Quantitative understanding of the initial stage of liquid to crystalline or amorphous phase transitions

Hao-De Dong; Peng Zhang; Ming-Yang Qin; Jian Hui; Hong Wang; Zi-Kui Liu; X.-D. Xiang

doi:10.59717/j.xinn-mater.2024.100086

The Innovation Materials > 2024 Vol. 2 > No. 3 > 100086

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Quantitative understanding of the initial stage of liquid to crystalline or amorphous phase transitions

1.
Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
2.
Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology, Shenzhen 518055, China
3.
School of Materials Science and Engineering, Materials Genome Initiative Center & Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University, Shanghai 200240, China
4.
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
5.
Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China

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Corresponding authors: hongwang2@sjtu.edu.cn (H. W.); liu@matse.psu.edu (Z. L.); xiangxd@sustech.edu.cn (X. X.)
Received Date: April 22, 2024

Accepted Date: August 07, 2024

Published Online: August 13, 2024

The Innovation Materials 2(3), https://doi.org/10.59717/j.xinn-mater.2024.100086 | Cite this article

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GRAPHICAL ABSTRACT

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PUBLIC SUMMARY

PUBLIC SUMMARY
1. The time-temperature transition (TTT) curve is the critical boundary between the glass and crystal phases.
  
  Relating critical interface energy as a function of critical viscosity enables a quantitative model of TTT.
  
  The model reveals a new liquid to solid glass phase transition at T₀, and the nature of a glassy substance.

ABSTRACT

ABSTRACT

In 2005, Science magazine listed the “nature of a glassy substance” as one of the 125 most challenging scientific questions of the century. A quantitative understanding of the time-temperature transition (TTT) curve for critical nucleation of amorphous materials is crucial to answering this question. Despite extensive efforts over the past 70 years, a quantitative model for the TTT curve remains elusive due to a lack of understanding of physical properties such as the interfacial energy at the incubation time t^* for critical nucleation. In this study, a relationship between the critical nucleation viscosity and the interfacial energy as a function of t^* is established and a quantitative TTT model is developed. The model demonstrates excellent agreement with experimental TTT data for various amorphous materials. Most importantly, it allows the accurate and definitive determination of T₀, the true minimum crystallization temperature at the lower end-point of the TTT curve, as well as the temperature below which the amorphous liquid-to-solid state transition occurs. This offers an unambiguous answer to the nature of glassy substances: Above T₀, a liquid with constant amorphous structure relaxation; and below T₀, a solid with stable amorphous structure.

