Volume 210, Issue 8

Elastic constants and thermal expansion were measured using large single crystals of monoclinic Na 2 H 4 (C 6 H 8 O 4 ) 3 · 2 H 2 O. These properties show a considerable anisotropy, which is strongly correlated to features of the crystal structure. Essential details of the structure are discussed by comparing results from a structure determination by neutron diffraction (Gao, Clancy, Weber, Craven, McMullan, 1991) with our results using X-ray diffraction. Special emphasis is given to the different models of disorder proposed in the neutron and the X-ray work, which have to be discussed in the light of different scattering properties of atoms for the two radiations used. The temperature dependence of the elasticity tensor is anomalous, indicating a ferroelastic phase transition at about 270K. The critical shear stiffness belongs to a transverse mode propagating along the twofold axis.

A crystal structure is usually described as the union of sets of symmetrically equivalent atoms, i.e. as the union of orbits. During a continuous or nearly continuous phase transition, symmetrically equivalent atoms of a crystal structure may become inequivalent, their site symmetries may be reduced, or both may happen simultaneously. The same effect may occur as the result of an applied external mechanical, electric, magnetic, etc. homogeneous field. Using the orbit approach, this phenomenon may be described as ‘Splitting of orbits due to symmetry reduction’. The splitting behavior is the same for orbits of the same Wyckoff position. Therefore, one may speak loosely of ‘Splitting of Wyckoff positions’. In a preceding paper (Part I) the dependence of orbit splitting on the index and on the kind of group-subgroup relation [unk] – [unk] between groups has been considered. General laws have been derived and applied to the possible group-subgroup relations of index 4. In this paper (Part II) the splitting rules are formulated as two lemmata and applied to group-subgroup relations of index 6. There are eight different types of such relations, seven of which occur between space groups. Restrictions for the possible splittings are due to groups intermediate between [unk] and [unk] and due to the size of the normalizer [unk][unk]([unk]). The possible kinds of splittings are calculated. With two exceptions all of them are covered by theoretical examples. Furthermore, many of them describe relations between actual crystal structures.

The crystal structure of MB 2 , MB 4 and MB 6 borides are analyzed on the basis of their metal arrays. In all of them, the identity of the parent metal can be recognized. Some of the compounds present metal fragments which maintain the topology and shortest M-M distances of the pure metal. In other compounds, these distances are absent but distances to the second and even third nearest neighbors are recognizable. This feature does not seem to depend either on the stoichiometry or the nature of the metal involved. For all the compounds, a geometrical mechanism is proposed, based on the formation of metastable metal structures.

The appearance of metal aggregates in the crystal structures of MB 2 , MB 4 and MB 6 borides is discussed in relation to other compounds showing saturated valences. A comparison with cluster-forming compounds and with Zintl phases, indicates that conceptual barriers, which separate different kinds of inorganic compounds, can be overcome. Clusters are found in fully ionic compounds and examples are given (MgB 4 ) where metals behave structurally as if they were Zintl anions. Partial redox processes between metals and non-metals could account for some of the reported features.

It is shown that the density of the p 3 packing of ellipses never exceeds the maximum density ϱ = π /[unk] through numerical computations and series expansions. This maximum density is attained only by the closest packing of circles, p 6 mm .

Arylmethylene thiocamphors are easily obtained from corresponding (+)-arylmethylene camphors by reaction with Lawesson reagent or P 4 S 10 . Crystals of o-methoxyphenylmethylene thiocamphor C 18 H 22 OS belong to space-group P 2 1 2 1 2 1 with a = 7.581(9) Å, b = 12.884(7) Å and c = 16.831(7) Å, Z = 4, T = 293 K. The final R is 0.055 for 1300 unique reflections. The cohesion of the crystal is the result of van der Waals interactions. This compound and all arylmethylene thiocamphors adopt the E configuration, more stable from the stereochemical point of view. The conjugated S = C – C = C system is skewed in the sense of a left handed helix. Furthermore, the aromatic ring is twisted (−32°). Exciton Circular Dichroism is consistent with this conformation.

The crystal and molecular structures of (endo, anti)-5-ethylidene-1,2,3,3,6,7-hexamethyl-6-(4-methoxyphenyl)-bicyclo[2.2.1]hept-2-ene (C 22 H 30 O) (DA-1) and (endo, anti)-1,3,4,5,6,7-hexamethyl-3-(4-methoxyphenyl)-bicyclo[2.2.1]hept-5-en-2-one (C 20 H 26 O 2 ) (DA-2) have been resolved by X-ray diffraction methods. DA-1 crystallizes in the monoclinic space group P 2 1 / a with a = 13.189(1) Å. b = 8.4285(2) Å, c = 18.033(2) Å and β = 109.155°(5) Å. Z = 4. DA-2 crystallizes in the orthorhombic space group Pbca with a = 11.546(1) Å, b = 16.750(1) Å and c = 17.986 Å. Z = 8. The structures were solved by direct methods and refined by least-square procedures to final R -values of 0.054 (DA-1) and 0.046 (DA-2) for 3244 (DA-1) and 1784 (DA-2) unique observed reflections with I ≥ 2 σ (I).