A variational model is formulated to study the effect of substitutional impurities in solids at very low temperature. The aim of this approach is to improve upon the independent harmonic oscillation assumption in the Einstein model. Since the impurities may vibrate partially independent of the media, an Einstein model is used to describe their motion, while the motion of impurities that correlates with the lattice and the collective motion of the host particles are characterized by a Debye model. By variationally determining the parameters of the model, this approach is used to investigate the effects of various impurities on the thermodynamical and structural properties of solid H2 and solid D2. The averaged effect of the anharmonicity in the pair potentials is included self‐consistently in the variational model. However, as suggested from the comparison between the model calculations and computer simulations, a detailed consideration of the anharmonicity is necessary for a highly quantized solid such as H2.  

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