We report on a detailed investigation of the crystal and electronic band structures and of the transport and thermodynamic properties of the Mo-based cluster compound Ag2Tl2Mo9Se11. This novel structure type crystallizes in the trigonal space group R3c and is built of a three-dimensional network of interconnected Mo9Se11 units. Single-crystal X-ray diffraction indicates that the Ag and Tl atoms are distributed in the voids of the cluster framework, both of which show unusually large anisotropic thermal ellipsoids indicative of strong local disorder. First-principles calculations show a weakly dispersive band structure around the Fermi level as well as a semiconducting ground state. The former feature naturally explains the presence of both hole-like and electron-like signals observed in Hall effect. Of particular interest is the very low thermal conductivity that remains quasi-constant between 150 and 800 K at a value of approximately 0.6 W·m(-1)·K(-1). The lattice thermal conductivity is close to its minimum possible value, that is, in a regime where the phonon mean free path nears the mean interatomic distance. Such extremely low values likely originate from the disorder induced by the Ag and Tl atoms giving rise to strong anharmonicity of the lattice vibrations. The strongly limited ability of this compound to transport heat is the key feature that leads to a dimensionless thermoelectric figure of merit ZT of 0.6 at 800 K.

X-ray characterization, electronic band structure, and thermoelectric properties of the cluster compound Ag2Tl2Mo9Se11.

The new isostructural K2Mo9S11 and Rb2Mo9S11 phases were prepared by solid-state reaction at 1500 °C in a sealed molybdenum crucible. Both compounds crystallize in the trigonal space group (SG) R3c, Z = 6, a = 9.271(1) A, c = 35.985(9) A and a = 9.356(2) A, c = 35.935(9) A for the K and Rb compounds, respectively, in the hexagonal setting. Their crystal structures were determined from single-crystal X-ray diffraction data and consist of interconnected Mo9S11 units forming an original and unprecedented three-dimensional framework. Extended Huckel tight-binding (EHTB) calculations carried out on K2Mo9S11 indicate that such compounds are electron-deficient and may be reduced without altering the arrangement of the Mo9S11 units. This was verified by the insertion of copper into K2Mo9S11 by topotactic oxydo-reduction reaction, which leads to the new metastable Cu2K1.8Mo9S11 compound (SG R3c, a = 9.4215(4) A, c = 35.444(2) A, Z = 6). The potassium nonstoichiometry of this quaternary phase was confirmed by dei...

Synthesis, Structural Evolution, and Theoretical and Physical Studies of the Novel Compounds M(2)Mo(9)S(11) (M = K, Rb) and Related Metastable Materials Cu(x)()K(1.8)Mo(9)S(11) (x = 0 or 2) Containing Bioctahedral Mo(9) Clusters.

A series of 12 carbocyclic α-amino acids has been prepared from four different racemic 2-alkylated cyclopentanones and ( R )-1-phenylethylamine as the chiral auxiliary by means of an asymmetric Strecker synthesis. The stereoselectivity was influenced by solvent, temperature and size of the substituent at the 2-position of the cyclopentanones. For the methyl and ethyl substituted amino acids all four possible stereoisomers could be obtained, whereas for the isopropyl and tertiary butyl compounds an unexpected side reaction prohibited the isolation of the cis configured amino acids. The 1,3-induction mechanism observed for the kinetically controlled α-amino nitrile formation in the 2-methyl and 2-ethyl series was overlayed by a 1,2-induction in the respective 2-isopropyl and 2-tertiary butyl series.

