J.J. Hoyt

Calculation of stress in atomistic simulation

Atomistic simulation is a useful method for studying material science phenomena. Examination of the state of a simulated material and the determination of its mechanical properties is accomplished by inspecting the stress field within the material. However, stress is inherently a continuum concept and has been proven difficult to define in a physically reasonable manner at the atomic scale. In this paper, an expression for continuum mechanical stress in atomistic systems derived by Hardy is compared with the expression for atomic stress taken from the virial theorem. Hardys stress expression is evaluated at a fixed spatial point and uses a localization function to dictate how nearby atoms contribute to the stress at that point; thereby performing a local spatial averaging. For systems subjected to deformation, finite temperature, or both, the Hardy description of stress as a function of increasing characteristic volume displays a quicker convergence to values expected from continuum theory than volume averages of the local virial stress. Results are presented on extending Hardys spatial averaging technique to include temporal averaging for finite temperature systems. Finally, the behaviour of Hardys expression near a free surface is examined, and is found to be consistent with the mechanical definition for stress.

Atomistic and continuum modeling of dendritic solidification

Abstract Due to its technological importance, modeling of dendrite growth in pure metals and alloys remains a significant challenge in the field of materials science. In this review recent achievements in the dendrite modeling problem, using two distinct length scale approaches, are summarized. At the nanometer scale, molecular dynamics and Monte Carlo techniques have been developed to extract two important properties of the solid–liquid interface: the kinetic coefficient and the solid–liquid interfacial free energy. Perhaps more importantly the atomistic simulation methods are capable of accurately determining the small, yet crucially important, anisotropies of these parameters. At the mesoscopic scale, advances in phase field modeling have largely overcome the numerical problem associated with the large disparity in length scales typically found in dendrite growth. It is demonstrated that, when the atomistic and continuum level approaches are combined, accurate and parameter free predictions of dendrite growth velocities are possible. In addition, extensions of atomistic and phase field modeling to the case of binary alloys are described.

Kinetic phase field parameters for the Cu–Ni system derived from atomistic computations

In the phase field model of binary solidification the mobility terms which appear in the governing rate equations can be estimated from the liquid diffusion coefficients of the pure elements and the velocity of the solid-liquid interface as a function of undercooling. Molecular dynamics simulations utilizing embedded atom potentials have been employed to compute the liquid diffusivities for pure Cu and Ni in the vicinity of their melting points. In both cases the diffusion coefficient is found to vary linearly with temperature and the results are in good agreement with experimental values which are available for Cu. The simulations were also employed to obtain the boundary velocities in three different low index growth directions. The results for Cu and Ni were found to be very similar, with the slope of the velocity-undercooling curve at small undercoolings varying in the range 45--18 cm/s/K. Anisotropy in the growth behavior was observed with V{sub 100} > V{sub 110} > V{sub 111}. The solid-liquid interface velocities were found to be a factor of 4--5 less than the theoretical upper limit derived previously.

Determination of the anomalous scattering factors for Cu, Ni and Ti using the dispersion relation

X-ray absorption spectra about the K edges of Ni, Cu and Ti have been measured at the Stanford Synchrotron Radiation Laboratory. The imaginary part of the atomic scattering factor f′′ was determined using the optical theorem and the real part f′ computed by the Kramers–Kronig dispersion relation. Methods for evaluating this integral as well as the effects on f′ of various experimental errors are investigated. The f′ results for Cu and Ni are compared to data from interferometry experiments.

Development of interatomic potentials appropriate for simulation of solid–liquid interface properties in Al–Mg alloys

Different approaches are analyzed for construction of semi-empirical potentials for binary alloys, focusing specifically on the capability of these potentials to describe solid–liquid phase equilibria, as a pre-requisite to studies of solidification phenomena. Fitting ab initio compound data does not ensure correct reproduction of the dilute solid-solution formation energy, and explicit inclusion of this quantity in the potential development procedure does not guarantee that the potential will predict the correct solid–liquid phase diagram. Therefore, we conclude that fitting only to solid phase properties, as is done in most potential development procedures, generally is not sufficient to develop a semi-empirical potential suitable for the simulation of solidification. A method is proposed for the incorporation of data for liquid solution energies in the potential development procedure, and a new semi-empirical potential developed suitable for simulations of dilute alloys of Mg in Al. The potential correctly reproduces both zero-temperature solid properties and solidus and liquid lines on the Al-rich part of the Al–Mg phase diagram.

On the coarsening of precipitates located on grain boundaries and dislocations

Abstract The Lifschitz-Slyozov-Wagner theory of particle coarsening is applied to the case in which all the precipitates lie on grain boundaries. Earlier studies of the grain boundary precipitate coarsening problem have assumed that all mass transfer is limited to the grain boundary region and have shown that in the long time limit the average particle size increases with time as t 1 4 . The present investigation considers diffusion of solute to occur both through the bulk material and along the grain boundary. Employing an asymptotic analysis due to Marqusee and Ross, one can show that the time dependent average particle size varies as t 1 3 and the coarsening rate constant depends on both the bulk and grain boundary diffusivities. The case of coarsening of precipitates lying on dislocations is also discussed and again cubic growth kinetics are found.

