Comparison of the anharmonic formalisms

The OPP formalism, though based on the assumption of independent motion, has the advantage of assigning a physical meaning to the terms in the expansion. By equating the OPP terms to the corresponding ones in the statistical expansions, the quasimoments and cumulants can be related to the parameters of the potential model, and their temperature dependence can be predicted. 

For a cubic site, relations between the cumulants and the coefficients of the OPP model have been derived by Kontio and Stevens (1982), and applied to the Al(4) atom in the alloy VA110 4.2 The coordination of Al(4) is illustrated in Fig. 2.4(a), while the potential along [111], derived from the thermal parameter refinement, is shown in Fig. 2.4(b). It is clear from these figures that higher than third-order terms contribute to the potential, because the deviation from the harmonic curve is not exactly antisymmetric with respect to the equilibrium configuration. The potential appears steeper at the higher temperature, which is opposite to what is expected on the basis of the thermal expansion of the solid. 

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