Free energy quasi-harmonic crystal

As noted earlier, this approach assumes the quasi-harmonic approximation which includes important anharmonic effects associated with the variation of free energy with volume (extrinsic anharmonicity). It does, however, neglect intrinsic anharmonicity which becomes important at elevated temperatures. To investigate crystals at high temperatures Molecular Dynamics (MD) can be used in which intrinsic anharmonic effects are treated explicitly. This method is considered in detail in Chapter 4. 

For the description of the temperature and stress-related behavior of the crystal we used the method of consistent quasi-harmonic lattice dynamics (CLD), which permits the determination of the equilibrium crystal structure of minimum free energy. The techniques of lattice dynamics are well developed, and an explanation of CLD and its application to the calculation of the minimum free-energy crystal structure and properties of poly(ethylene) has already been presented. ... 

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... 

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