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REFERENCES

[1]	So much more to know. (2005). Science 309 : 78-102. DOI: 10.1126/science.309.5731.78b. View in Article Google Scholar
[2]	Debenedetti, P.G. and Stillinger, F.H. (2001). Supercooled liquids and the glass transition. Nature 410: 259−267. DOI: 10.1038/35065704. View in Article CrossRef Google Scholar Scopus
[3]	Gao, Q. and Jian, Z. (2020). Predicting the thermodynamic ideal glass transition temperature in glass-forming liquids. Materials 13: 2151. DOI: 10.3390/ma13092151. View in Article CrossRef Google Scholar
[4]	Kawazoe, Y., Yu, J.-Z., Tsai, A.-P., et al. (1997). Phase diagrams and physical properties of nonequilibrium alloys. Subvol. A. (ed). Nonequilibrium phase diagrams of ternary amorphous alloys (Springer). View in Article Google Scholar
[5]	Kauzmann, W. (1948). The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43: 219−256. DOI: 10.1021/cr60135a002. View in Article CrossRef Google Scholar
[6]	Fellers, W.O. (1990). Materials science, testing, and properties for technicians (Prentice Hall). View in Article Google Scholar
[7]	Zhang, K., Zhang, Z., Pan, H., et al. (2024). Taming heat with tiny pressure. The Innovation 5: 100577. DOI: 10.1016/j.xinn.2024.100577. View in Article CrossRef Google Scholar Scopus
[8]	Welch, R.S., Zanotto, E.D., Wilkinson, C.J., et al. (2023). Cracking the kauzmann paradox. Acta Mater. 254: 118994. DOI: 10.1016/j.actamat.2023.118994. View in Article CrossRef Google Scholar
[9]	Gibbs, J.H. and DiMarzio, E.A. (1958). Nature of the glass transition and the glassy state. J. Chem. Phys. 28: 373−383. DOI: 10.1063/1.1744141. View in Article CrossRef Google Scholar Scopus
[10]	Uhlmann, D.R. (1972). A kinetic treatment of glass formation. J. Non-Cryst. Solids 7: 337−348. DOI: 10.1016/0022-3093(72)90269-4. View in Article CrossRef Google Scholar Scopus
[11]	Uhlmann, D.R. (1977). Glass formation. J. Non-Cryst. Solids 25: 42−85. DOI: 10.1016/0022-3093(77)90090-4. View in Article CrossRef Google Scholar Scopus
[12]	Turnbull, D. and Cohen, M.H. (2004). Concerning reconstructive transformation and formation of glass. J. Chem. Phys. 29: 1049−1054. DOI: 10.1063/1.1744654. View in Article CrossRef Google Scholar Scopus
[13]	Cohen, M.H. and Turnbull, D. (2004). Molecular transport in liquids and glasses. J. Chem. Phys. 31: 1164−1169. DOI: 10.1063/1.1730566. View in Article CrossRef Google Scholar Scopus
[14]	Davies, H.A. and Lewis, B.G. (1976). Metallic glasses and the avoidance of crystallization in metallic melts. Faraday Discuss. Chem. Soc. 61: 100−109. DOI: 10.1039/DC9766100100. View in Article CrossRef Google Scholar Scopus
[15]	Barmak, K. (2010). A commentary on: “Reaction kinetics in processes of nucleation and growth”*. Metall. Mater. Trans. A 41: 2711−2775. DOI: 10.1007/s11661-010-0421-1. View in Article CrossRef Google Scholar
[16]	Kelton, K.F. and Greer, A.L. (2010). Chapter 2 - The classical theory. Kelton, K.F. and Greer, A.L. (eds). Pergamon materials series (Pergamon), pp: 19-54. DOI: 10.1016/S1470-1804(09)01502-8. View in Article Google Scholar
[17]	Liu, Z.-K. (2023). Thermodynamics and its prediction and calphad modeling: Review, state of the art, and perspectives. Calphad 82: 102580. DOI: 10.1016/j.calphad.2023.102580. View in Article CrossRef Google Scholar
[18]	Turnbull, D. (1962). On the relation between crystallization rate and liquid structure. J. Phys. Chem. 66: 609−613. DOI: 10.1021/j100810a009. View in Article CrossRef Google Scholar Scopus
