Features Of Vacancy Formation Energy Determination of 5-d Transition Metals Of The First Principles Taking Into Account The Temperature Factor

Марк Михайлович Федоров, Ганна Дмитрівна Холмська, Сергій Іванович Сидоренко, Сергій Олександрович Замулко

Abstract


This work is devoted to investigation of the behavior of the most common structural defect that determines the properties of the material – vacancies – at high temperatures. Theoretical study of the temperature dependence of the vacancy formation energy in pure 5-d fcc and bcc transition metals Au, Pt and W by means of density functional theory (DFT). The feature of this work is usage of experimental values of lattice parameters for the respective temperatures. The article discusses contributions to the vacancy formation energy, the results of computer simulation show that all of them can play an important role. It is shown, that thermal excitation has a significant impact on the vacancy formation energy at high temperatures. Also the possibility of compensation effect, i.e. the simultaneous change of free energy contributions to the vacancy formation energy in the 5-d fcc and bcc transition metals Au, Pt and W was confirmed. Contribution of the free energy vibrations and thermal electronic excitation depending on the temperature gives a good picture of the effect thermal expansion. Calculated vacancy formation energies are in good agreement with previous theoretical and experimental research. The effect of the compensation of different contributions to the vacancy formation energy can explain equality of vacancy formation energy values at different temperatures, observed in experimental studies, and justifies temperature dependence neglecting when modeling the properties of pure 5-d fcc and bcc transition metals.

Keywords


Density functional theory; Vacancy formation energy; Ab initio; Free electronic energy of thermal expansion; Free vibration energy; 5-d transition metals

References


1. Z.D. Popovic et al., “On the vacancy for mation energy and volume of simple cubic metals,” J. Phys. F: Met. Phys., vol. 4, no. 3, 1974. doi: 10.1088/0305-4608/4/3/008

2. S.M. Kim and W.J.L. Buyers, "Temperature dependence of the vacancy for mation energy in aluminum and positronannihilation", Phys. Lett. A, vol. 49, pp. 181–182, 1974.

3. T.R. Mattsson and A.E. Mattsson, “Calculating the vacancy for mation energy in metals: Pt, Pd, and Mo,” Phys. Rev. B, vol. 66, p. 214110, 2002. doi: 10.1103/PhysRevB.66.214110.

4. B. Grabowski et al., “Formation energies of point defects at finite temperatures,” Phys. Status Solidi, vol. 248, pp. 1295–1308, 2011.

5. P.A. Korzhavyi et al., “Constitutional and thermal point defects in B2 NiAl,” Phys. Rev. B, vol. 61, p. 6003, 2000.

6. V.U. Nazarov et al., “On the relation between the scalarand tensor exchange-correlation kernels of the time-dependent density functional theory,” J. of Chem. Phys., vol. 133, p. 021101, 2010.

7. M. Mantina et al., “First-principles calculation of self-diffusion coefficients,” Phys. Rev. Lett., vol. 100, p. 215901, 2008.

8. Замулко С.О. Особливості визначення енергії формування вакансії у 4d перехідних металах із перших принципів. – Наукові вісті НТУУ “КПІ”. – 2014. – № 4. – С. 127–132.

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

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

11. M.J. Gillan, “Calculation of the vacancy for mation energy in aluminium,” J. Phys.: Condens. Matter, vol. 1, no. 4, p. 689, 1989. – doi:10.1088/0953-8984/1/4/005.

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

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

14. A.V. Ruban and V.I. Razumovskiy, “First-principles based thermodynamic model of phase equilibria in bcc Fe–Cr alloys,” Phys. Rev. B, vol. 86, p. 174111, 2012.

15. O.I. Gorbatov et al., “The role of magnetism in Cuprecipitation in a-Fe”, Phys. Rev. B, vol. 88, p. 174113, 2013.

16. G. Kresse et al., “Abinitio Force Constant Approachto Phonon Dispersion Relations of Diamondand Graphite”, Europhys. Lett., vol. 32, p. 729, 1995.

17. A. Togo et al., “First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 athighpressures”, Phys. Rev. B, vol. 78, p. 134106, 2008.

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

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


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DOI: http://dx.doi.org/10.20535/1810-0546.2015.1.48847

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