Volume 210, Issue 6

Following a lecture given 1959 by Max von Laue, the author demonstrates von Laue's final ideas about his discovery, the diffraction of X-rays by crystals. Its most important consequence? The discovery of electron diffraction. Its essence? Wave fields.

Using a triple-crystal arrangement, the Cu K α (111) and (333) X-ray reflection curves of dislocation-free Ge and Si have been measured in the symmetric and asymmetric Bragg case. Comparison with the corresponding curves derived from the Dynamical Theory of Ewald and v. Laue with consideration of absorption exhibits excellent coincidence of experimental and theoretical curves. In particular, the observed asymmetry of the reflection curves, resulting from absorption, is reproduced and fully explained by the theory.

X-ray topography provides a non-destructive method of mapping point-by-point variations in orientation and reflecting power within crystals. The discovery, made by several workers independently, that in nearly perfect crystals it was possible to detect individual dislocations by X-ray diffraction contrast started an epoch of rapid exploitation of X-ray topography as a new, general method for assessing crystal perfection. Another discovery, that of X-ray Pendellösung, led to important theoretical developments in X-ray diffraction theory and to a new and precise method for measuring structure factors on an absolute scale. Other highlights picked out for mention are studies of Frank-Read dislocation sources, the discovery of long dislocation helices and lines of coaxial dislocation loops in aluminium, of internal magnetic domain structures in Fe-3 wt.% Si, and of stacking faults in silicon and natural diamonds.

Using an analogy with three-connected networks of hyperbolically-curved single sheets, a method for construction of tetrahedral frameworks corresponding to interconnected, double-sheeted relatives of these is presented. The analogy is founded upon common application of the bond switch mechanism to the structures. Considering the simplest such examples, models of the frameworks sheathing the triply-periodic minimal surfaces P, D and G are given. For each of these cases the systems of tunnels and cavities thus formed are significantly larger than those for the established zeolite structures.

Two procedures to derive all types of sphere packings with three contacts per sphere are described. 52 such types have been found. They are characterized by their shortest meshs and related to Wells' three-connected nets, if possible. It is proved that there exists no sphere packing with contact number three and a density lower than 5.5%, i.e. the density of the Heesch-Laves packing.

The influence of surface relaxations on the intensity of microcrystals was investigated. Since the volume fraction of near surface atoms becomes appreciable for submicrometer crystals, it is important to estimate whether observed intensities of submicrometer crystals can be interpreted with standard structure refinement methods or whether surface relaxations produce a significant deviation from the intensities of the perfect crystal. Structure simulation techniques were applied in order to calculate the intensity of microcrystals of various sizes. Different models of surface relaxations were applied. Structure refinements on the data sets calculated for these models showed that submicrometer crystals down to 0.5 μm in diameter are not affected by surface relaxations. Smaller crystals below 0.1 μm in diameter are significantly affected by surface relaxations. Great care will have to be taken when refining observed intensities of these small crystals.

Single crystal X-ray determinations of the lattice constants of tugtupite (Na 8 [Al 2 Be 2 Si 8 O 24 ](Cl) 2 (idealized), tetragonal, I [unk], specimen from Ilimaussaq, Greenland) were performed using a modified Merrill-Bassett type high pressure diamond anvil cell. The maximum pressure reached was 6.2 GPa. The data obtained suggest that the compressibility of the crystal structure changes between 2 and 3 GPa; the bulk modulus K computes to 0.62 · 10 11 Nm −2 below and to 0.94 · 10 11 Nm −2 above this region. Plots of the relative volume reduction of tugtupite, sodalite and helvite illustrate that the reaction of the crystal structure of tugtupite and sodalite to pressure corresponds, whereas the structure of helvite is less compressible.

Crystals of Na 2 [Bi 2 Cu 3 O 4 (AsO 4 ) 2 ] · H 2 O and K 2 [Bi 2 Cu 3 O 4 (AsO 4 ) 2 ] · 2 H 2 O were synthesized under hydrothermal conditions at T ≤ 503 K. Their crystal structures were determined from single crystal X-ray data (Na 2 [Bi 2 Cu 3 O 4 (AsO 4 ) 2 ] · H 2 O: a = 9.716(1) Å, b = 5,203(1) Å, c = 13.362(2) Å, β = 115.03(1)°, Z = 2, space group C2, R = 0.033 and R w = 0.036 for 1683 reflections, sin ϑ / λ ≤ 0.707 Å −1 ; K 2 [Bi 2 Cu 3 O 4 (AsO 4 ) 2 ] · 2 H 2 O: a = 9.964(4) Å, b = 5.237(2) Å; c = 14.307(6) Å, β = 89.67(5)°, Z = 2, space group C 2, R = 0.053 and R w = 0.053 for 1437 reflections, sin ϑ / λ ≤ 0.707 Å −1 ). A pronounced C 2/ m pseudo-symmetry is observed especially for the potassium compound: non-space-group restrictions according to this local higher symmetry were applied to some of the structural parameters during the refinements. Both compounds form topologically the same [Bi 2 Cu 3 O 4 · (AsO 4 ) 2 ] layers, linked to each other by alkali atoms and by water molecules: The Bi(III) atoms are coordinated one side by four nearest neighbors, the Cu(II) atoms show a [4 + 1] and [4 + 2] coordination. The different stereochemical behavior of the alkali atoms Na and K obviously requires the incorporation of one and two H 2 O molecules per formula unit, respectively. Adjacent layers are shifted by a /2; in addition, the layers are more apart in K 2 [Bi 2 Cu 3 O 4 (AsO 4 ) 2 ] · 2 H 2 O as compared to Na 2 [Bi 2 Cu 3 O 4 (AsO 4 ) 2 ] · H 2 O, thus increasing the interlayer space.