[19]	Turnbull, D. and Fisher, J.C. (1949). Rate of nucleation in condensed systems. J. Chem. Phys. 17: 71−73. DOI: 10.1063/1.1747055. View in Article CrossRef Google Scholar Scopus
[20]	Liu, F., Chen, K., and Xue, D. (2023). How to fast grow large-size crystals. The Innovation 4: 100458. DOI: 10.1016/j.xinn.2023.100458. View in Article CrossRef Google Scholar Scopus
[21]	Zanotto, E.D. and James, P.F. (1985). Experimental tests of the classical nucleation theory for glasses. J. Non-Cryst. Solids 74: 373−394. DOI: 10.1016/0022-3093(85)90080-8. View in Article CrossRef Google Scholar Scopus
[22]	Turnbull, D. (1950). Formation of crystal nuclei in liquid metals. J. Appl. Phys. 21: 1022−1028. DOI: 10.1063/1.1699435. View in Article CrossRef Google Scholar Scopus
[23]	Hoffman, J.D. (1958). Thermodynamic driving force in nucleation and growth processes. J. Chem. Phys. 29: 1192−1193. DOI: 10.1063/1.1744688. View in Article CrossRef Google Scholar Scopus
[24]	Thompson, C.V. and Spaepen, F. (1979). On the approximation of the free energy change on crystallization. Acta Metall. 27: 1855−1859. DOI: 10.1016/0001-6160(79)90076-2. View in Article CrossRef Google Scholar Scopus
[25]	Porter, D.A., Easterling, K.E., and Sherif, M.Y. (2009). Phase transformations in metals and alloys (revised reprint) (CRC Press). View in Article Google Scholar
[26]	Krynicki, K., Green, C.D., and Sawyer, D.W. (1978). Pressure and temperature dependence of self-diffusion in water. Faraday Discuss. Chem. Soc. 66: 199−208. DOI: 10.1039/DC9786600199. View in Article CrossRef Google Scholar Scopus
[27]	Einstein, A. (1905). On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat. Ann. Phys. 17: 208. DOI: 10.1002/andp.19053220806. View in Article CrossRef Google Scholar
[28]	Garca-Coln, L.S., del Castillo, L.F., and Goldstein, P. (1989). Theoretical basis for the vogel-fulcher-tammann equation. Phys. Rev. B 40: 7040−7044. DOI: 10.1103/PhysRevB.40.7040. View in Article CrossRef Google Scholar
[29]	Waniuk, T.A., Busch, R., Masuhr, A., et al. (1998). Equilibrium viscosity of the Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 bulk metallic glass-forming liquid and viscous flow during relaxation, phase separation, and primary crystallization. Acta Mater. 46 : 5229-5236. DOI: 10.1016/S1359-6454(98)00242-0. View in Article Google Scholar
[30]	Hembree, W. (2015). High temperature rheology of Zr-based bulk metallic glass forming liquids. PhD thesis. (Saarland University). View in Article Google Scholar
[31]	Evenson, Z., Raedersdorf, S., Gallino, I., et al. (2010). Equilibrium viscosity of Zr–Cu–Ni–Al–Nb bulk metallic glasses. Scr. Mater. 63: 573−576. DOI: 10.1016/j.scriptamat.2010.06.008. View in Article CrossRef Google Scholar
[32]	Mukherjee, S., Kang, H.-G., Johnson, W., et al. (2004). Noncontact measurement of crystallization behavior, specific volume, and viscosity of bulk glass-forming Zr-Al-Co-(Cu) alloys. Phys. Rev. B 70: 174205. DOI: 10.1103/PhysRevB.70.174205. View in Article CrossRef Google Scholar Scopus
[33]	Mukherjee, S., Schroers, J., Zhou, Z., et al. (2004). Viscosity and specific volume of bulk metallic glass-forming alloys and their correlation with glass forming ability. Acta Mater. 52: 3689−3695. DOI: 10.1016/j.actamat.2004.04.023. View in Article CrossRef Google Scholar Scopus
[34]	Bai, F.X., Yao, J.H., Wang, Y.X., et al. (2017). Crystallization kinetics of an Au-based metallic glass upon ultrafast heating and cooling. Scr. Mater. 132: 58−62. DOI: 10.1016/j.scriptamat.2017.02.001. View in Article CrossRef Google Scholar Scopus
