Volume 126, Issue 1-3

The interpretation of certain electron-diffraction patterns leads to a crystal structure whereby rows of unit cells (termed elementary fibers) are statistically displaced lengthwise with respect to each others by half a translation period. The reason for this displacement is discussed by means of the example of tobermorite.

Koenenite 4NaCl · 4(Mg,Ca)Cl 2 · 5Mg(OH) 2 · 4Al(OH) 3 is built up of two trigonal substructures: [Na 4 (Ca,Mg) 2 Cl 12 ] 4− and [Mg 7 Al 4 (OH) 22 ] 4+ (space group R [unk] m and P [unk] m 1 respectively). In direction of the common c axis ( c = 3 · 10.88 Å or c = 10.88 Å respectively) NaCl-like chlorine double layers ( a cl = 4.072 Å) alternate with brucite-like OH double layers ( a OH = 3.052 Å). All possible octahedral sites are randomly occupied by the metal ions. The Cl double layers have the following rhombohedral sequence: – BC – AB – CA – BC –. Evidence of a common supercell could not be found. The [100] directions of both subcells form an angle of 28.3 ± .1°. The distances Me–Cl and Me–OH are 2.79 Å and 2.02 Å respectively, the distances between the layers are Cl–Cl = 3.02 Å, OH–OH = 1.99 Å and Cl–OH = 2.94 Å. The double layers of both lattices are held together by their opposite charge and by hydrogen bonds. The reliability index for 215 independent structure factors is R = 0.056.

The paper deals with a simple photographic method for determining lattice constants from non-indexed powder diagrams of tetragonal and hexagonal substances.

Basal cleavages of apophyllite crystals from different localities are etched in ammonium bifluoride, hydrofluoric acid, sodium hydroxide, potassium hydroxide and acetic acid. Etch patterns obtained are illustrated and interpreted. Correspondence in positions of the etch pits on matched cleavages etched with the same etchant and also with two different etchants is established. The pits are shown to nucleate at dislocation sites. Linear and intersecting boundaries observed on the basal plane are recorded and interpreted.

The crystal structure of the compound Li 2 (Si 0,25 Ge 0,75 ) 2 O 5 has been determined by means of Weissenberg photographs and refined by two-dimensional Fourier syntheses. The lattice parameters of the unit cell ( C 2 v 15 – Abm 2) are found to be: a = 5,99; b = 15,05; c = 4,94 Å. The crystal structure represents a new type of a double-chain, showing an identity period of two tetrahedra (Zweierdoppelketten). There is a structural relationship to the layer silicate Li 2 Si 2 O 5 The following average distances have been obtained: (Si,Ge)–O = 1,69 and Li–O = 1,94 Å.

LiAlSi 2 O 6 -II (“ β spodumene”) was found to be tetragonal, space group P 4 3 2 1 2 (or P 4 1 2 1 2), a = 7.541 ± 0.001, c = 9.156 ± 0.002 Å, Z = 4, D o = 2.365 and D c = 2.374 g/cm 3 . The bond lengths were determined with an accuracy of 0.006 Å for (Si,Al)–O bonds and 0.041 Å for Li–O bonds. The final R value was 6.2%. The structure consists of a three-dimensional aluminosilicate framework. The framework was confirmed to be isotypic with keatite. The Li atoms were found to be coordinated to four oxygen atoms. The distribution of Si and Al in the tetrahedra is random. The structure is dominated by interlocking 5-membered rings of (Si,Al) tetrahedra. All the five-membered rings run approximately parallel to either (010) or (100), and thus help to create zeolite-like channels. These channels account for the ion-exchange properties of LiAlSi 2 O 6 -II. Lithium atoms are stuffed in interstitial positions but occupy a general eight-fold site. The four lithium atoms per unit cell are distributed among four sets of paired sites of the eight-fold positions. An explanation for the unusually low thermal expansion behavior of LiAlSi 2 O 6 -II is given.

The phases of the three-dimensional structure factors of the crystal of para -chlorophenol have been determined by the use of B eursken 's method based on S ayre 's equation. The Cl–C, O–C, C–C bonds are 1.69 to 1.71, 1.38 to 1.41 and 1.36 to 1.42 Å respectively. Hydrogen bonding dominates the packing of the molecules and forms chains perpendicular to the twofold screw axis.

Crystal structure of an eighteen-layered polytype of cadmium iodide, grown from vapour phase, has been worked out. It is found to belong to the (22) n 11 series of CdI 2 polytypes, five members of which were previously known.