Using chemical transport reactions well-shaped crystals of In 2 (SO 4 ) 3 and Ga 2 (SO 4 ) 3 can be prepared in a temperature gradient ( T 2 → T 1 ) using Cl 2 as transport agent. The two modifications of In 2 (SO 4 ) 3 were formed by variation of the transport temperature. The low-temperature modification of In 2 (SO 4 ) 3 (898 K → 848 K) is isostructural to monoclinic Fe 2 (SO 4 ) 3 and crystallizes in P 2 1 / n with a = 8.570(2) Å, b = 8.908(2) Å and c = 12.0521(1) Å, β = 91.05(3)°, Z = 4. The high-temperature modification of In 2 (SO 4 ) 3 (1023 K → 973 K) as well as Ga 2 (SO 4 ) 3 (923 K → 873 K) is isostructural to rhombohedral Fe 2 (SO 4 ) 3 and crystallizes in the rhombohedral space group R [unk] with a = 8.440(2) (8.054(2)) Å, c = 23.093(2) (21.840(2)) Å, Z = 6 (hexagonal setting). The crystal structures were refined to a residual R 1 = 0.028 using 1710 unique reflections with F o ≥ 4 σ · ( F o ) for monoclinic In 2 (SO 4 ) 3 and to R 1 = 0.031(0.037) (571(587) unique reflections with F o ≥ 4 σ ( F o )) for rhombohedral In 2 (SO 4 ) 3 (Ga 2 (SO 4 ) 3 ). The structures consist of MO 6 -octahedra and SO 4 -tetrahedra, which are linked via common corners to a three-dimensional network.

The one-dimensionally disordered structure of the composite crystal of synthetic (LaS) 1.18 VS 2 has been determined based on the X-ray diffraction intensities collected by using monochromatized synchrotron radiation of wavelength 1.180 Å. The ordered (100) projection was refined based on 94 unique intensities collected on a diffractometer using Mo K α radiation; R = 0.067, R w = 0.084. The structure consists of interleaved layers of LaS and VS 2 , each of them forming a substructure which can be described based on a C -centred orthorhombic lattice with a 1 = 5.705(1) Å, b = 5.828(1) Å, c = 22.32(2) Å and Z = 8 for LaS and a 2 = 3.366(3) Å, b = 5.828(1) Å, c = 22.32(2) Å and Z = 4 for VS 2 . The b and c axes are common to both substructures. D x = 4.806 Mg m −3 . The structure of the (100) projection is isotypic with that of the orthorhombic (PbS) 1.18 TiS 2 ; plane group pgm , b ′ = b /2, c ′ = c . The La and S atoms of LaS are arranged like Na and Cl in the NaCl structure. The V atom is surrounded by six S atoms octahedrally. The LaS layers are related to each other through a twofold screw axis parallel to [100] with a screw translation of ±0.32 a 1 , while the nearest VS 2 layers are coupled by a glide plane perpendicular to [001] with a glide translation of ±0.25 a 2 . Stochastic change of the signs causes a one-dimensional disorder.

Ferrocenium heptaiodide (biscyclopentadienyliron(II)heptaiodide) [Cp 2 Fe]I 7 (Cp = η 5 -C 5 H 5 ) has been prepared by stoichiometric reaction of ferrocene and iodine in ethanol. It crystallizes at 298 K in the monoclinic space group P 2 1 / n with a = 15.155(7) Å, b = 9.455(3) Å, c = 15.416(4) Å, β = 102.03(3)°, V = 2160.6(13) Å 3 and Z = 4. The crystal structure has been refined by full matrix least-squares procedures to R = 0.049 for 2436 reflections. It contains complex cations Cp 2 Fe + with well ordered ligands in eclipsed arrangement and heptaiodide anions ∞ 1 (I 7 − ) building two parallel chains along [010] from pentaiodide units and connected by iodine molecules forming a rope like ribbon.

The title compound with M 2 = Mn 2 1 crystallizes in space group C 2/ c with a = 15.943(6) Å, b = 17.464(6) Å, c = 8.499(3) Å, β = 96.72(2)°, V = 2350(2) Å 3 . The homonuclear Mn–Mn bond length is 2.9332(11) Å. Title compound 2 with M 2 = MnRe crystallizes in space group C 2/ c with a = 16.058(2) Å, b = 17.535(4) Å, c = 8.593(2) Å, β = 96.44(1)°, V = 2404.3(8) Å 3 . The heteronuclear Mn–Re bond length is 3.0397(7) Å.