[35]	Reiner, M. (1964). The deborah number. Phys. Today 17: 62−62. DOI: 10.1063/1.3051374. View in Article CrossRef Google Scholar
[36]	Miedema, A.R. and Broeder, F.J.A.d. (1979). On the interfacial energy in solid-liquid and solid-solid metal combinations. Int. J. Mater. Res. 70: 14−20. DOI: 10.1515/ijmr-1979-700103. View in Article CrossRef Google Scholar
[37]	Boer, F.R.d., Mattens, W.C.M., Boom, R., et al. (1988). Cohesion in metals. Transition metal alloys (Amsterdam, Netherlands; North-Holland;). View in Article Google Scholar
[38]	Benedictus, R., Böttger, A., and Mittemeijer, E. (1996). Thermodynamic model for solid-state amorphization in binary systems at interfaces and grain boundaries. Phys. Rev. B 54: 9109. DOI: 10.1103/PhysRevB.54.9109. View in Article CrossRef Google Scholar Scopus
[39]	Kalb, J.A., Spaepen, F., and Wuttig, M. (2005). Kinetics of crystal nucleation in undercooled droplets of sb- and te-based alloys used for phase change recording. J. Appl. Phys. 98: 054910. DOI: 10.1063/1.2037870. View in Article CrossRef Google Scholar
[40]	Mukherjee, S., Zhou, Z., Schroers, J., et al. (2004). Overheating threshold and its effect on time–temperature-transformation diagrams of zirconium based bulk metallic glasses. Appl. Phys. Lett. 84: 5010−5012. DOI: 10.1063/1.1763219. View in Article CrossRef Google Scholar
[41]	Ericsson, A., Pacheco, V., Sahlberg, M., et al. (2020). Transient nucleation in selective laser melting of Zr-based bulk metallic glass. Mater. Des. 195: 108958. DOI: 10.1016/j.matdes.2020.108958. View in Article CrossRef Google Scholar Scopus
[42]	Hays, C.C., Schroers, J., Johnson, W.L., et al. (2001). Vitrification and determination of the crystallization time scales of the bulk-metallic-glass-forming liquid Zr_58.5Nb_2.8Cu_15.6Ni_12.8Al_10.3. Appl. Phys. Lett. 79 : 1605-1607. DOI: 10.1063/1.1398605. View in Article Google Scholar
[43]	Kim, Y.J., Busch, R., Johnson, W.L., et al. (1996). Experimental determination of a time–temperature‐transformation diagram of the undercooled Zr_41.2Ti_13.8Cu_12.5Ni_10.0Be_22.5 alloy using the containerless electrostatic levitation processing technique. Appl. Phys. Lett. 68 : 1057-1059. DOI: 10.1063/1.116247. View in Article Google Scholar
[44]	Zhao, J., Hui, J., Ye, Z., et al. (2022). Exploring “no man's land”—arrhenius crystallization of thin-film phase change material at 1 000 000 k s⁻¹ via nanocalorimetry. Adv. Mater. Interfaces 9: 2200429. DOI: 10.1002/admi.202200429. View in Article CrossRef Google Scholar
[45]	Orava, J., Greer, A.L., Gholipour, B., et al. (2012). Characterization of supercooled liquid Ge₂Sb₂Te₅ and its crystallization by ultrafast-heating calorimetry. Nat. Mater. 11: 279−283. DOI: 10.1038/nmat3275. View in Article CrossRef Google Scholar
[46]	Chen, B., ten Brink, G.H., Palasantzas, G., et al. (2017). Crystallization kinetics of gesbte phase-change nanoparticles resolved by ultrafast calorimetry. J. Phys. Chem. C 121: 8569−8578. DOI: 10.1021/acs.jpcc.6b11707. View in Article CrossRef Google Scholar
[47]	Gourvest, E., Pelissier, B., Vallée, C., et al. (2012). Impact of oxidation on Ge₂Sb₂Te₅ and gete phase-change properties. J. Electrochem. Soc. 159: H373. DOI: 10.1149/2.027204jes. View in Article CrossRef Google Scholar
[48]	Nozard, H. and Schiettekatte, F. (2021). Arrhenius behavior of crystallization at up to 184 000 k/s in Ge₂Sb₂Te₅ thin films. AIP Adv. 11: 085226. DOI: 10.1063/5.0058586. View in Article CrossRef Google Scholar
