D. Wolf

Formalism for the calculation of local elastic constants at grain boundaries by means of atomistic simulation

A new formalism for use in atomistic simulations to calculate the full local elastic‐constant tensor in terms of local stresses and strains is presented. Results of simulations on a high‐angle (001) twist grain boundary are illustrated, using both a Lennard–Jones potential for Cu and an embedded‐atom potential for Au. The two conceptionally rather different potentials show similar anomalies in all elastic constants, confined to within a few lattice planes of the grain boundary, with an especially dramatic reduction in the resistance to shear parallel to the grain‐boundary plane. It is found that the primary cause of the anomalies is the atomic disorder near the grain boundary, as evidenced by the slice‐by‐slice radial distribution functions for the inhomogeneous interface system.

Molecular dynamics calculation of free energy

The results of a systematic study of a recently proposed method by Frenkel and Ladd for calculating free energies via molecular dynamics are reported. Internal measures of the error, the effect of varying parameters, and comparison of the relative computational efficiency of the method compared to other methods is considered. In particular, agreement with the quasiharmonic method is shown for temperatures up to 75% of melting.

Anomalous elastic behavior in superlattices of twist grain boundaries in silicon

The elastic constants and moduli of superlattices of high‐angle twist grain boundaries on the two densest crystallographic planes of silicon are calculated using Stillinger and Weber’s three‐body potential. While in both cases the Young’s and shear moduli are found to be softened, the Poisson ratios and some elastic constants, in particular C33 (in the direction of the interface‐plane normal), are found to be hardened. It is shown that the elastic behavior is determined by the structural disorder at the interfaces, and that it cannot be understood in terms of the dimensional changes of the system alone. A comparison with similar calculations for metallic superlattices elucidates the role of the covalent nature of bonding of silicon on its elastic behavior.

Nucleation and kinetics of thermodynamic melting: A molecular dynamics study of grain-boundary induced melting in silicon

Abstract A molecular dynamics study of a silicon bicrystal illustrates that thermodynamic melting is rapidly nucleated at, and grows from a grain boundary. No premelting or disordering below the thermodynamic melting temperature is found. These observations are entirely consistent with experiment.

On the relevance of extrinsic defects to melting: A molecular dynamics study using an embedded atom potential

Three basic classes of theories of melting have been proposed. The first treats the phenomenon as a homogeneous, bulk process involving a lattice instability, in which the (temperature-dependent) normal modes of the lattice become unstable at sufficiently high temperature. The second involves a mechanical instability occurring when the concentration of intrinsic (i.e., thermally-generated) defects reaches a critical concentration. The third class, originating from experimental observation, describes melting as nucleating at extrinsic defects such as free surfaces, grain boundaries (GBs) etc. Several recent measurements demonstrate that when the surface conditions are modified, the melting point can be depressed or the solid can be substantially superheated. The implication is that melting is basically a heterogeneous process and the mechanism of nucleation at extrinsic defects generally determines the kinetics.