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

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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.