Thermal expansions of high-purity and OH−-doped NaCl at temperatures below 30 K

A variable transformer dilatometer has been used to obtain linear thermal-expansion coefficients for temperatures from 2 to 30 K for single crystals of pure (O${\mathrm{H}}^{-}$-free) NaCl and for NaCl crystals which contained 6.5 and 80 ppm of O${\mathrm{H}}^{-}$ substitutional impurities. The thermal expansions of the pure sample are well behaved, with a Grüneisen parameter which agrees well with the elastic-constant value (1.06) below 6 K, and which shows a pronounced minimum near 15 K. A relatively large anomalous contribution to the thermal-expansion coefficient of the 80-ppm sample increases with decreasing temperature and has a magnitude which is ten times that of the pure sample at 2.25 K. The large excess thermal expansions are similar in form to heat-capacity contributions which can be calculated from published energy-level diagrams for O${\mathrm{H}}^{-}$ in NaCl. The corresponding Grüneisen parameter for this impurity system is quite large (∼40), and hence provides a direct confirmation that tunneling must be involved in any description of the thermodynamic properties of these impurity states.