Elastic properties of para- and ferroelectric phases in the system Li2 − xNaxGe4O9

The elastic properties of single crystals of the ferroelectric family Li2 − xNaxGe4O9 with x = 1, 0.8, 0.6 and 0.4 were studied in the range between 100 and 360 K by ultrasonic resonance techniques. At room temperature a distinct anomalous reduction of all elastic constants cij occurs with increasing lithium content in an amount of up to 26% (c44). At 293 K the thermoelastic constants Tij = d(log cij)/dT and the piezoelastic constants Pij = dcij/dp (T, temperature; p, hydrostatic pressure) vary only slightly with composition, except T44 and P44, which in the case of x = 0.4 possess anomalous positive and negative signs, respectively. Approaching the transition temperature T0, which depends strongly on the composition, a softening of the constants c44, c55, c33 and c23 in an amount of about 5% is observed. Below T0 these constants increase with lower temperatures. In contrast, the constants c11, c22, c12 and c66 are much less affected by the transition process. Further, a strong anomalous negative thermal expansion appears along [0 0 1] below T0. These phenomena show that the transition process is related to bonding interactions along [0 0 1]. A comparison of the elastic properties of the Li2 − xNaxGe4O9 family with Li2Ge7O15 reveals unexpected large differences, particularly near the transition temperature.