A Fourier-transform computer program has been developed to calculate the x-ray diffraction effects expected from non-ideal crystals. The program evaluates the function [unk], where G ( HKL ) is the Fourier transform at a particular H , K , L coordinate in reciprocal space, f n is the atomic scattering factor of the n th atom, and x , y , z its coordinates in direct space. Diffraction profiles were calculated for biotite, muscovite, and montmorillonite crystallites 2, 3, 4, 5, 6, 8, 10, 20 and 30 layers thick, and for various models of graphite and periclase. The apparent basal spacings given by finite muscovite, montmorillonite, graphite, and periclase models deviate from the true values as the platelets become thinner. Diffraction profiles were also calculated for 30-layer packets of random mixed-layer muscovite-montmorillonite clays. The migration curves of the (001), (002), (003), (004) and (005) muscovite maxima and of the (001), (002), (003), (004), (005), (006), (007) and (008) montmorillonite maxima, obtained from those calculations, are in general agreement with the Hendricks-Teller formulation, although certain new details appear giving a more quantitative estimate of the diffraction effects. Diffraction profiles also give a very accurate measure of line broadening. Evaluation of the profiles for graphite gives the following relationship between half-width line broadening and crystal thickness: 2(sin θ ′−sin θ ″) = 0.90 λ / t , where t is the thickness of the crystal and θ ′ and θ ″ are, respectively, the values of theta at the large- and small- angle sides of the peak.

Alamosite, PbSiO 3 , has space group P 2/ n with cell parameters for the reduced cell a = 11.23 Å, b = 7.08 Å, c = 12.26 Å, and β = 113° 15′, with Z = 12. The structure has been determined using three-dimensional counterdiffractometer data. Refinement converged with R = 11.1%, including a number of reflections omitted due to extinction effects. The structure of alamosite is unique in that it consists partially of chains of tetrahedra extending parallel to [10[unk]] with a lattice translation repeat of twelve tetrahedra. The three independent Pb atoms are coordinated by 3 or 4 oxygen atoms, in each case the nearest oxygen neighbors being distributed on one side of the Pb atom, indicating covalency in Pb–O bonding. The Pb atoms and their coordinating oxygen atoms are related by an approximation to a 3 1 screw axis parallel to [010] so that they form a continuous spiral of bonded Pb, O atoms.

The relationship between lattice-types may be shown in a particularly instructive manner if W erner 's coordination theory be applied to the description of crystal structures as has already been done by P feiffer . If this be carried out in a systematic fashion and with due consideration to appropriate stoichiometric proportions between central atoms and ligands, a large group of structures is obtained the central atom of which is in the negative state of oxydation. Examples with oxygen as coordination centre confirm the value of this method for systematic purposes.

Two naturally-occurring low-iron pyrrhotite superstructures, based on the NiAs structure, have been confirmed. High-temperature precession photographs show that the transformation from the 4 C structure to the NiAs structure occurs at 225 ± 10°C and is unrelated to the magnetic transition above 300°C. A new superstructure, also based on the NiAs structure, has been produced by quenching.

The structure determined earlier from x-ray powder diffraction data has been confirmed but changed in detail by new data obtained for a tiny single crystal. Na(1) is displaced 0.4 Å into the large cavity from the center of a ring of six oxygen atoms, resulting in effective three-fold coordination with three oxygen atoms at 2.3 Å and three others at 3.0 Å. Na(2) is displaced 1 Å, nearly in the plane of the ring, from the center of a ring of eight oxygen atoms. The coordination is even more unusual with oxygen atoms at 2.5, 3.0, 3.4, 4.0 and 4.1 Å.

The atomic coordinates in Tl 2 O 3 were redetermined by neutron diffraction. They were refined by least-squares method to a R value of 0,090 including all reflections. The Tl–O distances are between 2.13 and 2.47 Å, the average of three different distances (2.26 Å) agrees with the value for six coordination.

The location of hydrogen atoms in ionic hydrates by calculations based upon energetics of crystal structures is discussed. Results are presented for two hydrates, BaCl 2 · 2H 2 O and NaBr · 2H 2 O.

On account of stacking faults occuring during growth, the cadmium iodide crystals are very frequently found to be disordered, showing ‘streaking’ on the x-ray diffraction photographs. The degree of disorder, α , of twenty CdI 2 polytypes has been evaluated according to J agodzinski 's theory of one-dimensional disorder based on the vibration entropy of crystals. The frequency-distribution curve of the polytypes shows two maxima, one for α ∼ 0.06 and the other for α ∼ 0.28. The results are in agreement with those from a similar investigation made by J agodzinski in silicon carbide, thus confirming that vibration entropy is the decisive factor in the explanation of polytypism phenomenon in crystals.

