Phase transitions in langbeinites I: Crystal chemistry and structures of K-double sulfates of the langbeinite type M 2 + + K2(SO4)3, M + +=Mg,Ni, Co,Zn, Ca

The crystal structures of the langbeinite type M ₂ ^{+ +} K₂(SO₄)₃ with M ^{+ +}=Mg, Ni, Co, Zn, Ca in their cubic phase (P 2 ₁ 3) and Ca₂K₂(SO₄)₃ in its orthorhombic phase (P 2 ₁ 2 ₁ 2 ₁) are determined. Whereas the SO₄-tetrahedra in these compounds are almost undistorted, the two symmetry-independent coordination polyhedra of M ^{+ +} are highly distorted octahedra with trigonal site symmetry in P 2 ₁ 3. The deformation of the oxygen octahedra and the off-centering of M ^{+ +} along the trigonal axis show systematic dependences on the ionic radii and the electronegativities of the M ^{+ +}-ions. The correlations are remarkably different for the two symmetry-independent M ^{+ +}-ions indicating different M ^{+ +} — O bonding. The octahedral deformations show also linear correlations with the phase transition temperatures (P 2 ₁ 3 — P 2 ₁ 2 ₁ 2 ₁) of the different compounds. This observation leads to a new model for the phase transition mechanism which is based on thermal instabilities of the M ^{+ +} — O and K — O polyhedral distortions. The cubic high temperature phase is characterized by high symmetric oxygen coordinations around M ^{+ +} which distort with decreasing temperature. At T _c the trigonal site symmetry is broken in such a way that the K — O coordination becomes denser at the expense of a wider and less symmetric M ^{+ +} — O coordination.