Collective motions of atoms in crystals

V. D. Negodin ; D. Yu. Fleita ; G. E. Norman

Matematičeskoe modelirovanie, Tome 35 (2023) no. 6, pp. 37-50.

Résumé

Collective motions of atoms in molecular dynamics model of classical Lennard-Jones crystal are under consideration in process of heating up to spinodal decomposition and subsequent cooling of the melt to spontaneous crystallization. Collective motions magnitude hysteresis was found. A new numerical method based on four-point correlator usage was used for studying collectivity in the motion of atoms in crystals. This correlator represents the mean cosine of angle between replacement vectors of two atoms over time $\tau$, which were initially close to each other. Two features were found: (a) correlator increases with temperature in monocrystal; (b) correlator in polycrystal, which was formed during crystallization, appeared to be higher than in initial monocrystal. Distributions of correlator's values over the angles between displacements were computed. Two contributions in atoms’ motions were distinguished: first is anisotropic, temperature independent and second is almost isotropic, which angular distribution has the form of the Boltzmann distribution. Excitation energies, which corresponds to second contribution, were calculated.

Détail

Keywords: molecular dynamics, correlation functions, Lennard-Jones system.
Mots-clés : collective motions

Bibliographie

[1] H. N.V. Temperley, J. S. Rowlinson, G. S. Rushbrooke, Physics of Simple Liquids, North-Holland Pub. Co., Amsterdam, 1968, 713 pp.

[2] A. V. Zatovskii, N. P. Malomuzh, I. Z. Fisher, “Hydrodynamic asymptotic form of the rotational motion correlation function of a molecule in a liquid”, Sov. Phys. JETP, 38 (1974), 146–150

[3] R.C. Balescu, Equilibrium and Non-Equilibrium Statistical Mechanics, Wiley, New York, 1975, 742 pp. | MR

[4] T. Egami, S. J.L. Billinge, Underneath the Bragg Peaks. Structural Analysis of Complex Materials, 2nd ed., Pergamon, Amsterdam, 2012, 422 pp.

[5] J. P. Hansen, I. McDonald, Theory of Simple Liquids. With Applications to Soft Matter, Academic Press, Oxford, 2013, 619 pp. | Zbl

[6] N. P. Malomuzh, T. V. Lokotosh, “Lagrange theory of thermal hydrodynamic fluctuations and collective diffusion in liquids”, Phys. A, 286 (2000), 474–488 | DOI

[7] L. A. Bulavin, T. V. Lokotosh, N. P. Malomuzh, “Role of the collective self-diffusion in water and other liquids”, J. Mol. Liq., 137:1–3 (2008), 1–24 | DOI

[8] W. Schirmacher, B. Schmid, “Theory of collective excitations in simple liquids”, Eur. Phys. J. Special Topics, 196:1 (2011), 3–13 | DOI

[9] Y. D. Fomin, E. Tsiok, V. N. Ryzhov, V. Brazhkin, “Anomalous behavior of dispersion of longitudinal and transverse collective excitations in water”, J. Mol. Liq., 287 (2019), 110992 | DOI

[10] N. V. Priezjev, “Heterogeneous relaxation dynamics in amorphous materials under cyclic loading”, Phys. Rev. E, 87 (2013), 052302 | DOI

[11] N. M. Chtchelkatchev, R. E. Ryltsev, “Complex singularities of the fluid velocity autocorrelation function”, JETP Lett., 102:10 (2015), 643–649 | DOI

[12] M. A. Orekhov, “Coordination Numbers of Bivalent Ions in Organic Solvents”, Rus. J. of Phys. Chem. A, 95 (2021), 2059–2064 | DOI

[13] D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed., Academic Press, Orlando, 2001, 664 pp.

