Volume 215, Issue 1

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

Synthetic buckhornite, [Pb 2 BiS 3 ][AuTe 2 ], was grown from melts in connection with the search for high-temperature superconductive materials. Chemical analyses were performed by electron-microprobe investigations. The crystal structure was determined from 726 single-crystal X-ray reflections of a twinned crystal. The refinement gave R(F)=0.101 for 33 variable parameters. The space group is Pmmn, a=4.108(3) Å, b=12.308(9) Å, c=9.331(6) Å, Z=2. The atomic arrangement features a pronounced layer structure formed by two different sheets. (a) Planar Au [4Te] Te 4 configurations are edge-connected to ribbons in [100]; they are linked by Te···Te contacts to planar nets parallel to (001). Te and Au atoms are in a distorted square arrangement. (b) Slices of (Pb,Bi)S are sandwiched between these AuTe 2 layers. They form SnS-archetype layers. The present paper proves that buckhornite, [(Pb 2 Bi) Σ3 S 3 ] [(Te 2 Au) Σ3 ], and nagyagite, [(Pb 3 (Pb,Sb) 3 ) Σ6 S 6 ][(Te,Au) 3 ] are members of a homologous series. Both compounds have comparable Au—Te layers. However, ordering of Au and Te atoms was verified in buckhornite only. In buckhornite two (Pb,Bi)S sheets form one slice of the SnS-archetype whereas in nagyagite four (Pb,Sb)S layers form the corresponding slice with a thickness of two SnS-archetype slabs.

The high pressure behaviour of the room temperature modification of cesium sulfate, β-Cs 2 SO 4 , has been studied by powder x-ray diffraction and by ab initio calculations based on density functional theory. The powder x-ray diffraction experiments were carried out using a diamond anvil cell mounted on an image plate system. The pressure dependence of the unit cell parameters was obtained for pressures up to 4.5 GPa. A fit with a 3 rd -order Birch-Murnaghan equation of state gave a bulk modulus, B 0 =28.4(1.0)GPa, with a pressure derivative B´ 0 =5.1(6). Quantum mechanical calculations have been used to study structural changes induced by compression.

Crystal structure determinations on a series of R 2 SnCl 2 (bipy)[bipy is 2,2'-bipyridyl] compounds show that these adopt a common structural motif in the solid-state with the Sn-bound organic substituents occupying mutually trans positions in a distorted octahedral geometry. A comparison of the experimental Sn–Cl and Sn–N bond distances with the moderated (i.e. by changing the nature of R) Lewis acidities of the tin atoms shows a general correlation, i.e. longer distances with decreasing Lewis acidity, but with a relatively large spread of values. In order to examine the role of crystal packing effects on the derived geometric parameters, gas-phase structures for these compounds have been modeled employing ab initio molecular orbital theory. These calculations showed that within individual compounds the two Sn–Cl distances are equal as are the two Sn–N distances, in contrast to the solid-state results. Further, a better correlation between the Sn–Cl and Sn–N bond distances and the Lewis acidity of the tin atom was found. These key results are attributed to the influence of crystal packing forces on the geometric parameters about the tin center in the solid-state.

The crystal structure of C 22 H 32 BrN 2 NiO 2 was ab initio solved from conventional X-ray powder data by combination of few powder diffraction techniques. After the intensity estimating procedure based on texture method, the orientation and approximate position of the molecule was found by the Patterson methods. Next, Patterson and direct method search program PATSEE was used to locate the molecule more precisely. Missing atoms of flexible groups and final refinement was performed by Rietveld method. The structure consists of flat molecules connected by van der Waals forces. The compound crystallises in the monoclinic space group P21/c (No. 14) with a=10.362(3) Å, b=18.468(3) Å, c=12.066(3) Å, β = 124.53(1)°, Z=4, and contains 28 atoms in asymmetric unit.

The crystal structures of several 1,1´,3,3´-tetramethyl-2,2´-diimidazolium dication salts were determined at low temperatures. The dihedral angles between the planes of the two five-membered rings vary between 64° in the bromide salt and up to 80° in the ketone adduct tetraphenylborates, indicating some conformational flexibility around the central C–C bond of the 1,1´,3,3´-tetramethyl-2,2´-diimidazolium dication. Semiempirical calculations predict the conformation with a dihedral angle of 90° to be most favourable and the conformations within the crystal structures to be results of packing effects. In tetra phenyl borate salts of ketone and diketone adducts, the oxygen centers coordinate to the dication from above as well as below the defined molecular least squares plane and form chains of alternating dications and ketones. Since this packing motif is found in tetraphenylborate salts with different ketones, it might prove to be a robust supramolecular synthone in crystal engineering.

