R. Najafabadi

Elastic step interactions on vicinal surfaces of fcc metals

Abstract The structural and energetic properties of [100] and [110] steps on the (001) surface of fcc metal have been determined by T = 0 atomistic simulations. The interactions between [100] steps and between [110] steps on the (001) surface are determined from the surface energy of a series of (01 n ) and (11 m ) surfaces, respectively. For step spacings larger than three fcc lattice parameters ( R > 3 a 0 ), we find that the interaction energy between two similar steps on the (001) surface can be reasonably represented by the functional form R −2 , in agreement with the prediction of a simple linear elastic analysis based upon a line dipole force model of a step. However, we observe qualitative differences between the displacement fields determined by the two methods. For R a 0 , on the other hand, we find that the interaction between steps deviates significantly from the form R −2 . These deviations demonstrate that both dipole and quadrupole force distributions are necessary to account for step-step interactions for spacings as small as a fraction of a lattice parameter up to infinite step spacings. We show that a [100] step on the (001) surface in Au and Pt (but not in Ag, Au, Cu, or Pd) may lower the surface energy by transforming into a zig-zagged [110] step.

Thermodynamics of solid and liquid embedded‐atom‐method metals: A variational study

We present results of variational calculations of the Helmholtz free energy and the thermodynamic properties of a series of metallic liquids and solids (Ag, Au, Cu, Ni, Pd, Pt) described by embedded‐atom‐method potentials. For the solids, we use a variational procedure based on an Einstein‐model reference state. The free energies of liquids are calculated with an approximate variational method proposed by Ross. At the respective melting points, the present results for the Helmholtz free energy are within about 1% of the results of accurate Monte Carlo (MC) calculations with the same interaction potentials, both for the fluid and the solid. The average error in the melting points calculated with the present procedure relative to Monte Carlo results is about 7.5%. The internal energies and entropies are compared to MC results, and show, in general, good agreement.

A new method for the simulation of alloys: Application to interfacial segregation

Abstract We present a new, accurate method for determining the properties of defects in alloys at finite temperature, including equilibrium segregation. This method is based upon a point approximation for the configurational entropy, an Einstein model for vibrational contributions to the free energy and may be employed with any type of description of atomic interactions. The atomic structure, segregation and thermodynamics of a defect in an alloy is determined by minimizing the free energy with respect to atomic coordinates and composition of each site at constant chemical potential. In order to test the accuracy of this approach, we compare our results with accurate Monte Carlo determinations. Overall, very good agreement for segregation to free surfaces and grain boundaries in CuNi alloys is obtained. One of the main advantages this new method enjoys over other methods such as Monte Carlo, is the efficiency with which the atomic structure of a defect, segregation and thermodynamic properties can be determined. This efficiency is obtained in the framework of a very straightforward method and with little loss in accuracy.

Polycrystalline surface properties from spherical crystallites: Ag, Au, Cu and Pt

We have performed a series of atornistic simulations of nearly spherical, crystalline (fee) clusters of Ag, Au, Cu and Pt as a function of temperature and cluster size. Since both a spherical cluster and a random polyctystal expose all possible surfaces equally, this provides a plausible approach for determining the surface properties of random (non-textured) polycrystalline metals and to find a simple expression to relate these average surface properties to the oft calculated properties of high symmetry/low index surfaces. Atomic clusters with radii greater than approximately 4~2, yield cluster average surface energies and surface stresses are within a few percent of those obtained from very large clusters. The variation of the cluster average surface properties with cluster size is dominated by a geometrical effect associated with the discrete spacing between atomic planes and that the differences associated with differences in the atomic bonding between different elements is small, at least for the four elements considered herein. Comparison of the cluster average surface free energy with those of the more commonly studied high symmetry flat {loo), {110), and the (111) surfaces suggest two useful approximations for the average surface free

Finite temperature vacancy formation thermodynamics: local harmonic and quasiharmonic studies

The vacancy formation thermodynamics in six FCC metals Ag, Au, Cu, Ni, Pd and Pt are determined from atomistic simulations as a function of temperature. The investigation is performed using the embedded atom method interatomic potentials and the finite temperature properties are determined within the local harmonic and the quasiharmonic frameworks. The temperature dependence of the vacancy formation free energy, entropy, enthalpy and vacancy formation volume are determined. The authors find that the temperature dependence of the vacancy formation energy can make a significant contribution to the vacancy concentration at high temperatures. An additional goal of the study is to evaluate the accuracy of the local harmonic method under circumstances in which the excess entropy associated with the formation of a defect is very small. The data demonstrate that while the errors associated with determining the vacancy formation entropy in the local harmonic model are large, a simple extension to the local harmonic method yields thermodynamic properties comparable to that obtained in the quasiharmonic model, but with much higher computational efficiency.