[14] G. E. Norman, V. V. Stegailov, “Stochastic theory of the classical molecular dynamics method”, Math. Mod. and Comp. Sim., 5:4 (2013), 305–333 | MR | Zbl

[15] P. H. Poole, C. Donati, S. C. Glotzer, “Spatial correlations of particle displacements in a glass-forming liquid”, Phys. A, 261 (1998), 51–59 | DOI | MR

[16] N. Lacevic, F. W. Starr, T. B. Schroder, S. C. Glotzer, “Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function”, J. Chem. Phys., 119 (2003), 7372–7387 | DOI

[17] V. Voloshin, G. Malenkov, Y. Naberukhin, “Collective motions in computer models of water. Large-scale and long-time correlations”, J. Struct. Chem., 54:2 (2013), S233–S251

[18] A. V. Anikeenko, G. G. Malenkov, Yu. I. Naberukhin, “Visualization of the collective vortex-like motions in liquid argon and water: Molecular dynamics simulation”, J. Chem. Phys., 148:9 (2018), 094508 | DOI | DOI

[19] A. V. Anikeenko, Yu. I. Naberukhin, “Large-scale and long-term correlations in collective motions of atoms of liquid argon. Computer simulation”, JETP Lett., 106:5 (2017), 290–294 | DOI

[20] A. Anikeenko, G. Malenkov, Y. Naberukhin, “Visualization of vortex movements in a molecular dynamics model of liquid argon”, Dokl. Phys. Chem., 472:1 (2017), 16–18 | DOI

[21] G. E. Norman, V. V. Pisarev, D. I. Fleita, “Singularity at the point of transition from equilibrium to metastable states of a metallic melt”, JETP Lett., 109:10 (2019), 667–670 | DOI

[22] V. Negodin, Y. Polyachenko, D. Fleyta, V. Pisarev, G. Norman, “Kinetic singularities at transition points from equilibrium to metastable states of the Lennard-Jones particle system”, J. Mol. Liq., 322 (2021), 114954 | DOI

[23] G. E. Norman, D. I. Fleita, “Collective Motion of Atoms in a Superheated Crystal and a Supercooled Melt of a Simple Metal”, JETP Lett., 111:4 (2020), 245–250 | DOI

[24] A. Travesset, “Phase diagram of power law and Lennard-Jones systems: Crystal phases”, J. Chem. Phys., 141 (2014), 164501 | DOI

[25] C. Vega, F. J. Blas, A. Galindo, “Extending Wertheim's perturbation theory to the solid phase of Lennard-Jones chains: Determination of the global phase diagram”, J. Chem. Phys., 116:17 (2002), 7645–7655 | DOI

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

[27] V. Stegailov, E. Dlinnova, T. Ismagilov, M. Khalilov, N. Kondratyuk, D. Makagon, A. Semenov, A. Simonov, G. Smirnov, A. Timofeev, “Angara interconnect makes GPU-based Desmos supercomputer an efficient tool for molecular dynamics calculations”, The Int. J. of High Perf. Comp. Appl., 33:3 (2019), 507–521 | DOI

[28] E. Dlinnova, S. Biryukov, V. Stegailov, “Energy consumption of MD calculations on hybrid and CPU-only supercomputers with air and immersion cooling”, Par. Comp. Tech. Tr., Adv. in Par. Comp., 36, 2020, 574–582

[29] A. Shamsutdinov, M. Khalilov, T. Ismagilov, A. Piryugin, S. Biryukov, V. Stegailov, A. Timofeev, “Performance of Supercomputers Based on Angara Interconnect and Novel AMD CPUs/GPUs”, Int. Conf. on Mat. Mod. and Supercomp. Tech., 2020, 401–416 | MR

[30] I. Z. Fisher, Statistical theory of liquids, Univ. of Chicago Press, Chicago, 1964, 335 pp.

[31] G. R. Stewart, “Measurement of low-temperature specific heat”, Rev. of Scientific Instr., 54 (1983), 1–11 | DOI

[32] Seung-Kyo Oh, “Modified Lennard-Jones Potentials with a Reduced Temperature-Correction Parameter for Calculating Thermodynamic and Transport Properties: Noble Gases and Their Mixtures (He, Ne, Ar, Kr, and Xe)”, J. of Thermod., 2013 (2013), 828620

[33] L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, v. 5, Statistical Physics, Butterworth-Heinemann, Oxford, 1980, 564 pp. | MR

[34] A. Kh. Khrgian, Fizika atmosfery, Gidrometeoizdat, L., 1969, 645 pp.

[35] L. A. Maksimov, A. V. Mikheenkov, I. Ya. Polishuk, Lektsii po statisticheskoy fizike, uchebnoe posobie, MFTI, M., 2015, 328 pp.

[36] V.L. Ginzburg, D.V. Sivukhin, L.M. Levin, E.S. Chetverikova, Problems in Undergraduate Physics, v. III, Optics, Pergamon Press, Oxford, 1965, 280 pp.