Amplitude Instability of Charged Particles in a Body-Centered Cubic Cell
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Amplitude Instability of Charged Particles in a Body-Centered Cubic Cell O. S. Vaulinaa,b a
Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia bMoscow
Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia e-mail: [email protected] Received April 5, 2019; revised April 5, 2019; accepted April 23, 2019
Abstract—The conditions for the formation of amplitude instabilities in 3D Yukawa systems consisting of nine charged particles in a body-centered cubic (bcc) cell have been investigated. The criterion for the formation of amplitude instability has been sought using an analytic approach based on determining the point of inflection of the potential energy of the system during deviation of particles from their equilibrium position. The results have been compared with melting criteria for extended bcc lattices.
DOI: 10.1134/S1063776119080168
1. INTRODUCTION The formation of various instabilities in nonideal media is of permanent interest in various branches of science and technology [1–9]. A slight variation of control parameters in initially equilibrium systems may substantially change their physical characteristic due to the evolution of dissipative and/or dispersive instabilities [7–14]. In addition, systems of interacting particles may lose stability upon an increase in the amplitude of their deviations from initially equilibrium positions (due to evolution of amplitude instability), for example, due to an increase in the temperature of particles. Most methods for determining criteria of formation of various instabilities in nonideal media are based either on analysis of linearized equation of motion of interacting particles or on the search for the minimum of the potential energy of a system [10–20]. The former approach is limited by the necessary condition of smallness of deviation (displacement) of particles from their equilibrium position, while the latter approach is more fundamental and is often used for determining the melting criterion and conditions of the formation of various crystal lattices [11, 17–20]. The impossibility of using linearized equations of motion correctly for describing nonlinear processes (emerging, for example, upon an increase in the particle temperature) has led to wide employment of various phenomenological criteria in the theory of melting of crystal lattices (Liedeman criterion, Hansen criterion, etc. [1, 2, 20, 21]). How-
ever, these criteria often cannot be used for smallsize cluster systems [20, 22]. In this study, for analyzing the conditions for variation of physical characteristics of body-centered cubic (bcc) clusters upon an increase in temperature of particles, their amplitude stability (i.e., the stability to any (and not only small) deviations of particles from their equilibrium positions) is tested. This approach is based on the search for the point of inflection of the potential energy of the system upon an increase in displacements of interacting particles and
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