New mechanism of structuring associated with the quasi-merohedral twinning by an example of Ca$_{1-x}$La$_x$F$_{2+x}$ ordered solid solutions

Merohedry is considered an inseparable property of atomic structures, and uses for the refinement of structural data in a process of correct determination of structure of compounds. Transformation of faulty structures stimulated by decreasing of systemic cumulative energy leads to generation of merohedral twinning type. Ordering is accompanied by origin of antiphase domains. If ordering belongs to the CuAu type, it is accompanied by tetragonal distortions along different $\langle$100$\rangle$ directions. If a crystal consists of mosaic of nanodimensional antiphase domains, the conjugation of antiphase domains with different tetragonality leads to monoclinic distortions, at that, conjugated domains are distorted mirrorly. Similar system undergoes further transformation by means of quasi-merohedral twinning. As a result of quasi-merohedry, straight-lines of lattices with different monoclinic distortions are transformed into coherent lattice broken-lines providing minimization of the cumulative energy. Structuring is controlled by regularities of the self-organization. However stochasticity of ordering predetermines the origin areas where few domains with different tetragonality contact which leads to the origin of faulty fields braking regular passage of structuring. Resulting crystal has been found structurally non-uniform, furthermore structural non-uniformity permits identifying elements and stages of a process. However there is no precondition preventing arising the origin of homogenous states. Effect has been revealed in Ca$_{1-x}$La$_x$F$_{2+x}$ solid solution, but it can be expected that distortions of regular alternation of ions similar to antiphase domains can be obtained in non-equilibrium conditions in compounds and similar effect of the quasi-merohedry can falsify results of structural analysis.