Negative thermal expansion and valence fluctuation in quasi-one-dimensional platinum compounds.

Abstract

Negative thermal expansion observed along the chain direction in [Pt(${\mathrm{NH}}_{3}$${)}_{4}$][Pt${X}_{2}$(${\mathrm{NH}}_{3}$${)}_{4}$]) $_{4}$] (${\mathrm{HSO}}_{4}$${)}_{4}$, where X=Cl or Br, is explained from the viewpoint of the valence fluctuation of Pt atoms. The present crystals are considered essentially ionic system with the mean valencies of ${\mathrm{Pt}}^{3+\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Pt}}^{3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, and the valence fluctuation is treated in two different approaches: slow and rapid fluctuation. In both cases, minimization of the (free) energy provides the contraction of ${\mathrm{Pt}}^{3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$-X distance and expansion of ${\mathrm{Pt}}^{3+\mathrm{\ensuremath{\delta}}}$-X distance with increasing temperature leading to the overall negative thermal expansion, in agreement with experiment.