The orthorhombic-to-monoclinic phase transition in NbCrP – Peierls distortion of the chromium chain

The equiatomic metal-rich phosphide NbCrP shows a structural phase transition around 125 K. The structures of the high- and low-temperature modifications were refined from single crystal X-ray diffractometer data of an un-twinned crystal: TiNiSi type, Pnma, a = 619.80(2), b = 353.74(4), c = 735.24(6) pm, wR = 0.0706, 288 F 2 values, 20 variables at 240 K and P121/c1, a = 630.59(3), b = 739.64(4), c = 933.09(5) pm, β = 132.491(6)°, wR = 0.0531, 1007 F 2 values, 57 variables at 90 K. The structural phase transition is of a classical Peierls type. The equidistant chromium chain in HT-NbCrP (353.7 pm Cr–Cr) splits pairwise into shorter (315.2 pm) and longer (373.2 pm) Cr–Cr distances. This goes along with a strengthening of Cr–P bonding. The superstructure formation is discussed on the basis of a group–subgroup scheme. Electronic structure calculations show a lifting of band degeneracy. Protection of the non-symmorphic symmetry of space group Pnma is crucial for the phase transition. The estimated charge modulation is consistent with the interpretation as Peierls transition.

Synthesis and magnetic properties of the extended RE4Pd9Al24 series (RE = Sc, Y, Ce–Nd, Sm, Gd–Lu)

The existing RE4Pd9Al24 series (triclinic, space group P$\overline{1}$) with RE = Gd–Tm has been extended to the rare earth elements Sc, Y, Ce–Nd, Sm, Yb and Lu. The samples were synthesized from the elements via arc-melting followed by annealing. Phase-purity was checked by powder X-ray diffraction experiments, which were also utilized to refine the lattice parameters. The structure can be described as composed of layers with a stacking of [PtAl2] (A) and [RE2Al3] (B) slabs in an ABAAB sequence. As two different structure types (P$\overline{1}$ and R$\overline{3}$m) have been reported for this composition, a group-subgroup scheme using the Bärnighausen formalism has been established in order to link the two. The magnetic properties of the X-ray-pure samples were investigated by susceptibility and magnetization measurements. Gd4Pd9Al24 shows the highest transition temperature to antiferromagnetism of TN = 22.0(1) K, however, a broad feature is observed. This is in line with a low-dimensional ordering caused by the layer-like structure and the flat honeycomb arrangement of the Gd atoms.

Structure variations within RSi2 and R 2 TSi3 silicides. Part I. Structure overview

Here, structural parameters of various structure reports on RSi2 and R 2 TSi3 compounds [where R is an alkaline earth metal, a rare earth metal (i.e. an element of the Sc group or a lathanide), or an actinide and T is a transition metal] are summarized. The parameters comprising composition, lattice parameters a and c, ratio c/a, formula unit per unit cell and structure type are tabulated. The relationships between the underlying structure types are presented within a group–subgroup scheme (Bärnighausen diagram). Additionally, unexpectedly missing compounds within the R 2 TSi3 compounds were examined with density functional theory and compounds that are promising candidates for synthesis are listed. Furthermore, a correlation was detected between the orthorhombic AlB2-like lattices of, for example, Ca2AgSi3 and the divalence of R and the monovalence of T. Finally, a potential tetragonal structure with ordered Si/T sites is proposed.

The polymorphs of the Na+ ion conductor Na3PS4 viewed from the perspective of a group-subgroup scheme

The Na+ solid state electrolyte Na3PS4 is currently being investigated due to its high ionic conductivity and its synthesis-dependent crystal structure. Na3PS4 adopts a tetragonal low-temperature modification with space group P 4̅21c that transforms to a cubic high-temperature modification with space group I 4̅3m (Tl3VS4 type). These two modifications are related by a group-subgroup scheme. The symmetry reduction proceeds via a translationengleiche transition from I 4̅3m to I 4̅2m and subsequently via a klassengleiche transition to P 4̅21c. The tetragonal phase with space group I 4̅2m corresponds to the K2HgSnSe4 type. The group-subgroup scheme of this tetragonal branch of the Bärnighausen tree is discussed along with the crystal chemical consequences and results of diffraction experiments. The structure of K3SbSe4 (space group R 3c) belongs to the rhombohedral branch of the aristotype Tl3VS4.

