton K F 2012 Phys. Rev. Lett. 109 185901 Google Scholar
[89]	Louzguine-Luzgin D V, Inoue A 2007 J. Mater. Res. 22 1378 Google Scholar
[90]	Uhlmann D R 1983 J. Am. Ceram. Soc. 66 95 Google Scholar
[91]	Jackson K A 2002 Interface Sci. 10 159 Google Scholar
[92]	Ediger M D, Harrowell P, Yu L 2008 J. Chem. Phys. 128 034709 Google Scholar
[93]	Gutzow I, Schmelzer J 1995 The Vitreous State (Berlin-New York: Springer)
[94]	Busch R, Schroers J, Wang W H 2007 MRS Bull. 32 620 Google Scholar
[95]	Wang L M, Tian Y, Liu R, Wang W 2012 Appl. Phys. Lett. 100 261913 Google Scholar
[96]	Senkov O N, Miracle D B, Mullens H M 2005 J. Appl. Phys. 97 103502 Google Scholar
[97]	Turnbull D 1981 Metall. Trans. B 12 217 Google Scholar
[98]	Li D, Herlach D M 1996 Phys. Rev. Lett. 77 1801 Google Scholar
[99]	Wang Q, Wang L M, Ma M Z, Binder S, Volkmann T, Herlach D M, Wang J S, Xue Q G, Tian Y J, Liu R P 2011 Phys. Rev. B 83 014202 Google Scholar
[100]	Hoffmann H J 2005 Phys. Chem. Glasses 46 570
[101]	Gao P, Tu W, Li P, Wang L M 2018 J. Alloys Compd. 736 12 Google Scholar
[102]	Pelton A D, Degterov S A, Eriksson G, Robelin C, Dessureault Y 2000 Metall. Mater. Trans. B 31 651 Google Scholar
[103]	Hillert M 2008 Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis (London: Cambridge University Press)
[104]	Qian H 1998 J. Chem. Phys. 109 10015 Google Scholar
[105]	Meyer W V, Neldel H 1937 Z. Tech. Phys. 18 588
[106]	Constable F H 1925 Proc. R. Soc. London, Ser. A 108 355 Google Scholar
[107]	Exner O 1964 Collection Czechoslov. Chem. Commun. 29 1094 Google Scholar
[108]	Cornish-Bowden A 2002 J. Biosci. 27 121 Google Scholar
[109]	Barrie P J 2012 Phys. Chem. Chem. Phys. 14 327 Google Scholar
[110]	Graziano G 2004 J. Chem. Phys. 120 4467 Google Scholar
[111]	赖国华, 周仁贤, 韩晓祥, 郑小明 2005 化学通报 12 928 Google Scholar Lai G H, Zhou R X, Han X X, Zheng X M 2005 Chem. Bull. 12 928 Google Scholar
[112]	Galwey A K 1977 Adv. Catal. 26 247
[113]	Starikov E B, Nordén B 2007 J. Phys. Chem. B 111 14431 Google Scholar
[114]	Ryu S, Kang K, Cai W 2011 Proc. Natl. Acad. Sci. U. S. A. 108 5174 Google Scholar
[115]	Sharp K 2001 Protein Sci. 10 661 Google Scholar
[116]	Eyring H 1935 J. Chem. Phys. 3 107 Google Scholar
[117]	Liu L, Guo Q X 2001 Chem. Rev. 101 673 Google Scholar
[118]	Pan A, Biswas T, Rakshit A K, Moulik S P 2015 J. Phys. Chem. B 119 15876 Google Scholar
[119]	Shimakawa K, Abdel-Wahab F 1997 Appl. Phys. Lett. 70 652 Google Scholar
[120]	Song H W, Guo S R, Lu D Z, Xu Y, Wang Y L, Lin D L, Hu Z Q 2000 Scr. Mater. 42 917 Google Scholar
[121]	Wang Y J, Ishii A, Ogata S 2013 Acta Mater. 61 3866 Google Scholar
[122]	Wang Y J, Zhang M, Liu L, Ogata S, Dai L H 2015 Phys. Rev. B 92 174118 Google Scholar
[123]	Lu J, Ravichandran G, Johnson W L 2003 Acta Mater. 51 3429 Google Scholar
[124]	Wang L M, Tian Y J, Liu R P, Richert R 2008 J. Chem. Phys. 128 084503 Google Scholar
[125]	Kubaschewski O, Evans A L, Alcock C B 1967 Metallurgical thermochemistry (New York: Pergamon Press) p427
[126]	Swalin R A, Arents J 1962 J. Electrochem. Soc. 109 308C Google Scholar
[127]	Angell C A 1997 J. Res. Natl. Inst. Stand. Technol. 102 171 Google Scholar
[128]	Greet R J, Magill J H 1967 J. Phys. Chem. 71 1746 Google Scholar
[129]	Reiner M 1964 Phys. Today 17 62
[130]	Blackburn F R, Wang C Y, Ediger M D 1996 J. Phys. Chem. 100 18249 Google Scholar
[131]	Senkov O N, Miracle D B 2003 J. Non-Cryst. Solids 317 34 Google Scholar
[132]	Yang X, Liu R, Yang M, Wang W H, Chen K 2016 Phys. Rev. Lett. 116 238003 Google Scholar
[133]	Wei D, Yang J, Jiang M Q, Dai L H, Wang Y J, Dyre J C, Douglass I, Harrowell P 2019 J. Chem. Phys. 150 114502 Google Scholar
[134]	Han D, Wei D, Yang J, Li H L, Jiang M Q, Wang Y J, Dai L H, Zaccone A 2020 Phys. Rev. B 101 014113 Google Scholar
[135]	Nettleton R E, Green M S 1958 J. Chem. Phys. 29 1365 Google Scholar
[136]	Mittal J, Errington J R, Truskett T M 2006 J. Chem. Phys. 125 076102 Google Scholar