[49]	Jeyasingh, R., Fong, S.W., Lee, J., et al. (2014). Ultrafast characterization of phase-change material crystallization properties in the melt-quenched amorphous phase. Nano Lett. 14: 3419−3426. DOI: 10.1021/nl500940z. View in Article CrossRef Google Scholar Scopus
[50]	Pries, J., Wei, S., Wuttig, M., et al. (2019). Switching between crystallization from the glassy and the undercooled liquid phase in phase change material Ge₂Sb₂Te₅. Adv. Mater. 31: 1900784. DOI: 10.1002/adma.201900784. View in Article CrossRef Google Scholar
[51]	Glade, S.C., Busch, R., Lee, D.S., et al. (2000). Thermodynamics of Cu₄₇Ti₃₄Zr₁₁Ni₈, Zr_52.5Cu_17.9Ni_14.6Al₁₀Ti₅ and Zr₅₇Cu_15.4Ni_12.6Al₁₀Nb₅ bulk metallic glass forming alloys. J. Appl. Phys. 87 : 7242-7248. DOI: 10.1063/1.372975. View in Article Google Scholar
[52]	Heinrich, J., Busch, R., and Nonnenmacher, B. (2012). Processing of a bulk metallic glass forming alloy based on industrial grade Zr. Intermetallics 25: 1−4. DOI: 10.1016/j.intermet.2012.02.011. View in Article CrossRef Google Scholar Scopus
[53]	Gallino, I., Shah, M.B., and Busch, R. (2007). Enthalpy relaxation and its relation to the thermodynamics and crystallization of the Zr_58.5Cu_15.6Ni_12.8Al_10.3Nb_2.8 bulk metallic glass-forming alloy. Acta Mater. 55 : 1367-1376. DOI: 10.1016/j.actamat.2006.09.040. View in Article Google Scholar
[54]	Busch, R., Kim, Y.J., and Johnson, W.L. (1995). Thermodynamics and kinetics of the undercooled liquid and the glass transition of the Zr_41.2Ti_13.8Cu_12.5Ni_10.0Be_22.5 alloy. J. Appl. Phys. 77 : 4039-4043. DOI: 10.1063/1.359485. View in Article Google Scholar
[55]	Bünz, J. and Wilde, G. (2013). Direct measurement of the kinetics of volume and enthalpy relaxation of an Au-based bulk metallic glass. J. Appl. Phys. 114: 223503. DOI: 10.1063/1.4843716. View in Article CrossRef Google Scholar Scopus
[56]	Angell, C.A. (1997). Entropy and fragility in supercooling liquids. J. Res. Natl. Inst. Stand. Technol. 102: 171−185. DOI: 10.6028/jres.102.013. View in Article CrossRef Google Scholar Scopus
[57]	Tatsumisago, M., Halfpap, B.L., Green, J.L., et al. (1990). Fragility of Ge-As-Se glass-forming liquids in relation to rigidity percolation, and the kauzmann paradox. Phys. Rev. Lett. 64: 1549−1552. DOI: 10.1103/PhysRevLett.64.1549. View in Article CrossRef Google Scholar
[58]	Abiad, M.G., Carvajal, M.T., and Campanella, O.H. (2009). A review on methods and theories to describe the glass transition phenomenon: Applications in food and pharmaceutical products. Food Eng. Rev. 1: 105−132. DOI: 10.1007/s12393-009-9009-1. View in Article CrossRef Google Scholar
[59]	Zhong, L., Wang, J., Sheng, H., et al. (2014). Formation of monatomic metallic glasses through ultrafast liquid quenching. Nature 512: 177−180. DOI: 10.1038/nature13617. View in Article CrossRef Google Scholar Scopus
[60]	Evenson, Z., Schmitt, T., Nicola, M., et al. (2012). High temperature melt viscosity and fragile to strong transition in Zr–Cu–Ni–Al–Nb(Ti) and Cu₄₇Ti₃₄Zr₁₁Ni₈ bulk metallic glasses. Acta Mater. 60: 4712−4719. DOI: 10.1016/j.actamat.2012.05.019. View in Article CrossRef Google Scholar
[61]	Klement, W., Willens, R.H., and Duwez, P.O.L. (1960). Non-crystalline structure in solidified gold–silicon alloys. Nature 187: 869−870. DOI: 10.1038/187869b0. View in Article CrossRef Google Scholar
[62]	Lu, Z.P. and Liu, C.T. (2002). A new glass-forming ability criterion for bulk metallic glasses. Acta Mater. 50: 3501−3512. DOI: 10.1016/S1359-6454(02)00166-0. View in Article CrossRef Google Scholar Scopus
