15 new multicomponent solid solutions with stoichiometry 122 were synthesized in different systems {Ca,Sr,Ba}-{La,Ce,Gd,Yb}-{Fe,Co,Ni}-Ge. Their crystal structures are built up from layers of edge-shared deformed [TGe4] tetrahedra (T = Fe, Co, Ni) alternating with nets of alkaline-earth or rare-earth metal atoms. Structural instability was observed for the solid solution Sr1-xBaxNi2Ge2. The tetragonal CeAl2Ga2-type structure (space group I4/mmm) remains stable up to x = 0.5 under ambient conditions. With increasing Ba content, the c-parameter and the volume of the unit cell, as well as the degree of deformation of the [NiGe4] tetrahedra (flattened with the tetrahedron angle ? = 122.63-125.56° with respect to the ideal value of 109.5°) increase. Upon further increasing the Ba content, the degree of deformation of the tetrahedra reaches a critical value and the structure becomes modulated (x = 0.5-0.8). Finally, for x > 0.8 the orthorhombic BaNi2Ge2-type structure (Pnma) is stable under ambient conditions. The structure of this phase, as refined on Sr0.12(2)Ba0.88(2)Ni2Ge2, changes from orthorhombic to tetragonal when it is heated (Pnma [< 568 K] > modulated structure > I4/mmm [> 588 K]).The family of iron-based superconducting pnictides is in part represented by the structure type CeAl2Ga2 (122-type). The transition to the superconducting state in compounds with this structure type usually appears when the composition is close to a “structural instability”. In spite of the structural instability noted for the germanide Sr1-xBaxNi2Ge2,superconductivity was not observed. Electron doping in the compound SrNi2Ge2 (synthesis of the solid solution Sr1-xLaxNi2Ge2), or creation of structural vacancies in the antimonide SrNi2-xSb2 (x = 0.15-0.28) did also not induce superconductivity. Investigation of the magnetic properties indicated paramagnetic behavior for the majority of the samples. Interestingly, the diamagnetic signal observed at 60 K for a mixture of 122-type Sr1-xLaxCo2Ge2 and 113-type La1-xSrxCoGe3, became stronger after heating of the sample in air, which could be connected with superconductivity. Investigation of the magnetic properties of the 113-type phase La1-xSrxCoGe3 (BaNiSn3, I4mm) indicated weak paramagnetism, while the 148-type phase CaFe4Al8 (CeMn4Al8, I4/mmm) exhibits several intrinsic magnetic transitions. At room temperature it is paramagnetic, but orders antiferromagnetically at 170 K, and shows a spin-glass transition, combined with ferromagnetic ordering, or canting of antiferromagnetically ordered spins from their antiparallel directions, at lower temperatures. The phase equilibria in the systems {Ce,Gd,Yb}-Fe-Ge-Sb were studied in the region of 0-33.3 at.% rare-earth metal at 773 K and diagrams were constructed; no quaternary compounds were found. The binary compounds RSb with cubic NaCl-type structures take part in most of the phase equlibria. The existence of many superconducting compounds with Frank-Kasper polyhedra, and the linear relation between the weighted average coordination number and the icosahedron content, known as the Yarmolyuk-Kripyakevich phenomenon, motivated a more detailed analysis of this class of structures. The atoms in these structures are surrounded by P- (16 vertices), Q- (15 vertices), R- (14 vertices), or X-type (12 vertices) Frank-Kasper polyhedra. The structural formulas can be written as (R3X)i(PX2)j(Q2R2X3)k, which represents a combination of the types Cr3Si (space group Pm-3n) – R3X, MgZn2 (P63/mmc) – PX2, and Zr4Al3 (P6/mmm) – Q2R2X3. Considering the Yarmolyuk-Kripyakevich criterion, solutions of the equation N12 = 2•N16 + 7/6•N15 + 1/3•N14, which defines the numbers of different polyhedra, were derived. It was found that, among the different possible combinations obeying the Yarmolyuk-Kripyakevich rule, only one combination has so far been experimentally observed for a particular number of icosahedra. In most cases the simplest combination, with minimal average coordination number and lowest number of fragments (i.e. i + j + k) is preferred. By distributing all known combinations (R3X)i(PX2)j(Q2R2X3)k into groups, and considering the number of different fragments they contain, regularities were derived. The values of i, j and k revealed a series, where every number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8 …, known as Fibonacci sequence. The family was extended by the synthesis of a quaternary stannide Nb4.4V1.5Ni6Sn0.9 (P63/mmc, a = 4.9433(5), c = 17.935(3) A), which represents a new structure type.