[137]	Tiwari G P, Juneja J M, Iijima Y 2004 J. Mater. Sci. 39 1535 Google Scholar
[138]	Tiwari G P 1978 Met. Sci. Heat Treat. 12 317
[139]	Jackson K A 1969 Crystal Growth Kinetics and Morphology. In Kinetics of Reactions in Ionic Systems (Boston: Springer) p229
[140]	Li Y, Guo Q, Kalb J A, Thompson C V 2008 Science 322 1816 Google Scholar
[141]	Tallon J L 1980 Phys. Lett. A 76 139 Google Scholar
[142]	Tallon J L 1989 Nature 342 658 Google Scholar
[143]	Chen W, Wang Y, Qiang J, Dong C 2003 Acta Mater. 51 1899 Google Scholar
[144]	Yuan C C, Yang F, Xi X K, Shi C L, Holland-Moritz D, Li M Z, Hu F, Shen B L, Wang X L, Meyer A, Wang W H 2020 Mater. Today 32 26 Google Scholar
[145]	Saini M K, Jin X, Wu T, Liu Y, Wang L M 2018 J. Chem. Phys. 148 124504 Google Scholar
[146]	卢柯 1992 金属学报 2 8 Lu K 1992 Acta Metall. Sin. 2 8
[147]	Wang L, Li Z, Chen Z, Zhao Y, Liu R, Tian Y 2010 J. Phys. Chem. B 114 12080 Google Scholar
[148]	Zhang Y, Li P, Gao P, Tu W, Wang L M 2017 J. Mater. Sci. 52 2924 Google Scholar
[149]	Kang H, Wang L M unpublished
[150]	Tu W, Li X, Chen Z, Liu Y D, Labardi M, Capaccioli S, Paluch M, Wang L M 2016 J. Chem. Phys. 144 174502 Google Scholar
[151]	Wunderlich B 1960 J. Phys. Chem. 64 1052 Google Scholar
[152]	Moynihan C T, Angell C A 2000 J. Non-Cryst. Solids 274 131 Google Scholar
[153]	Takeda K, Yamamuro O, Tsukushi I, Matsuo T, Suga H 1999 J. Mol. Struct. 479 227 Google Scholar
[154]	Mishra R K, Dubey K S 1997 J. Therm. Anal. 50 843 Google Scholar
[155]	Chang S S, Bestul A B 1972 J. Chem. Phys. 56 503 Google Scholar
[156]	Wang L M, Angell C A, Richert R 2006 J. Chem. Phys. 125 074505 Google Scholar
[157]	Li P, Gao P, Liu Y, Wang L M 2017 J. Alloys Compd. 696 754 Google Scholar
[158]	Ubbelohde A R 1978 The Molten State of Matter: Melting and Crystal Structure (Chichester: John Wiley & Sons)
[159]	Oriani R A 1951 J. Chem. Phys. 19 93 Google Scholar
[160]	Martinez L M, Angell C A 2001 Nature 410 663 Google Scholar
[161]	Lu Z P, Bei H, Liu C T 2007 Intermetallics 15 618 Google Scholar
[162]	Battezzati L, Greer A L 1989 Acta Metall. 37 1791 Google Scholar
[163]	Lide D R 2004 CRC Handbook of Chemistry and Physics (Cleveland: CRC Press)
[164]	Gao F, He J, Wu E, Liu S, Yu D, Li D, Zhang S, Tian Y 2003 Phys. Rev. Lett. 91 015502 Google Scholar
[165]	Carter C B, Norton M G 2013 Ceramic Materials: Science and Engineering (New York: Springer-Verlag)
[166]	Kelton K F 1991 Solid State Phys. 45 75 Google Scholar
[167]	Kelton K F, Greer A L 1988 Phys. Rev. B 38 10089 Google Scholar
[168]	Wang L M, Velikov V, Angell C A 2002 J. Chem. Phys. 117 10184 Google Scholar
[169]	Ichitsubo T, Matsubara E, Yamamoto T, Chen H S, Nishiyama N, Saida J, Anazawa K 2005 Phys. Rev. Lett. 95 245501 Google Scholar
[170]	Ngai K L 2011 Relaxation and Diffusion in Complex Systems (New York: Springer)
[171]	Kolodziejczyk K, Paluch M, Grzybowska K, Grzybowski A, Wojnarowska Z, Hawelek L, Ziolo J D 2013 Mol. Pharmacol. 10 2270 Google Scholar
[172]	Mauro J C, Yue Y Z, Ellison A J, Gupta P K, Allan D C 2009 Proc. Natl. Acad. Sci. U. S. A. 106 19780 Google Scholar
[173]	Wu T, Jin X, Saini M K, Liu Y D, Ngai K L, Wang L M 2017 J. Chem. Phys. 147 134501 Google Scholar
[174]	Sarjeant P T, Roy R 1968 Mater. Res. Bull. 3 265 Google Scholar
[175]	Mukherjee S, Schroers J, Zhou Z, Johnson W L, Rhim W K 2004 Acta Mater. 52 3689 Google Scholar
[176]	Li P F, Wang L M unpublished.
[177]	Bureau B, Boussard-Pledel C, Lucas P, Zhang X, Lucas J 2009 Molecules 14 4337 Google Scholar
[178]	Zhang Y, Gong H, Li P, Tian Y, Wang L M 2017 Mater. Lett. 194 149 Google Scholar
[179]	Zanotto E D, Cassar D R 2017 Sci. Rep. 7 1 Google Scholar
[180]	翟玉春 2017 非平衡态热力学 (北京: 科学出版社) Zhai Y C, 2017 Non-Equilibrium Thermodynamics (Beijing: Science Press) (in Chinese)
[181]	Li Z, Pan S, Zhang S, Feng S, Li M, Liu R, Tian Y, Wang L M 2019 Intermetallics 109 97 Google Scholar
[182]	Wang Y, Yao J, Li Y 2018 J. Mater. Sci. Technol. 34 605 Google Scholar

