Klaas Derk Bronsema

The crystal-structure of vanadium ditelluride, v1+xte2

Abstract Vanadium ditelluride, V1.04Te2, has a Cd(OH)2-type structure with unit cell dimensions ah = 3.638 A and ch = 6.582 A above the transition temperature Tt of 482 K. Below Tt the structure is monoclinic, space group C2 m , with cell dimensions am = 18.984 A(≈3ah√3), bm = 3.5947 A (≈ah), cm = 9.069 A (≈√(3a2h + c2h)), β = 134.62°. This low-temperature form is isostructural with NbTe2 and TaTe2 (which do not show a phase transition); the vanadium atoms form double zigzag chains with VV distances of 3.316 A, which distort the Te lattice. Complex diffraction patterns were observed due to the simultaneous occurrence of the distortion of the Cd(OH)2-type structure of vanadium ditelluride in three equivalent directions. Similar patterns were found for the Nb and Ta ditellurides.

The preparation, crystal-structures and properties of the potassium vanadium sulfides kxv5s8 (0.5 less-than-or-equal-to x less-than-or-equal-to 0.7)

The crystal structures of the potassium vanadium sulphides K0.7V5S8 and K0.5V5S8 (=KV10S16) have been determined. K0.7V5S8 has a C-centered monoclinic unit cell of dimensions a=17.499(3) A, b=3.2986(6) A, c=8.489(1) A, s=103.98(1)°, spacegroup C2/m; isomorphous with TIV5S8; K0.5V5S8 has essentially the same structure, but due to ordering of the K atoms, the monoclinic b-axis is doubled, thus forming a superstructure. The cell parameters are: a=17.462(4) A, b=6.556(2) A, c=8.4595(9) A, s=103.86(1)°, spacegroup P2. The structures are characterized by a three-dimensional framework of VS6 octahedra with channels in which the K atoms are situated. Both compounds exhibit metallic behaviour.

X-ray study of the second-order phase transition of Ag0.35TiS2: A phase transition characterized by two order parameters

Abstract Ag 0.35 TiS 2 shows a second-order phase transition with T c = 298.0 K from a a √3 × a √3 × 2 c superstructure, space group P 3 1c , to a disordered Cd(OH) 2 NiAs intermediate structure with unit cell a × a × c and space group P 3 m1 . In the disordered structure silver atoms occupy fractionally the sites of triangular lattice planes. Below T c silver atoms occupy special sites in space group P 3 1c : Ag(α) at ±(0, 0, 1 4 ) , Ag(β) at ±( 2 3 , 1 3 , 1 4 ) , and Ag(γ) at ±( 1 3 , 2 3 , 1 4 ) . The order is characterized by two order parameters η 1 = n ( β ) − n ( γ ) and η 2 = n ( β ) + n ( γ ) − 2 n ( α ), where n ( α ), n ( β ), and n ( γ ) are the occupancies of the α, β, and γ sites, respectively. Single-crystal X-ray diffraction of the ordered structure showed the occupancies n ( α ) = 0.172, n ( β ) = 0.861, n ( γ ) = 0 at 100 K and n ( α ) = 0.180, n ( β ) = 0.786, n ( γ ) = 0.069 at 255 K. Critical exponents β 1 and β 2 of the order parameters η 1 and η 2 were determined from the temperature dependence of the intensities of the superreflections 101 and 102, respectively; the values obtained, β 1 = 0.41 and β 2 = 0.81, are between those predicted by P. Bak ( Phys. Rev. Lett. 44, 889 (1980)) from scaling laws: β 1 = 0.33 and β 2 = 0.86, and from mean field theory: β 1 = 0.5, β 2 = 1.0. The temperature dependence of the order parameters in the temperature range 100–298 K is compared with that from a Bragg-Williams (mean field) model, the energy being written in terms of nearest-neighbor repulsive interactions, e 1 for atoms at distance a and e 2 for atoms at distance c ; e 1 > e 2 because c > a . The space group of the observed structure, P 3 1c , is discussed in (3 + 1)D superspace, which gives an alternate description for the symmetry of this commensurately modulated phase. Finally, some related phases are discussed.

