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Abstract: We consider the thermal expansion, change of sound velocity with pressure andtemperature, and the Poisson ratio of lattices which have rigid unitspolyhedra very large stiffness to change in bond-length and to bond-anglevariations connected to other such units through relatively compressiblepolyhedra. We show that in such a model, the potential energy for rotations ofthe rigid units can occur only as a function of the combination ${\boldsymbol\Theta} i \equiv {\boldsymbol \theta} i - abla \times {\bf u} i-2$, where${\boldsymbol \theta i} $ are the orthogonal rotation angles of the rigid unit$i$ and ${\bf u} i$ is its displacement. Given such new invariants in thetheory of elasticity and the hierarchy of force constants of the model, anegative thermal expansion coefficient as well as a decrease in the elasticconstants of the solid with temperature and pressure is shown to follow. Theseare consistent with the observations.



Author: Yan He, Vladimir Cvetkovic, C. M. Varma

Source: https://arxiv.org/



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