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图 1 基于体系焓H或者体积V变化表达的非晶转变示意图. 1—3代表不同的冷速得到的非晶态

Figure 1. Schematic of glass transition behaviors addressed by enthalpy or volume. Numbers of 1—3 define glassy states obtained at different quenching rates.

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图 2 非晶与液态的部分能量图景示意图

Figure 2. Schematic diagram of partial energy landscape of a glass and liquid.

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图 3 四种二元金属合金体系在共晶成分上的混合熵^[78]

Figure 3. Entropies of mixing in four types of binary metallic alloys at their eutectic compositions^[78].

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图 4 金属合金液固Gibbs自由能差在过冷区内温度关系^[30,94], T_l为液相线温度

Figure 4. Temperature dependence of the difference of liquid-crystal Gibbs free energies in supercooled liquid regions of metallic alloys. T_l is the liquidus temperature^[30,94].

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图 5 具有正、负混合热金属二元共晶体系中的过剩熔化熵^[101]

Figure 5. Excess entropies of fusion in binary eutectic alloys showing positive and negative enthalpies of mixing^[101].

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图 6 具有正、负混合热二元小分子共晶体系的过剩熔化熵. 左图为混合热测量曲线, 右图为共晶相图　(a), (b)、共晶点以及纯组元熔化熵(c), (d)和共晶成分过剩熔化熵(e), (f)^[101]

Figure 6. Excess entropies of fusion in binary molecular eutectics of positive and negative enthalpies of mixing. Experimental measurements of the enthalpy of mixing is shown in left panel. (a) and (b) in the right panels are the phase diagrams; (c) and (d) show the entropies of fusion of eutectics and pure components; (e) and (f) give the excess entropies of fusion of eutectics^[101].

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图 7 基于准化学模型在1000 ℃下计算的AB二元体系的摩尔混合热与混合熵. 假设A与B配位数为2, 短程序Δg_A-B分别为定值0, –21, –42和–84 kJ/mol四种情况^[102]

Figure 7. Calculated enthalpies and entropies of mixing in a A-B binary system in terms of quasi-chemical model with the fixed coordination number of two but varied short-range ordering Δg_A-B of 0, –21, –42 and 84 kJ/mol^[102].

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图 8 中间化合物Cu₅₀Zr₅₀在　(a) 玻璃态(I)和过(b)冷液态(II)弛豫激活动力学中的焓-熵补偿效应^[122]

Figure 8. Enthalpy-entropy compensation behaviors for the activation behaviors of the relaxation dynamics in the glassy (I) (a) and supercooled liquid (II) (b)states of intermetallic Cu₅₀Zr₅₀^[122].

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图 9 单羟基醇分子体系中非晶转变温度T_g与沸点T_b之间的关系^[58]

Figure 9. Relationship between the glass transition temperature T_g and boiling temperature T_b of glass forming monoalcohols^[58].

