Vacancy Formation Energy In Metals Research Articles

Vacancy Formation Energy of Metals

In this work, we investigated and discussed the experimental and theoretical data of the vacancy formation energy Ev. The results of calculations in the continuum model of the solids and the model of interaction between a pair of neutral atoms, as well as the results of ab initio methods using various exchange – correlation functionals, are analyzed. It was found that the experimental and theoretical values of the vacancy formation energy have an adjusted coefficient of determination R2 close to 0.80. The relationship between the calculated vacancy formation energy and the sublimation enthalpy most closely corresponds to the relation Ev = ΔHs/3 for the results obtained on the basis of continuum model and model of interaction between a pair of atoms. The vacancy formation energy most closely correlates with the melting enthalpy ΔHm. The adjusting coefficient of determination R2 of this relation is 0.87 in comparison with 0.71 and 0.84 for the sublimation enthalpy and the evaporation enthalpy, respectively.

The Vacancy Energy in Metals: Cu, Ag, Ni, Pt, Au, Pd, Ir and Rh

The predictive calculations of vacancy formation energies in metals: Cu, Ag, Ni, Pt, Au, Pd, Ir and Rh are presented. The energy is given as a function of electron density. Density functional theory underestimates the vacancy formation energy when structural relaxation is included. The unrelaxed mono-vacancy formation, unrelaxed di-vacancy formation, unrelaxed di-vacancy binding and low index surface energies of the fcc transition metals Cu, Ag, Ni, Pt, Au, Pd, Ir and Rh has been calculated using embedded atom method. The values for the vacancy formation energies agree with the experimental value. We also calculate the elastic constants of the metals and the heat of solution for the binary alloys of the selected metals. The average surface energies calculated by including the crystal angle between planes (hkl) and (111) correspond to the experiment for Cu, Ag, Ni, Pt and Pd. The calculated mono-vacancy formation energies are in reasonable agreement with available experimental values for Cu, Ag, Au and Rh. The values are higher for Pt and Ir while smaller values were recorded for Ni and Pd. The unrelaxed di-vacancy binding energy calculated agrees with available experimental values in the case of Cu, Ni, Pt and Au.

Vacancy formation energies in metals: A comparison of MetaGGA with LDA and GGA exchange–correlation functionals

We report on the results of density-functional-theory based calculations of the vacancy formation energies in metals using the revised Tao–Perdew–Staroverov–Scuseria (revTPSS) functional (Pedrew et al., 2009), which is a self-consistent semilocal meta-generalized gradient approximation functional. The motivation for this work is to determine if the improved accuracy of surface energies for revTPSS compared to local and generalized gradient approximation functionals also leads to improved vacancy formation energies since vacancies can be viewed as internal surfaces. In addition, we report on the lattice constants, cohesive energies and bulk moduli predicted by revTPSS. By comparing the vacancy formation energies and bulk properties, the performance of revTPSS is assessed against four functionals: the local spin density approximation (LSDA), Perdew, Burke and Ernzerhof (PBE), Perdew–Wang-91 (PW91), and PBE for solids (PBEsol). Using an automated computational approach, we calculate the vacancy formation energies and the macroscopic properties of 34 metal systems for the five functionals. For macroscopic properties (lattice constants, cohesive energies and bulk modulus), we find the results for revTPSS typically lie between LDA and PBE with a mean absolute percentage deviation of 1.1% and 12.1% from the experimental data for lattice constants and cohesive energies respectively. Further, it is found that revTPSS predicts higher vacancy formation energies when compared to the four other functionals surveyed. We have observed the following order for the functionals with respect to the computed vacancy formation energies, Efxc:EfrevTPSS>EfPBEsol∼EfLDA>EfPBE>EfPW91. We also consider the effects of a surface-energy error correction that has been proposed for standard LDA and GGA functionals. This correction increases the vacancy formation energies of LDA, PBE and PW91 functionals. The revTPSS computed VFEs are greater than the surface-energy-corrected PBE VFEs by a mean relative difference of 14.8%.