[63]	Lu, Z.P., Bei, H., and Liu, C.T. (2007). Recent progress in quantifying glass-forming ability of bulk metallic glasses. Intermetallics 15: 618−624. DOI: 10.1016/j.intermet.2006.10.017. View in Article CrossRef Google Scholar Scopus
[64]	Schwarz, R.B. and Johnson, W.L. (1983). Formation of an amorphous alloy by solid-state reaction of the pure polycrystalline metals. Phys. Rev. Lett. 51: 415−418. DOI: 10.1103/PhysRevLett.51.415. View in Article CrossRef Google Scholar Scopus
[65]	Chang, H., Takeuchi, I., and Xiang, X.-D. (1999). A low-loss composition region identified from a thin-film composition spread of (Ba_1−x−ySr_xCa_y)TiO₃. Appl. Phys. Lett. 74: 1165−1167. DOI: 10.1063/1.123475. View in Article CrossRef Google Scholar
[66]	Takeuchi, I., Chang, H., Gao, C., et al. (1998). Combinatorial synthesis and evaluation of epitaxial ferroelectric device libraries. Appl. Phys. Lett. 73: 894−896. DOI: 10.1063/1.122030. View in Article CrossRef Google Scholar Scopus
[67]	Wang, J., Yoo, Y., Gao, C., et al. (1998). Identification of a blue photoluminescent composite material from a combinatorial library. Science 279: 1712−1714. DOI. DOI: 10.1126/science.279.5357.1712. View in Article CrossRef Google Scholar
[68]	Xiang, X.D. (1998). Combinatorial synthesis and high throughput evaluation of functional oxides-a integrated materials chip approach. Mater. Sci. Eng. B 56: 246−250. DOI: 10.1016/S0921-5107(98)00221-9. View in Article CrossRef Google Scholar
[69]	Schultz, P.G. and Xiang, X.-D. (1998). Combinatorial approaches to materials science. Curr. Opin. Solid State Mater. Sci. 3: 153−158. DOI: 10.1016/S1359-0286(98)80081-8. View in Article CrossRef Google Scholar Scopus
[70]	Xiang, X.D. (1998). Combinatorial synthesis and high throughput evaluation of functional materials: An integrated materials chip approach to discovery, optimization and study of advanced materials. Mater. Today 1: 23−26. DOI: 10.1016/S1369-7021(98)80009-6. View in Article CrossRef Google Scholar
[71]	Xiang, X.-D. (1999). Combinatorial materials synthesis and high-throughput screening: An integrated materials chip approach to mapping phase diagrams and discovery and optimization of functional materials. Biotechnology and Bioengineering 61: 227−241. DOI: 3.0.CO;2-F">10.1002/(SICI)1097-0290(1998)61:4<227::AID-CC5>3.0.CO;2-F. View in Article CrossRef Google Scholar
[72]	Xiang, X.-D. (1999). Combinatorial materials synthesis and screening: An integrated materials chip approach to discovery and optimization of functional materials. Annu. Rev. Mater. Res. 29: 149−171. DOI: 10.1146/annurev.matsci.29.1.149. View in Article CrossRef Google Scholar
[73]	Yoo, Y.-K., Duewer, F., Yang, H., et al. (2000). Room-temperature electronic phase transitions in the continuous phase diagrams of perovskite manganites. Nature 406: 704−708. DOI: 10.1038/35021018. View in Article CrossRef Google Scholar Scopus
[74]	Li, J., Duewer, F., Gao, C., et al. (2000). Electro-optic measurements of the ferroelectric-paraelectric boundary in Ba_1−xSr_xTiO₃ materials chips. Appl. Phys. Lett. 76: 769−771. DOI: 10.1063/1.125889. View in Article CrossRef Google Scholar
[75]	Fister, L. and Johnson, D.C. (1992). Controlling solid-state reaction mechanisms using diffusion length in ultrathin-film superlattice composites. J. Am. Chem. Soc. 114: 4639−4644. DOI: 10.1021/ja00038a029. View in Article CrossRef Google Scholar
