非静水应力下晶体中的化学压力与空位
Chemical pressure and vacancies in crystals under nonhydrostatic stress
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中文总结 AI 辅助
本文提出了一种新的晶体组分-应力耦合机制，推导了相关控制方程，通过模拟发现其与Larché-Cahn理论在表面牵引力变形体系中定性一致，重力变形体系偏差更显著。
中文摘要 AI 辅助
非均匀应力是晶体中空位扩散的驱动力，反过来，空位的非均匀分布会诱导产生应力。晶体中组分-应力耦合的公认理论是Larché-Cahn（LC）理论，该理论中组分由晶格位点的粒子数定义，每个位点最多容纳1个粒子，耦合通过在应力的本构关系中向弹性应变添加组应变项来建模。本文提出的另一种机制是让位点结合能随空间（变形）密度变化，这会产生化学压力，该压力会叠加到弹性应力上。使用非平衡连续介质热力学方法推导了该模型的控制方程，化学压力梯度具有双重作用：既作为迁移的漂移力，又作为弹性应力的柯西方程中的有效内部体力。本文的实际评估限于平衡性质，研究了外部施加的非静水应力的影响，其形式为表面牵引力或体力密度（重力），模型系统为具有固定晶格位点数的单组分晶体，粒子数可变但始终少于晶格位点数，线性弹性响应由标准Lamé应力张量建模。表面牵引力变形系统的结果与LC理论定性一致，仅弹性模量表达式存在差异，而重力变形晶体的偏差更为显著。
英文摘要
Inhomogeneous stress is a driving force for diffusion of vacancies in crystals. The other way around a non-uniform distribution of vacancies induces stress. The accepted theory of composition-stress coupling in crystals is Larché-Cahn (LC) theory. Composition is defined in terms of the population of lattice sites with a limit of one-particle per site. Coupling is modelled by adding a compositional strain term to the elastic strain in the constitutive relation for stress. An alternative mechanism, proposed here, is letting the site binding energy vary with spatial (deformed) density. This generates a chemical pressure adding to the elastic stress. The governing equations for this model are derived using non-equilibrium continuum thermodynamic methods. The gradient of the chemical pressure has a dual function acting both as the drift force for migration and as an effective internal one body force in the Cauchy equation for the elastic stress. The practical evaluation presented in the paper is restricted to equilibrium properties. We examine the effect of externally applied non-hydrostatic stress, either in the form of surface tractions or a one-body force density (gravitation). The model system is a one component crystal with a fixed number of lattice sites. The number of particles can be variable but is always smaller than the number of lattice sites. The linear elastic response is modelled by the standard Lamé stress tensor. The results for systems deformed by surface tractions are in qualitative agreement with LC theory allowing for differences in the expression for the elastic moduli. Deviations are more serious for the crystal deformed by gravitation.
发表机构
- Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素夫·哈米德化学系）
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