Microscopic approaches to the nonlinear mechanics of driven defect-rich crystals

我们将研究硬质和软质晶体在大应力和大变形的非线性和非平衡区的弹性和塑性性质。将三个研究小组聚集在一起，使我们能够从微观原理出发考虑三种不同的互补方法，以便计算这些系统的弹性系数和输运系数，并推导出缺陷晶体中弹性、塑性和输运现象的宏观方程。这些方法是(1)带有投影算子的统计力学概念，(2)经典密度泛函理论，和(3)有效的计算机模拟。众所周知，位错是晶格的拓扑缺陷，其弹塑性性质受位错的影响很大，并且具有很高的流动性。然而，对于不改变晶格结构的点缺陷对弹性和输运的影响却知之甚少，这些点缺陷对应于空位、间隙颗粒或单个晶格上的几个颗粒。虽然在宏观层面上，标准弹性理论描述了七种模式(声波和扩散热传输)，但马丁、帕罗迪和珀尔尚以及弗莱明和科恩的两部开创性著作在40多年前就已经表明，一定存在第八种模式来描述点缺陷的扩散。关于这第八个模式及其与微观层面上的应变的耦合，人们知之甚少。最近的兴趣源于发现了具有巨大缺陷密度的晶体，其中每个粒子在其相邻粒子中平均经历了接近一个缺陷的情况。为此，我们的项目将主要集中在点缺陷上，并阐述点缺陷在非线性和非平衡区中的扩散运动及其对材料弹塑性性质的影响的微观理解。我们将特别考虑软晶体材料和团簇晶体，它们具有丰富的缺陷，并有望显示出强大的影响。

We will investigate the elastic and plastic properties of hard and soft matter crystals in the nonlinear and non-equilibrium regime for large stresses and large deformations. Bringing together three research groups, allows us to consider three different complementary approaches starting from microscopic principles in order to calculate elastic and transport coefficients of these systems and to derive the macroscopic equations for elastic, plastic, and transport phenomena in defective crystals. These approaches are (1) statistical mechanics concepts with projection operators, (2) classical density functional theory, and (3) efficient computer simulations. It is well known that the elastic and plastic properties are strongly influenced by dislocations which are topological defects of the crystal lattice and are highly mobile. However, less is known about the effect on elasticity and transport arising frompoint defects which do not change the lattice structure and which correspond to vacancies, interstitial particles, or several particles on a single lattice site. While on a macroscopic level standard elastic theories describe seven modes (sound waves and diffusive heat transport), two seminal works by Martin, Parodi, and Pershan and by Fleming and Cohen have shown already more than forty years ago that there must be an eighth mode which describes the diffusion of point defects. Little is known about this eighth mode and its coupling to strains on the microscopic level. Recent interest results from the discovery of crystals with giant defect densities, where each particle experiences on average close to one defect among its neighbors. For this reason, our project will mainly focus on point defects and elaborate a microscopic understanding for their diffusive motion and their influence on the elastic and plastic properties of the material in the nonlinear and the non-equilibrium regime. We will especially consider soft crystalline materials and cluster crystals which are defect-rich and are expected to show strong effects.