Calculation Features from First Principles of the Diffusion Activation Energy for the Systems Ag–Mo and Mo–Ag
DOI:
https://doi.org/10.20535/1810-0546.2015.4.51253Keywords:
Density functional theory, Vacancy formation energy, Migration energy, Diffusion activation energy, First principles calculations, Silver–molybdenumAbstract
Background. We investigated diffusion coefficient parameters for a vacancy diffusion mechanism in the presence of two point defects (vacancies and impurity atoms), taking into account the temperature factor, and conducted by means of computer simulations based on density functional theory (DFT).
Objective. Development of theoretical concepts of the mechanisms of diffusion at the atomic and subatomic levels, including the temperature dependence of the vacancy formation energy, the migration energy, and the diffusion activation energy in the metallic systems Ag–Mo and Mo–Ag.
Methods. The calculations were performed in VASP, using the full-potential projector augmented wave (PAW) method, and a PBE-sol generalized gradient approximation. Optimization of the structure geometry was carried out by relaxation of the ions' positions in a super cell made by 64 atoms. A specific feature of the calculations was the application of experimental values for the lattice parameters of the core element matrix at relevant temperatures.
Results. The peculiarities of calculating the vacancy formation energy, the migration energy, and the diffusion activation energy from first principles are presented. It is shown that thermal excitation has a significant impact on the vacancy formation energy, the migration energy, and the diffusion activation energy at high temperatures. Also, the possibility of a compensation effect has been found, namely, the simultaneous changing of the various free energy contributions to the energy of vacancy formation in metallic systems Ag–Mo and Mo–Ag. Evaluation of the contributions of free vibration energy, electronic thermal excitation energy, and energy of pair interactions depending on temperature helps to clarify the picture of the effect of material’s thermal expansion.
Conclusions. The estimated vacancy formation energy, the migration energy, and the diffusion activation energy are in good agreement with previously reported theoretical and experimental data. The presence of the mutual compensation of different contributions to the vacancy formation energy in the metallic complex systems has been confirmed. Confirming the existence and the characteristics of a compensation effect for the system Mo–Ag requires more research.References
V. Alexandrov et al., “Ab initio modeling of bulk and intragranular diffusion in Ni alloys”, J. Phys. Chem. Lett., vol. 6, p. 1618, 2015.
M. Mantina et al., “First-principles calculation of self-diffusion coefficients”, Phys. Rev. Lett., vol. 100, p. 4, 2008.
M. Mantina et al., “3d transition metal impurities in aluminum: A first-principles study”, Phys. Rev. B., vol. 80, p. 184111, 2009.
M. Mantina et al., “First-principles impurity diffusion coefficients”, Acta Mater., vol. 57, pр. 4102–4108, 2009.
S. Ganeshan et al., “First-principles study of self-diffusion in hcp Mg and Zn”, Comput. Mater. Sci., vol. 50, pp. 301–307, 2010.
S. Ganeshan et al., "First-principles calculations of impurity diffusion coefficients in dilute Mg alloys using the 8-frequency model”, Acta Mater., vol. 59, p. 3214–3228, 2008.
S. Shang et al., “Anomalous energy pathway of vacancy migration and self-diffusion in hcp Ti”, Phys. Rev. B., vol. 83, p. 514, 2011.
C. Freysoldt et al., “First-principles calculations for point defects in solids”, Rev. Mod. Phys., vol. 86, p. 253, 2010.
B. Grabowski et al. “Formation energies of point defects at finite temperatures”, Physica Status Solidi B, vol. 248, pp. 1295–1308, 2011.
P.A. Korzhavyi et al., “Constitutional and thermal point defects in B2 NiAl”, Phys. Rev. B., vol. 61, p. 6003, 2000.
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.
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.
V.U. Nazarov et al., “On the relation between the scalar and tensor exchange-correlation kernels of the time-dependent density functional theory”, J. Chem. Phys., vol. 133, p. 021101, 2010.
P. Hohenberg and W. Kohn, “Inhomogeneous electron gas”, Phys. Rev. B., vol. 136, p. B864, 1964.
W. Kohn and L.J. Sham, “Self-consistent equations including exchange and correlation effects”, Phys. Rev. B., vol. 140, p. A1133, 1965.
G. Kresse et al., “VASP the GUIDE” Computational Physics, Faculty of Physics, Universität Wien, Sensengasse 8, A-1130 Wien, Austria Vienna, April 23, 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 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.
O.I. Gorbatov et al., “The role of magnetism in Cu precipitation in a-Fe”, Phys. Rev. B., 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. Phonopy Manual [Online]. Available: http://phonopy.sourceforge.net.
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.
T.R. Mattsson et al., “Quantifying theanomalous 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”, Phys. Rev. B., vol. 79, p. 054304, 2009.
S.О. Zamulko, “Definition peculiarities of energy of vacancy formation in 4d-transition metals from first principles”, Naukovi Visti NTUU KPI, no. 4, pp. 127–132, 2014 (in Ukrainian).
M.M. Fedorov et al., “Definition peculiarities of energy of vacancy formation in 5-d transition metals from first principles, regard temperature factor”, Naukovi Visti NTUU KPI, no. 1, pр. 74–78, 2015 (in Ukrainian).
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 totalenergy 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 trap in gin silver and nickel”, J. Phys. F: Met. Phys., vol. 7, p. 1985, 1977.
G. Henkelman et al., “A climbing image nudged elastic band method for finding saddle points and minimum energy paths”, J. Chem. Phys., vol. 113, p. 9901, 2000.
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