Atomistic simulation of the coexistence of liquid-vapor phase states for gold and determination of critical parameters

V. I. Mazhukin ; O. N. Koroleva ; M. M. Demin ; A. V. Shapranov ; A. A. Aleksashkina

Matematičeskoe modelirovanie, Tome 34 (2022) no. 3, pp. 101-116.

Résumé

The work is devoted to the study (on the example of gold) of the properties of metals near the critical point. Long-term studies testify to the complexity of the problem and its importance both for constructing theoretical ideas about the behavior of metastable states of a highly superheated liquid phase of metals, and for developing a number of technological applications in the field of materials science, the impact of concentrated energy flows on a substance, etc. Metastable states of a superheated liquid and a saturated pair in the vicinity of the critical point have not been sufficiently studied. When approaching the critical point, the properties of matter change dramatically due to strong stochastic fluctuations of parameters (primarily density). Molecular dynamics methods are a relevant tool for determining critical parameters. For gold, they were used to obtain a liquid– vapor coexistence curve, from which the critical parameters were then determined: temperature, density, and pressure. In the calculations, the potential of the family of "embedded atoms" (EAM) was used as the interaction potential of particles. The value of the critical temperature $T_{cr}$ was determined from the results of MD simulation using the method of the maximum size of the averaged cluster on the temperature curve passing through the critical region. The value of the critical pressure $P_{cr}$ was obtained from the results of MD simulation from the temperature dependence of the saturated vapor pressure $P_{sat}(T)$. The value of the critical density $\rho_{cr}$ was obtained from the results of MD simulation of the liquid-vapor coexistence curve using the empirical rule of the rectilinear diameter. The simulation results of this work are compared with the results of estimation of the critical parameters of gold by other authors using different approaches.

Détail

Keywords: molecular dynamics modeling, liquid-vapor coexistence curve, critical parameters, gold.

Bibliographie

[1] N. Elahi, M. Kamali, M. H. Baghersad, “Recent biomedical applications of gold nanoparticles: A review”, Talanta, 184 (2018), 537–556 | DOI

[2] M. P. Vukalovich, I. I. Novikov, Termodinamika, Mashinostroenie, M., 1972

[3] R. Winter, C. Pilgrim, F. Hensel, C. Morkel, W. Gläser, “Structure and dynamics of expanded liquid alkali metals”, J. Non-Crystalhne Sohds, 156-158 (1993), 9–14 | DOI

[4] F. Hensel, E. Marceca, W. C. Pilgrim, “The metal-non-metal transition in compressed metal vapours”, J. Physics: Condensed Matter, 10:49 (1998), 11395–11404 | DOI

[5] F. Hensel, G. F. Hohl, D. Schaumloffel, W. C. Pilgrim, E. U. Franck, “Empirical regularities in behaviour of the critical constants of fluid alkali metals”, J. Phys. Chem., 214:6 (2000), 823–831

[6] J. Jüngst, B. Knuth, F. Hensel, “Observation of singular diameter in the coexistence curve of metals”, Phys. Rev. Lett., 55 (1985), 2160–2163 | DOI

[7] G. R. Gathers, “Dynamic methods for investigating thermophysical properties of matter at very high temperatures and pressures”, Reports on Progress in Physics, 49:4 (1986), 341–396 | DOI

[8] G. Pottlacher (Ed.), High Temperature Thermophysical Properties of 22 Pure Metals, Edition keeper, Pab., 2010

[9] M. M. Martyniuk, “Parametry kriticheskoi tochki metallov”, J. fiz. himii, 57:4 (1983), 810–821

[10] K. Boboridis, G. Pottlacher, H. Jager, “Determination of the Critical Point of Gold”, International Journal of Thermophysics, 20:4 (1999), 1289–1297 | DOI

[11] G. Pottlacher, W. Schröer, “Estimation of critical data and phase diagrams of pure molten metals”, High Temperatures, High Pressures, 2014, 201–215

[12] V. E. Fortov, A. N. Dremin, A. A. Leont'ev, “Evaluation of the parameters of the critical point”, High Temperature, 13:5 (1975), 984–992

[13] A. A. Likalter, “On the critical parameters of metals”, High Temperature, 23:3 (1985), 371–377

[14] G. Lang, “Critical temperatures and temperature coefficients of the surface tension of liquid metals”, Zeitschrift fuer Metallkunde, 68:3 (1977), 213–218

[15] E. M. Apfelbaum, V. S. Vorob'ev, “The similarity relations set on the basis of symmetrization of the liquid — vapor phase diagram”, J. Phys. Chem. B, 119 (2015), 8419 | DOI

[16] E. M. Apfelbaum, V. S. Vorob'ev, “The Wide-Range Method to Construct the Entire Coexistence Liquid-Gas Curve and to Determine the Critical Parameters of Metals”, J. Phys. Chem. B, 119:35 (2015), 11825–11832 | DOI

[17] S. Blairs, M. H. Abbasi, “Correlation between surface tension and critical temperatures of liquid metals”, Journal of Colloid and Interface Science, 304 (2006), 549–553 | DOI

[18] G. Kaptay, “On the Order-Disorder Surface Phase Transition and Critical Temperature of Pure Metals Originating from BCC, FCC, and HCP Crystal Structures”, Int. J. Thermophys, 33 (2012), 1177–1190 | DOI