[76]	Abrosimova, G.E., Matveev, D.V., and Aronin, A.S. (2022). Nanocrystal formation in homogeneous and heterogeneous amorphous phases. Phys.-Usp. 65: 227−244. DOI: 10.3367/UFNe.2021.04.038974. View in Article CrossRef Google Scholar Scopus
[77]	Andrievski, R.A. and Glezer, A.M. (2009). Strength of nanostructures. Phys.-Usp. 52: 315−334. DOI: 10.3367/UFNe.0179.200904a.0337. View in Article CrossRef Google Scholar Scopus
[78]	Greer, A.L. (2001). Partially or fully devitrified alloys for mechanical properties. Mater. Sci. Eng. A 304-306: 68−72. DOI: 10.1016/S0921-5093(00)01449-0. View in Article CrossRef Google Scholar
[79]	Sun, L.G., Wu, G., Wang, Q., et al. (2020). Nanostructural metallic materials: Structures and mechanical properties. Mater. Today 38: 114−135. DOI: 10.1016/j.mattod.2020.04.005. View in Article CrossRef Google Scholar Scopus
[80]	Kou, H., Lu, J., and Li, Y. (2014). High-strength and high-ductility nanostructured and amorphous metallic materials. Adv. Mater. 26: 5518−5524. DOI: 10.1002/adma.201401595. View in Article CrossRef Google Scholar Scopus
[81]	Wu, G., Chan, K.-C., Zhu, L., et al. (2017). Dual-phase nanostructuring as a route to high-strength magnesium alloys. Nature 545: 80−83. DOI: 10.1038/nature21691. View in Article CrossRef Google Scholar Scopus
[82]	Zhu, J., Hu, Z., Guo, S., et al. (2023). Non-epitaxial growth of highly oriented transition metal dichalcogenides with density-controlled twin boundaries. The Innovation 4: 100502. DOI: 10.1016/j.xinn.2023.100502. View in Article CrossRef Google Scholar Scopus
[83]	Zhao, W., Yan, Y., Chen, X., et al. (2022). Combining printing and nanoparticle assembly: Methodology and application of nanoparticle patterning. The Innovation 3: 100253. DOI: 10.1016/j.xinn.2022.100253. View in Article CrossRef Google Scholar Scopus
[84]	Li, S., Dong, M., Peng, M., et al. (2022). Crystal-phase engineering of pdcu nanoalloys facilitates selective hydrodeoxygenation at room temperature. The Innovation 3: 100189. DOI: 10.1016/j.xinn.2021.100189. View in Article CrossRef Google Scholar
[85]	Wuttig, M. and Yamada, N. (2007). Phase-change materials for rewriteable data storage. Nat. Mater. 6: 824−832. DOI: 10.1038/nmat2009. View in Article CrossRef Google Scholar Scopus
[86]	Wöltgens, H.W. (2003). Combinatorial material synthesis applied to Ge-Sb-Te based phase change materials. PhD thesis (RWTH Aachen University). View in Article Google Scholar
[87]	Wang, W.H. (2009). Bulk metallic glasses with functional physical properties. Adv. Mater. 21: 4524−4544. DOI: 10.1002/adma.200901053. View in Article CrossRef Google Scholar Scopus
[88]	Wang, W.H., Dong, C., and Shek, C.H. (2004). Bulk metallic glasses. Mat. Sci. Eng. R. 44: 45−89. DOI: 10.1016/j.mser.2004.03.001. View in Article CrossRef Google Scholar Scopus
[89]	Torquato, S. (2000). Hard knock for thermodynamics. Nature 405: 521−523. DOI: 10.1038/35014711. View in Article CrossRef Google Scholar Scopus

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Dong H., Zhang P., Qin M., et al., (2024). Quantitative understanding of the initial stage of liquid to crystalline or amorphous phase transitions. The Innovation Materials 2(3): 100086. https://doi.org/10.59717/j.xinn-mater.2024.100086

Dong H., Zhang P., Qin M., et al., (2024). Quantitative understanding of the initial stage of liquid to crystalline or amorphous phase transitions. The Innovation Materials 2(3): 100086. https://doi.org/10.59717/j.xinn-mater.2024.100086

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