Phenomenological potentials for the refractory metals Cr, Mo and W (original) (raw)
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In this work, we have successfully applied one of the most effective semi-empirical interatomic potentials called embedded atom method EAM to calculate some thermodynamics properties of refractory metals (Nb, Ta, Mo and W). Our theoretical calculated values for mono-vacancy formation energy are in excellent agreement with the available experimental values. Among these metals, the highest f v E 1 is obtained for W. It is well known that the value of the mono-vacancy formation energy of each metal is directly proportional to its cohesive energy. i.e. the lower the cohesive energy is, the lower the mono-vacancy formation energy and vice versa. The trend exhibited by these metals whose mono-vacancy migration energies were computed revealed that migration energies are small but cannot be negative. The mono-vacancy activation energy was obtained by summing the mono-vacancy formation energy and mono-vacancy migration energy together. For all the metals considered, W has the largest values for mono-vacancy formation energy, mono-vacancy migration energy and mono-vacancy activation energy followed by Mo and then Ta. This could be as a result of parameter β used in the calculation. We used 8 as β for both W and Mo, while β = 6 for all other metals. The values for di-vacancy formation energy are larger than their corresponding mono-vacancy formation energy but still lower than corresponding cohesive energy of each metal. The binding energies were computed from mono-vacancy formation and di-vacancy formation energies. The obtained values for Nb and Ta metals are in good agreement with Zhang et al but there are no experimental values for these two metals. Experimental values are highly needed before conclusion can be drawn.
The quantum sutton-chen many-body potential for properties of fcc metals
1998
The simple Sutton-Chen Philos. Mag. Lett. 61, 139 (1990)] (SC) type many-body force eld leads to an accurate description of many properties of metals and their alloys. We h a ve modi ed SC to include quantum corrections (e.g., zero-point energy) in comparing properties to experiment, leading to the quantum Sutton-Chen, or Q-SC force eld. We have applied the Q-SC description to nine face-centered cubic (fcc) metals (Al, Ni, Cu, Rh, Pd, Ag, Ir, Pt, and Au). The Q-SC parameters were optimized to describe the lattice parameter, cohesive energy, b u l k m o d ulus, elastic constants, phonon dispersion, vacancy formation energy, a n d surface energy. These potentials were tested by calculating the equation of state, thermal expansion, and speci c heat. We nd generally good agreement with all properties, indicating that this Q-SC type force eld should be useful in molecular dynamics and Monte Carlo simulations of metallic alloys. To illustrate the application of these parameters, we show h o w they have been used for predicting the viscosity of liquid metal alloys, and alloy melting and solidi cation (to form crystal or glass).
Model potential based on tight-binding total-energy calculations for transition-metal systems
Physical review, 1995
A semiempirical model potential to simulate properties of fcc transition metals is proposed. The attractive part of the potential has been obtained from a tight-binding Hamiltonian that takes into account the symmetry of the d orbitals and leads to a 2/3 power dependence on the effective coordination (or second moment of the local density of states) instead of the usual square-root dependence. The repulsive interaction is assumed to be of the Born-Mayer type. In order to use this potential for specific materials, four parameters are adjusted with experimental data. We present two different parametrizations and calculate bulk, defect, surface, and cluster properties comparing with experiment, ab initio calculations, and the usual second-moment approximation.
Tight-binding potentials for transition metals and alloys
Physical Review B, 1993
The parameters of many-body potentials for fcc and hcp transition metals, based on the secondmornent approximation of a tight-binding Hamiltonian, have been systematically evaluated. The potential scheme, cast in analytical form, allows us to reproduce correctly the thermal behavior of transition metals making use of a small set of adjustable parameters. The large cutoff, which extends the range of the interactions up to the fifth-neighbor distance, ensures good quantitative agreement with the experimental data up to temperatures close to the melting point. The ability of the potentials to describe real systems has been checked by calculating point-defect properties, lattice dynamics, and finite-temperature behavior, and by comparing the results with other potential schemes. Application of this scheme to bcc transition metals has proved unsuccessful. Examples of derivation of many-body potentials for a few transition-metal alloys with cubic structure are also reported.