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图 10 简单二元相图(理想混合且固溶度为零)中液相线与熔化熵关系

Figure 10. Dependence of the liquidus on entropy of fusion in hypothetical binary phase diagrams featured by the ideal mixing and negligible solid solubility.

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图 11 四个二元碲基窄带隙合金的非晶形成能力图和相图. 左图为SnTe分别与Bi₂Te₃　(a), Sb₂Te₃ (b), In₂Te₃(c)和Ga₂Te₃ (d)构成的二元体系不同组分熔体淬火样品的XRD图, 右图为相对应的二元相图, 显示固溶度的变化趋势^[148]

Figure 11. Phase diagrams and glass forming ability in four binary Tellurium-based alloys. Left panel shows the XRD patterns of the samples obtained by water-quenching in the SnTe alloys with Bi₂Te₃ (a), Sb₂Te₃ (b), In₂Te₃ (c) and Ga₂Te₃ (d). Binary phase diagrams are presented in the right panel showing the variation of solid solubility^[148].

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图 12 金属合金与小分子非晶形成体系归一化熔化熵与熔点粘度关系^[150], 实线表示数据趋势

Figure 12. Dependence of the melting viscosity on entropy of fusion in metallic and molecular glass-formers. Solid line guides the eye^[150].

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图 13 不同非晶形成体系的约化熔化熵与经典非晶形成参量T_g/T_m关系

Figure 13. Dependence of the reduced glass transition T_g/T_m on entropy of fusion in various glass forming systems.

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图 14 金属与无机材料的归一化熔化熵. n为一个分子中的原子数

Figure 14. Normalized entropies of fusion in various metallic and inorganic materials. The parameter of n defines the atomic number of a molecule.

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图 15 金属合金的熔化熵与非晶形成临界冷却速率的关系. 实验数据基于文献^[95], 曲线由(19)式计算确定

Figure 15. Dependence of the critical cooling rate of glass formation on entropy of fusion in metallic alloys. The data are obtained from Ref. 95 and, the solid curve is calculated in terms of equation (19).

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图 16 硫族化合物熔化熵与非晶形成临界冷却速率的关系. 实线是参考(19)式的拟合曲线

Figure 16. Dependence of the critical cooling rate of glass formation on entropy of fusion in glass forming chalcogenides. The solid line is the fitting curve using equation (19).

