### Definition Peculiarities of Energy of Vacancy Formation in 4d-Transition Metals from First Principles

#### Abstract

#### Keywords

#### Full Text:

PDF (Українська)#### References

*K.N. Grew and W.K.S. Chiu,* “Review of Modeling and Simulation Techniques Across the Length Scales for the Solid Oxide Fuel Cell,” J. Power Sources, vol. 199, pp. 1–13, 2012.

*T.R. Mattsson and A.E. Mattsson,* “Calculating the vacancy formation energy in metals: Pt, Pd, and Mo”, Phys. Rev. B, vol. 66, p. 214110, 2002.

*K.F. McCarty et al.,* “Vacancies in. Solids and the Stability of Surface Morphology”, Nature (London), vol. 412, p. 622, 2001.

*Gh.A. Nematollahi et al., *“Thermodynamics of carbon solubility in ferrite and vacancy formation in cementite in strained pearlite”, Acta Materialia, vol. 61, p. 1773, 2013.

*L. Ventelon et al.,* “*Ab initio* investigation of radiation defects in tungsten: Structure of self-interstitials and specificity of di-vacancies compared to other bcc transition metals”, J. Nuclear Mater., vol. 425, p. 16, 2012.

*B. Grabowski et al.,* “Formation energies of point defects at finite temperatures”, Phys. Status Solidi B, vol. 248, p. 1295, 2011.

*P.A. Korzhavyi et al.,* “First-principles calculations of the vacancy formation energy in transition and noble metals”, Phys. Rev. B, vol. 59, p. 11693, 1999.

*A.E. Mattsson et al.,* “Electronic surface error in the Si interstitial formation energy”, Ibid, vol. 77, p. 155211, 2008.

*R. Nazarov et al., *“Vacancy formation energies in fcc metals: influence of exchange-correlation functionals and correction schemes”, Ibid, vol. 85, p. 144118, 2012.

*A.J. Hatt et al.,* “Harmonic and anharmonic properties of Fe and Ni:Thermal expansion, exchange-correclation errors, and magnetism”, Ibid, vol. 82, p. 134418, 2010.

*M. Mantina et al.,* “First-principles calculation of self-diffusion coefficients”, PRL, vol. 100, p. 215901, 2008.

*T.R. Mattsson et al.,* “Quantifying the anomalous self-diffusion in molybdenum with first-principles simulations”, Phys. Rev. B, vol. 80, p. 224104, 2009.

*D. Simonovic and M.H.F. Sluiter,* “Impurity diffusion activation energies in Al from first principles”, Ibid, vol. 79, p. 054304 2009.

*P. Hohenberg and W. Kohn,* “Inhomogeneous Electron Gas”, Ibid, vol.136, p. B864, 1964.

*W. Kohn and L.J. Sham,* “Self-Consistent Equations Including Exchange and Correlation Effects”, Phys. Rev., vol. 140, p. A1133, 1965.

*P. Giannozzi et al.,* “QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials”, J. Phys.: Condens. Matter, vol. 21, p. 395502, 2009.

*P.E. Blochl, *“Projector augmented-wave method”, Phys. Rev. B, vol. 50, p. 17953, 1994.

*J. Perdew et al.,* “Restoring the density-gradient expansion for exchange in solids and surfaces”, Phys. Rev. Lett., vol. 100, p. 136406, 2008.

*H.J. Monkhorst and J.D. Pack,* “On Special Points for Brillouin Zone Integrations”, Phys. Rev. B, vol. 13, p. 5188, 1976.

*M.J. Gillan,* “Calculation of the vacancy formation energy in aluminium”, J. Phys.: Condens. Matter, vol. 1, p. 689, 1989.

*B. Grabowski et al.,* “Formation energies of point defects at finite temperatures”, Phys. Status Solidi B, vol. 248, p. 1295, 2011.

*D.E. Turner et al.,* “Energetics of vacancy and substitutional impurities in aluminum bulk and clusters”, Phys. Rev. B, vol. 55, p. 13842, 1997.

*A.V. Ruban, V.I. Razumovskiy, *“First-principles based thermodynamic model of phase equilibria in bcc Fe-Cr alloys”, Ibid, vol. 86, p. 174111, 2012.

*O.I. Gorbatov et al.,* “The role of magnetism in Cu precipitation in α-Fe”, Ibid, vol. 88, p. 174113, 2013.

*G. Kresse et al.,* “*Ab initio* Force Constant Approach to Phonon Dispersion Relations of Diamond and Graphite”, Europhys. Lett., vol. 32, p. 729, 1995.

*A. Togo et al.,* “First-principles calculations of the ferroelastic transition between rutile-type and CaCl_{2}-type SiO_{2} at high pressures”, Phys. Rev. B, vol. 78, p. 134106, 2008.

*A. Togo.* (2009). Phonopy v.1.8.5 [Online]. Avaliable: http://phonopy.sourceforge.net

*Y. Kraftmakher,* “Equilibrium vacancies and thermophysical properties of metals”, Phys. Rep., vol. 299, p. 79, 1998.

*H.M. Polatoglou et al.,* “Vacancy-formation energies at the (111) surface and in bulk Al, Cu, Ag, and Rh”, Phys. Rev. B, vol. 48, p. 1877, 1993.

*T. Korhonen et al.,* “Vacancy-formation energies for fcc and bcc transition metals”, Phys. Rev. B, vol. 51, p. 9526, 1995.

*M.J. Mehl and D.A. Papaconstantopoulos,* “Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals”, Phys. Rev. B, vol. 54, p. 4519, 1996.

*J.L. Campbell et al.,* “Temperature dependence of positron trapping in silver and nickel”, J. Phys. F: Met. Phys., vol. 7, p. 1985, 1977.

*A.E. Mattsson et al.,* “The AM05 density functional applied to solids”, J. Chem. Phys., vol. 128, p. 084714, 2008.

*I-K Suh et al.,* “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction Mo, Ag”, J. Mater. Sci., vol. 23, p. 757, 1988.

*J.W. Arblaster, *“Crystallographic Properties of Palladium”, Platinum Metals Rev., vol. 56, p. 181, 2012.

*X. Tang and B. Fultz,* “First-principles study of phonon linewidths in noble metals”, Phys. Rev. B, vol. 84, p. 054303, 2011.

*C.V. Pandya et al.,* “Lattice Mechanical Properties of Pd, Pt and Ni – A Model Potential Approach”, J. Korean Physical Soc., vol. 38, p. 377, 2001.

*V.A. Korshunov,* “Determination of the phonon density of states from the thermodynamic functions of a crystal: Nickel, palladium, and platinum”, Soviet Physics J., vol. 22, is. 8, pp. 903–905, 1979.

*V.L. Moruzzi et al.*, “Calculated thermal properties of metals”, Phys. Rev. B, vol. 37, p. 790, 1988.

#### GOST Style Citations

DOI: https://doi.org/10.20535/1810-0546.2014.4.28329

### Refbacks

- There are currently no refbacks.

Copyright (c) 2017 NTUU KPI