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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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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