The Ferroelectric Transition in GERMANIUM(X)LEAD(1 - EXAFS Investigation of the Germanium and Lead Sites.

Ge_{rm x}Pb _{rm 1-x}Te alloys undergo a ferroelectric phase transition from a high temperature cubic phase to a low temperature trigonal phase. The phase transition is second order and is caused by softening of a zone-center transverse optical phonon. This alloy system exhibits several experimental results not found in other IV-VI alloys. For small x, the transition temperature is a strong non-linear function of temperature, the resistivity has a logarithmic dependence on temperature, and there is a Schottky-type specific heat. These results suggest that Ge plays an important role in the phase transition in Ge_{rm x}Pb _{rm 1-x}Te alloys. EXAFS studies on the Ge K-edge in alloys from x = 0.01 to 0.30 and in the trigonal and cubic phases have been performed. The EXAFS results show that Ge is displaced from the Pb site by 0.73 +/- 0.03 A at all temperatures in the cubic phase, and by 0.60 +/- 0.04 A for x = 0.18 to 0.71 +/- 0.03 A for x = 0.01 at 10K in the trigonal phase. Since Ge atom is always off-site, the phase transition implies a long-range ordering of local dipoles along the trigonal c-axis below the transition. The displacive character of the phase transition is established by direct determination of the sublattice shift by Pb L_3-edge EXAFS studies. At 6K, the magnitude of the shift is 0.12 +/- 0.02 A for x = 0.10 alloy and 0.13 +/- 0.02 A for x = 0.18 alloy, which have transition temperatures 243 +/- 16K and 314 +/- 4K respectively. Several short-range anharmonic potentials in which the Ge atom moves have been considered. A symmetric one -dimensional double-well potential along the < 111> direction with a barrier height ~80 meV at the center of the cell adequately describes the room temperature data. The low-temperature behavior cannot be explained by this potential nor by a triple-well potential with three possible Ge sites along <111 >, nor by a distribution of Ge between two symmetric double-well potentials, one along <111> and the other along <100 >. A model of the phase transition in Ge _{rm x}Pb_ {rm 1-x}Te alloys is proposed, taking into account the order-disorder and displacive characters of the transition. The model may be applicable to many other displacive ferroelectric alloys in which the substitutional atom and the host atom have large size difference.