Band 129, Heft 5-6

Crystals of Zn(NO 3 ) 2 · 2H 2 O were prepared by evaporation of ZnO solutions in HNO 3 (fuming). The crystals are monoclinic with a = 5.754 ± 0.006, b = 5.978 ± 0.005, c = 8.557 ± 0.005, β = 91°2′ ± 20′ and Z = 2 formula units per unit cell. The space group is P 2 1 / c – C 2 h 5 . The crystal has been refined by least-squares calculations to a final R value of 9.3 %. Hydrogen atoms were located by difference syntheses. The zinc atoms are surrounded by a distorted octahedron composed of four oxygen atoms belonging to the nitrate ions and of two oxygen atoms belonging to two water molecules. The zinc-oxygen distances have values between 2.03 and 2.22 Å, the N–O distances are 1.22, 1.23 and 1.24 Å. Zinc nitrate dihydrate has a layer structure. The layers are parallel to (100) and are linked together by hydrogen bonds (2.93 Å). Each H 2 O molecule forms two hydrogen bonds with oxygen atoms of the nitrate groups (2.84, 2.93 Å).

The structure of interstitial solid solutions in zirconium-oxygen alloys over the composition range 15.0 to 28.5 at.% O has been studied using x-ray, neutron and electron diffraction techniques. The superstructure observed in alloys of 25.0 to 28.5 at.% O corresponds to that observed by H olmberg and D agerhamn . A different ordered arrangement which can be described in terms of a one-dimensional long-period superstructure occurs in alloys of 15.0 to 25.0 at.% O with a periodicity which increases with oxygen content. In alloys of 25.0 at.% O, both types of ordered arrangements occur, separately and coexisting, depending on heat treatment.

The twinning of tetragonal leucite (Albano, Italy) has been studied by means of high-temperature precession photographs. Reciprocal-lattice points on both sides of the diagonal net plane are shifted in the two opposite directions, in such a way that the tetragonal symmetry of the lattice remains, when the temperature decreases from ca. 650°C. There are two possibilites in the direction of the shift. These two possibilities are realized separately and with the same a priori probabilities in the crystals.

The stress-optical coefficients C λ 1 = ( n 3 /2) ( q 11 – q 12 ), C λ 2 = ( n 3 /2) ( q 11 – q 13 ) and C λ 3 = ( n 3 /2) q 44 of the alums CH 3 NH 3 Al(SO 4 ) 2 · 12H 2 O (MASD), CH 3 NH 3 Al(SeO 4 ) 2 · 12H 2 O (MASeD) and CsAl(SO 4 ) 2 · 12H 2 O were measured over the range of wavelengths from 250 to 580 μ m, and those of CsFe(SO 4 ) 2 · 12H 2 O were measured over the range of 400 to 580 μ m, by a general intensity method which has been developed by the author. These coefficients exhibit large dispersion in the ultraviolet in the case of the first three alums. Besides, these crystals which belong to class m 3 are found to become negative biaxial under a stress along a cube edge; the dispersion of the optic-axial angle with wavelength is clearly established. The trend of the dispersion curves suggests that at still shorter wavelengths the first two of these alums may behave as positive biaxial.

X-ray investigations of (Mn 1– x Fe x ) 2 O 3 show that for all x ≦ 0.38 the bixbyite structure is not correct. Near x = 0.01 occurs a structural transition. Probable space groups are P 2 1 3– T 4 for x < 0.01 and I 2 1 3– T 5 for x > 0.01.

Single crystals of one form of β Ta 2 O 5 and of the A form of KPO 3 have been grown. The unit-cell dimensions have been determined, and x-ray and morphological data in combination allowed a unique space-group assignment for both: Pna 2 for β Ta 2 O 5 and R [unk] for A KPO 3 .

A peak-search technique has been developed and evaluated for an automatic diffractometer. The instrument is a Buerger-Supper diffractometer with analyzing electronics and is driven through an IBM 1710 control computer. Indices and angular settings are precomputed and stored. After stepping to γ ( hkl ) and ϕ ( hkl ), 0.5 second counts are made at fixed increments of Δϕ on either side of the computed ϕ positions. From the ϕ search, scan rates and background-counting times are computed to give desired accuracy. The peak width and background positions are determined from second-order differences and curvatures computed from the peak half-height outward on either side of the peak. The background positions are accurately located on the radiation streak at all 2 θ angles with an ω search and it is not necessary to use monochromators or balanced filters. A check method uses the search data to compute an alternate width to be used if necessary when μ / γ is large or when peak shapes are unusual. The ϕ search data is used to select optional modes of measurement for an individual reflection based on the integrated peak to background ratio, R . Moderate-to-intense peaks are scanned. Weak peaks ( R < 1.5) may either be scanned, or peak intensities may be measured and converted to integrated intensities by interpolation. Very weak or unobserved peaks are scanned over the entire search range. The ϕ search data also yields exact ϕ values of the peaks for cell-dimension refinement. The γ search, an optional procedure, causes correction of errors in the γ setting and gives precise values for γ . The search data and error-corrective procedures allow unrefined cell dimensions to be used, hence speeding the data collection. Measurement of test data indicates that, if an ω of ϕ search only is performed, the data-collection rate for a given accuracy is at least as fast as the rate without the search and with fixed scan times. When searching over two angles, the data collection rate is reduced by about 20 percent to about 27 reflections per hour with a medium-to-large crystal.

