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

Сергій Олександрович Замулко

Abstract


In this paper a study of the temperature dependence of the vacancy formation energy in bulk fcc 4d-transition metals Ag and Pd using DFT was presented. Peculiarity of this work is the use of experimental values of the lattice parameters for the respective temperatures. This paper discusses the various contributions to the vacancy formation energy and shows that they can play an important role. It was shown that thermal excitation has a significant impact on the vacancy formation energy at high temperatures. The possibility of the existence of the compensation effect, i.e. the simultaneous changes in the contributions of the free energy and the vacancy formation energy in the fcc 4d-transition metals Ag and Pd, which were investigated from first principles. Taking in to account free oscillation energy and electronic thermal excitation depending on the temperature allows obtaining a qualitative picture of the effect of thermal expansion. The vacancy formation energy is in good agreement with previous theoretical and experimental studies. The effect of mutual compensation of different contributions to the vacancy formation energy can explain the constant value of the vacancy formation energy at any temperature and justifies the neglect of the temperature dependence of the simulation properties.

Keywords


Density functional theory; The energy of formation of vacancies; The first principles; Electronic thermal exitation; Vibration energy

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 CaCl2-type SiO2 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