Group-subgroup Scheme Research Articles

The monoclinic superstructure of the M 2Pt6Al15 series (M=Ca, Sc, Y, La, Lu)

Abstract The five ternary intermetallic compounds M 2Pt6Al15 (M=Ca, Sc, Y, La, Lu) were prepared from the elements by arc-melting. The crystal structure was determined via single crystal X-ray diffraction. The title compounds crystallize in a superstructure of the RE 0.67Pt2Al5 type structure (P63/mmc) in the monoclinic crystal system with space group P121/m1 (Sc2Pt6Al15: a=734.19(2), b=1628.96(10), c=734.19(2) pm, β=119.999(3)°; wR=0.0356, 3034 F 2 values, 68 variables). The superstructure can be derived by the superspace formalism using (3+2)D or (3+1)D interpretations of the diffraction data. The structural relation to the subcell structure is discussed on the basis of a group-subgroup scheme. In the crystal structure strongly bonded [Pt2Al4] δ− slabs are alternatingly stacked with ordered layers containing M atoms and Al3 triangles.

Monoclinic superstructure of Pr3Rh4Ge4

Abstract Pr3Rh4Ge4 was synthesized by melting of the elements in an arc-melting furnace followed by annealing in a sealed tantalum ampoule in a muffle furnace. Structure refinement was based on temperature dependent single-crystal X-ray diffractometer data. At ambient temperature Pr3Rh4Ge4 adopts the U3Ni4Si4 type structure with strongly enhanced anisotropic displacement parameters for Rh1. Below 230 K additional reflections start to appear and at 110 K the structure could be described with the (3+1)D superspace group I2/m(α0γ)00; α=1/2, γ=1/2; (Z=2). This commensurately modulated structure could be refined with 1448 F 2 values, 39 variables and residuals of wR=0.0417 for the main reflections and wR=0.1520 for the satellites of 1st order, [a=408.36(2), b=421.12(3) and c=2504.4(2) pm]. The commensurate description could be transformed to a 3D supercell with space group A2/m and Z=4: a=816.72(2), b=421.12(3), c=2537.5(1) pm, β=99.26(1)°, 1448 F 2 values, 69 variables and wR=0.0499. The relation of the U3Ni4Si4 type structure, the (3+1)D modulated and the 3D supercell is discussed on the basis of a group–subgroup scheme. Temperature dependent magnetic susceptibility data reveal Curie–Weiss paramagnetism with an experimental moment of 3.72(2) μB/Pr atom and a Weiss constant of –12.6(5) K. No magnetic ordering is evident down to 3 K.

RE 13Pd25+x Zn28–x (RE = Y, Ho–Lu) – A 4 × 4 × 4 tungsten superstructure with short Pd/Zn dumbbells as structural motif

Abstract The rare earth-based zinc compounds RE 13Pd25+x Zn28–x (RE = Y, Ho–Lu) were synthesized from the elements in sealed niobium ampoules with a maximum reaction temperature of 1470 K followed by different annealing sequences. The structures of all compounds were refined from single crystal X-ray diffraction data, indicating substantial Zn/Pd mixing on one 8c and one 24g zinc site. Exemplarily, the homogeneity range of the solid solution Yb13Pd25+x Zn28–x was manifested from samples of different starting compositions and five single crystal data sets. The RE 13Pd25+x Zn28–x structures are cubic, space group I4̅3m with lattice parameters ranging from 1295 to 1307 pm, as a function of the rare earth element and the Zn/Pd mixing. Hierarchically, one can derive the RE 13Pd25+x Zn28–x structures from the simple bcc packing. A group–subgroup scheme was developed for this new 4 × 4 × 4 tungsten superstructure which shows vacancy ordering and dumbbell formation. Temperature dependent magnetic susceptibility measurements show diamagnetism for a Lu13Pd29Zn24 sample and Curie–Weiss paramagnetism for Tm13Pd29Zn24 down to 3 K.

