First-principles local stress in crystalline and amorphous metals.

Atomic size is perhaps the most commonly used concept to describe material properties. Advances in the understanding of materials are hindered by the available choices of simplifying concepts that can be used. However, the precise definition of atomic size is not easy, and often controversial. Atomic level stress provides a new interpretive tool that draws on the rich formalism of solid mechanics for use with density functional calculations to advance a deeper understanding of the properties of materials. We discuss atomic level stresses in liquids and glasses and make comparisons with ordered and disordered crystals. Somewhat surprisingly, even ordered compounds that are under no macroscopic stress and whose individual atoms are completely relaxed, i.e., no force acting on them, can have substantial atomic level stresses. On top of concepts such as the ionicity or covalency, the atomic level stresses add to the arsenal of analysis tools that are available to interpret the results of density functional calculations.

Applications of a general random-walk theory for confined diffusion.

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.