Applicability of the broken-bond rule to the surface energy of the fcc metals
Surface Science, 2002
We apply the Green's function based full-potential screened Korringa-Kohn-Rostoker method in conjunction with the local density approximation to study the surface energies of the noble and the fcc transition and sp metals. The orientation dependence of the transition metal surface energies can be well described taking into account only the broken bonds between first neighbors, quite analogous to the behavior we recently found for the noble metals [see cond-mat/0105207]. The and surfaces of the sp metals show a jellium like behavior but for the more open surfaces we find again the noble metals behavior but with larger deviation from the broken-bond rule compared to the transition metals. Finally we show that the use of the full potential is crucial to obtain accurate surface energy anisotropy ratios for the vicinal surfaces.
Thermal and mechanical properties of some fcc transition metals
Physical Review B, 1999
The temperature dependence of thermodynamic and mechanical properties of six fcc transition metals ͑Ni, Cu, Ag, Au, Pt, Rh͒ are studied using molecular dynamics ͑MD͒ simulations. The structures are described at elevated temperatures by the force fields developed by Sutton and co-workers within the context of the tight binding approach. In these simulations the thermodynamic and mechanical properties are calculated in the temperature range between 0 to 1500 K using the statistical fluctuation expressions over the MD trajectories.
Modelisation of transition and noble metal vicinal surfaces: energetics, vibrations and stability
The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces, i.e., surface energy, step energy, kink energy and electronic interactions between steps, is studied at 0K from electronic structure calculations in the tight-binding approximation using a {\it s, p} and {\it d} valence orbital basis set. Then, the surface phonon spectra of copper are investigated in the harmonic approximation with the help of a semi-empirical inter-atomic potential. This allows to derive the contribution of phonons at finite temperatures to the step free energy and to the interactions between steps. The last part is devoted to the stability of vicinal surfaces relative to faceting with special attention to the domain of orientations (100)-(111). Semi-empirical potentials are shown to be not realistic enough to give a reliable answer to this problem. The results derived from electronic structure calculations predict a variety of behaviors and, in particular, a possible faceting into two othe...
Journal of Physics and Chemistry of Solids, 1992
A theoretical study of the lattice contribution to the heat capacity and thermal expansion coefficient for FCC transition metals is presented. Anomalous features in the phonon spectra, such as the Kohn anomalies or the negative dispersion at small wave vectors, are shown to manifest themselves qualitatively in the temperature dependence of the Debye temperature and the Grtineisen coefficient. A compilation of experimental data supports the theoretical prediction of anomalies in the phonon spectra of iridium and rhodium.
Cohesive energy of 3d transition metals: Density functional theory atomic and bulk calculations
Physical review. B, Condensed matter, 1996
We report generalized gradient approximation ͑GGA͒ cohesive energies for 3d metals. The problem of obtaining atomic reference energies in density-functional theory is considered. The effect of going to nonspherical atomic charge distributions is much larger at the GGA than at the local-density approximation ͑LDA͒ level, but allowing fractional occupations of 3d and 4s shells has negligible effect. When nonsphericity effects are taken into account in the atomic reference energies, the average absolute error of 0.3 eV in the GGA cohesive energies is much smaller than the LDA error of 1.3 eV. The working of the GGA is analyzed in terms of the cohesive energy density and the charge inhomogeneity division of the exchange energy. The lowgradient limit in the GGA functionals is not important as regions with charge inhomogeneity sϽ0.2 have negligible contributions. ͓S0163-1829͑96͒10531-2͔
Modelling of transition and noble metal vicinal surfaces: energetics, vibrations and stability
Journal of Physics: Condensed Matter, 2003
The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces, i.e., the surface energy, step energy, kink energy and electronic interactions between steps, is studied at 0 K from electronic structure calculations in the tight binding approximation using an s, p and d valence orbital basis set. Then, the surface phonon spectra of copper are investigated in the harmonic approximation with the help of a semi-empirical inter-atomic potential. This allows one to derive the contribution of phonons at finite temperatures to the step free energy and to the interactions between steps. The last part is devoted to the stability of vicinal surfaces relative to faceting with special attention paid to the domain of orientations (100)-(111). Semi-empirical potentials are shown to be not realistic enough to give a reliable answer for this problem. The results derived from electronic structure calculations predict a variety of behaviours and, in particular, a possible faceting into two other vicinal orientations. Finally, temperature effects are discussed. Comparisons are made with other theoretical works and available experiments.