Ni4 and Ni3Ga clusters as building units in Ca3Ni4Ga4 and Sr3Ni3□Ga4

Abstract The gallides Ca3Ni4Ga4 and Sr3Ni3Ga4 were synthesized from arc-melted NixGay precursor alloys and the respective alkaline earth metal in sealed niobium tubes in an induction furnace. Redetermination of the Ca3Ni4Ga4 structure from X-ray single crystal diffractometer data confirmed the X-ray powder data: Na3Pt4Ge4 type, I4̅3m, a=740.6(1) pm, wR2=0.0245, 169 F2 values, 9 variables. The nickel atoms build tetrahedral Ni4 clusters (256 pm Ni–Ni) that are end-on coordinated by gallium atoms (234 pm Ni–Ga). These [Ni4Ga4] units show a bcc packing and leave cavities Ca@Ga4Ni4Ga4 for the calcium atoms. Sr3Ni3Ga4 crystallizes with a new structure type: R3m, a=1039.8(2), c=698.2(1) pm, wR2=0.1048, 636 F2 values, 23 variables. The structure shows twinning by inversion with a domain ratio of 79/21. The structures of Sr3Ni3Ga4 and Ca3Ni4Ga4 are related by a group–subgroup scheme (R3m is a translationengleiche subgroup of I4̅3m). The 8c Ni and Ga subcell sites split into site 3a and 9b each. This allows formation of ordered Ni3Ga tetrahedra (264 pm Ni–Ga) along with ordered gallium vacancies.

Chromium substitution effect on structural and electrochemical behavior of Li-Cr-Ni-O oxides

The chromium-substituted LiCr x Ni1−x O2 oxides were prepared from lithium hydroxide monohydrate (LiOH·H2O), NiO, and Cr2O3. The structure of Li1.5Cr0.5NiO3 phase has been investigated by means of X-ray single crystal and powder diffraction (space group P-3m1, a = 2.9256(1), c = 7.1539(2) A). The relations between Li1.5Cr0.5NiO3 structure, rhombohedral LiNiO2, and NiO are described by a group-subgroup scheme on the basis of Barnighausen formalism. Electronic structures were calculated applying the TB-LMTO-ASA 4.7 program. The maximum of electron localization function (ELF) was obtained around the oxygen atoms. Features of the crystal structure of the trigonal Li1.5Cr0.5NiO3 phase cause lower electrode capacity compared to rhombohedral LiNiO2.

SrAu4Ga3: a further example with Ga3 units and a Lonsdaleite-related gold substructure

The gallide SrAu4Ga3 was obtained by induction melting of the elements in a sealed tantalum tube and subsequent annealing in a muffle furnace. SrAu4Ga3 is isotypic with Ba3Ag14.6Al6.4. Its structure was refined from single crystal X-ray diffractometer data: $${P}{\bar{6}}$$ 2m, a = 860.9(3) pm, c = 720.4(2) pm, wR = 0.0342, 678 F values, and 30 variables. The gold atoms build a distorted lonsdaleite-related (hexagonal diamond) substructure and the cavities left by this network are filled in an ordered manner by the strontium atoms as well as Ga3 and (Ga,Au)3 triangles. The latter have Ga–Ga and Ga/Au–Ga/Au distances of 305 and 262 pm, respectively. Consequently one can topologically describe the SrAu4Ga3 structure as an ordered substitution variant of the Zintl phase CaIn2. This structural relationship is discussed on the basis of a group–subgroup scheme.

Phase Transition Mechanisms in LixCoO2 (0.25 ≤ x ≤ 1) Based on Group–Subgroup Transformations

The basic structural chemistry of O3–LixCoO2 (0.25 ≤ x ≤ 1) oxides is reviewed. Crystal chemical details of selected compositions and group–subgroup schemes are discussed with respect to phase transitions upon electrochemical or chemical deintercalation of the lithium atoms. Furthermore, the theoretical crystal structures of LixCoO2 supercells (x = 0.75, 0.5, 0.33, and 0.25) are reported for the first time based on the combination of transmission electron microscopy (TEM) and X-ray (XRD) or neutron diffraction (ND) experiments. Li0.75CoO2 and Li0.25CoO2 supercells crystallize with the space group R3m, a4 = 5.6234 A and 5.624 A, and c4 = 14.2863 A and 14.26 A, respectively, whereas the Li0.5CoO2 supercell crystallizes with the space group P21/m, a7 = 4.865 A, b7 = 2.809 A, c7 = 9.728 A, and β7 = 99.59°. The Li0.33CoO2 supercell may crystallize in different unit cells (hexagonal or orthorhombic or monoclinic). For Li0.75CoO2, the TEM superstructure reflections are due to only one type of lithium and vacanc...

