<i>Ab initio</i>thermodynamics of metals: Al and W

We apply the pseudopotential density functional perturbation theory approach along with the quasiharmonic approximation to calculate the thermal expansion of tungsten and two important metallic alloys, NiAl and PdTi. We derive the theory for anisotropic crystal structures and test the approximation that the anisotropic effects of thermal expansion are equivalent to negative pressure -this simplifies the calculation enormously for complex structures. Throughout, we find excellent agreement with experimental results.

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“…The calculated phonon frequencies are in good agreement with experiment ( Fig. 1) and with a recent calculation [6]. Fig.…”

Section: Anisotropic Strain -Tungstensupporting

confidence: 89%

First-principles thermodynamics of transition metals: W, NiAl, and PdTi

2003

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“…in the work of Reith et al 6 for the pair of Fe atoms in fcc-Cu, in the work of (Table II) determined using values of the Grüneisen parameter which were obtained from literature data for the volume expansion coefficient, the bulk modulus, the density, and the specific heat capacity. [87][88][89][90] Details are given in the Supplemental Material.…”

Section: B Influence Of Defects On Vibrational Frequenciesmentioning

confidence: 99%

First-principles calculation of defect free energies: General aspects illustrated in the case of bcc Fe

2015

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Modeling of nanostructure evolution in solids requires comprehensive data on the properties of defects such as the vacancy and foreign atoms. Since most processes occur at elevated temperatures not only the energetics of defects in the ground state but also their temperaturedependent free energies must be known. The first-principles calculation of contributions of phonon and electron excitations to free formation, binding, and migration energies of defects is illustrated in the case of bcc-Fe. First of all, the ground state properties of the vacancy, the foreign atoms Cu, Y, Ti, Cr, Mn, Ni, V, Mo, Si, Al, Co, O, and the O-vacancy pair are determined under constant volume (CV) as well as zero pressure (ZP) conditions, and relations between the results of both kinds of calculations are discussed. Second, the phonon contribution to defect free energies is calculated within the harmonic approximation using the equilibrium atomic positions determined in the ground state under CV and ZP conditions. In most cases the ZPbased free formation energy decreases monotonously with temperature, whereas for CV-based data both an increase and a decrease were found. The application of a quasi-harmonic correction to the ZP-based data does not modify this picture significantly. However, the corrected data are valid under zero-pressure conditions at higher temperatures than in the framework of the purely harmonic approach. The difference between CV-and ZP-based data D. Murali, M. Posselt, M. Schiwarth: First-principles calculation of defect free energies… MS#BD12759 2 is mainly due to the volume change of the supercell since the relative arrangement of atoms in the environment of the defects is nearly identical in the two cases. A simple transformation similar to the quasi-harmonic approach is found between the CV-and ZP-based frequencies.Therefore, it is not necessary to calculate these quantities and the corresponding defect free energies separately. In contrast to ground state energetics the CV-and ZP-based defect free energies do not become equal with increasing supercell size. Third, it was found that the contribution of electron excitations to the defect free energy can lead to an additional deviation of the total free energy from the ground state value or can compensate the deviation caused by the phonon contribution. Finally, self-diffusion via the vacancy mechanism is investigated. The ratio of the respective CV-and ZP-based results for the vacancy diffusivity is nearly equal to the reciprocal of that for the equilibrium concentration. This behavior leads to almost identical CV-and ZP-based values for the self-diffusion coefficient. Obviously, this agreement is accidental. The consideration of the temperature dependence of the magnetization yields self-diffusion data in very good agreement with experiments.

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“…A common practice is to use the power law or the Taylor expansion of phonon energy versus the deviation of volume from equilibrium, either linear or up to the second order term (e.g. [1]). In this work it has been shown that the lattice constant dependence of phonon energies is almost linear (see Fig.…”

Section: Methodsmentioning

confidence: 99%

“…Several papers have appeared so far in which the ab initio calculations of crystal thermodynamics have been reported (e.g. [1][2][3][4]). The computational procedure involves the evaluation of the total energy and phonon energies, which are then used to calculate the phonon partition function, the fundamental quantity in statistical thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of Fcc Al Crystal from First Principles - Performance of Local Density and Generalized Gradient Approximations

2007

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Phonon dispersion relations in fcc Al crystal were calculated from first principles using density functional perturbation theory, as implemented in ABINIT code. The results are compared with experimental data as well as with the results of previously done ab initio calculations based on the direct method. A slightly better agreement of density functional perturbation theory phonons with experiment can be observed. The ab initio phonon energies were used to evaluate the partition function of the crystal, using the Monkhorst-Pack integration scheme. The quasiharmonic approximation was applied to relate the temperature dependent part of the free energy to volume. The lattice constant dependence of phonon energies was found to be almost linear, so the second order polynomial was considered as sufficient to approximate the dependence. A few examples of thermodynamic characteristics were evaluated: isobaric specific heat, linear thermal expansion coefficient, isothermal bulk modulus, and compared with the experimental data. The calculation was done both in the local density and the generalized gradient approximations for the exchange-correlation energy. The agreement with the experimental data appears to be very satisfactory, although better in the local density approximation than in the generalized gradient approximation.

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Ab initiothermodynamics of metals: Al and W

Cited by 99 publications

References 28 publications

First-principles thermodynamics of transition metals: W, NiAl, and PdTi

First-principles thermodynamics of transition metals: W, NiAl, and PdTi

First-principles calculation of defect free energies: General aspects illustrated in the case of bcc Fe

Thermodynamics of Fcc Al Crystal from First Principles - Performance of Local Density and Generalized Gradient Approximations

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