Linear thermal expansion tensor in KRE(WO4)2 (RE=Gd, Y, Er, Yb) monoclinic crystals

KGd(WO4)(2) crystal is monoclinic, space group C2/c with the unit cell parameters determined by single crystal diffraction a=10.652(4) Angstrom, b=10.374(6) Angstrom c=7.582(2) Angstrom and beta = 130.80(2) degrees [1]. KRE(WO4)(2) (RE=Gd, Y, Er and Yb) are isostructural compounds. The crystals were grown by the TSSG (Top Seeded Solution Growth) slow cooling technique. The linear thermal expansion coefficients along a given crystallographic direction can be determined by measuring the increase of the lattice parameters with the temperature changes. The unit cell parameters of KREW as a function of the temperature were measured from X-ray powder diffraction analysis. The linear thermal expansion coefficients in a given crystallographic direction are alpha=(partial derivativeL/partial derivativeT)/L, where L is the initial parameter at 25 degreesC, and AL is the change in this parameter when the temperature is changed by AT. The alpha (ij) are the slopes and conform the linear thermal expansion tensor in the crystallophysical system. By diagonalising this tensor, we obtained linear thermal expansion tensor in the principal system X'(1), X'(2), X'(3). The principal axis with maximum thermal expansion X'(3). was calculated and found at delta rotating anti-clockwise from c axis with the b positive axis pointing us.