[19] A. L. Khomkin, A. S. Shumikhin, “The thermodynamics and transport properties of transition metals in critical point”, High Temp. High Press, 46:4-5 (2017), 367–380

[20] H. Kanno, “New empirical formula for estimating critical temperature of element from solid properties”, Journal of Inorganic and Nuclear Chemistry, 38:8 (1976), 1573–1575 | DOI

[21] V. I. Mazhukin, A. A. Samokhin, M. M. Demin, A. V. Shapranov, “Explosive boiling of metals upon irradiation by a nanosecond laser pulse”, Quantum Electronics, 44:4 (2014), 283–285 | DOI

[22] V. I. Mazhukin, A. A. Samokhin, A. V. Shapranov, M. M. Demin, “Modeling of thin film explo-sive boiling surface evaporation and electron thermal conductivity effect”, Mater. Res. Express, 2:1 (2015), 016402, 9 pp. | DOI

[23] M. M. Demin, O. N. Koroleva, A. V. Shapranov, A. A. Aleksashkina, “Atomistic modeling of the critical region of copper using a liquid-vapor coexistence curve”, Math. Montis, 46 (2019), 52–61 | DOI | MR

[24] M. V. Shugaev, C. Y. Shih, E. T. Karim, C. Wu, L. V. Zhigilei, “Generation of nanocrystalline surface layer in short pulse laser processing of metal targets under conditions of spatial confinement by solid or liquid overlayer”, Appl. Surf. Sci., 417 (2017), 54–63 | DOI

[25] D. I. Zhukhovitskii, V. V. Zhakhovsky, “Thermodynamics and the structure of clusters in the dense Au vapor from molecular dynamics simulation”, J. Chem. Phys., 152 (2020), 224705 | DOI

[26] V. V. Zhakhovskii, N. A. Inogamov, Yu. V. Petrov, S. I. Ashitkov, K. Nishihara, “Molecular dynamics simulation of femtosecond ablation and spallation with different interatomic potentials”, Appl. Surf. Sci., 255 (2009), 9592–9596 | DOI

[27] C. Desgranges, L. Widhalm, J. Delhommelle, “Scaling Laws and Critical Properties for FCC and HCP Metals”, J. Phys. Chem. B, 2016, 1–24

[28] E. M. Apfelbaum, V. S. Vorob'ev, “The Zeno line for Al, Cu, and U”, J. Phys. Chem. B, 120 (2016), 4828–4833 | DOI

[29] J. K. Singh, J. Adhikari, S. K. Kwak, “Vapor-liquid phase coexistence curves for Morse fluids”, Fluid Phase Equilib., 248 (2006), 1–6 | DOI

[30] A. A. Likalter, “Critical points of metals of three main groups and selected transition metals”, Physica A: Statistical Mechanics and its Applications, 311 (2002), 137–149 | DOI

[31] L. V. Al'tshuler, A. V. Bushman, M. V. Zhernokletov, V. N. Zubarev, A. A. Leont'ev, V. E. Fortov, “Unloading isentropes and the equation of state of metals at high energy densities”, JETP, 51:2 (1980), 373–383 | MR

[32] D. A. Young, B. J. Alder, “Critical point of metals from the van der Waals model”, Phys. Rev. A, 3:1 (1971), 364–371 | DOI

[33] A. A. Likalter, “Equation of state of metallic fluids near the critical point of phase transition”, Phys. Rev. B, 53 (1996), 4386 | DOI

[34] S. Blairs, Mh. Abbasi, “Internal-pressure approach for the estimation of critical-temperatures of liquid-metals”, Acustica, 79:1 (1993), 64–72

[35] V. P. Skripov, Metastable Liquids, Halsted Press, John Wiley Sons, New York, 1974

[36] V. A. Kirillin, V. V. Sychev, A. E. Sheidlin, Tekhnicheskaia termodinamika, Izd-vo MEI, M., 2008

[37] F. Hensel, “35 years Liquid Metals conferences: what do we and what do we not yet understand about liquid metals”, J. Non-Cryst. Solids, 312-314 (2002), 1–7 | DOI

[38] V. I. Mazhukin, O. N. Koroleva, A. V. Shapranov, M. M. Demin, A. A. Aleksashkina, “Oprede-lenie teplofizicheskikh svoistv zolota v oblasti fazovogo perehoda plavlenie-kristallizatciia. Molekuliarno-dinamicheskiy podhod”, Matematicheskoe modelirovanie, 34:1 (2022), 59–80 | DOI | Zbl

[39] L. Verlet, “Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules”, Phys. Rev., 159 (1967), 98–103 | DOI

[40] V. I. Mazhukin, A. V. Shapranov, “Matematicheskoe modelirovanie protcessov nagreva i plavleniia metallov. Chast I. Model i vychislitelnyi algoritm”, Keldysh Institute Preprints, 2012, 031, 27 pp.

[41] H. J. C. Berendsen, J. P.M. Postma, W. F. van Gunsteren, A. DiNola, J. R. Haak, “Molecular dynamics with coupling to an external bath”, J. Chem. Phys., 81 (1984), 3684–3690 | DOI

[42] M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 2002

[43] V. I. Mazhukin, A. V. Shapranov, O. N. Koroleva, A. V. Rudenko, “Molecular dynamics simulation of critical point parameters for silicon”, Math. Montis., 31 (2014), 56–76

[44] S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics”, J. Comput. Phys., 117:1 (1995), 1–19 | DOI | Zbl