Probing the hidden order in glasses
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摘要: 通过探究玻璃态物质中原子结构的径向空间关联形式及对应的晶体相晶格结构，发现它们之间存在密切联系，这一特点通过数值模拟和实验所获得的玻璃材料都得到了很好的验证．相关结果表明，结构同源性同样存在于玻璃固体与其对应晶体相之间，进而提出了从同源性视角出发探讨非晶物理与材料学的问题，可为更深入地理解玻璃固体中的原子结构及其结构物性关系提供新的思路．Abstract: This work aims to explain how materials like glass are structured, one of the most important puzzles in the field of complex physical systems． The atomic packing formula in glass materials is found to correlate with lattice structure and symmetry of their crystalline counterparts, this holds well both in numerical and realistic experimental glass systems． This indicates that structure homology also exists between a glassy solid and its parent crystal, leading us to the proposal that, in the study of glass physics and material science, thinking in terms of homology may open new doors to understanding the nature of atomic structures and structure-property relationships in glass materials．
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图 1 温度T = 300 K时玻璃态Ni和Fe的原子结构PCF曲线及相关结果显示
注：a和b分别是温度为300 K时，通过MD模拟得到的玻璃态g-Ni和g-Fe及晶体态c-Ni和c-Fe的原子空间关联函数；c和d分别为对应样品角分布信息；e为玻璃与晶体的典型原子结构构型．
表 1 原子空间PCF中的第1峰峰位
$ {\mathit{R}}_{1} $ 和$ {\mathit{R}}_{\mathit{i}}/{\mathit{R}}_{1} $ 玻璃态/非晶态 R1/nm R2/R1 R3/R1 R4/R1 R5/R1 Ni glass 0.245 1.74($ \sqrt{3} $) 1.98($ \sqrt{4} $) 2.63($ \sqrt{7} $) 3.46($ \sqrt{12} $) Fe glass 0.248 1.65($ \sqrt{8/3} $) 2.00($ \sqrt{4} $) 2.58($ \sqrt{20/3} $) 3.47($ \sqrt{12} $) Amorphous Si 0.238 1.61($ \sqrt{8/3} $) 2.42($ \thickapprox\sqrt{19/3} $) 2.91($\thickapprox\sqrt{8} $) 3.12($ \thickapprox\sqrt{9} $) 注：Ni glass和Fe glass数据来源于MD模拟；Amorphous Si的数据则取自实际实验室衍射数据[23]． 
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表 2 fcc（F）、bcc（B）和金刚石晶格结构的相对原子位置信息
类别 $ {\mathit{R}}_{1}^{0} $ $ {\mathit{R}}_{2}^{0} $ $ {\mathit{R}}_{3}^{0} $ $ {\mathit{R}}_{4}^{0} $ $ {\mathit{R}}_{5}^{0} $ $ {\mathit{R}}_{6}^{0} $ $ {\mathit{R}}_{7}^{0} $ $ {\mathit{R}}_{8}^{0} $ $ {\mathit{R}}_{9}^{0} $ $ {\mathit{R}}_{10}^{0} $ $ {\mathit{R}}_{11}^{0} $ $ {\mathit{R}}_{12}^{0} $ $ {\mathit{R}}_{13}^{0} $ $ {\mathit{R}}_{14}^{0} $ F 1 $ \sqrt{2} $ $ \sqrt{3} $ $ \sqrt{4} $ $ \sqrt{5} $ $ \sqrt{6} $ $ \sqrt{7} $ $ \sqrt{8} $ $ \sqrt{9} $ $ \sqrt{10} $ $ \sqrt{11} $ $ \sqrt{12} $ $ \sqrt{13} $ $ \sqrt{15} $ B 1 $ \sqrt{4/3} $ $ \sqrt{8/3} $ $ \sqrt{11/3} $ $ \sqrt{4} $ $ \sqrt{16/3} $ $ \sqrt{19/3} $ $ \sqrt{20/3} $ $ \sqrt{8} $ $ \sqrt{9} $ $ \sqrt{32/3} $ $ \sqrt{35/3} $ $ \sqrt{12} $ $ \sqrt{40/3} $ D 1 $ \sqrt{8/3} $ $ \sqrt{11/3} $ $ \sqrt{16/3} $ $ \sqrt{19/3} $ $ \sqrt{8} $ $ \sqrt{9} $ $ \sqrt{32/3} $ $ \sqrt{35/3} $ $ \sqrt{40/3} $ $ \sqrt{43/3} $ $ \sqrt{16} $ $ \sqrt{17} $ $ \sqrt{56/3} $ 注： $ {R}_{1}^{0} $被设定为1；$ {R}_{i}^{0} $ （$i = 1,2,\cdots,14 $）是第$ i $近邻原子的相对距离．
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表 3 各种金属玻璃PCF的第1峰位
$ {\mathit{R}}_{1} $ 和约化后的第2峰位$ {\mathit{R}}_{2}/{\mathit{R}}_{1} $ ，以及这些金属玻璃经退火后的结晶析出相金属玻璃 R1/nm R2/R1 退火后的晶体析出相 参考文献 Zr44.5Al10Cu20Ni8 Ti7.5 0.304 1.68 CuZr2 (bcc-type)
NiZr2 (bcc-type)
CuZr (bcc-type)
NiZr (bcc-type)
Fe (bcc-type)[26] Zr57Al10Cu20Ni8 Ti5 0.311 1.66 [26] Zr58Al10Cu20Ni8 Ti4 0.311 1.68 [26] Zr59Al10Cu20Ni8 Ti3 0.311 1.66 [26] Zr60Al10Cu20Ni8 Ti2 0.312 1.67 [26] Fe82B18 0.257 1.65 [27，28] Cu60Zr30Ti10 0.269 1.74 CuTi (fcc-type)
MgZn-type (hcp)
Al (fcc-type)[29，30] Zr41Ti14Cu12.5Ni10Be22.5 0.272 1.73 [30，31] Cu47Ti33Zr11Ni8Si1 0.275 1.74 [32] Al90Fe5Nb5 0.315 1.74 [33]
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