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

Abstract 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).

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

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

Magnetic Properties of RE3Pd6Sb5 (RE = Pr, Nd,Gd) and a Group-Subgroup Scheme for Ce3Pd6Sb5 and Yb5Cu11Sn8

The Ce3Pd6Sb5-type antimonides RE3Pd6Sb5 (RE = Pr, Nd, Sm, Gd, Tb) were synthesized by arc-melting and subsequent annealing in sealed silica ampoules in a high-frequency furnace. The new compounds Sm3Pd6Sb5 (a = 1337.0(5), b = 441.5(1), c = 988.6(3) pm) and Tb3Pd6Sb5 (a = 1328.8(4), b = 439.9(2), c = 976.6(5) pm) were characterized by powder X-ray diffraction data. The RE3Pd6Sb5 antimonides adopt an ordered defect structure that derives from the CaBe2Ge2 type. Their crystal chemistry is compared to the structures of Ce8Rh17Sb14 and Yb5Cu11Sn8 on the basis of group-subgroup schemes. Temperature-dependent magnetic susceptibility data of the samples with RE = Pr, Nd and Gd show Curie-Weiss paramagnetism of the trivalent rare earths. Low-field susceptibility measurements reveal magnetic ordering at low temperatures.

Structure Refinement and Magnetic Properties of Ce2RuAl3 and a Group-Subgroup Scheme for Ce5Ru3Al2

The hexagonal Laves phase Ce2RuAl3 (≡ CeRu0.5Al1.5) was synthesized by high-frequencemelting of the elements in a sealed tantalum tube and subsequent annealing. The structure was refined from single-crystal X-ray diffraction data: MgZn2 type, P63/mmc, Z = 2, a = 565.38(9), c = 888.3(1) pm, wR2 = 0.0231, 193 F2 values and 13 parameters. The 2a (0.824 Ru + 0.176 Al) and 6h (0.956 Al + 0.044 Ru) Wyckoff positions show mixed occupancies leading to the composition CeRu0.48Al1.52 for the investigated crystal. The aluminum atoms build up Kagomé networks at z = 1/4 and z = 3/4 which are connected to a three-dimensional network by the ruthenium atoms. The cerium atoms fill cavities of coordination number 16 (3 Ru + 9 Al + 4 Ce) within the [RuAl3] network. The Ce2RuAl3 sample orders ferromagnetically at TC = 8.0(1) K. The cerium-rich aluminide Ce5Ru3Al2 shows unusually short Ce-Ru distances of 253 and 260 pm for the Ce1 position as a result of intermediate cerium valence. The structural distortions are discussed on the basis of a group-subgroup scheme for Pr5Ru3Al2 (space group I213) and the superstructure variant Ce5Ru3Al2 (space group R3).

RE8Rh 17Sb 14 ( RE = La, Ce, Pr, Nd) with a CaBe 2Ge 2-related superstructure through rhodium–antimony-ordering and vacancy formation

The new antimonides RE 8Rh 17Sb 14 ( RE = La, Ce, Pr, Nd) were synthesised by arc-melting. Crystals can be grown in a high-frequency furnace. The RE 8Rh 17Sb 14 phases were characterized by powder X-ray diffraction. They crystallize with a tetragonal, CaBe 2Ge 2-related superstructure which was refined for Ce 8Rh 17Sb 14 on the basis of single crystal X-ray diffractometer data: I4 cm, a = 1239.8 (3), c = 2101.8 (8) pm, w R = 0.065, 2924 F values, and 109 parameters. The rhodium and antimony atoms and vacancies show full ordering on the [Be 2Ge 2] substructure, leading to a composition of Ce 8Rh 17Sb 14 CeRh 2.13Sb 1.75. The superstructure formation is discussed on the basis of a group-subgroup scheme together with the related structures of CePt 2+xSb 2−y, CeNi 1.91As 1.94 and URh 1.6As 1.9. Temperature dependent susceptibility measurements show Pauli paramagnetism for La 8Rh 17Sb 14 and Curie–Weiss paramagnetism for RE 8Rh 17Sb 14 ( RE = Ce, Pr, Nd). No magnetic ordering was detected down to 2.5 K.

