1. Doping of alkaline earth fluorides MF 2 (M = Ca, Cd, Sr, Ba) with a fluorite structure by trivalent ions R (R are the rare earth, yttrium or scandium, ions) with a concentration of more than 0.1 mol % leads to the formation of detectable rare earth clusters in the crystal, which include the groups of interstitial fluorine ions and are coherently conjugate with the host lattice [1,2].Two types of cluster structures are most known in MF 2 -RF 3 solid solutions. In the first one, the octahe dron composed of 6 R and M ions in cationic positions embraces a cuboctahedron of 12 anions situated at the edges of the initial fluorine cube [1][2][3][4][5][6][7][8], and therefore the nearest neighborhood of the R(M) ion is a square antiprism or a Thomson cube (Fig. 1). Such an octa hedral cluster [R 6 -x M x F 36 ] or the cluster [R 6 -x M x F 37 ], which includes a fluorine ion situated inside the anionic cuboctahedron, substitutes the fragment [M 6 F 32 ] of the regular structure of fluorite thus weakly distorting the lattice. The presence of M ions in the rare earth octahedron provides electroneutrality of the cluster. Larger structural elements, the {M 8 [R 6 F 68 ]} and {M 8 [R 6 F 69 ]} superclusters, which include the above octahedral clusters, are the mini mum cubic parts of the crystal containing all types of structural defects.Another most known type of clusters, tetrahedral one, includes 4 R and M ions in cationic positions and the tetrahedron of interstitial F -ions around the cen tral fluorine vacancy (see Fig. 1 in [2]). This cluster is described by the formula [M 4 -x