The crystal and molecular structure of the title compound, C 22 H 21 O 8 has been elucidated at room temperature by single crystal X-ray diffraction technique. The colorless crystals are orthorhombic, space group P2 1 2 1 2 1 , with unit cell parameters a= 10.538(1) Å, b= 11.203(1) Å,c=16.855(2) Å, Z= 4, D c = 1.380 g cm -3 . The structure was solved by direct methods and refined by a full-matrix least-squares procedure to final R= 0.042 for 1241 observed reflections with I ≥ 3σ(I). The structure of the molecule consists of a fused ring system containing four (A, B, C and D) rings with a pendant methoxy phenyl (E) ring. The conformations of dioxolen (A) ring, both phenyl (B and E) rings, the cyclohexane (C) ring and the lactone (D) ring are envelope, planar, distorted boat and envelope, respectively. The plane of the phenyl (E) ring is about 72° from the mean least-squares plane of rings A, B, C and D. The molecules are connected in a head to tail fashion by O–H...O hydrogen bonds.

The title compound, C 22 H 19 N 3 crystallizes in the triclinic space group P1 with a= 8.310(1) Å, b= 9.890(1) Å, c= 12.007(1) Å, α =92.17(1)°, β= 97.32(1)°, γ =106.72(1)°; Z=2; D x =1.3270(3) (gcm-3); R=0.068 for 1618 observed reflections [I ≥ 2σ (I)]. The angle between the least squares planes formed by the N1–C2–N3 and C4–C5–C6 atoms of the pyrimidine ring is 30.1(3)°. The dihydropyrimidine ring adopts a distorted boat conformation. The dihedral angle between the two phenyl rings is 48.4(1)°. The pyrazole ring in the title compound is distorted from planarity with a maximum deviation of 0.153(3) Å for C4. Two molecules form a dimere with 1. There are the shortest four inter- and two intramolecular hydrogen bonds in the structure and {four intermolecular [N1–H1= 0.860(3) Å, N1...O2 i = 2.902(3) Å, H1...O2 i = 2.129(2) Å, N1–H1...O2 i =.149.3(2)°, C4–H4=.0.981(3) Å, C4...O70= 2.895(4) Å, H4...O70= 2.460(2) Å, C4–H4...O70= 106.5(2)°; C65–H65= 0.930(3) Å, C65...O70 ii = 3.346(4) Å, H65...O70 ii = 2.540(2) Å, C65–H65...O70 ii = 145.2(2)° and C71–H71A= 1.02(3) Å, C71...O50= 3.188(6) Å, H71A...O50= 2.51(3) Å, C71–H71A...O50=123(2)°; (i) ≡ 1-x,2-y, -z, (ii) ≡ -x, 2-y, -1-z] and two intramolecular [C4–H4= 0.980(3) Å, C4...O70= 2.895(3) Å, H4...O70= 2.460(2) Å, C4–H4...O70= 106.5(2)° and C71–H71A= 1.026(3) Å, C71...O50= 3.189(5) Å, H71...O5= 2.51(3) Å, C71–H71A...O50= 123(2)°]}.

[Me 3 PhN][ClO 4 ], [Me 3 PhN][BF 4 ], [MePh 3 P] [ClO 4 ], and [MePh 3 P][BF 4 ] were synthesized and their structures and thermodynamic data of transitions were determined. [Me 3 PhN][ClO 4 ]: P2 1 /c, a= 852.7(3) pm, b= 580.9(2) pm, c=2260.1(8) pm, β =96.65(3)° and Z= 4. [Me 3 PhN][BF 4 ]: P2 1 2 1 2 1 , a= 584.82(8) pm, b= 835.04(8) pm, c=2258.5(2) pm, and Z=4. [MePh 3 P]·[ClO 4 ]: P2 1 /c, a= 1491.0(3) pm, b= 1378.6(1) pm, c= 1791.6(2)pm, β = 90.66(1)° and Z= 8. [MePh 3 P] ·[BF 4 ]: P2 1 /c, a=1487.4(2)pm, b= 1377.5(1)pm, c= 1768.7(1)pm, β = 91.00(1)° and Z= 8. Two solid-solid phase transitions were detected in DSC for both trimethylphenylammonium compounds. Modification III of [Me 3 PhN][BF 4 ] and the modification II of [Me 3 PhN][ClO 4 ] are isotypic. The latter phase has lattice parameters of a= 2260.6(7) pm, b= 852.7(3) pm, and c= 586.3(2) pm at 373 K. No phase transitions were observed in the phosphonium compounds in the range 153-600 K.