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[1]	Anderson P W 1995 Science 267 1615 Google Scholar
[2]	Angell C A, Ngai K L, McKenna G B, McMillan P F, Martin S 2000 J. Appl. Phys. 88 3113 Google Scholar
[3]	汪卫华 2013 物理学进展 33 177 Wang W H 2013 Prog. Phys. 33 177
[4]	Turnbull D 1969 Contemp. Phys. 10 473 Google Scholar
[5]	Turnbull D, Cohen M H 1960 Modern Aspects of the Vitreous State (London: Butterworth)
[6]	Uhlmann D R 1977 J. Non-Cryst. Solids 25 42 Google Scholar
[7]	Schmentzer J 2005 Nucleation Theory and Applications (New York: Wiley-VCH)
[8]	Kalikmanov V I 2013 Nucleation Theory (Netherlands: Springer)
[9]	Klement W, Willens R H, Duwez P O L 1960 Nature 187 869
[10]	Jiang Z, Hu X, Zhao X 1982 J. Non-Cryst. Solids 52 235 Google Scholar
[11]	Peker A, Johnson W L 1993 Appl. Phys. Lett. 63 2342 Google Scholar
[12]	Highmore R J, Greer A L 1989 Nature 339 363 Google Scholar
[13]	Ottou Abe M T, Viciosa M T, Correia N T, Affouard F 2018 Phys. Chem. Chem. Phys. 20 29528 Google Scholar
[14]	Atawa B, Correia N T, Couvrat N, Affouard F, Coquerel G, Dargent E, Saiter A 2019 Phys. Chem. Chem. Phys. 21 702
[15]	Kauzmann W 1949 Chem. Rev. 43 219
[16]	Angell C A 1995 Science 267 1924 Google Scholar
[17]	Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200 Google Scholar
[18]	Mukherjee S, Schroers J, Johnson W L, Rhim W K, 2005 Phys. Rev. Lett. 94 245501 Google Scholar
[19]	Lu Z P, Ma D, Liu C T, Chang Y A 2007 Intermetallics 15 253 Google Scholar
[20]	Yang B, Du Y, Liu Y 2009 Trans. Nonferrous Met. Soc. China 19 78 Google Scholar
[21]	Chattopadhyay C, Satish Idury K S N, Bhatt J, Mondal K, Murty B S 2016 Mater. Sci. Technol. 32 380 Google Scholar
[22]	Mondal K, Chatterjee U K, Murty B S 2003 Appl. Phys. Lett. 83 671 Google Scholar
[23]	Chen H S 1980 Rep. Prog. Phys. 43 353 Google Scholar
[24]	Kim D, Lee B J, Kim N J 2004 Intermetallics 12 1103 Google Scholar
[25]	Sun K H 1947 J. Am. Ceram. Soc. 30 277 Google Scholar
[26]	Rawson H 1956 Proc. IV Intern. Congress on Glass (Paris: Impremenic Chaix) p62
[27]	Xia L, Li W H, Fang S S, Wei B C, Dong Y D 2006 J. Appl. Phys. 99 026103 Google Scholar
[28]	Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817 Google Scholar
[29]	Takeuchi A, Inoue A 2000 Mater. Trans., JIM 41 1372 Google Scholar
[30]	Busch R, Liu W, Johnson W L 1998 J. Appl. Phys. 83 4134 Google Scholar
[31]	Singh P K, Dubey K S 2010 J. Therm. Anal. Calorim. 100 347 Google Scholar
[32]	Adam G, Gibbs J H 1965 J. Chem. Phys. 43 139 Google Scholar
[33]	Perepezko J H 2004 Prog. Mater. Sci. 49 263 Google Scholar
[34]	Fecht H J, Johnson W L 2004 Mater. Sci. Eng. A 375 2
[35]	Battezzati L 1994 Mater. Sci. Eng. A 178 43 Google Scholar
[36]	Battezzati L, Castellero A, Rizzi P 2007 J. Non-Cryst. Solids 353 3318 Google Scholar
[37]	Gallington L C, Bongiorno A 2010 J. Chem. Phys. 132 174707 Google Scholar
[38]	Gutzow I, Schmelzer J W P, Petroff B 2008 J. Non-Cryst. Solids 354 311 Google Scholar
[39]	Ji X, Pan Y 2007 J. Non-Cryst. Solids 353 2443 Google Scholar
[40]	Fultz B 2010 Prog. Mater. Sci. 55 247 Google Scholar
[41]	van de Walle A, Ceder G 2002 Rev. Mod. Phys. 74 11 Google Scholar
[42]	Manzoor A, Pandey S, Chakraborty D, Phillpot S R, Aidhy D S 2018 NPJ Comput. Mater. 4 47 Google Scholar
[43]	Ohsaka K, Trinh E H 1995 Appl. Phys. Lett. 66 3123 Google Scholar
[44]	Goldstein M, 1969 J. Chem. Phys. 51 3728 Google Scholar
[45]	Stillinger F H 1995 Science 267 1935 Google Scholar
[46]	Angell C A 2005 Phil. Trans. R. Soc. A 363 415 Google Scholar
[47]	Sastry S, Debenedetti P G, Stillinger F H 1998 Nature 393 554 Google Scholar
[48]	Bhatt J, Wu J, Xia J H, Wang Q, Dong C, Murty B S 2007 Intermetallics 15 716 Google Scholar