One‐, Two‐, and Three‐Dimensional Order in and Four‐Dimensional Description of KxV5S8 (0.5 ≦ x ≦ 0.7)

The C-centered monoclinic (average) structure of KxV5S8 (0.5 ≦ x ≦ 0.7) is characterized by a three-dimensional V5S8 framework with channels containing the K atoms. For K0.5V5S8 at room temperature a superstructure is found due to ordering of the K atoms. This superstructure is analyzed on basis of a (3 + 1) dimensional space group in terms of an occupational modulation accompanied by a displacive modulation with small amplitude. At increasing temperature the superreflections of K0.5V5S8 are first broadened into lines and eventually into planes in reciprocal space, indicating a loss of three- and two-dimensional order of the K atoms, respectively. For crystals KxV5S8 with x ≥ 0.5 electron-diffraction experiments show incommensurate planes of diffuse scattering, even at liquid-nitrogen temperature, indicating only one-dimensional order of the K atoms. Die monokline (mittlere) C-Zentrums-Struktur von KxV5S8 (0.5 ≦ x ≦ 0.7) ist durch ein dreidimensionales V5S8-Gerust mit Kanalen, die die K-Atome enthalten, charakterisiert. Fur K0,5V5S8 wird bei Zimmertemperatur eine Superstruktur gefunden, die auf die Ordnung der K-Atome zuruckzufuhren ist. Diese Superstruktur wird auf der Basis einer (3 + 1)-dimensionalen Raumgruppe mit einer Besetzungsmodulation, die von einer verschobenen Modulation mit geringer Amplitude begleitet ist, analysiert. Bei ansteigender Temperatur werden die Superreflexionen von K0,5V5S8 zuerst in Linien und eventuell in Ebenen im reziproken Raum verbreitert, was den Verlust der drei- bzw. zweidimensionalen Ordnung der K-Atome anzeigt. Fur KxV5S8-Kristalle mit x ≥ 0,5 zeigen Elektronenbeugungsexperimente inkommensurable Ebenen diffuser Streuung, sogar bei der Temperatur des flussigen Stickstoff, was eine nur eindimensionale Ordnung der K-Atome anzeigt.

Structure of a Non-Stoichiometric Chromium Silver Sulphide

Ag0.37Crr21S2, rhombohedral, R3m, a = 3.4325 (1), c =- 37.190 (1) A (in hexagonal setting), Z = 6. The structure was determinined using singlecrystal X-ray data from 908 independent reflections; the least-squares refinement of the positional and thermal parameters and the population parameters of Ag and Cr led to a final R e = 0.102. It is a layer compound with hexagonal layers of atoms. Layers of S form a close packing of the type (hcch) 3, forming CrS 2 sandwiches with Cr in octahedral coordination. The gaps between these sandwiches are alternately occupied by Cr (2 x 0.21 Cr per site), also in octahedral coordination, and by Ag in tetrahedral holes. Both tetrahedral holes are partly occupied by 0.37 Ag; Ag is distributed over several sites within the S tetrahedra.

Four-dimensional structure determination of the incommensurate modulated compound (Nd4Ca2)Ti6O20

The structure of the incommensurate modulated compound (Nd4Ca2)Ti6O20 has been analyzed on the basis of a four-dimensional description in the space group or S(1–2)2mc+e4 (a=3.832A, b=36.64A, c=5.436A, q∗=0.49a∗, Z=2). The modulation involves rotations of the TiO6 octahedra of the perovskite-like structure around the [010] direction, coupled with a substitutional modulation of the NdCa species. R-factors are respectively 0.087, 0.070 and 0.113 for all, main and satellite reflections(1699 observed intensities).