Rare earth-ruthenium-magnesium intermetallics

Eight new intermetallic rare earth-ruthenium-magnesium compounds have been synthesized from the elements in sealed niobium ampoules using different annealing sequences in muffle furnaces. The compounds have been characterized by powder and single crystal X-ray diffraction. Sm9.2Ru6Mg17.8 (a=939.6(2), c=1779(1) pm), Gd11Ru6Mg16 (a=951.9(2), c=1756.8(8) pm), and Tb10.5Ru6Mg16.5 (a=942.5(1), c=1758.3(4) pm) crystallize with the tetragonal Nd9.34Ru6Mg17.66 type structure, space group I4/mmm. This structure exhibits a complex condensation pattern of square-prisms and square-antiprisms around the magnesium and ruthenium atoms, respectively. Y2RuMg2 (a=344.0(1), c=2019(1) pm) and Tb2RuMg2 (a=341.43(6), c=2054.2(7) pm) adopt the Er2RuMg2 structure and Tm3Ru2Mg (a=337.72(9), c=1129.8(4) pm) is isotypic with Sc3Ru2Mg. Tm3Ru2Mg2 (a=337.35(9), c=2671(1) pm) and Lu3Ru2Mg2 (a=335.83(5), c=2652.2(5) pm) are the first ternary ordered variants of the Ti3Cu4 type, space group I4/mmm. These five compounds belong to a large family of intermetallics which are completely ordered superstructures of the bcc subcell. The group-subgroup scheme for Lu3Ru2Mg2 is presented. The common structural motif of all three structure types are ruthenium-centered rare earth cubes reminicent of the CsCl type. Magnetic susceptibility measurements of Y2RuMg2 and Lu3Ru2Mg2 samples revealed Pauli paramagnetism of the conduction electrons.

Universal smooth k-tame central extension

This chapter describes the construction of canonical central extensions that are analogues for perfect smooth connected affine k-groups of the simply connected central cover of a connected semisimple k-group. A commutative affine k-group scheme of finite type is k-tame if it does not contain a nontrivial unipotent k-subgroup scheme. The chapter establishes good properties of the universal smooth k-tame central extension, noting that the property “locally of minimal type” is inherited by pseudo-reductive central quotients of pseudo-reductive groups. Although inseparable Weil restriction does not generally preserve perfectness, the chapter shows that the formation of the universal smooth k-tame central extension interacts with derived groups of Weil restrictions.

Solid Solutions RE16Rh11–xZx (RE = La, Ce, Pr, Nd, Sm; Z = Ga, Zn, Cd, In, Sn, Sb, Pb, Bi) – Centrosymmetric n = 2 Variants of Parthé’s Homologous Series A5n+6B3n+5

Several samples of solid solutions RE16Rh11-xZx (RE = La, Ce, Pr, Nd, Sm; Z = Ga, Zn, Cd,In, Sn, Sb, Pb, Bi) were synthesized by high-frequency melting of the elements in sealed tantalum ampoules. The samples were characterized by powder X-ray diffraction, and the structures of eight compounds were refined on the basis of single-crystal X-ray diffractometer data. The compounds crystallize with a centrosymmetric variant (space group P4⁄mbm) of the Ca16Sb11 type (P4̄ 21m). The relation between both structure types is discussed on the basis of a group-subgroup scheme. Only for La16Rh8Sn3 we observed full rhodium-tin ordering. The striking structural motif is a chain of face-sharing square prisms (filled with tin) and anti-prisms (filled with rhodium). The La16Rh8Sn3 structure is closely related to the structure types W5Si3, Ca16Sb11, Y3Rh2, Sm26Co11Ga6, Pu31Pt20, and Yb36Sn23 and is the centrosymmetric n = 2 member of Parthé’s A5n+6B3n+5 series. 119Sn Mössbauer spectra resolved the two crystallographically independent tin sites of La16Rh8Sn3, while a Pr16Rh9Sb2 sample shows only a singlet in its 121Sb Mössbauer spectrum.

Intermediate-valent Cerium in Ce2Ru4Mg17 and a Group-Subgroup Scheme for La9Ru4In5 and Ce9Ru4Ga5

Ce2Ru4Mg17 was synthesized by high-frequency melting of the elements in a sealed tantalum ampoule. This magnesium-rich compound crystallizes with a new tetragonal structure type: I4̄2m, a = 986.75(8), c = 1008.7(1) pm, wR2 = 0.0513, 909 F2 values and 34 variables. The striking structural motifs in the Ce2Ru4Mg17 structure are slightly bent CeRu2 units with short Ce-Ru distances of 231 pm and additionally a short Ce-Ce distance of 307 pm. These features are a direct consequence of the cerium valence. The CeRu2 units are embedded in a magnesium-rich matrix with a broad range of Mg-Mg distances (291 - 361 pm). Temperature-dependent magnetic susceptibility data show intermediate-valent behavior of the cerium atoms (0.23(5) μB per Ce atom) and no magnetic ordering down to 3 K, indicative of almost tetravalent cerium in Ce2Ru4Mg17. The ceriumrich gallide Ce9Ru4Ga5 shows an unusually short Ce-Ru distance of 237 pm for the Ce2 position as a result of an intermediate cerium valence. The structural distortions are discussed on the basis of a group-subgroup scheme for La9Ru4In5 (space group I4/mmm) and the superstructure variant Ce9Ru4Ga5 (space group I4mm).