パラジウム系水素透過合金膜の耐久性に及ぼす周期表第5族および第6族金属の添加効果

The alloying effects of group 5 and 6 metals on the durability for Pd-based hydrogen permeable membranes are investigated systematically. The surface defects, so called Kirkendall voids, that cause a gas leakage, are formed around iron particles adhered on the Pd-based metal membrane during hydrogen permeation reaction. It is found that the formation of these surface defects are inhibited by the addition of only 1 mol% of group 5 or 6 metals into palladium in hydrogen atmosphere at less than 873 K. The growth rate of the crystal grain of Pd-20 mol%Ag-1 mol%W alloy is slower than Pd-22 mol%Ag alloy at 973 K, indicating that the inter-diffusion of metal atoms is delayed by the addition of tungsten into palladium. The vacancy formation energies of metals increase almost linearly with their melting temperatures. Thus, it can be understood that the improvement of the durability against the iron particles may attributable to the decrement of the inter-diffusion rate through the modification of the vacancy formation energy by the addition of group 5 or 6 metals into palladium.

Calculating the vacancy formation energy in metals: Pt, Pd, and Mo

The predictive power of first-principles calculations of vacancy formation energies in metals (Pt, Pd, Mo) is improved by adding a correction for the intrinsic surface error in current implementations of density functional theory. The derived correction is given as a function of electron density; it can be explicitly applied to a wide range of systems. Density functional theory, contrary to claims in previous work, underestimates the vacancy formation energy when structural relaxation is included. This is the case whether using the local density- or the generalized gradient approximation for the exchange-correlation energy. With corrections for the intrinsic surface error we reach excellent agreement between calculated values using the two exchange-correlation functionals. Our final values for the three vacancy formation energies are 1.16, 1.70, and 2.98 eV for Pt, Pd, and Mo, respectively. The numbers are in good agreement with experimental data. We also calculate the barrier for vacancy diffusion in Pt to 1.43 eV.

First-principles calculations for point-defect energies in metals and phase diagrams of binary alloys

We discuss the present status of the first-principles electronic-structure calculations for defect energies in metals. The calculations apply density functional theory in the generalized-gradient approximation of Perdew and Wang, together with a full-potential version of Korringa–Kohn–Rostoker Green's function method, developed by the Jülich group. It is shown that: (1) the present calculations reproduce very well the experimental results for vacancy formation energies in metals, as well as the bulk properties such as equilibrium lattice parameters and bulk moduli of metals; and (2) the type of the phase diagram of a binary A–B alloy can be characterized by the interaction energies between a pair of impurity B (A) atoms in the host metal A (B). The observed temperature dependence of the solid solubility limit of Rh in Pd is also reproduced very well by the free-energy calculations based on the cluster variation method with the pair- (up to the eighth neighbor) and many-body (up to a tetrahedron of first-nearest neighbors) interaction energies, all of which are determined by the present first-principles calculations.

Vacancy Formation Energy of Metals Determined by Using Positron Age-Momentum Correlation Technique

Vacancy Formation Energy of Metals Determined by Using Positron Age-Momentum Correlation Technique

第一原理計算手法による材料物性研究 ＦＰ‐ＫＫＲ‐Ｇｒｅｅｎ関数法による金属の平衡格子定数・体積弾性率・原子空孔形成エネルギーの第一原理計算

第一原理計算手法による材料物性研究 ＦＰ‐ＫＫＲ‐Ｇｒｅｅｎ関数法による金属の平衡格子定数・体積弾性率・原子空孔形成エネルギーの第一原理計算

Calculation of the vacancy formation energy of metals

Models of elastic continuum and paired rigid bonds were used to determine the vacancy formation energy of metals. The relaxation displacements of the atoms around the vacancy resulting in a reduction of the vacancy formation energy were calculated using the paired potential of the Johnson type. The energy consumed for these processes was calculated using quantum mechanics and the Schottky mechanism. The model of the paired bonds agreed with the model of rigid continuum. Experimental and calculated values of the formation energy are tabulated for 54 metals classified according to fcc, bcc, and hcp lattice structure.

Comments on Faber's Expression for the Vacancy Formation Energy in Metals

Comments on Faber's Expression for the Vacancy Formation Energy in Metals

Relaxation and Formation Energy of Vacancies in Metals

AbstractAn expression for the vacancy formation energy in metals is obtained taking into account the associated lattice distortions. For the purpose of finding the electrostatic energy Ewald's method was generalized specially for a lattice with a vacancy. Equations are found for the calculation of the displacements around the vacancy.

THE FORMATION ENERGY OF VACANCY OF METAL

The formation energy of vacancy is calculated from, the surface tension of solid. It is found that the theoretical values of vacancy formation energy of metals agree with its experimental values, the vacancy formation energies of metals are directly proportional to its energies of self-diffusion and melting points, and the ratio of the energy of vacancy formation to the energy of self-diffusion, determined by one of the above proportional relations, is 0.43. Besides that, the vacancy formation energy is also a periodic function of atomic number.