C woodward dr trinkle lg hector jr dl olmsted

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C. Woodward, D.R. Trinkle, L.G. Hector, Jr., D.L. Olmsted, “Prediction of Dislocation Cores in Aluminum from Density Functional Theory,” Physical Review Letters 100 (2008) 045507. J. A. Yasi, L.G. Hector, Jr., D.R. Trinkle, “First-principles Data for Solid- Solution Strengthening of Magnesium: From Geometry and Chemistry to Properties,” Acta Materialia 58 (2010) 5704. G. Leyson, W.A. Curtin, L.G. Hector, Jr., C. Woodward, “Quantitative Prediction of Solute Strengthening in Aluminum Alloys,” Nature Materials published on-line, August, 2010. S. Ganeshan, L.G. Hector, Jr., Z.-K. Liu, “First-principles Calculations of Impurity Diffusion Coefficients in Dilute Mg alloys with the 8 frequency model, “ Acta Materialia , in review.
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We Need Material Properties in All Cases: So What are Examples of Quantities that can be Predicted with DFT Inputs? Components of the elasticity tensor (C ij ) C v (T)and C p (T): heat capacities Thermodynamic functions: enthalpy of formation, free energy, zero point energy, vibrational entropy. Binding energies Critical Point in Phase Transitions (e.g. Cerium) Yield strength (as function of solute chemistry) Dielectric properties (Born charge tensor components, dielectric tensor components) Thermal expansion tensor ( ij ) Magnetism Transition state barriers Diffusion coefficients (self- and impurity) Work of Separation/Adhesion Negative Possion’s ratio (auxetic materials) *Y Wang, et al. Phys. Rev. B 78 (2008) 104113/1-9. T-V Phase Diagram for Ce*
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Components of the Elasticity Tensor, C ij : Why Important? Fundamental intrinsic material properties Important components of Hooke’s law/elasticity If you want to predict dislocation core structures starting with anisotropic elasticity theory, you will need the C ij Useful for predicting mechanical instability If one knows the C ij , then one knows the sounds speeds Indicative of bonding in solids (cf. diamond with Lithium) With the C ij , one can calculate polycrystalline: Young's Modulus, E (a proportionality constant between uniaxial stress and strain; Poisson's Ratio, (the ratio of transverse to axial strain); bulk modulus, B (measure of the incompressibility); shear Modulus, G (measure of a resistance to shear) Thermodynamic stability can influenced by elastic constants* * M. Baldi et al. Phys. Rev. Lett. 102 (2009) 226102
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Energy-Based Formulation Expression for the energy U in a harmonic approximation is  i j j i ij C U U 0 2 ) ( 2 where i and j run over the 6 components of the strain. However, we don’t actually know the strain! We know what we applied, but the initial structure has some strain typically. Let the initial strain be S and the applied strain be e , then ) ( ) ( 2 ) ( 2 0 S e C S e T U e U e S ε and C ij determined individually or as sums from second derivatives of U w.r.t. displacements!
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Stress-Based Formulation* With an arbitrary (unknown) initial strain E and the corresponding stress , we applied strains e.
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  • VASP, density functional theory

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