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The crystal structures of rare-earth metal sesquisulfides and some related compounds (Tm 5 S 7 , Tm 8 S 11 , Tm 15 S 22 ) of orthorhombic or monoclinic symmetry with the mirror plane perpendicular to the translation of 3.7 Å – 4.1 Å have been studied using an analysis of close-packed atomic nets. The cation and the anion matrices have been shown to possess a similar construction for all compounds. A system of parallel mirror planes (∼2 Å apart) causes all atoms to be located only in these planes; in fact, this means that a crystal structure becomes pseudo two-dimensional. It was found that in each structure there were sets of cation close-packed crystallographic planes perpendicular to the mirror planes; when intersecting they form a node net close to the ideal 3 6  net. Because of the proximity of the neighbouring mirror planes the cation node in one mirror plane corresponds with a vacancy in the adjacent mirror plane. Hence the cation matrices can be represented by a single-layer hexagonal structure whose basal planes split into the two mirror planes with half the cations moving onto each of the mirror planes (the AA′ type according to our classification). The anion matrices have a similar construction but they are less regular and on a smaller scale. Each structure type has an inherent law governing the distribution of atoms and vacancies in the net and the proper conditions for the compatibility between the cation and anion matrices that determine the unit cell dimensions. So, the system of the nearest mirror planes is the main factor which regulates the atomic arrangement, that is, keeps to the minimum the number of arbitrarily changed coordinates or, more properly, degrees of a freedom of the structure.

Peculiarities of crystal structures of rare-earth metal sulfides with the period 4 Å