Band 226, Heft 3 -

We describe generalized polyhedra of icosahedron type with analytic mathematics (exponential summation method) using the ordinary (Platon and Archimedes) polyhedra and their interpenetrations (mixed polyhedra). To this we add the Hardy devation for enhancing the topology within each structure type. The findings are compared with the structures of some viruses.

The intermetallic compounds RE 2 Cu 2 Cd ( RE = Ce, Pr, Nd) were synthesized by induction-melting of the elements. Nd 2 Cu 2 Cd is dimorphic with a tetragonal Mo 2 B 2 Fe high- (HT) and a monoclinic, Mn 2 B 2 Al 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: P 4/ mbm , a = 764.7(3), c = 385.3(2) pm, wR 2 = 0.0529, 288 F 2 values, 12 variables for HT-Nd 2 Cu 2 Cd and C 2/ 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-Nd 2 Cu 2 Cd. Both modifications are simple 1:1 intergrowth variants with slightly distorted CsCl and AlB 2 related slabs of compositions NdCd and NdCu 2 . Formation of the monoclinic superstructure is discussed on the basis of a group sub-group scheme. Monoclinic Ce 2 Cu 2 Cd ( a = 859.1(5), b = 743.0(3), c = 1520.6(7) pm, β = 106.37(5)°, 1243 F 2 values, 48 variables) and Pr 2 Cu 2 Cd ( 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. Ce 2 Cu 2 Cd, Pr 2 Cu 2 Cd, LT- and HT-Nd 2 Cu 2 Cd show Curie-Weiss paramagnetism and magnetic ordering at low temperatures.

A well crystallized sample of EuAu 2 Ge 2 was synthesized by arc-melting of the elements. The structure was refined on the basis of single crystal X-ray diffracto meter data: ThCr 2 Si 2 type, I 4/ mmm , a = 447.3(1), c = 1034.0(4) pm, wR 2 = 0.0575, 148 F 2 values and 9 variables. The gold atoms have tetrahedral germanium coordination (261 pm Au—Ge). These AuGe 4/4 tetrahedra share four common edges, leading to layers which are connected via Ge—Ge bonds (247 pm). The europium atoms fill cages of coordination number 16 within the [Au 2 Ge 2 ] δ – polyanion. Temperature dependent susceptibility measurements show a magnetic moment of 7.79(1) μ B /formula unit. Together with the 151 Eu Mössbauer spectroscopic data (isomer shift of –11.43 mm/s at 77 K), the magnetic data point to stable divalent europium. EuAu 2 Ge 2 orders antiferromagnetically at T N1 = 5.5(1) K, followed by a spin-reorientation at T N2 = 3.5 K. A metamagnetic step occurs around 20 kOe in the 4 K magnetization isotherm.

Nonstoichiometric REE Al 2.07 (B 4 O 10 )O 0.60 ( REE = La, Pr) borates have been crystallized and analyzed by means of single crystal X-ray diffraction. The compounds resulted to be isostructural within hexagonal space group P -62 m (n. 189), with the following unit cell parameters: a = 4.6170(1) Å, c = 9.3640(3) Å and V = 172.87(1) Å 3 (La); a = 4.5990(1) Å; c = 9.3270(2) Å and V = 170.87(1) Å 3 (Pr). REE cations make up a trigonal prismatic coordination, by means of six REE -O bonds under 2.5 Å; aluminium cation is five-coordinated, displaying a square pyramidal coordination, while the boron atom forms BO 4 tetrahedral units. The present borates belong to the structural type of NdAl 2.07 (B 4 O 10 )O 0.60 dimetaborate [1]: thus, the three-dimensional framework can be described as a structure packed down crystallographic axis c , with layers of six-membered rings of B tetrahedra alternated by inter-layers REE cations and layers of Al polyhedra. An intricate network of Al···O and REE ···O interactions complete the array.

An inclusion in a diamond from the Juina area, Brazil was investigated in situ by single-crystal X-ray diffraction. It consists of six different phases: garnet, orthopyroxene and four individuals of diopsidic clinopyroxene. The application of the ALIGN-program helped to obtain accurate crystallographic data sets.

Well-shaped needles of the metal-rich phosphide Ce 13 Ir 34.4 P 24 were synthesized by a reaction of the elements in a lead flux (1 : 2 : 2 : 60 molar ratio, 1370 K, slow cooling rate of 2 K/h). Ce 13 Ir 34.4 P 24 was characterized by X-ray powder and single crystal data: new structure type C 2/ m (mS144–1.2), a = 4512.2(9), b = 398.51(8), c = 1331.1(2) pm, β = 105.01(2)°, wR 2 = 0.0326, 3554 F 2 values and 186 variables. The structure is built up from a complex three-dimensional [Ir 34.4 P 24 ] δ – polyanion in which the seven crystallographically independent cerium atoms fill distorted hexagonal cavities. Geometrically the Ce 13 Ir 34.4 P 24 structure can be described as an intergrowth variant of ThCr 2 Si 2 , SrPtSb, and CeMg 2 Si 2 related slabs, similar to Lu 3 Ir 7 P 5 , Sm 15 Ir 33 P 26 , and Ce 4 Ir 14 P 9 .

