Relationship Between Atomic Structure and Mechanical Properties of Interfaces and Free Surfaces

从原子和连续体的角度研究晶界和双晶的力学性能。通过与详细的原子模拟的比较，建立了在原子尺度上对晶界非均质性质的连续描述的有效性。这导致了局部稳定、亚稳和不稳定晶界结构的分类，并在给定双晶的多个晶界结构中识别出物理上更合理的结构。这项研究建立在这些发现的基础上，并继续强调原子论和连续统理论之间的关系。将对界面区域和自由表面的内应力进行详细的研究，这些内应力通常是相当大的。本文将研究弹性模量的四阶张量丧失正确定性或强椭圆性的含义，以及相应的局部负应变能或分岔和不连续的可能性。对于原子非均质连续体模型的有效性质，将发展出更好的界限或估计。该理论将应用于两种不同金属之间的晶界和界面，自由表面，薄膜和衬底之间的界面，以及合金的影响，表现为偏析和/或有序，对弹性性能。材料的机械性能的研究通常使用连续的方法，即使已知材料是由离散的元素，如原子和分子组成的。其力学性能取决于晶粒间的晶界结构和双晶的存在。从原子的角度研究晶界的结构是可能的。然而，很少有工作将晶界的原子研究与连续体方法联系起来。这项拨款就是要做到这一点。我们将采用一种一致的方法从原子的角度来研究晶界，然后将其与连续体描述联系起来。

Research will be conducted on the mechanical properties of grain boundaries and bicrystals from both atomistic and continuum points of view. The validity of a continuum description of the heterogeneous nature of grain boundaries at the atomic scale has been established through comparisons with detailed atomistic simulations. This has led to the classification of locally stable, metastable and unstable grain boundary structures and identification of the physically more reasonable structure among the multiple ones found for a given bicrystal. The research builds on these findings and continues to emphasize the relation between atomistic and continuum theories. A detailed study of the internal stresses in interface regions and at free surfaces, which can generally be of significant magnitude, will be undertaken. The implication of the loss of positive definitieness or strong ellipticity for the fourth-order tensor of elastic moduli and the corresponding possibiity, respectively, of locally negative strain energies or bifurcations and discontinuities will be studied. Better bounds or estimates for the effective properties of the atomically heterogeneous continuum model will be developed. The theory wil be applied to grain boundaries and interfaces between two different metals, free surfaces, interfaces between thin films and substrates, and the influence of alloying, manifested in segregation and/or ordering, on elastic properties. %%% Studies of the mechanical properties of materials usually use a continuum approach even though materials are known to be made up of discrete elements such as atoms and molecules. The mechanical properties are dependent on the structure of grain boundaries bewteen crystal grains and on the existence of bicrystals. It is possible to study the structure of grain boundaries from an atomistic approach. However, there is very little work which connects the atomistic study of grain boundaries with the continuum approach. This grant proposes to do just this. A consistent approach will be taken to study grain boundaries from an atomistic point of view and then connect this with the continuum description.