Volume 115, Issue 3-4

With the axial ratios a : b : c = 0.8676: 1: 0.9585, the morphological space group of phosphoferrite-reddingite (Fe 2+ , Mn) 3 (PO 4 ) 2 · 3H 2 O – (Mn, Fe 2+ ) 3 (PO 4 ) 2 · 3H 2 O on re-examination is found to be P ( m or n ) nb , contrary to previous reports. The structural space group, redetermined by the precession method (M rose , priv. comm.), also differs from previous results and is Pcnb . The difference between morphological and structural symmetries lies only in the nature of the symmetry planes (100). In the bc projection the mesh ( b , c ), already halved along c by the effect of the c glide plane, must also be halved along b by fortuitous values of atomic coordinates. The mesh ( b /2, c /2) is a pseudomesh of the projected structure, it is a true mesh of the projected bond assemblage.

In addition to the frequently used relation [unk] the following one is applicable to iso-electronic pairs of equivalent ions: [unk] The factor K has a constant mean value 0.778 for all monovalent ions resembling the noble gases. The corresponding value for bivalent ions resembling the noble gases is 0.689. It follows that the relation given below holds for two pairs I and II of iso-electronic ions having the same valency: [unk] This relation makes possible the direct calculation of all four ionic radii from the ionic distances of the four compounds in question without knowledge of a basic radius. Ionic radii for the halides of the alkalis and alkaline earths calculated solely from the ionic distances and according to the last-named equation agree satisfactorily with the subtractively or theoretically computed action radii of the ions as given by G oldschmidt , P auling or Z achariasen and hitherto used in crystal chemistry.

The lack of fast convergence sometimes encountered during a least-squares refinement can be attributed to two factors that may be present in addition to the interaction of two or more parameters. One may be caused by the linear approximation of the structure-amplitude function, which actually may have appreciable curvature. This can be eliminated by a damping factor computable from the experimental data. Another possible cause contributing to retarded convergence is related to an“image” atom symmetrical to the real atom with respect to the extreme of the structure-amplitude function. This effect can be eliminated by the selection of data according to a criterion developed in this paper. These approaches should lead to a maximum rate of convergence within a range of 2 πhΔx i that is nearly as large as the maximum possible range inherent in the basic premises of the technique.

The infra-red spectra of layer structures synthesized under controlled high-temperature, high-pressure conditions in sealed noble-metal systems have been examined in the region 400–5000 cm −1 (25–2 μ ). By complete replacement of an ion, e.g., Mg 2+ by Ni 2+ or Fe 2+ , Al 3+ by Ga 3+ or Fe 3+ , and Si 4+ by Ge 4+ it was possible to assign the main absorption bands of layer-structure silicates. Bands involving various OH-vibrations were located by complete replacement of OH − by OD − . The results obtained in this study suggest certain other relations between the bonds involved and IR spectra of the complex crystalline phases.

Estimates are made of the single-bond and double-bond oovalent radii of V (V) and of the corresponding V–O bond lengths for tetrahedral, five-fold, and octahedral coordination of O around V. The possible nature of the V–O bonds in V 2 O 5 and in other structures containing pentavalent vanadium is discussed.

The notions Colour-Symmetry Group and Colour Group are defined. A simple method is given, by which all possible colour groups corresponding to a given symmetry group can be found.

By condensation on hot substrates and by annealing above 204°C selenium crystallizes in the direction of the chain molecules (needles, crystals like round paving-stones). From the fluid or amorphous phase selenium crystallizes perpendicular to the chain molecules (biconvex crystals, fibrilles, spherulithes). The biconvex crystals are macroscopical examples for crystal seeds of substances consisting of chain molecules. They may become cores of spherulithes if the growth proceeds in a sheaf-like manner. In thin layers rows of fine fibrilles are formed by trans-crystallization at about 115°C. Such layers show a fibre texture ([100] – fibre axis). The plane of cleavage is (10[unk]0).

The measurement of integrated intensities directly by conventional diffraction arrangements is not possible because the specimen crystals are normally smaller than the incident beam cross section. If a micro-source and a bent-crystal monochromator are used, however, the crystal can be made to intercept the entire incident beam and it is possible to measure the integrated intensity for all reflections. It is also shown how the necessary geometrical conditions for several arrangements can be satisfied.