Order-disorder transitions at and segregation to (001) Ni-Pt surfaces

Abstract Order-disorder transitions at and segregation to the (001) surface of Ni-Pt alloys have been investigated by a recently developed free energy simulation method, where the atomic interactions are described using the embedded atom method (EAM) potentials. On the Ni-rich side of the phase diagram, we observe a second order, order-disorder phase transition on the (001) surfaces at temperatures well above the bulk phase transition temperature. At the transition temperature, the first (002) atomic plane changes from a disordered plane to an ordered one with the c(2 × 2) pattern. The second (002) plane changes from a disordered plane to a nearly pure Ni plane. Subsequent planes retain their essentially bulk-like, disordered structure. We also observe first order, order-disorder surface phase transitions on the Pt-rich side of the phase diagram. At the transition temperatures, the first and third (002) planes become nearly pure Pt and the second plane becomes nearly pure Ni. The effect of the surface transitions on the thermodynamic properties of the surfaces, such as enthalpy and vibrational and configurational entropy, are also investigated. It is shown that the ordering surface transition upon cooling the Ni-rich sample is enthalpically driven. The present simulations also show the importance of including atomic vibrations in surface segregation studies. Atomic vibrations have been typically omitted in previous lattice gas descriptions of surface segregation.

Segregation to ∑5 [001] twist grain boundaries in ni-cu alloys

Abstract Atomistic simulations of segregation to the ∑5 [001] twist boundary in Ni-Cu alloys have been performed for a wide range of temperature and composition all within the solid solution region of the phase diagram. In addition to the grain boundary segregation profile, grain boundary structures, free energies, enthalpies, and entropies were determined. These simulations were performed within the framework of the free energy simulation method, in which an approximate free energy functional is minimized with respect to atomic coordinates and atomic site occupation. For all alloy bulk compositions (0.05≤ C ≤0.95) and temperatures (400≤ T(K) ≤ 1000) examined, Cu segregates strongly to the grain boundary. The width of the segregation profile is limited to approximately two atomic planes on each side. The resultant segregation profiles are shown to be in poor agreement with classical segregation theories. The grain boundary thermodynamic properties depend sensitively on the magnitude of the grain boundary ...

SEGREGATION TO AND STRUCTURE OF (001) TWIST GRAIN BOUNDARIES IN Cu-Ni ALLOYS

The segregation, thermodynamic, and structural properties of (001) twist boundaries in Cu-Ni alloys have been examined within a wide range of misorientations and temperatures. Cu always segregates to the boundary. The concentration of the first layer adjacent to the boundary increases monotonically with misorientation and no obvious cusps are observed. All other thermodynamic properties vary smoothly with the misorientation, with the exception of the vibrational entropy of the boundaries without segregation. The unsegregated vibrational entropy shows a large peak at the misorientation corresponding to the El7 boundary and two minima around the ~13 and E5 boundary orientations. The concentration distribution within the plane of the grain boundaries can be described by the same structural unit model established for (001) twist boundaries in pure materials. Regions of large tensile stress show greater segregation than do regions of compressive stress. Regions of large shear stress tend to show reduced segregation compared with regions of small shear stress.

Determination of vacancy and atomic diffusivities in solid solution alloys

A Monte Carlo procedure is applied to determine the vacancy and tracer diffusion constants in binary solid solutions. The Monte Carlo method uses vacancy jump frequencies which are calculated using an atomistic simulation method (the First Shell-Black/White model) and are tabulated for all possible jumps in all possible local environments. A simpler, more computationally efficient model, the First Shell-Gray model, is also presented. Comparison of the vacancy diffusion constants, the pre-exponential factors and the migration energies in the Cu-Ni alloys obtained using the First Shell-Gray model and the more accurate but much less computationally efficient Monte Carlo simulation method suggests that the First Shell-Gray model is adequate to predict the diffusion behavior over the entire temperature range. The agreement between the two models is even better at high temperatures where the differences among the Cu jump frequencies and Ni jump frequencies are not as important as at low temperatures. Therefore, treating the atoms in the Cu-Ni alloy as mean-field atoms is an adequate approximation in predicting vacancy and atomic diffusion behavior. The effect of the temperature and alloy composition on the tracer and vacancy correlation factors and the short range order are also investigated.

Statistical mechanical-atomistic determination of vacancy formation free energies in Cu-Ni alloys

Abstract Atomistic and statistical mechanical methods are combined to determine the vacancy formation free energy in binary solid solutions. The first-shell grey model is based on the assumption that all the atoms are effective or mean-field atoms, but with the concentration of the first shell different from the bulk. Comparison of the vacancy formation free energy and the average local concentration profile around the vacancy obtained from the first-shell grey model and the more accurate but much less computationally efficient first-shell black-white model (where the mean-field approximation is not used) suggest that only the composition of the first atomic shell adjacent to the vacancy must be determined. The temperature dependence of the vacancy formation free energy for a Cu-Ni system can be efficiently determined using the first-shell grey atom approximation. Our results show that the vacancy has a strong tendency to form in Cu-rich regions of the Cu-Ni alloy at low temperatures and low Cu bulk conce...