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Strain Functionals for Characterizing Atomistic Geometries

Edward Kober (Los Alamos National Laboratory)

From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A

Wed 9:00 - 10:30

CIT 165

The development of a set of strain tensor functionals that are suitable for characterizing atomistic structures in atomistic simulations is described. The target application is to characterize general deformation processes in polycrystalline materials with random orientations. The approach is to recast the atomic coordinates in terms of atomic “neighborhoods” and describe those neighborhoods by Taylor’s series expansions. The coefficients of those expansions can be derived from the corresponding moments of the neighborhood that are defined by the local strain. The neighborhoods are defined using a Maximum Entropy (ME) method that establishes a non-arbitrary definition of an atomic neighborhood that is smooth and differentiable, and achieves a unitary transformation. To first order, this neighborhood definition is a Gaussian weighting function that has a width defined by the local atomic spacing. For general analysis, it is useful to recast the resulting moments in terms of Rotationally Invariant Functions (RIF), which are the basis elements of the three-dimensional rotationally invariant space group, SO(3). These are specific polynomial combinations of the solid harmonic functions (also called 3D Zernike functions), which are similar to functions used for pattern recognition and image processing. The expansions are carried out to fourth order to enable the distinctions between crystal habitats, analogous to the fourth order stiffness/compliance tensors. This is also at the convergence limit of the Taylor expansion of the Gaussian neighborhood. Other commonly used metrics such as the Steinhardt order parameters and the centrosymmetry parameter can be shown to be essentially subsets of this formally complete expansion basis. The net result is the definition of an n-th order strain map with essentially atomic level resolution, where defect structures of arbitrary geometry can be readily identified.