Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, CB2 3RA Cambridge, UK.
Soft Matter. 2017 Sep 20;13(36):6079-6089. doi: 10.1039/c7sm00843k.
The mechanical, thermal and vibrational properties of defective crystals are important in many different contexts, from metallurgy and solid-state physics to, more recently, soft matter and colloidal physics. Here we study two different models of disordered fcc crystal lattices, with randomly-removed bonds and with vacancies, respectively, within the framework of non-affine lattice dynamics. We find that both systems feature the same scaling of the shear modulus with the newly defined inversion-symmetry breaking (ISB) parameter, which shows that local inversion-symmetry breaking around defects is the universal root source of the non-affine softening of the shear modulus. This finding allows us to derive analytical relations for the non-affine (zero-frequency) shear modulus as a function of vacancy concentration in excellent agreement with numerical simulations. Nevertheless, due to the different microstructural disorder, the spatial fluctuations of the local ISB parameter are different in the vacancy and bond-depleted case. The vacancy fcc exhibits comparatively a more heterogenous microstructural disorder (due to the broader distribution of coordination number Z), which is reflected in a different scaling relation between boson peak frequency in the DOS and the average Z[combining macron]. These differences are less important at low vacancy concentrations, where the numerical DOS of the vacancy fcc can be well described theoretically by coherent-potential approximation, developed here for the bond-depleted fcc lattice in 3d.
有缺陷晶体的力学、热学和振动特性在许多不同的背景下都很重要，从冶金学和固态物理到最近的软物质和胶体物理。在这里，我们在非仿射晶格动力学的框架内研究了两种不同的无序面心立方晶格模型，分别是随机去除键和空位。我们发现，这两个系统的剪切模量与新定义的反转对称性破坏（ISB）参数的标度相同，这表明缺陷周围的局部反转对称性破坏是剪切模量非仿射软化的普遍根本原因。这一发现使我们能够推导出空位浓度与非仿射（零频）剪切模量之间的解析关系，与数值模拟结果非常吻合。然而，由于微观结构的不同，空位和键缺失情况下局部 ISB 参数的空间波动是不同的。空位面心立方结构表现出相对更不均匀的微观结构无序（由于配位数 Z 的分布更宽），这反映在 DOS 中玻色峰频率与平均 Z[组合]之间的不同标度关系上。在低空位浓度下，这些差异并不重要，此时空位面心立方结构的数值 DOS 可以通过我们在这里为 3d 中的键缺失面心立方晶格开发的相干势近似理论很好地描述。