The measured x and z parameters of single-layer lizardite from Raduša chromite Mine, Yugoslavia, indicate a distortion of the basic serpentine layer similar to that found in chrysotiles. Composite crystals of lizardite from the same locality are characterized by the domains. The layers within a domain are related to those in the next one by a rotation of 60° or 180°, the number of domains in each orientation varying from crystal to crystal.

It is proved that the pgg -packing of ellipses never can have exactly the maximum density ϱ = [unk]. This maximum density is reached only, if all ellipses are parallel (= cmm -packing) or if they become circles (=closest packing of circles p 6 m ).

It is shown that a general method of approach, based on statistical considerations, can be formulated to deal with the problem of devising weighting schemes for different situations in crystal-structure analysis. This approach leads readily to the well known method of applying a weighting function for the improvement of a Fourier synthesis when a part of the structure is known. The method is applied to a new case, namely that of defining the “best Patterson” function to locate the heavy-atom vectors from a pair of isomorphous crystals. The possible application of this method of approach for the treatment of unobserved reflections is pointed out.

Fe 2 B- and Mn 4 B-type compounds are described for the first time in terms of structural frameworks of close-packed M 4 tetrahedra with ten nearest neighbors. The physical significance of the metal tetrahedra is discussed. Assignment of a quasi-spherical radius to the M 4 units enables a fairly accurate calculation of unit-cell dimensions. Various packing models leading to a coordination of ten are examined.

By generalizing the concept of OD structures (“order-disorder structures”) in spaces of any number of dimensions, structures with generalized symmetry (such as antisymmetry) may be treated. Antiferroelectric and antiferromagnetic crystals should form such OD structures. Some examples are mentioned.

Good quality natural crystals of calcium fluoride obtained from Amba Dungar mines of Chhota Udepur, Gujarat State, India, were cleaved, and a number of matched pairs were obtained. One piece from each pair was irradiated with different doses of neutrons in the swimming-pool Aspara Reactor at Trombay, India. After irradiation, the irradiated and their non-irradiated counterparts were matched. They were then etched simultaneously in 0.28 N perchloric acid for the same period. The etch patterns produced were studied optically. They were successively etched for three different periods, and the sizes and the depths of the pits on the nonirradiated and irradiated cleavages were measured. It is observed that (i) the irradiated cleavages etch at a faster rate than non-irradiated cleavages and, (ii) the rate of etching increases with increase in the dose of irradiation. A crystal plate 3.86 mm thick, irradiated with a dose of 1.3 · 10 10 n/cm 2 , was selected and cleaved into five thinner plates. All of them were etched simultaneously for the same period and the etch rate measured on them. As one proceeds within the body of the crystal it is observed that the etch rates on the faces increase with increase in the distance from the outer surface. The implications are discussed.

The application of matrix methods to the computation of Fourier syntheses of the electron density in crystals is described. Examples are given for plane group p 2 and for space group P 2 1 / c .

Calcium-fluoride cleavages obtained from natural and synthetic crystals have been etched; the etch patterns, studied with an electron microscope by preparing single-stage carbon replicas shadowed with chromium. It is observed that no correlation of the etch patterns exist on the two sides of thin plates. The electron micrographs have revealed unusual round bottomed pits, and pits with slightly deformed structure; these have been attributed to the nature of imperfections at which they are nucleated. It is observed that pits divide, and thus pits are formed within the pits. By taking electron micrographs of the etch pattern on corresponding regions of matched pairs, it is shown that there is one-to-one correspondence, in number and position, of etch pits if the division of the etch pits is ignored; nevertheless correlation in the division of the etch pits is not observed. Thus it is conjectured that there exists a dislocation network in the body of calcium fluoride. The implications are discussed.

Spiral patterns have been produced by thermally etching NaCl single crystals at 780°C for 8 hours. By drawing a schematic diagram it is shown that the spiral pattern indicates the sites of helical dislocation perpendicular to the cleavage face. Observations have been made on the spiral etch pattern to obtain the pitch, as well as the diameter, of the helical-dislocation cone. The calculated pitch and the diameter of the helix are 0.4 μ and 6 μ respectively.

l (+)-cysteine hydrochloride monohydrate crystallizes in the space group P 2 1 2 1 2 1 , with a = 19.48 Å, b = 7.12 Å, c = 5.52 Å. The structure was determined in projections and refined with three-dimensional data to R = 0.124 for observed reflections. Interesting features of the structure are, ( a ) a possible S–H···Cl bond, the sulfur atom acting as a donor and, ( b ) the carboxyl-oxygen atom O(2) not taking part in hydrogen bonding. The molecule assumes a nonzwitterion form. Its conformation, relative to other similar sulfur-containing amino acids, is discussed.