[49]	Ramakrishna Rao B, Gandhi A S, Vincent S, Bhatt J, Murty B S 2012 Trans. Indian Inst. Met. 65 559 Google Scholar
[50]	Zachariasen W H 1932 J. Am. Chem. Soc. 54 3841 Google Scholar
[51]	Johnson W L, Na J H, Demetriou M D 2016 Nat. Commun. 7 1
[52]	Jiusti J, Zanotto E D, Cassar D R, Andreeta M R B 2020 J. Am. Ceram. Soc. 103 921 Google Scholar
[53]	Minaev V S 1978 Amorphous Semiconductors-78 (Prague: AS ChSSR) p71
[54]	de Oliveira M F, Pereira F S, Bolfarini C, Kiminami C S, Botta W J 2009 Intermetallics 17 183 Google Scholar
[55]	Benson S W 1947 J. Chem. Phys. 15 367 Google Scholar
[56]	Myers R T 1979 J. Phys. Chem. 83 294 Google Scholar
[57]	Wessel M D, Jurs P C 1995 J. Chem. Inf. Comput. Sci. 35 841 Google Scholar
[58]	Wang L M, Richert R 2007 J. Phys. Chem. B. 111 3201 Google Scholar
[59]	Turnbull D, Cohen M H 1958 J. Chem. Phys. 29 1049 Google Scholar
[60]	郑兆勃 1979 金属学报 15 155 Zheng Z B 1979 Acta. Metall. Sin. 15 155
[61]	Hrubý A 1972 J. Phys. B 22 1187
[62]	Inoue A 2000 Acta Mater. 48 279 Google Scholar
[63]	Song W X, Zhao S J 2015 J. Chem. Phys. 142 144504 Google Scholar
[64]	Miedema A R, de Châtel P F, de Boer F R 1980 Phys. B+C 100 1 Google Scholar
[65]	Basu J, Murty B S, Ranganathan S 2008 J. Alloys Compd. 465 163 Google Scholar
[66]	Das N, Kulkarni U D, Pabi S K, Murty B S, Dey G K 2008 Defect Diffus. Forum 279 147 Google Scholar
[67]	Bhatt J, Dey G K, Murty B S 2008 Metall. Mater. Trans. A 39 1543 Google Scholar
[68]	Ray P K, Akinc M, Kramer M J 2008 22 nd Annu. Conf. Foss. Energy Mater (Pittsburgh) 2008 p474
[69]	Weeber A W 1987 J. Phys. F: Met. Phys. 17 809 Google Scholar
[70]	Pan Y, Zeng Y, Jing L, Zhang L, Pi J 2014 Mater. Des. 55 773 Google Scholar
[71]	Miracle D B 2006 Acta Mater. 54 4317 Google Scholar
[72]	Egami T, Waseda Y 1984 J. Non-Cryst. Solids 64 113 Google Scholar
[73]	Gargarella P, de Oliveira M F, Kiminami S, Pauly S, Kühn U, Bolfarini C, Botta W J, Eckert J 2011 J. Alloys Compd. 50 9
[74]	Hu Y C, Schroers J, Shattuck M D, O’Hern C S 2019 Phys. Rev. Mater. 3 085602 Google Scholar
[75]	Greer A L 1993 Nature 366 30
[76]	Zhang W, Liaw P K, Zhang Y 2018 Sci. China Mater. 61 2 Google Scholar
[77]	Lei Z, Liu X, Wu Y, Wang H, Jiang S, Wang S, Hui X, Wu Y, Gault B, Kontis P, Raabe D, Gu L, Zhang Q, Chen H, Wang H, Liu J, An K, Zeng Q, Nieh T G, Lu Z 2018 Nature 563 546 Google Scholar
[78]	Zhao L R, Li Z J, Gao Y Q, Bo H, Liu Y D, Wang L M 2016 Intermetallics 71 18 Google Scholar
[79]	Gibbs J H, DiMarzio E A 1958 J. Chem. Phys. 28 373 Google Scholar
[80]	Mansoori G A, Carnahan N F, Starling K E, Leland Jr T W 1971 J. Chem. Phys. 54 1523 Google Scholar
[81]	Takeuchi A, Amiya K, Wada T, Yubuta K, Zhang W, Makino A 2013 Entropy 15 3810 Google Scholar
[82]	Guo J, Bian X, Li X, Zhang C 2010 Intermetallics 18 933 Google Scholar
[83]	Li X, Song K, Wu Y, Ji H, Wang L 2013 Mater. Lett. 107 17 Google Scholar
[84]	Vincent S, Peshwe D R, Murty B S, Bhatt J 2011 J. Non-Cryst. Solids 357 3495 Google Scholar
[85]	Wang L M, Richert R 2007 Phys. Rev. Lett. 99 185701 Google Scholar
[86]	Wang W H 2012 Prog. Mater. Sci. 57 487 Google Scholar
[87]	Stillinger F H, Debenedetti P G 1999 J. Phys. Chem. B 103 4052 Google Scholar
[88]	Bendert J C, Gangopadhyay A K, Mauro N A, Kelton K F 2012 Phys. Rev. Lett. 109 185901 Google Scholar
[89]	Louzguine-Luzgin D V, Inoue A 2007 J. Mater. Res. 22 1378 Google Scholar
[90]	Uhlmann D R 1983 J. Am. Ceram. Soc. 66 95 Google Scholar
[91]	Jackson K A 2002 Interface Sci. 10 159 Google Scholar
[92]	Ediger M D, Harrowell P, Yu L 2008 J. Chem. Phys. 128 034709 Google Scholar
[93]	Gutzow I, Schmelzer J 1995 The Vitreous State (Berlin-New York: Springer)
[94]	Busch R, Schroers J, Wang W H 2007 MRS Bull. 32 620 Google Scholar
