Influence of size and pressure on the temperature dependencies of thermodynamic properties of platinum
Institute of Physics named after H.I. Amirkhanova – subdivision of Dagestan Federal Research Center of the Russian Academy of Sciences
Abstract: Based on the parameters of the pair interatomic interaction potential of the Mie-Lennard- Jones for Pt , and using the RP-model of the nanocrystal, the temperature, pressure and size dependencies of the following properties are studied: elastic modulus, thermal expansion coefficient, isobaric heat capacity, and surface energy. The calculation of the equation of state showed good agreement with experiment. The equation of state was calculated along five isotherms: T=300, 1300, 1500 , 1700 , 1900 K. For the first time, calculations of the temperature dependences of the above properties of Pt in the range from 0 to 1500 K along 0 and 50 GPa isobars were performed from a unified standpoint. Calculations of these dependencies were carried out for both macro- and cubic nanocrystals of 306 atoms. It is shown that with an isobaric-isothermal decrease in the nanocrystal size, the values of the elastic modulus and surface energy decrease, while the values of the thermal expansion coefficient and isobaric heat capacity increase over the investigated temperature range.
Keywords: platinum, nanocrystal, size dependencies, equation of state, surface energy
- Sergey P. Kramynin – Junior Researcher, Institute of Physics named after H.I. Amirkhanova – subdivision of Dagestan Federal Research Center of the Russian Academy of Sciences
Kramynin, S.P. Influence of size and pressure on the temperature dependencies of thermodynamic properties of platinum / S.P. Kramynin // Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials. — 2021. — I. 13. — P. 465-474. DOI: 10.26456/pcascnn/2021.13.465. (In Russian).
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1. Magomedov M.N. Temperature and Pressure Dependences of the Surface Energy for a Macro- and Nanocrystal, Physics of the Solid State, 2021, vol. 63, issue 9, pp. 1595-1609. DOI: 10.1134/S1063783421090250.
2. Magomedov M.N. On the statistical thermodynamics of a free-standing nanocrystal: silicon, Crystallography Reports, 2017, vol. 62, issue 3, pp. 480-496. DOI: 10.1134/S1063774517030142.
3. Magomedov M.N. Study of properties of fcc- Au–Fe alloys in macro- and nano-crystalline states under various P–T -conditions, Journal of Physics and Chemistry of Solids, 2021, vol. 151, art. no. 109905, 12 p. DOI: 10.1016/j.jpcs.2020.109905.
4. Fei Y., Li J., Hirose K. et al. A critical evaluation of pressure scales at high temperatures by in situ X-ray diffraction measurements, Physics of the Earth and Planetary Interiors, 2004, vol. 143-144, pp. 515-526, DOI: 10.1016/j.pepi.2003.09.018.
5. Zha C.-S., Mibe K., Bassett W.A. et al. P–V–T equation of state of platinum to 80 GPa and 1900 K from internal resistive heating/x-ray diffraction measurements, Journal of Applied Physics, 2008, vol. 103, issue 5, pp. 054908-1-054908-10. DOI: 10.1063/1.2844358.
6. Dorogokupets P.I., Sokolova T.S., Danilov B.S., Litasov K.D. Near-absolute equations of state of diamond, Ag, Al, Au, Cu, Mo, Nd, Pt, Ta, W and W for quasi-hydrostatic conditions, Geodynamics & Tectonophysics, 2012, vol. 3, no. 2, pp. 129-166. DOI: 10.5800/ GT-2012-3-2-0067. (In Russian).
7. Holmes N.C., Moriarty J.A., Gathers G.R., Nellis W.J. The equation of state of platinum to 660 GPa ( 6,6 Mbar), Journal of Applied Physics, 1989, vol. 66, issue 7, pp. 2962-2967. DOI: 10.1063/1.344177.
8. Marsh S. LASL shock hugoniot data. Berkeley, Los Angeles, London, University of California Press, 1980, XIX, 658 p.
9. Jin K., Wu Q., Geng H. et al. Pressure–volume–temperature equations of state of Au and Pt up to 300 GPa and 3000 K: internally consistent pressure scales, High Pressure Research, 2011, vol. 31, issue 4, pp. 560-580. DOI: 10.1080/08957959.2011.611469.
10. Dewaele A., Loubeyre P., Mezouar M. Equations of state of six metals above 94 GPa, Physical Review B, 2004, vol. 70, issue 9, pp. 094112-1-094112-8. DOI: 10.1103/PhysRevB.70.094112.
11. Ono S., Brodholt J.P., Price G.D. Elastic, thermal and structural properties of platinum, Journal of Physics and Chemistry of Solids, 2011, vol. 72, issue 3, pp. 169-175. DOI: 10.1016/j.jpcs.2010.12.004.
12. Elkin V.M., Mikhaylov V.N., Ovechkin A.A., Smirnov N.A. A wide-range multiphase equation of state for platinum, Journal of Physics: Condensed Matter, 2020, vol. 32, no. 43, art. no. 435403, 12 p. DOI: 10.1088/1361-648X/aba428.
13. Collard S.M., McLellan R.B. High-temperature elastic constants of platinum single crystals, Acta Metallurgica et Materialia, 1992, vol. 40, issue 4, pp. 699-702. DOI: 10.1016/0956-7151(92)90011-3.
14. Karbasi A., Saxena S.K., Hrubiak R. The thermodynamics of several elements at high pressure, Calphad, 2011, vol. 35, issue 1, pp. 72-81. DOI: 10.1016/j.calphad.2010.11.007.
15. El'kin V.M., Mikhajlov V.N., Mikhajlova T.Yu. Poluempiricheskoe dvukhfaznoe uravnenie sostoyaniya platiny (tverdaya faza, zhidkost') s uchetom ispareniya [Semi-empirical two-phase equation of state for platinum (solid phase, liquid) taking into account evaporation], Voprosy atomnoj nauki i tekhniki. Seriya: Teoreticheskaya i prikladnaya fizika [Nuclear science and technology. Series: Theoretical and Applied Physics], 2016, no. 1, pp. 38-52. (In Russian).
16. Povzner A.A., Filanovich A.N. Effect of phonon anharmonicity on the thermophysical and elastic properties of platinum, High Temperature, 2011, vol. 49, issue 5, pp. 674-678. DOI: 10.1134%2FS0018151X11050178.
17. Kramynin S.P. Zavisimost' teplofizicheskikh svojstv niobiya ot razmera nanokristalla [Change in the baric dependences of the thermophysical properties of a niobium nanocrystal with a change in size], Fiziko- khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2019, issue 11, pp. 315-325. DOI: 10.26456/pcascnn/2019.11.315. (In Russian).
18. Kramynin S.P. Razmernye zavisimosti svojstv splava Mo–W [The size dependencies of properties of Mo–W alloy of equiatomic composition], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2020, issue 12, pp. 128-135. DOI: 10.26456/pcascnn/2020.12.128. (In Russian).