论文标题
位错堆积的统计力学
Statistical Mechanics of Dislocation Pileups in Two Dimensions
论文作者
论文摘要
脱位堆积直接通过相互作用位错的排列和集体运动直接影响晶体固体的材料特性。我们研究了这些有序的缺陷结构的统计力学，这些缺陷结构嵌入了二维晶体中，其中错位本身形成了一维晶格。特别是，堆积体现了一类新的不均匀晶体，其特征在于晶格间距的空间变化。 By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocation positions onto the eigenvalues of recently studied random matrix ensembles, we uncover two types of one-dimensional phase transitions in dislocation pileups: a thermal depinning transition out of long-range translational order from the pinned-defect phase, due to a periodic Peierls potential, to a浮动缺失状态，最后是从准范围熔化的浮动缺陷相位到缺陷液。我们还发现了可以通过一维结构因子直接观察到这些过渡的一组过渡温度，在该因素中，Delta功能braggs在固定缺失到浮动缺陷过渡的悬挂率上扩展到代数呈差异化的bragg峰，然后依次消失，因为这是一种接近两型层次熔融式融化的宿主晶体。我们为结构因子和径向分布函数计算一组依赖温度的临界指数，并使用随机矩阵理论获得均匀和不均匀堆积的确切形式。
Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in two dimensional crystals, where the dislocations themselves form one-dimensional lattices. In particular, pileups exemplify a new class of inhomogeneous crystals characterized by spatially varying lattice spacings. By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocation positions onto the eigenvalues of recently studied random matrix ensembles, we uncover two types of one-dimensional phase transitions in dislocation pileups: a thermal depinning transition out of long-range translational order from the pinned-defect phase, due to a periodic Peierls potential, to a floating-defect state, and finally the melting out of a quasi-long range ordered floating defect-solid phase to a defect-liquid. We also find the set of transition temperatures at which these transitions can be directly observed through the one-dimensional structure factor, where the delta function Bragg peaks, at the pinned-defect to floating-defect transition, broaden into algebraically diverging Bragg peaks, which then sequentially disappear as one approaches the two-dimensional melting transition of the host crystal. We calculate a set of temperature-dependent critical exponents for the structure factor and radial distribution function, and obtain their exact forms for both uniform and inhomogeneous pileups using random matrix theory.
