Mikhail I. Mendelev

Development of new interatomic potentials appropriate for crystalline and liquid iron

Two procedures were developed to fit interatomic potentials of the embedded-atom method (EAM) form and applied to determine a potential which describes crystalline and liquid iron. While both procedures use perfect crystal and crystal defect data, the first procedure also employs the first-principles forces in a model liquid and the second procedure uses experimental liquid structure factor data. These additional types of information were incorporated to ensure more reasonable descriptions of atomic interactions at small separations than is provided using standard approaches, such as fitting to the universal binding energy relation. The new potentials (provided herein) are, on average, in better agreement with the experimental or first-principles lattice parameter, elastic constants, point-defect energies, bcc–fcc transformation energy, liquid density, liquid structure factor, melting temperature and other properties than other existing EAM iron potentials.

Development of an interatomic potential for phosphorus impurities in α-iron

We present the derivation of an interatomic potential for the iron–phosphorus system based primarily on ab initio data. Transferability in this system is extremely problematic, and the potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Some preliminary molecular dynamics calculations show that P strongly affects point defect migration.We present the derivation of an interatomic potential for the iron phosphorus system based primarily on {\it ab initio} data. Transferrability in this system is extremely problematic, and the potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Some preliminary molecular dynamics calculations show that P strongly affects point defect migration.

Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid Al and Cu

We investigate the application of embedded atom method (EAM) interatomic potentials in the study of crystallization kinetics from deeply undercooled melts, focusing on the fcc metals Al and Cu. For this application, it is important that the EAM potential accurately reproduces melting properties and liquid structure, in addition to the crystalline properties most commonly fit in its development. To test the accuracy of previously published EAM potentials and to guide the development of new potential in this work, first-principles calculations have been performed and new experimental measurements of the Al and Cu liquid structure factors have been undertaken by X-ray diffraction. We demonstrate that the previously published EAM potentials predict a liquid structure that is too strongly ordered relative to measured diffraction data. We develop new EAM potentials for Al and Cu to improve the agreement with the first-principles and measured liquid diffraction data. Furthermore, we calculate liquid-phase diffusivities and find that this quantity correlates well with the liquid structure. Finally, we perform molecular dynamics simulations of crystal nucleation from the melt during quenching at constant cooling rate. We find that EAM potentials, which predict the same zero-temperature crystal properties but different liquid structures, can lead to quite different crystallization kinetics. More interestingly, we find that two potentials predicting very similar equilibrium solid and liquid properties can still produce very different crystallization kinetics under far-from-equilibrium conditions characteristic of the rapid quenching simulations employed here.

Development of suitable interatomic potentials for simulation of liquid and amorphous Cu―Zr alloys

We present a new semi-empirical potential suitable for molecular dynamics simulations of liquid and amorphous Cu–Zr alloys. To provide input data for developing the potential, new experimental measurements of the structure factors for amorphous Cu64.5Zr35.5 alloy were performed. In this work, we propose a new method to include diffraction data in the potential development procedure, which also includes fitting to first-principles and liquid density and enthalpy of mixing data. To refine the new potential, we used first-principles and liquid enthalpy of mixing data published earlier combined with the densities of liquid Cu64.5Zr35.5 measured over a range of temperatures. We show that the potential predicts a liquid-to-glass transition temperature that agrees reasonably well with experimental data. Finally, we compare the new potential with two previously developed semi-empirical potentials for Cu–Zr alloys and examine their comparative and contrasting descriptions of structure and properties for Cu64.5Zr35.5 liquids and glasses.

Using atomistic computer simulations to analyze x-ray diffraction data from metallic glasses

We propose a method of using atomistic computer simulations to obtain partial pair correlation functions from wide angle diffraction experiments with metallic liquids and their glasses. In this method, a model is first created using a semiempirical interatomic potential and then an additional atomic force is added to improve the agreement with experimental diffraction data. To illustrate this approach, the structure of an amorphous Cu64.5Zr35.5 alloy is highlighted, where we present the results for the semiempirical many-body potential and fitting to x-ray diffraction data. While only x-ray diffraction data were used in the present work, the method can be easily adapted to the case when there are also data from neutron diffraction or even in combination. Moreover, this method can be employed in the case of multicomponent systems when the data of several diffraction experiments can be combined.

Development of an interatomic potential for the simulation of phase transformations in zirconium

In recent years, some 30 studies have been published on the molecular dynamics (MD) of zirconium, primarily of its twinning deformation and response to radiation damage. Its low thermal neutron absorption makes it uniquely suited for the latter application. Surprisingly, currently used interatomic potentials do not encapsulate the unique properties of Zr, namely its high stacking-fault energy, anomolous self-diffusion, melting and phase transformation under temperature and pressure (or alloying). Ab initio calculations have shown deficiencies in the description of point defects, both vacancies and interstitials, using existing interatomic potentials, deficiencies that can now be rectified by refitting. Here, we show the calculation of phase transitions self-consistently and present a potential for Zr that correctly reproduces the energetics of our extended database of ab initio configurations and high-temperature phase transitions. The potential has an analytic many-body form, making it suitable for existing large-scale MD codes. We also present a best-fit potential for the hcp structure and its defects.

Effect of Fe segregation on the migration of a non-symmetric Σ5 tilt grain boundary in Al

We present an analysis, based upon atomistic simulation data, of the effect of Fe impurities on grain boundary migration in Al. The first step is the development of a new interatomic potential for Fe in Al. This potential provides an accurate description of Al–Fe liquid diffraction data and the bulk diffusivity of Fe in Al. We use this potential to determine the physical parameters in the Cahn–Lucke–Stuwe (CLS) model for the effect of impurities on grain boundary mobility. These include the heat of segregation of Fe to grain boundaries in Al and the diffusivity of Fe in Al. Using the simulation-parameterized CLS model, we predict the grain boundary mobility in Al in the presence of Fe as a function of temperature and Fe concentration. The order of magnitude and the trends in the mobility from the simulations are in agreement with existing experimental results.

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.

Development of interatomic potentials appropriate for simulation of liquid and glass properties of NiZr2 alloy

A new interatomic potential for the Ni–Zr system is presented. This potential was developed specifically to match experimental scattering data from Ni, Zr and NiZr2 liquids. Both ab initio and published thermodynamic data were used to optimise the potential to study the liquid and amorphous structure of the NiZr2 alloy. This potential has the C 16 phase, being more stable than C 11b phase in the NiZr2 alloy, consistent with experiments. The potential leads to the correct glass structure in the molecular dynamics simulation and, therefore, can be used to study the liquid–glass transformation in the NiZr2 alloy.

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.