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Reflections of the reciprocal lattice row [-9 -5 1] of TlGaSe2 at 126K, 114K and 104K corresponding to the paraelectric, intermediate incommensurate and ferroelectric commensurate modulated phases, respectively. Also shown is a larger section of the reciprocal lattice row measured at 51K in the ferroelectric phase. The position sensitive detector allows a three dimensional representation of the reflections. Gamma and v correspond to the horizontal and vertical directions in the plane of the multidetector whereas omega is the rotation angle of the crystal.
In the incommensurate phase the pairs of satellites are displaced from the superlattice positions corresponding to the wave vector k=(0, 0, ¼) by small amounts whereas in the commensurate modulated phase they appear exactly on the superlattice positions. About 9000 principal and satellite reflections were measured in the ferroelectric phase. The structure determination of the low temperature ferroelectric phase using these intensity data showed that systematic displacements of the Tl atoms from the positions of the paraelectric phase parallel to [0 0 1] take place in the modulated phase. The ²[Ga4Se10] layers remain practically unmodified. The prism changes its coordination number from CN6 to CN7. The reason for the shifts of the Tl atoms is the induced stereochemical activity of the lone pair of Tl+ at the ferroelectric phase transition. All Tl atoms from two neighbouring ¹[TlSe6] units along [0 0 1] are shifted in the same direction by the same amount. The prism units form a block. The unit cell is built of eight such blocks stacked along [0 0 1]. The shifts of two consecutive blocks are alternatively parallel to [-1 -1 0] and [1 -1 0]. The present structure model explains the quadrupling of the c axis and shows that it is the stereochemical activity of the Tl+ ion and not the chalcogenide ion which is responsible for the appearance of ferroelectricity.