Three-dimensional intensities were collected on a coesite crystal from the same synthetic material which was used for the original structure determination 1 . The structure was refined with least-squares methods, giving a final R value of 7.6%, slightly different atomic positions and more significantly changed thermal data than originally obtained.

The relation of the probability factors defining an interstratified structure and Reichweite is described. The m th s-t transition probability P st ( m ) and the short-range order parameter σ ( m ) are proved to be shown by [unk]. Some model buildings of the interstratified structure for g = 1 and g = 2 are tried by using the electronic computer.

At room-temperature γ Na 2 Si 2 O 5 is monoclinic, pseudotetragonal with the lattice constants a = 23.46 4 Å, b = 7.08 7 Å, c = 26.12 0 Å, β = 116°41′ and 8 formula units in the pseudotetragonal cell. Due to disorder there was no possibility to distinguish between the space groups Pc – C s 2 or P 2/ c – C 2 h 4 and P 2 1 / c – C 2 h 5 . The pseudotetragonal symmetry is I 4 1 / a – C 4 h 6 . One of the high-temperature forms of γ Na 2 Si 2 O 5 probably is tetragonal. A new orthorhombic modification of sodium disilicate, δ Na 2 Si 2 O 5 , was found with a = 12.07 0 Å, b = 8.37 5 Å, c = 4.84 0 Å, Z = 4. The space group is Pnmm – D 2 h 13 or Pn 2 1 m – C 2 v 7 . Whereas structural relations are to be expected between δ and β Na 2 Si 2 O 5 , such relations to silicate structures with “Zweiereinfachschichten” cannot be deduced simply from lattice constants for the γ modification.

Two structural propositions of vaterite are examined using infrared spectroscopy. The carbonate ion has C s -site symmetry in the structure presented by M eyer (1959), but C 2 v according to K amhi (1963). Observed infrared spectra are characterized by (1) the activation and splitting of v 1 and (2) the splitting of v 3 , which support C 2 v symmetry.

The values of bond lengths are in most instances reasonably well known and can be predicted with some certainty. The direct use of this information in structure analyses has been found particularly useful in studies of aluminosilicate structures. The interatomic distance D is a function only of the coordinates of the atoms involved and the unit-cell constants. With framework structures it is found that the number of crystallographically independent interatomic distances exceeds the number of coordinates to be determined. Therefore, given an approximate initial solution, it is possible to compute the coordinates of framework atoms by means of least-squares adjustments of interatomic distances to prescribed values. The refined coordinates found thereby define an idealized structure with respect to prescribed interatomic distances (and fixed unit-cell constants) which is called the D structure. A general computer program has been developed for these refinements. D refinement can be applied to the analysis of pseudosymmetric framework structures, i.e. the lowering of the symmetry in structure determinations. Fourier maps of the initial high-symmetry structure yield the magnitudes but not the signs of the atomic displacements from the high-symmetry positions. The probable signs of the displacements may be obtained by D refinement. Other applications of D refinement include the calculation of reasonably accurate trial coordinates and the determination of possible Si/Al distributions in aluminosilicate frameworks. We have noted that whenever D refinement has not proceeded, either the trial structure or the assumed symmetry has been incorrect.

A KCl-quadruplet is described, which was observed during an investigation on whisker-growth. The fourfold axis of twinning is parallel to [211].

The crystal structure of the garnet {Mn 3 }[Fe 2 ](Ge 3 )O 12 has been refined by least-squares calculations applied to single-crystal data collected with a Buerger-Supper-Pace-Picker automatic diffractometer. The Ge–O distance is 1.77 ± 0.02 Å (limits of error), about 0.03 Å longer than the Ge–O distance in quartz-type GeO 2 . This is in accord with the analogous Si–O distances. The Fe–O distance is 2.00 ± 0.02 Å in good agreement with the analogous distance in three iron garnets. The Mn–O distances are 2.30 and 2.42 ± 0.02 Å. The structural results are in accord with the absence of ferrimagnetism in the {Mn 3 }[Fe 2 ](Ge 3 )O 12 garnet.

The theoretical results concerning the normalized discrepancy index and other statistical parameters such as correlation functions are tested on hypothetical models in projection. Some practical aspects of using these parameters, in particular, the normalized discrepancy index are discussed. Graphical methods have been developed for the estimation of errors in the coordinates of atoms which form only a part of the structure.

New photographic data have been obtained for intermediate plagioclase both at temperature and after cooling. When considered with earlier observations, these confirm that at temperatures up to about 1000°C immediate reversible changes can be observed in the diffraction pattern; at higher temperatures permanent changes in the pattern are induced. A tentative structural interpretation of the two ranges of behaviour is outlined.