Alderson A, Evans K E
Centre for Materials Research and Innovation, University of Bolton, Deane Road, Bolton BL3 5AB, UK.
J Phys Condens Matter. 2009 Jan 14;21(2):025401. doi: 10.1088/0953-8984/21/2/025401. Epub 2008 Dec 9.
Analytical expressions have been developed in which the elastic behaviour of the α-quartz and α-cristobalite molecular tetrahedral frameworks of both silica and germania are modelled by rotation, or dilation or concurrent rotation and dilation of the tetrahedra. Rotation and dilation of the tetrahedra both produce negative Poisson's ratios (auxetic behaviour), whereas both positive and negative values are possible when these mechanisms act concurrently. Concurrent rotation and dilation of the tetrahedra reproduces with remarkable accuracy both the positive and negative ν(31) Poisson's ratios observed for silica α-quartz and α-cristobalite, respectively, when loaded in the x(3) direction. A parametric fit of the concurrent model to the germania α-quartz experimental ν(31) Poisson's ratio is used to predict ν(31) for germania α-cristobalite, for which no experimental value exists. This is predicted to be +0.007. Strain-dependent ν(31) trends, due to concurrent rotation and dilation in the silica structures, are in broad agreement with those predicted from pair-potential calculations, although significant differences do occur in the absolute values. With the model of concurrent dilation and rotation of the tetrahedra we predict that an alternative uniaxial stress (σ(3))-induced phase exists for both silica, α-quartz and α-cristobalite, and germania, α-cristobalite, having geometries in reasonable agreement with β-quartz and idealized β-cristobalite, respectively.
已经开发出解析表达式，其中通过四面体的旋转、膨胀或同时旋转和膨胀来模拟二氧化硅和氧化锗的α-石英和α-方石英分子四面体框架的弹性行为。四面体的旋转和膨胀都会产生负泊松比（负泊松比行为），而当这些机制同时作用时，正负值都是可能的。当在x(3)方向加载时，四面体的同时旋转和膨胀分别以极高的精度再现了在二氧化硅α-石英和α-方石英中观察到的正ν(31)泊松比和负ν(31)泊松比。将同时模型对氧化锗α-石英实验ν(31)泊松比进行参数拟合，以预测氧化锗α-方石英的ν(31)，因为没有其实验值。预测该值为+0.007。由于二氧化硅结构中的同时旋转和膨胀，应变相关的ν(31)趋势与对势计算预测的趋势大致一致，尽管在绝对值上确实存在显著差异。利用四面体同时膨胀和旋转的模型，我们预测对于二氧化硅的α-石英和α-方石英以及氧化锗的α-方石英，存在另一种单轴应力（σ(3)）诱导相，其几何形状分别与β-石英和理想化的β-方石英合理一致。