Refined Crystal Structure and Idealized Structure of Mixed-Valent Eu4F5(CN2)2: Transition Possible

The new europium fluoride carbodiimide Eu(4)F(5)(CN(2))(2) was synthesized by solid state reaction from mixtures of EuF(3) and Li(2)(CN(2)) at 700 °C. The crystal structure as refined by single crystal X-ray diffraction (P ̅42(1)c, no. 114, a = 16.053(1) Å, c = 6.5150(6) Å, Z = 8) reveals three crystallographically distinct [N═C═N](2-) ions in the structure of mixed-valent Eu(4)F(5)(CN(2))(2). The presence of one Eu(3+) and three Eu(2+) per formula unit Eu(4)F(5)(CN(2))(2) is confirmed by magnetic measurements and (151)Eu-Mössbauer spectroscopy. The arrangement of Eu ions and gravity centers of [NCN](2-) ions in the structure of Eu(4)F(5)(CN(2))(2) follow the motif formed by atoms in the CuAl(2)-type structure. A possible high-symmetry structure of Eu(4)F(5)(CN(2))(2) is discussed on the basis of a group-subgroup scheme.

Bismuth flux crystal growth of RERh6P4 (RE = Sc, Yb, Lu): new phosphides with a superstructure of the LiCo6P4 type

The rhodium-rich phosphides RERh6P4 (RE = Sc, Yb, Lu) were synthesized from the constituent elements in bismuth fluxes and their structures were refined from X-ray single-crystal diffractometer data: P3, a = 6.968(2), c = 3.666(2) A, wR (F 2) = 0.0481, 895 F 2 for ScRh6P4; a = 6.971(1), c = 3.673(1) A, wR (F 2) = 0.0614, 700 F 2 for YbRh6P4; a = 6.971(2), c = 3.682(1) A, wR (F 2) = 0.0828, 722 F 2 for LuRh6P4 with 37 variables per refinement. All three crystals are twinned. The twinning and the structural relationship with the aristotype LiCo6P4, space group $$P\bar 6m2$$ are discussed on the basis of a group–subgroup scheme. The RERh6P4 phosphides belong to the large number of metal-rich compounds with a metal-to-phosphorus ratio near 2:1. The isolated phosphorus atoms have trigonal prismatic metal coordination by RE and Rh atoms. The high rhodium content leads to a pronounced rhodium substructure (278–293 pm Rh–Rh in ScRh6P4). From a geometrical point of view, the RERh6P4 structures can be viewed as intergrowth variants of slightly distorted ThCr2Si2-related slabs as realized for KRh2P2.

Structural chemistry of superconducting pnictides and pnictide oxides with layered structures

The basic structural chemistry of superconducting pnictides and pnictide oxides is reviewed. Crystal chemical details of selected compounds and group subgroup schemes are discussed with respect to phase transitions upon charge-density formation, the ordering of vacancies, or the ordered displacements of oxygen atoms. Furthermore, the influences of doping and solid solutions on the valence electron concentration are discussed in order to highlight the structural and electronic flexibility of these materials.

Dimorphic Nd2Cu2Cd – structures and magnetic properties of RE 2Cu2Cd (RE = Ce, Pr, Nd)

