Low temperature thermal expansion in sphalerite type and chalcopyrite type multinary semiconductors

The lattice parameters and linear thermal expansion coefficients a and c of multinary 2 ZnX x CuBIIIX2 1 x mixed cystals cubic Zn2x CuIn 1 xSe2 and tetragonal Zn2x CuGa 1 xS2 were determined by neutron diffraction in the temperature region 1.5 300K. With decreasing temperature the lattice constants in the mixed crystals decrease but show a flat minimum at a certain temperature, reflecting a change in sign of the linear thermal expansion coefficient. Because of the negative linear thermal expansion coefficients negative Grüneisen parameters may be expected in the low temperature region and as a consequence the existence of low energy lattice vibrational modes. For tetragonal Zn2x CuGa 1 xS2 mixed crystals the lattice constants a and c vary independently with temperature as expected from the axial symmetry of the crystal. Moreover the linear thermal expansion coefficients follow the inequality a gt; c in the whole temperature range. The tetragonal distortion of the chalcopyrite structure 2 c a decreases non linearly with decreasing temperature and has a positive temperature coefficient in the whole temperature range studie