Carbocyclic α-amino acids: asymmetric Strecker synthesis of a series of 2-alkylated 1-aminocyclopentanecarboxylic acids

Calculations of the integrated diffracted intensity for Renninger experiments, i.e. calculations of ψ-scan profiles scanning through three-beam positions, are reported. The fundamental equations of the dynamical theory are solved by means of an eigenvalue procedure and boundary conditions consistent with the diffraction geometry. It is shown that for noncentrosymmetric structures the three-beam ψ-scan profiles bear information on both the magnitude, defined in the range 0 ≤ |φ| ≤ 180°, and the sign of the triplet phase involved in the three-beam interference. In general, the ψ-scan profiles can be separated into two parts: a phase-dependent part ('ideal' profile) due to the interference effect and a symmetric phase-independent Umweganregung or Aufhellung profile due to the mean energy flow in a three-beam case. Both parts can be calculated by summing up the ψ-scan profiles for + φ and -φ, one profile being reversed with respect to the three-beam point. As a result, the experimentally best suited three-beam cases for triplet phase determination should involve structure factors of nearly equal magnitude.

On the quantitative determination of triplet phases by X‐ray three‐beam diffraction

We present here the synthesis, crystal structure, and magnetic and resistivity studies of a remarkable ternary reduced molybdenum oxide Pr4Mo9O18. Its structure was determined on single crystal by X-ray diffraction in the space group R3m (ah = 11.3600(7) A, ch = 50.392(8) A, Vh = 5631.8(9) A3, Zh = 15; arh = 18.032(1) A, αrh = 36.720(3)°). The crystal stucture contains, in addition to the common triangular Mo3 cluster, the new Mo7, Mo13, and Mo19 clusters. Contrary to the previous high-nuclearity molybdenum clusters, the Mo13 and Mo19 present hemispherical and spherical geometries, respectively, while the Mo7 is planar. These four clusters with their oxygen environments form three different slabs parallel to the ab plane. The first slab is composed of Mo3 and Mo7 clusters in equal proportions. An infinite metallic plane based on connected Mo3 and Mo13 clusters forms the second slab. The Mo13 aggregate presents a hemispherical geometry and results from the cis-edge-sharing of three Mo6 octahedra having one...

Pr4Mo9O18, an Atypical, Novel, Ternary Reduced Molybdenum Oxide Containing Unusual Mo7, Mo13, and Mo19 Clusters. Synthesis, Crystal Structure, and Physical Properties

Direct measurements of triplet phase relationships for non-centrosymmetric light-atom organic structures with medium-size unit cells are reported. The phase information can be extracted from the three- beam profiles of a Renninger ψ-scan experiment. The measurements were carried out with a special ψ-circle diffractometer installed on a rotating Cu-anode generator. The incident-beam divergence is reduced to 0.02°. The experimental results confirm the theoretical considerations of paper I of this work [Hummer & Billy (1986). Acta Cryst. A42, 127-133]. As triplet phases of +90° can be distinguished, the absolute structure can be determined unambiguously. The measurements show that the triplet-phase-dependent interference effects may be superposed on phase-independent Umweganregung or Aufhellung effects. By a comparison of the ψ-scan profiles of two centrosymmetrically related three-beam cases, the triplet phases of which have opposite signs, it is possible to evaluate the phase-independent effects and to determine the value of the triplet phase with an accuracy of at least 90°.

Direct determination of triplet phases and enantiomorphs of non‐centrosymmetric structures. II. Experimental results

Recent progress in experimental triplet phase determination by the method of three-beam diffraction for non-centrosymmetric light-atom structures is reported. The measurements were carried out with a special ψ-circle diffractometer installed at the DORIS II storage ring in Hamburg. Experimental results confirm the theoretical considerations. In general, the ψ-scan profiles consist of a phase-independent Umweganregung or Aufhellung part superimposed on a phase-dependent part due to the three-beam interference, which contains the phase information. Experimentally, Umweganregung and Aufhellung effects can be evaluated by comparison of the two centrosymmetrically related three-beam cases. It is shown that with moderate phase-independent effects the triplet phase can be determined with an accuracy of about 45°.

H. Bondza

Papers

Direct determination of triplet phases and enantiomorphs of non‐centrosymmetric structures. II. Experimental results

Direct measurements of triplet phase relationships of organic non-centrosymmetric structures using synchrotron radiation

Determination of invariant reflection phases by four-beam X-ray diffraction