Formulae are derived for calculating the differences in density between an heterogeneous mixture of elements and an ordered phase of the same chemical composition. The parameters used were the degrees of space-filling of the appropriate crystal lattices and the changes in shortest distances between atoms. The latter magnitude served as a measure of changes in the size of the atoms. A detailed discussion for Laves phases using a previously derived formula for changes in atomic distances shows that an increase in density as compared to the elementary state is characteristic of the group of Laves phases. It may, therefore, be assumed that an increase in stability goes hand in hand with this rise in density.

Abstraft As a part of a detailed study of the structures and crystal chemistry of the aluminum silicate minerals the crystal structure of andalusite, Al 2 SiO 5 , has been refined. Twelve cycles of least-squares refinement on the IBM 704 computer reduced the disagreement factor, R , for 354 hkl reflections from an initial value of 43.9% to a final value of 5.7%. The original structure determined by T aylor 1 was found to be fundamentally correct. Chains of aluminum octahedra sharing edges lie parallel to the c axis. These octahedra depart appreciably from regularity; two of the Al-O bond distances are 1.83 Å, two are 1,89 Å, and the two Al-O distances normal to the c axis are 2.09 Å. The octahedral chains are linked together by a framework of silicon tetrahedra and five-coordinated aluminum groups. The Si-O bond distances are 1.64 Å, 1.62 Å, 1.63 Å, and 1.63 Å. The Al-O bond distances in the five-coordinated group are 1.82 Å, 1.82 Å, 1.82 Å, 1.84 Å and 1.88 Å. The five-coordinated groups occur in pairs sharing an edge whose length is 2.25 Å.

B ridgman's AgNO 3 II crystallizes in the hexagonal (rhombohedral) system with a unit cell of a rh = 6.427 Å, α rh = 23° 52′. The rhombohedral unit cell contains 2AgNO 3 , and the calculated density at 164°C is 4.237 g/cm 3 . AgNO 3 II melts at T = 9.1 P + 212°C, where P is the pressure in kilobars ( P < 15).

X-ray investigation of numerous inclusion compounds showed, that many of the adducted organic components, especially relatively long-chain aliphatic compounds, are “crystallized” within the urea host. Several types of “guest structures” were observed, as well as transitions between those arrangements of parallel molecule rows without phase relations and those with a three-dimensional order. In addition many superstructure phenomena were found connected with changes in the normal urea host structure. All inclusion compounds of dicarboxylic acids investigated till now have molecular ratios which can be expressed by relatively small integers.

CoSO 4 · H 2 O crystallizes in the monoclinic system with a unit cell of a = 7.502 Å, b = 7.518 Å, c = 6.970 Å, β = 115°59′. The unit cell contains 4[CoSO 4 · H 2 O], the space group is A 2/ a − C 2 h 6 and the calculated density is 3.253 g/cm 3 .

R umanova and S kipetrova (1959) have described the structure of lawsonite in Ccmm . R umanova and B elov (1960) have shown that even the structure described by W ickman (1947) in the space group C 222 1 has this symmetry, a fact unnoticed by both W ickman and P abst (1959). Thus the supposed “false symmetry” of lawsonite is its true symmetry. P abst's example could at most be considered a hypothetical one and even that only if O II and O III of W ickman were non-equivalent, as by a parameter shift of one of these. B arclay and C ox (1960) have commented on the improbable Si-O distances in the Wickman structure. These are slightly improved in the R umanova and S kipetrova structure.

Reflections which are expected to be extinguished due to the “false symmetry effect” may be observed in favourable cases if the electronic density distribution does not follow exactly the false symmetry.

In a recent publication B urnham and B uerger 1 have described a very detailed refinement of the crystal structure of andalusite. This new work confirms and extends results obtained by less sophisticated methods in 1939 2 , which had not come to the notice of B urnham and B uerger .

In experiments on the etching of cadmium iodide crystals, convincing evidence has been obtained that an etch-pit is preferentially created at the site of a dislocation. Spiral steps are clearly seen along with the etch-pit. A tentative explanation is suggested.