Title: Negative thermal expansion and entropic elasticity in ScF3 type empty perovskites
While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). NTE is common in polymers and biomolecules, where it stems from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids had been widely believed to be different, with phonon anharmonicity and specific lattice vibrations that preserve geometry of the coordination polyhedra – rigid unit motions (RUMs) – as leading contenders for explaining NTE. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus . We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion, which is only constrained by the rigid Sc-F bonds. These experimental findings lead us to a quantitative, quasi-harmonic theory of NTE in terms of entropic elasticity of a Coulomb floppy network crystal, which is applicable to a broad range of open framework solids featuring floppy network architecture . The theory is in remarkable agreement with experimental results in ScF3, accurately describing NTE, phonon frequencies, entropic compressibility, and structural phase transition governed by entropic stabilization of criticality. We thus find that NTE in a family of insulating ceramics stems from the same simple and intuitive physics of entropic elasticity of an under-constrained floppy network that has long been appreciated in soft matter and polymer science, but broadly missed by the “hard” condensed matter community. Our results reveal the formidable universality of the NTE phenomenon across soft and hard matter [1,2].
 D. Wendt, et al., Sci. Adv. 5: eaay2748. (2019).
 A. V. Tkachenko, I. A. Zaliznyak. arXiv:1908.11643 (2019).
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