Specific heat anharmonic effects

In an attempt both to include quantum corrections and to treat anharmonic effects, Etters, Kanney, Gillis, and Kaelberger have calculated the thermodynamic properties of clusters using the self-consistent phonon approximation. - Within this approximation they calculated internal energies, free energies, specific heats, and entropies for argon clusters. 

Beyond the Harmonic Approximation Thus far, our analysis has been entirely predicated upon the harmonic approximation advanced in eqn (5.2). On the other hand, real crystals are characterized by nonlinear force laws and the resulting anharmonic effects are part of the story from the outset. If we confine our interest to the specific heat, we see that much may be made of the harmonic approximation. However, if we aim to press our modeling efforts further, for example, to consider the thermal expansion or the thermal conductivity, we will see that the harmonic approximation does not suffice. Let us flesh out the logic in the case of the coefficient of thermal expansion. Our first ambition will be to demonstrate that the harmonic approximation predicts... 

At temperatures where the dominant phonon wavelengths of interchain modes are of the order of the cross-link distance, a pronounced effect of cross-linking on thermal conductivity and thermal expansion was found. Both quantities were strongly determined by anharmonic contributions of the binding potential. Elastic mechanical parameters or specific heat, which can be described in the harmonic approximations, showed no influence of cross-linking. The interpretation that the... 

In Chap.5, anharmonic effects are considered. After an illustration of anharmonicity with the help of the diatomic molecule, we derive the free energy of the anharmonic linear chain and discuss the equation of state and the specific heat. The quasi-harmonic approximation" worked out in detail for the linear chain is then applied to three-dimensional crystals to obtain the equation of state and thermal expansion. The self-consistent harmonic approximation" is the basis for treating the effects of strong anharmonicity. At the end of this chapter we give a qualitative discussion of the response... 

Anharmonic Effects on the Specific Heat and Elastic Constants... 

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