The temperature dependence of the elastic stiffness coefficients of natural orthorhombic Mg-cordierite was studied between 295 K and 1573 K using resonant ultrasound spectroscopy. The measurements revealed a continuous decrease of all the elastic constants with increasing temperature. The bulk modulus softens from about 129(2) GPa at 295 K to 110(2) GPa at 1473 K. Irreversible anomalies in the temperature evolution of the resonance frequencies of certain eigenmodes were observed above 920 K due to the escape of volatiles and the occurrence of microcracks. However, the dehydrated samples still showed integrity on the macroscopic scale. Therefore, despite the occurence of the micro-cracks, a reasonable quantitative analysis of the high-temperature RUS data of cordierite samples was still feasible. The thermal expansion was studied between 100 K and 1570 K using dilatometry. The new data are consistent with earlier experimental results and confirm the expansion of the a and b unit cell parameters and the contraction of the c parameter with increasing temperature. Posäsible contributions of the Al/Si disorder to the elastic properties of Mg-cordierite were estimated on the basis of force-field and quantum mechanical calculations. The behaviour of individual elastic stiffness coefficients was followed across the order/disorder transition by Monte Carlo simulations. The simulations predicted a decrease in the bulk modulus with increasing Al/Si disorder. However, this effect is much smaller than that observed experimentally. The measured decrease in the elastic stiffness coefficients is mainly due to phonon softening effects.

Given that many zeolites crystallize in habits that lead to preferred orientation, and that there is a ±60° tilt limitation in many electron microscope goniometer stages, collection of a three 3-D electron diffraction data set from these materials is severely restricted. To overcome this, preparative measures must be taken to produce other sample orientations. Using a number of MWW framework zeolites (MCM-22, MCM-22P, MCM-49, ITQ-1) as examples, thin-sectioned views onto the edge stacking of lamellar layers can be prepared by a number of methods. While ultamicrotomy is a traditional approach to this problem, sections are often very thick and sparsely distributed. Other extreme mechanical processing techniques, such as extrusion and jet milling produce numerous thin crystals with the desired orientation. Dealumination, initiated by steaming, calcination or low pH, also yields a similar result. Additional intensity data from the ‘missing cone’ in addition to those obtained by tilting hexagonal plate crystals provides a more complete data set and hence a more easily interpreted structure analysis. Crystallographic phase determination by maximum entropy and likelihood, followed by Fourier refinement, yields a structural model very close to that of the known MWW framework.

A crystal chemistry approach was carried out in order to decipher the mechanisms involved in phase transitions of zirconia. A detailed analysis of structures, based on structural sheets of half fluorite cell thick and described in terms of SDF and HDF (for slightly and highly distorted fluorite) sheets is proposed for the first time. This approach allowed clarifying the relationships between tetragonal, orthorhombic and monoclinic forms. This concept permits to propose simple structural relationships between the structures of the different polymorphs. These relationships and their correlated transformation pathways were confirmed using symmetry group relations. The results were compared to those obtained by the phenomenological approach of the tetragonal → monoclinic ( T → M ) martensitic phase transition. The different lattice correspondences are revisited and discussed. For the first time, some fine structural models were proposed to describe the pathways of atomic displacements taking place during each possible phase transitions. The T → M phase transition is the main transformation pathway. It may solely gives rise to the C -type lattice correspondence, the (100) M || (100) T and [001] M || [001] T relationship allowing the minimum structural changes during the transformation. The B -type variant with (100) M || (100) T and [010] M || [001] T may be developed from an indirect pathway involving either a ferroelastic phase transition by domain switching taking place in the T phase before the T → M phase transition operates or a two stage process involving a combined T → O and O → M successive and independent transitions. The orthorhombic phase is an alternative form to the monoclinic one and is in no way an intermediate phase.

In order to find out the consequences of a methyl substitution on the crystalline packing behaviour of the parent compound 2,6-diphenyl-4-nitrophenol, three analogous nitrophenols being substituted at different positions of the lateral phenyl rings were comparatively studied with regard to their crystal structures. While the molecular structures do not suggest marked differences, the network structures do, showing dependency on the presence and positional substitution of the methyl groups. This is revealed by the formation of weakly O—H…π bonded dimers or supramolecular chains, more strongly hold together through interacting OH and nitro groups.

The synthesis, characterization, and X-ray crystal structure of two new compounds were determined: N -butyl-5-(4-methyl-1,2,3-thiadiazol-5-yl)-1,3,4-thiadiazol-2-amine ( 1 ) crystallizes in the monoclinic space group P 2 1 / n with a = 5.222(1), b = 15.010(3), c = 15.343(3) Å, β = 93.30(3)°, Z = 4 and 5-isoquinolin-3-yl- N -(2-methylphenyl)-1,3,4-thiadiazol-2-amine ( 2 ) crystallizes in the monoclinic space group P 2 1 / c with a = 7.455(2), b = 17.113(5), c = 12.199(3) Å, β = 94.68(2)°, Z = 4. In both structures, intermolecular N—H···N hydrogen bonds link two neighbouring molecules into a centrosymmetric R 2 2 (8) dimer.

The crystal structures of two new compounds were determined: 4-ethyl-3-(4-methyl-1,2,3-thiadiazol-5-yl)- s -triazole-5-thione ( 1 ), P 2 1 / n , a = 10.433(2), b = 7.975(2), c = 13.100(3) Å, β = 110.70(3)° and 4-carboxymethyl-3-(4-methyl-1,2,3-thiadiazol-5-yl)- s -triazole-5-thione ( 2 ), P 2 1 / c , a = 6.444(1), b = 14.721(3), c = 11.067(2) Å, β = 93.50(3)°. In both structures, the molecules form ähydrogen-bonded dimers through N1—H1n···S1 (triaäzole···S=C-triazole) interactions. The crystal structure of 1 is further stabilized by intermolecular C—H···N and S···S interactions, while in 2 , C—H···N/O, O—H···N/S, S···S/O and π···π interactions are observed.