X-ray diffuse scattering associated with ferroelectric microregions in KTa1-xNbxO3

X-ray diffuse scattering for single crystals of KTa1-xNbxO3 (x = 0, 0.007 a nd 0.011) has been measured. For the sample of x = 0.011, peculiar x-ray di ffuse scattering is observed above the phonon-frozen-in temperature (30 K). By an analysis of the diffuse scattering intensities, the average radius o f the ferroelectric microregions is found to row up to around 4 nm with dec reasing temperature from 100 K down to 30 K. Anisotropic distributions of t he diffuse scattering indicate off-centred shift of Nb and Ta ions to the < 111 > -direction. Moreover, lattice constants for x = 0.011 below 30 It ex hibit negative expansion, which is found neither in pure KTaO3 nor in KTa1- xNbxO3 (x = 0.007) at low temperatures. These results are successfully expl ained by introducing the effective classical potential (ECP) method for the anharmonic oscillators. The quantum contribution to mean square displaceme nt of Nb and Ta ions from an average position is also calculated by the ECP method.