Abstract
A method has been proposed for calculating the lattice parameter of binary substitutional solid solutions, which takes into account the presence of pressure (p) in alloys. The method has been applied to SiGe and CuAu alloys. It has been shown that, at p = 0, the deviation from Vegard’s law (Δl) results from the difference in compressibility and atomic volume between the pure constituent components of the alloys. With increasing pressure, Δl increases. According to our calculations, the Δl(p) of SiGe becomes positive at p0 = 0.685 GPa.
Similar content being viewed by others
REFERENCES
Fournet, G., Étude de la loi de Vegard, J. Phys. Radium, 1953, vol. 14, no. 6, pp. 374–380. https://doi.org/10.1051/jphysrad:01953001406037400
Dismukes, J.P., Ekstrom, L., and Paff, R.J., Lattice parameter and density in germanium–silicon alloys, J. Phys. Chem., 1964, vol. 68, no. 10, pp. 3021–3027. https://doi.org/10.1021/j100792a049
Pulikkotil, J.J., Chroneos, A., and Schwingenschlögl, U., Structure of Sn1 –xGex random alloys as obtained from the coherent potential approximation, J. Appl. Phys., 2011, vol. 110, no. 3, paper 036105. https://doi.org/10.1063/1.3618671
Magomedov, M.N., On the nature of the covalent bond in crystals of carbon family elements, Russ. J. Inorg. Chem., 2004, vol. 49, no. 12, pp. 1906–1916.
Okamoto, H., Chakrabarti, D.J., Laughlin, D.E., and Massalski, T.B., The Au–Cu (gold–copper) system, Bull. Alloy Phase Diagrams, 1987, vol. 8, no. 5, pp. 454–473. https://doi.org/10.1007/BF02893155
Holzapfel, W.B., Progress in the realization of a practical pressure scale for the range 1–300 GPa, High Press. Res., 2005, vol. 25, no. 2, pp. 87–96. https://doi.org/10.1080/09511920500147501
Stankus, S.V., Khairulin, R.A., and Tyagel’skii, P.V., The thermal properties of germanium and silicon in condensed state, High. Temp., 1999, vol. 37, no. 4, pp. 529–534. https://doi.org/ mi.mathnet.ru/tvt2324
Electronic database. http://www.ioffe.ru/SVA/NSM/ Semicond/SiGe/thermal.html
Amano, T., Beaudry, B., Gschneidner, K., Jr., Hartman, R., Vining, C., and Alexander, C., High-temperature heat contents, thermal diffusivities, densities, and thermal conductivities of n-type SiGe (GaP), p-type SiGe (GaP), and p-type SiGe alloys, J. Appl. Phys., 1987, vol. 62, no. 3, pp. 819–823. https://doi.org/10.1063/1.339712
Ravi, V., Firdosy, S., Caillat, T., Brandon, E., Van Der Walde, K., Maricic, L., and Sayir, A., Thermal expansion studies of selected high-temperature thermoelectric materials, J. Electron. Mater., 2009, vol. 38, no. 7, pp. 1433–1442. https://doi.org/10.1007/s11664-009-0734-2
Pavlova, L., Shtern, Y., and Kirilenko, E., Thermal expansion of bulk nanostructured n-type SiGe nanocomposite from 300 to 1400 K, J. Mater. Sci., 2017, vol. 52, no. 2, pp. 921–934. https://doi.org/10.1007/s10853-016-0387-5
Magomedov, M.N., On the calculation of the Debye temperature and crystal–liquid phase transition temperature of a binary substitution alloy, Phys. Solid State, 2018, vol. 60, no. 5, pp. 981–988. https://doi.org/10.1134/S1063783418050190
Magomedov, M.N., Changes in the thermodynamic properties of a Si–Ge solid solution at a decrease of the nanocrystal size, Phys. Solid State, 2019, vol. 61, no. 11, pp. 2145–2154. https://doi.org/10.1134/S1063783419110210
ACKNOWLEDGMENTS
I am grateful to S.P. Kramynin, N.Sh. Gazanova, and Z.M. Surkhaeva for their assistance with this study and useful discussions.
Funding
This work was supported by the Russian Foundation for Basic Research (project no. 18-29-11013_mk) and the Presidium of the Russian Academy of Sciences (program no. 6, grant no. 2-13).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Magomedov, M.N. On Deviations from Vegard’s Law at Increasing Pressure in Alloys. Inorg Mater 56, 903–908 (2020). https://doi.org/10.1134/S0020168520090125
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0020168520090125