[95]	Wang L M, Tian Y, Liu R, Wang W 2012 Appl. Phys. Lett. 100 261913 Google Scholar
[96]	Senkov O N, Miracle D B, Mullens H M 2005 J. Appl. Phys. 97 103502 Google Scholar
[97]	Turnbull D 1981 Metall. Trans. B 12 217 Google Scholar
[98]	Li D, Herlach D M 1996 Phys. Rev. Lett. 77 1801 Google Scholar
[99]	Wang Q, Wang L M, Ma M Z, Binder S, Volkmann T, Herlach D M, Wang J S, Xue Q G, Tian Y J, Liu R P 2011 Phys. Rev. B 83 014202 Google Scholar
[100]	Hoffmann H J 2005 Phys. Chem. Glasses 46 570
[101]	Gao P, Tu W, Li P, Wang L M 2018 J. Alloys Compd. 736 12 Google Scholar
[102]	Pelton A D, Degterov S A, Eriksson G, Robelin C, Dessureault Y 2000 Metall. Mater. Trans. B 31 651 Google Scholar
[103]	Hillert M 2008 Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis (London: Cambridge University Press)
[104]	Qian H 1998 J. Chem. Phys. 109 10015 Google Scholar
[105]	Meyer W V, Neldel H 1937 Z. Tech. Phys. 18 588
[106]	Constable F H 1925 Proc. R. Soc. London, Ser. A 108 355 Google Scholar
[107]	Exner O 1964 Collection Czechoslov. Chem. Commun. 29 1094 Google Scholar
[108]	Cornish-Bowden A 2002 J. Biosci. 27 121 Google Scholar
[109]	Barrie P J 2012 Phys. Chem. Chem. Phys. 14 327 Google Scholar
[110]	Graziano G 2004 J. Chem. Phys. 120 4467 Google Scholar
[111]	赖国华, 周仁贤, 韩晓祥, 郑小明 2005 化学通报 12 928 Google Scholar Lai G H, Zhou R X, Han X X, Zheng X M 2005 Chem. Bull. 12 928 Google Scholar
[112]	Galwey A K 1977 Adv. Catal. 26 247
[113]	Starikov E B, Nordén B 2007 J. Phys. Chem. B 111 14431 Google Scholar
[114]	Ryu S, Kang K, Cai W 2011 Proc. Natl. Acad. Sci. U. S. A. 108 5174 Google Scholar
[115]	Sharp K 2001 Protein Sci. 10 661 Google Scholar
[116]	Eyring H 1935 J. Chem. Phys. 3 107 Google Scholar
[117]	Liu L, Guo Q X 2001 Chem. Rev. 101 673 Google Scholar
[118]	Pan A, Biswas T, Rakshit A K, Moulik S P 2015 J. Phys. Chem. B 119 15876 Google Scholar
[119]	Shimakawa K, Abdel-Wahab F 1997 Appl. Phys. Lett. 70 652 Google Scholar
[120]	Song H W, Guo S R, Lu D Z, Xu Y, Wang Y L, Lin D L, Hu Z Q 2000 Scr. Mater. 42 917 Google Scholar
[121]	Wang Y J, Ishii A, Ogata S 2013 Acta Mater. 61 3866 Google Scholar
[122]	Wang Y J, Zhang M, Liu L, Ogata S, Dai L H 2015 Phys. Rev. B 92 174118 Google Scholar
[123]	Lu J, Ravichandran G, Johnson W L 2003 Acta Mater. 51 3429 Google Scholar
[124]	Wang L M, Tian Y J, Liu R P, Richert R 2008 J. Chem. Phys. 128 084503 Google Scholar
[125]	Kubaschewski O, Evans A L, Alcock C B 1967 Metallurgical thermochemistry (New York: Pergamon Press) p427
[126]	Swalin R A, Arents J 1962 J. Electrochem. Soc. 109 308C Google Scholar
[127]	Angell C A 1997 J. Res. Natl. Inst. Stand. Technol. 102 171 Google Scholar
[128]	Greet R J, Magill J H 1967 J. Phys. Chem. 71 1746 Google Scholar
[129]	Reiner M 1964 Phys. Today 17 62
[130]	Blackburn F R, Wang C Y, Ediger M D 1996 J. Phys. Chem. 100 18249 Google Scholar
[131]	Senkov O N, Miracle D B 2003 J. Non-Cryst. Solids 317 34 Google Scholar
[132]	Yang X, Liu R, Yang M, Wang W H, Chen K 2016 Phys. Rev. Lett. 116 238003 Google Scholar
[133]	Wei D, Yang J, Jiang M Q, Dai L H, Wang Y J, Dyre J C, Douglass I, Harrowell P 2019 J. Chem. Phys. 150 114502 Google Scholar
[134]	Han D, Wei D, Yang J, Li H L, Jiang M Q, Wang Y J, Dai L H, Zaccone A 2020 Phys. Rev. B 101 014113 Google Scholar
[135]	Nettleton R E, Green M S 1958 J. Chem. Phys. 29 1365 Google Scholar
[136]	Mittal J, Errington J R, Truskett T M 2006 J. Chem. Phys. 125 076102 Google Scholar
[137]	Tiwari G P, Juneja J M, Iijima Y 2004 J. Mater. Sci. 39 1535 Google Scholar
[138]	Tiwari G P 1978 Met. Sci. Heat Treat. 12 317
[139]	Jackson K A 1969 Crystal Growth Kinetics and Morphology. In Kinetics of Reactions in Ionic Systems (Boston: Springer) p229