Abstract The intermetallic compounds RE 2Cu2Cd (RE = Ce, Pr, Nd) were synthesized by induction-melting of the elements. Nd2Cu2Cd is dimorphic with a tetragonal Mo2B2Fe high- (HT) and a monoclinic, Mn2B2Al related low-temperature (LT) modification. The reconstructive phase transition is confirmed by DTA measurements showing a fully reversible phase transition commencing around 931(2) K. Both structures were refined on the basis of single crystal X-ray diffractometer data: P4/mbm, a = 764.7(3), c = 385.3(2) pm, wR2 = 0.0529, 288 F 2 values, 12 variables for HT-Nd2Cu2Cd and C2/c, a = 847.6(2), b = 740.4(2), c = 1509.3(5) pm, β = 106.31(2)°, 1180 F 2 values, 48 variables for LT-Nd2Cu2Cd. Both modifications are simple 1:1 intergrowth variants with slightly distorted CsCl and AlB2 related slabs of compositions NdCd and NdCu2. Formation of the monoclinic superstructure is discussed on the basis of a group sub-group scheme. Monoclinic Ce2Cu2Cd (a = 859.1(5), b = 743.0(3), c = 1520.6(7) pm, β = 106.37(5)°, 1243 F 2 values, 48 variables) and Pr2Cu2Cd (a = 855.8(4), b = 742.1(3), c = 1519.7(5) pm, β = 106.35(3)°, 1238 F 2 values, 48 variables) crystallize directly from the melt. Ce2Cu2Cd, Pr2Cu2Cd, LT- and HT-Nd2Cu2Cd show Curie-Weiss paramagnetism and magnetic ordering at low temperatures.

SrNi7.90(8)In5.10(8) – a new superstructure in the NaZn13 family

Abstract SrNi7.90(8)In5.10(8) was synthesized by induction melting of the elements in a sealed tantalum tube in a water-cooled silica sample chamber. The structure was refined on the basis of single crystal X-ray diffractometer data: Cccm, a = 1615.2(4), b = 1822.3(4), c = 1238.5(4) pm, wR2 = 0.1481, 4144F 2 values and 150 variables). The striking structural motifs of the SrNi7.90In5.10 structure are one-dimensional [Ni7] cluster units (242–286 pm Ni—Ni) which are surrounded by indium atoms. The structural relationship to the other NaZn13 superstructures is discussed on the basis of a group-subgroup scheme.

Non-centrosymmetric Ce3OCl[AsO3]2

The arsenite chloride Ce3OCl[AsO3]2 was synthesized in the form of colorless crystals from arsenic and cerium dioxide in a NaCl / KCl flux at 850 ◦C. Ce3OCl[AsO3]2 crystallizes with the noncentrosymmetric tetragonal Gd3OCl[AsO3]2 type, space group P42nm. The structure was refined from single crystal diffractometer data: a = 12.8590(6), c = 5.5627(3) Å, wR2 = 0.0429, 1463 F2 values, and 65 variables. The structure is built up from chains of trans edge-sharing OCe4/2 tetrahedra. The [AsO3]3− units coordinate to these chains via the oxygen atoms. Their lone-pairs point all to a common channel. Formation of the non-centrosymmetric superstructure is most likely driven by geometrical constraints and is discussed on the basis of a group-subgroup scheme

Zirconium–aluminium ordering in Zr 5Ni 4Al—a new superstructure in the family of U 3Si 2 related intermetallics

Zr 5Ni 4Al was synthesized by arc-melting of the elements and subsequent annealing in an induction furnace at 1360–1440 K. This aluminide crystallizes according to X-ray diffraction data of a twinned crystal with an ordered version of the Zr 3Al 2 type: P4 2/ m, a=716.7(3), c=659.8(4) pm, w R2=0.1174, 824 F 0 2 values, 28 variables. Due to the ordering of the zirconium and aluminium atoms, the space group symmetry is reduced from P4 2/ mnm (Zr 3Al 2) to P4 2/ m (Zr 5Ni 4Al), leading to merohedric twinning with a twin ratio of 52.5: 47.5 ( twin matrix 010 100 00 1 ¯ ) . The Zr 5Ni 4Al structure is an intergrowth of slightly distorted AlB 2 and CsCl/W related slabs of compositions ZrNi 2, ZrAl, and Zr 2 with an Ni–Ni distance of 257 pm in the distorted AlB 2 slab. A metastable Zr 3Al 2 type ( P4 2/ mnm) form of Zr 5Ni 4Al showing a disordered distribution of ZrAl and Zr 2 slabs was obtained by crystallizing a metallic glass of the composition Zr 50Ni 40Al 10 at 770 K. Further annealing at higher temperature led to the formation of ordered Zr 5Ni 4Al. The crystal chemical peculiarities of the different forms of Zr 5Ni 4Al are discussed on the basis of a group-subgroup scheme.