Lattice symmetry relaxation as a cause for anisotropic line broadening and peak shift in powder diffraction.

In powder diffraction, lattice symmetry relaxation causes a peak to split into several components which are not resolved if the degree of desymmetrization is small (pseudosymmetry). Here the equations which rule peak splitting are elaborated for the six minimal symmetry transitions, showing that the resulting split peaks are generally broader and asymmetric, and suffer an hkl-dependent displacement with respect to the high-symmetry parent peak. These results will be of help in Rietveld refinement of pseudosymmetric structures where an exact interpretation of peak deformation is required.

The structure of kaliophilite KAlSiO4, a long-lasting crystallographic problem.

Kaliophilite is a feldspathoid mineral found in two Italian magmatic provinces and represents one of the 12 known phases with composition close to KAlSiO4. Despite its apparently simple formula, the structure of this mineral revealed extremely complex and resisted structure solution for more than a century. Samples from the Vesuvius-Monte Somma and Alban Hills volcanic areas were analyzed through a multi-technique approach, and finally the crystal structure of kaliophilite was solved using 3D electron diffraction and refined against X-ray diffraction data of a twinned crystal. Results were also ascertained by the Rietveld method using synchrotron powder intensities. It was found that kaliophilite crystallizes in space group P3 with unit-cell parameters a = 27.0597 (16), c = 8.5587 (6) Å, V = 5427.3 (7) Å3 and Z = 54. The kaliophilite framework is a variant of the tridymite topology, with alternating SiO4 and AlO4 tetrahedra forming sheets of six-membered rings (63 nets), which are connected along [001] by sharing the apical oxygen atoms. Considering the up (U) and down (D) orientations of the linking vertex, kaliophilite is the first framework that contains three different ring topologies: nine (1-3-5) (UDUDUD) rings, six (1-2-3) (UUUDDD) rings and twelve (1-2-4) (UUDUDD) rings. This results in a relatively open (19.9 tetrahedra nm-3) channel system with multiple connections between the double six-ring cavities. Such a framework requires a surprisingly large unit cell, 27 times larger than the cell of kalsilite, the simplest phase with the same composition. The occurrence of some Na for K substitution (3-10%) may be related to the characteristic structural features of kaliophilite. Micro-twinning, pseudo-symmetries and anisotropic hkl-dependent peak broadening were also detected, and they may account for the elusive character of the kaliophilite crystal structure.