[140]	Li Y, Guo Q, Kalb J A, Thompson C V 2008 Science 322 1816 Google Scholar
[141]	Tallon J L 1980 Phys. Lett. A 76 139 Google Scholar
[142]	Tallon J L 1989 Nature 342 658 Google Scholar
[143]	Chen W, Wang Y, Qiang J, Dong C 2003 Acta Mater. 51 1899 Google Scholar
[144]	Yuan C C, Yang F, Xi X K, Shi C L, Holland-Moritz D, Li M Z, Hu F, Shen B L, Wang X L, Meyer A, Wang W H 2020 Mater. Today 32 26 Google Scholar
[145]	Saini M K, Jin X, Wu T, Liu Y, Wang L M 2018 J. Chem. Phys. 148 124504 Google Scholar
[146]	卢柯 1992 金属学报 2 8 Lu K 1992 Acta Metall. Sin. 2 8
[147]	Wang L, Li Z, Chen Z, Zhao Y, Liu R, Tian Y 2010 J. Phys. Chem. B 114 12080 Google Scholar
[148]	Zhang Y, Li P, Gao P, Tu W, Wang L M 2017 J. Mater. Sci. 52 2924 Google Scholar
[149]	Kang H, Wang L M unpublished
[150]	Tu W, Li X, Chen Z, Liu Y D, Labardi M, Capaccioli S, Paluch M, Wang L M 2016 J. Chem. Phys. 144 174502 Google Scholar
[151]	Wunderlich B 1960 J. Phys. Chem. 64 1052 Google Scholar
[152]	Moynihan C T, Angell C A 2000 J. Non-Cryst. Solids 274 131 Google Scholar
[153]	Takeda K, Yamamuro O, Tsukushi I, Matsuo T, Suga H 1999 J. Mol. Struct. 479 227 Google Scholar
[154]	Mishra R K, Dubey K S 1997 J. Therm. Anal. 50 843 Google Scholar
[155]	Chang S S, Bestul A B 1972 J. Chem. Phys. 56 503 Google Scholar
[156]	Wang L M, Angell C A, Richert R 2006 J. Chem. Phys. 125 074505 Google Scholar
[157]	Li P, Gao P, Liu Y, Wang L M 2017 J. Alloys Compd. 696 754 Google Scholar
[158]	Ubbelohde A R 1978 The Molten State of Matter: Melting and Crystal Structure (Chichester: John Wiley & Sons)
[159]	Oriani R A 1951 J. Chem. Phys. 19 93 Google Scholar
[160]	Martinez L M, Angell C A 2001 Nature 410 663 Google Scholar
[161]	Lu Z P, Bei H, Liu C T 2007 Intermetallics 15 618 Google Scholar
[162]	Battezzati L, Greer A L 1989 Acta Metall. 37 1791 Google Scholar
[163]	Lide D R 2004 CRC Handbook of Chemistry and Physics (Cleveland: CRC Press)
[164]	Gao F, He J, Wu E, Liu S, Yu D, Li D, Zhang S, Tian Y 2003 Phys. Rev. Lett. 91 015502 Google Scholar
[165]	Carter C B, Norton M G 2013 Ceramic Materials: Science and Engineering (New York: Springer-Verlag)
[166]	Kelton K F 1991 Solid State Phys. 45 75 Google Scholar
[167]	Kelton K F, Greer A L 1988 Phys. Rev. B 38 10089 Google Scholar
[168]	Wang L M, Velikov V, Angell C A 2002 J. Chem. Phys. 117 10184 Google Scholar
[169]	Ichitsubo T, Matsubara E, Yamamoto T, Chen H S, Nishiyama N, Saida J, Anazawa K 2005 Phys. Rev. Lett. 95 245501 Google Scholar
[170]	Ngai K L 2011 Relaxation and Diffusion in Complex Systems (New York: Springer)
[171]	Kolodziejczyk K, Paluch M, Grzybowska K, Grzybowski A, Wojnarowska Z, Hawelek L, Ziolo J D 2013 Mol. Pharmacol. 10 2270 Google Scholar
[172]	Mauro J C, Yue Y Z, Ellison A J, Gupta P K, Allan D C 2009 Proc. Natl. Acad. Sci. U. S. A. 106 19780 Google Scholar
[173]	Wu T, Jin X, Saini M K, Liu Y D, Ngai K L, Wang L M 2017 J. Chem. Phys. 147 134501 Google Scholar
[174]	Sarjeant P T, Roy R 1968 Mater. Res. Bull. 3 265 Google Scholar
[175]	Mukherjee S, Schroers J, Zhou Z, Johnson W L, Rhim W K 2004 Acta Mater. 52 3689 Google Scholar
[176]	Li P F, Wang L M unpublished.
[177]	Bureau B, Boussard-Pledel C, Lucas P, Zhang X, Lucas J 2009 Molecules 14 4337 Google Scholar
[178]	Zhang Y, Gong H, Li P, Tian Y, Wang L M 2017 Mater. Lett. 194 149 Google Scholar
[179]	Zanotto E D, Cassar D R 2017 Sci. Rep. 7 1 Google Scholar
[180]	翟玉春 2017 非平衡态热力学 (北京: 科学出版社) Zhai Y C, 2017 Non-Equilibrium Thermodynamics (Beijing: Science Press) (in Chinese)
[181]	Li Z, Pan S, Zhang S, Feng S, Li M, Liu R, Tian Y, Wang L M 2019 Intermetallics 109 97 Google Scholar
[182]	Wang Y, Yao J, Li Y 2018 J. Mater. Sci. Technol. 34 605 Google Scholar

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