Influence of strong anharmonicity on the dynamical properties of a crystal with BCC lattice

Abstract

The correlative method of unsymmetrized self-consistent eld CUSF is used to study dynamical characteristics of a strongly anharmonic crystal with body-centered cubic lattice, namely, the interatomic and mean square relative displacements. We present the general formulae for crystals with anharmonicity, including the strong one, up to fourth anharmonic terms. Taking into account the second order of the method we calculate correlations in this lattice between the nearest, second, third, fourth and fth neighbors. The in uence of more distant i n teractions is discussed. The results are compared with those obtained previously for an weakly anharmonic BCC crystal. We use the Schi potencial for Na and also Lennard-Jones potentials for comparison. I IntroductionThe quadratic correlation moments of atomic positions QCM as well as their mean square relative displacements MSRD expressing the e ective amplitude of the atomic vibrations are the most important features of lattice dynamics 1, 2 .Using the dynamical theory of crystal lattice, QCM and MSRD have been calculated in the harmonic approximation 2 . However, this approximation is not more valid at high temperatures due to anharmonic e ects which are of considerable importance. Here the correlative method of unsymmetrized self-consistent eld CUSF 3, 4 , 5 , 6 , 7, 8 is used to study the inuence of anharmonic e ects on the QCM and MSRD 9, 10 , including strongly anharmonic ones. The general expressions for QCM and MSRD are presented taking into account anharmonic terms up to the fourth order. Recently, they have been applied to weakly anharmonic crystal with face-and body centered cubic lattices 11, 12 and also to strongly anharmonic FCC crystal 13 . In the present paper we study a strongly anharmonic BCC crystal, namely solid Na. II General RelationsIn CUSF, the mean square relative displacements between two atoms i and j in a crystal, can be written as c D aa ij = q ia , q ja 2 = q 2 ia + q 2 ja , 2C aa ij ; 1 where a denotes the Cartesian components of atomic displacements and C aa ij = q ia q ja is the correlation moment.We consider a perfect crystal with pairwise central interactions U r; :::;r N = 1 2 X i6 =j jr i ,r j j : 2

An overview of the interatomic correlation moments and the mean square relative atomic displacements in anharmonic crystals

“…As this takes place, the strong anharmonicity significantly affects the interatomic correlations. It can be noticed as well that a drastic rise in C xx (1), in the vicinity of T S , corresponds to the general concept about the behavior of fluctuations and correlations of physical quantities near the spinodal [52]. …”

“…The melting temperature of Na is 373 K. For temperatures less than 50 K, Na has another crystal structure. For this reason, we investigated the QCM and MSRD in the temperature range between 50 K and 373 K [49,52]. It is seen that some momenta are negative, implying that the corresponding atoms oscillate in such a direction for the most part opposite in phase.…”

“…We note that CUSF yields good results for thermodynamic properties of strongly anharmonic crystals with various lattices and bonds: for van der Waals crystals [28,42], ionic crystals [30], fullerites [54,55] and also for Sodium [41,50,52] based on an effective interionic potential [58]. The CUSF is applicable not only to perfect, strongly anharmonic crystals, but also to crystals with lattice defects and surfaces as well [29,[33][34][35][36], allowing to study structural, dynamical and thermodynamical properties and providing a good agreements to available experimental data up to the melting temperatures [55]).…”

Interatomic correlations moments of atoms in the two-dimensional hexagonal lattice by using Morse and Lenard–Jones potentials

“…Based on the Correlative Method of Unsymmetrized Self-Consistent Field (CUSF, for short) [3][4][5][6][7] general formulae were derived for quadratic correlation moments between atomic displacements from lattice points in crystals taking into account anharmonic terms up to the fourth order [8][9][10], and have used them for calculations of these characteristics in the linear chain [9,11], twodimensional [10] and three-dimensional [12][13][14][15][16][17] models.…”