An embedded-atom method interatomic potential for Pd-H alloys

Palladium hydrides have important applications. However, the complex Pd–H alloy system presents a formidable challenge to developing accurate computational models. In particular, the separation of a Pd–H system to dilute (α) and concentrated (β) phases is a central phenomenon, but the capability of interatomic potentials to display this phase miscibility gap has been lacking. We have extended an existing palladium embedded-atom method potential to construct a new Pd–H embedded-atom method potential by normalizing the elemental embedding energy and electron density functions. The developed Pd–H potential reasonably well predicts the lattice constants, cohesive energies, and elastic constants for palladium, hydrogen, and PdHx phases with a variety of compositions. It ensures the correct hydrogen interstitial sites within the hydrides and predicts the phase miscibility gap. Preliminary molecular dynamics simulations using this potential show the correct phase stability, hydrogen diffusion mechanism, and mechanical response of the Pd–H system.

Determination of the crystal-melt interface kinetic coefficient from molecular dynamics simulations

The generation and dissipation of latent heat at the moving solid–liquid boundary during non-equilibrium molecular dynamics (MD) simulations of crystallization can lead to significant underestimations of the interface mobility. In this work we examine the heat flow problem in detail for an embedded atom description of pure Ni and offer strategies to obtain an accurate value of the kinetic coefficient, μ. For free-solidification simulations in which the entire system is thermostated using a Nose–Hoover or velocity rescaling algorithm a non-uniform temperature profile is observed and a peak in the temperature is found at the interface position. It is shown that if the actual interface temperature, rather than the thermostat set point temperature, is used to compute the kinetic coefficient then μ is approximately a factor of 2 larger than previous estimates. In addition, we introduce a layered thermostat method in which several sub-regions, aligned normal to the crystallization direction, are indepently thermostated to a desired undercooling. We show that as the number of thermostats increases (i.e., as the width of each independently thermostated layer decreases) the kinetic coefficient converges to a value consistent with that obtained using a single thermostat and the calculated interface temperature. Also, the kinetic coefficient was determined from an analysis of the equilibrium fluctuations of the solid–liquid interface position. We demonstrate that the kinetic coefficient obtained from the relaxation times of the fluctuation spectrum is equivalent to the two values obtained from free-solidification simulations provided a simple correction is made for the contribution of heat flow controlled interface motion. Finally, a one-dimensional phase field model that captures the effect of thermostats has been developed. The mesoscale model reproduces qualitatively the results from MD simulations and thus allows for an a priori estimate of the accuracy of a kinetic coefficient determination for any given classical MD system. The model also elucidates that the magnitude of the temperature gradients obtained in simulations with a single thermostat depends on the length of the simulation system normal to the interface; the need for the corrections discussed in this paper can thus be gauged from a study of the dependence of the calculated kinetic coefficient on system size.

Kinetic coefficient of steps at the Si(111) crystal-melt interface from molecular dynamics simulations.

Nonequilibrium molecular dynamics simulations are applied to the investigation of step-flow kinetics at crystal-melt interfaces of silicon, modeled with the Stillinger-Weber potential [Phys. Rev. B 31, 5262 (1985)]. Step kinetic coefficients are calculated from crystallization rates of interfaces that are vicinals of the faceted (111) orientation. These vicinal interfaces contain periodic arrays of bilayer steps, and they are observed to crystallize in a step-flow growth mode at undercoolings lower than 40 K. Kinetic coefficients for both [110] and [121] oriented steps are determined for several values of the average step separation, in the range of 7.7-62.4 A. The values of the step kinetic coefficients are shown to be highly isotropic, and are found to increase with increasing step separation until they saturate at step separations larger than approximately 50 A. The largest step kinetic coefficients are found to be in the range of 0.7-0.8 m(sK), values that are more than five times larger than the kinetic coefficient for the rough (100) crystal-melt interface in the same system. The dependence of step mobility on step separation and the relatively large value of the step kinetic coefficient are discussed in terms of available theoretical models for crystal growth kinetics from the melt.

Thermodynamic properties of coherent interfaces in f.c.c.-based Ag–Al alloys: a first-principles study

The thermodynamic properties of coherent interphase boundaries (IPBs) between the Al-rich-matrix and Guinier-Preston-zone (GP-zone) precipitate phases in Ag-Al are studied from first principles. The cluster-variation-method (CVM), with effective-cluster-interaction (ECI) parameters derived from the results of ab initio total energy calculations, is used to compute the interfacial free energies ({gamma}) and composition profiles of flat {l_brace}111{r_brace} and {l_brace}100{r_brace} IPBs as a function of temperature (T). The calculated values of {gamma} increase monotonically from zero to 35 (37)mJ/M{sup 2} for {l_brace}111{r_brace}({l_brace}100{r_brace}) IPBs as T is lowered from the critical temperature (calculated to be 760 K) to 450 K. Monte-Carlo simulations, based on the same set of ECIs used in the CVM work, have been performed to compute GP-zone morphologies at 450 K. Simulated precipitate shapes are found to be anisotropic, consistent with experimental observations. The CVM is used also to compute the gradient coefficient ({kappa}) in the Cahn-Hilliard coarse-grained free energy. Calculated values of {kappa} are found to display non-negligible concentration and temperature dependencies, in contrast to the predictions of regular-solution theory.