Elastic Properties of NaCl: OH at Low Temperatures

Low temperature behavior of elastic constants ( C 11 - C 12 )/2, C 44 and C 11 of NaCl crystals with OH impurity ions of various concentrations up to 650 ppm has been studied by means of an ultrasonic method. Pronounced softenings of the elastic constants below 50 K with minimum points around 0.8 K have been observed. The interaction between the elastic strain and the quadrupolar moments of the quantum tunneling states of an OH ion was found to be essential for the elastic anomalies. A variational method was employed to obtain the tunneling states of an OH ion in an off-center potential, and the quadrupolar moments of the states were calculated. The linear response theory for the quadrupolar moments has been adopted to explain the softening of the elastic constant.