The Einstein specific heat model for finite systems

E. Boscheto, M. de Souza and A. López-Castillo

Physica A: Statistical Mechanics and its Applications, 2016, vol. 451, issue C, 592-600

Abstract: The theoretical model proposed by Einstein to describe the phononic specific heat of solids as a function of temperature consists of the very first application of the concept of energy quantization to describe the physical properties of a real system. Its central assumption lies in the consideration of a total energy distribution among N (in the thermodynamic limit N→∞) non-interacting oscillators vibrating at the same frequency (ω). Nowadays, it is well-known that most materials behave differently at the nanoscale, having thus some cases physical properties with potential technological applications. Here, a version of the Einstein model composed of a finite number of particles/oscillators is proposed. The main findings obtained in the frame of the present work are: (i) a qualitative description of the specific heat in the limit of low-temperatures for systems with nano-metric dimensions; (ii) the observation that the corresponding chemical potential function for finite solids becomes null at finite temperatures as observed in the Bose–Einstein condensation and; (iii) emergence of a first-order like phase transition driven by varying N.

Keywords: Specific heat; Einstein model; Finite size systems (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:451:y:2016:i:c:p:592-600

DOI: 10.1016/j.physa.2016.02.010

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