The crystal and molecular structure of tetrakis(2-fluorobenzoato-O,O´)-bis(2-fluorobenzoate-O) dicopper(II) - C 42 H 26 Cu 2 F 60 O 12 - has been determined at room temperature. The blue-green crystals are monoclinic, space group P2 1 /n (No.14), with unit cell parameters a=10.633(3) Å, b= 12.528(3) Å, c=14.729(3) Å, β = 91.62(4)°, Z= 2, D m = 1.62 and D x = 1.64 g/cm 3 . The final R value for independent reflections is equal to 0.045. The structure consists of two centrosymmetric units [Cu 2 (2FbzO) 4 (2HFbzO) 2 ] (abbreviation 2FbzO stands for 2-fluorobenzoate, abbr. 2HFbzO for 2-fluorobezoic acid). These units are mutually held by Van der Waals forces. Within the binuclear unit the Cu atom is pentacoordinated by four carboxylic O atoms in the basal plane of tetragonal pyramid (Cu–O bond lengths being 1.962(3) Å, 1.963(2) Å, 1.958(2) Å and 1.996(2) Å and one apical O atom from HFbzO molecule, with Cu-O bond length 2.193(2) Å. The apical Cu(II)–O bond length predicted by bond valence method is 2.16 Å. The Cu...Cu distance is 2.6086(8) Å and the displacement of Cu atom from the basal plane is 0.1905(6) Å. Nonbonding character of Cu(II)...Cu(II) contact in 16 binuclear carboxylic complexes is proved.

The title compound, cis-[PtCl 4 (H 2 O) 2 ]·(18-cr-6)·2H 2 O(3), crystallizes from water in the orthorhombic space group Pbcn with lattice constants a= 7.9842(12) Å, b=16.550(3) Å, c= 18.027(4) Å, Z= 4. The crystal structure was solved by direct methods. The refinement converged to final wR2= 0.0485 for 2307 data (R1= 0.0187 for 1672 observed reflections). The platinum complex cis-[PtCl 4 (H 2 O) 2 ] exhibits crystallographically imposed C 2 symmetry with small deviations from C 2v symmetry, only. Each of the two aqua ligands forms an O-H...O hydrogen bond to a water molecule in such a way that H 4 O 2 units are yielded. Their three terminal hydrogen atoms form O-H...O hydrogen bonds to three oxygen atoms of the crown ether molecule. Thus, the crystal is threaded by chains built up of 18-crown-6/cis-[PtCl 4 (H 2 O) 2 ]·2H 2 O units. The crown ether exhibits crystallographically imposed C i symmetry and D 3d symmetry in rough approximation. The Raman and IR spectra of 3 are as expected for a complex [PtCl 4 (H 2 O) 2 ] with aqua ligands in mutual cis position.

Large single crystals of ammonium bis(nitrilotriacetato)zirconate, (NH 4 ) 2 [Zr{N(CH 2 COO) 3 } 2 ] (to be written (NH 4 ) 2 [Zr(NTA) 2 ), were grown. Linear optical properties were measured (indices of refraction and transparency range) and the phase matching conditions for second harmonic generation process were determined. Crystal structures of the zirconate and the isomorphic hafnate were solved from single crystal X-ray diffraction data (P3 1,2 ; Z= 3; Zr: a= 9.582(1)Å, c= 16.611(4)Å, Hf: a= 9.5846(5)Å, c=16.5920(8)Å and the geometry of the complex groups [Zr(NTA) 2 ] 2- and [Hf(NTA) 2 ] 2- was analysed.