Lower limit to the thermal conductivity of disordered crystals
David G. Cahill, Susan K. Watson, R. O. Pohl
Abstract
Measurements of the thermal conductivity above 30 K of mixed crystals with controlled disorder, (KBr${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(KCN${)}_{\mathit{x}}$, (NaCl${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$, (NaCn${)}_{\mathit{x}}$ ${\mathrm{Zr}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Y}}_{\mathit{x}}$${\mathrm{O}}_{2\mathrm{\ensuremath{-}}\mathit{x}/2}$, and ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$${\mathrm{F}}_{2+\mathit{x}}$, support the idea of a lower limit to the thermal conductivity of disordered solids. In each case, as x is increased, the data approach the calculated minimum conductivity based on a model originally due to Einstein. These measurements support the claim that the lattice vibrations of these disordered crystals are essentially the same as those of an amorphous solid.