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  Schorr, S. ; Sheptyakov, D.: Low-temperature thermal expansion in sphalerite-type and chalcopyrite-type multinary semiconductors. Journal of Physics: Condensed Matter 20 (2008), p. 104245/1-5

10.1088/0953-8984/20/10/104245

Abstract:
The lattice parameters and linear thermal expansion coefficients α_a and α_c of multinary 2(ZnX)_x(CuB^IIIX₂)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 α_a > α_c in the whole temperature range. The tetragonal distortion Δ of the chalcopyrite structure ( Δ = 2 – c/a) decreases non-linearly with decreasing temperature and has a positive temperature coefficient α_Δ in the whole temperature range studied.