Cell constants, diffraction

The two structurally similar polymorphs of (R,S)-ethambutol dihydrochloride have been shown to bear an enantiotropic relationship, and can reversibly interconvert in a single crystal transformation mode [27]. It was reported that despite the identity in space group type and similarity in unit cell constants, the two forms could be distinguished on the basis of their X-ray powder diffraction and solid-state nuclear magnetic resonance properties. Interestingly, while the (polymorphic forms, the (R,S)-diastereomer was only obtained in two different polymorphs. 

The unit cell constant of the zeolites were determined by X-ray diffraction using CuKo( radiation and following ASTM procedure D-3942-80. The estimated standard deviation was - 0.01 A. The... 

Effect of Steam Treatment. X-ray diffraction analyses indicated that ZSM-5 retained in excess of 90% of its crystallinity after the steam treatment described in the methods section. Unit cell constant of the REY zeolite in Super-D declined from 24.658. to 24.38a due to the steam treatment. Independent measurements... 

The crystal chemistry of BajRC C has been systematically studied by single-crystal and powder diffraction methods with R = La, Pr,... Yb, in addition to the conventional yttrium compound [(52)(53) (54) and references therein]. With the exception of La, Pr, and Tb, the substitution of Y with rare-earth metals has little or no effect on the superconductivity, with the values of Tc ranging from 87 to 95K. Also, a relatively small change is observed in the cell constants of these compounds. The La, Pr, and Tb-substituted materials are not superconductors. A detailed structural analysis of the Pr case (52) did not show any evidence of a superstructure or the presence of other differences with the atomic configuration of the yttrium prototype. 

Several octahedral crystals were ground to powder and studied by the Guinier-Hagg technique (Cu radiation). All diffraction lines could be indexed on the basis of a cubic cell with a = 4.560 0.001 A., which is within experimental error of that reported previously for MnSi, 4.558 0.001 A.2 In view of the similarity of the cell constants of the ground crystals to those of previous preparations, significant replacement of manganese by copper is not indicated. This was checked on a few crystals by emission spectrographic analysis which indicated an upper limit of ca. 1% of copper. 

Kistenmacher and Marsh determined the crystal and molecular structure of indomethacin by single crystal x-ray diffraction methods(23). Although not explicitly stated by Kistenmacher and Marsh, the crystals grown from anhydrous acetonitrile are most likely Form I. They reported that the crystals are triclinic, space group PI, with cell constants a = 9.295(2)A, b = 10.979(1)A, C = 9.742(1)A,... 

The x-ray diffraction patterns were made with a Picker diffractometer, using Ni-filtered CuK radiation and glass-slide mounts. To derive accurate unit cell constants, slow-scan x-ray patterns were internally standardized with NaCl, KC1, or Si. The integrated intensities were obtained by measuring the area under each peak with a planimeter. 

Takaki Y., Taniguchi T., Nakata K. and Yamaguchi H., Program for Finding the Unit-cell Constants and the Space Group from X-ray Powder Diffraction Data - The Case Where Approximate Unit-cell Contants are Known, J.Ceram. Soc. Jpn., 97 (1989)pp.763-766. 

Nonstoichiometry is a pervasive aspect of oxide chemistry, particularly where the cation can assume two or more valences or aliovalent cation substitutions are facile. These can be classified into three rather broad ranges. Class 1 includes systems where the nonstoichiometry approaches or exceeds that which caimot be detected by classical methods of chemical analysis (i.e., less than 1 part in 1000) but may manifest itself in dramatic changes in electrical or optical properties. Class n includes systems where the nonstoichiometry is of the order of several mole % and readily discernible by chemical analysis, density measurements, or X-ray diffraction measurements of unit cell constants. Class 111 are those systems with broad ranges of nonstoichiometry such as the alkah metal tungsten bronzes. 

The determination of previously unknown unit cell constants (viz., a, b, c, a, (i, y) from the various interlayer spacing values obtained from the powder diffraction profile... 

There have been a number of reports of polymorphic systems in which the reader might be led to expect some similarity in the powder pattern of two polymorphs because they crystallize in the same space group. There is no physical basis for this expectation. Except for the systematic absences of certain reflections due to space group symmetry polymorphic structures in the same space group and different cell constants will have different powder diffraction patterns. On the other hand, polymorphs with similar cell constants but different space groups may exhibit some similarity in X-ray powder diffraction patterns, but these cases are very rare vide infra). See also Section 2.4.3. 

Herbstein (2001). The cell constants forthe reduced cell are based on those reported by Colapietroet aZ. (1984) and DomenicanocZaZ. (1990) (for Form 1) and by Fischer et al. (1986) (by neutron diffraction) for Form II. Since they follow the convention for reporting reduced cells (International Tables 1987) they appear in a different order from the original also by convention the cell angles are defined as acute. 

Hexanitrophenylamine HND, although toxic, has been employed in underwater explosives together with TNT and aluminium powder (Meyer 1987). Two polymorphs were characterized by McCrone (1952), including a listing of the X-ray powder diffraction lines for Form I, which he determined to be orthorhombic, with cell constants essentially matching those reported later by Dickinson and Holden (1977). The latter also apparently carried out the structure analysis (CSD Refcode HNIDPA) but no coordinates are given. 

Earlier, we had reported the exchange of benzene with benzene-dg in the channels of 6 without the destraction of crystallinity. We have extended this study to other guests like toluene, m-xylene, undecane, benzyl alcohol, 2,6-di-ten-butylphenol and ( )-l-phenylethanol."" Cell constants determined by X-ray powder diffraction after exchange were close to the original cell constants. Optical micrographs showed that there was no dissolution and reformation of the crystals during the period of exchange. 

A process even more challenging than structure determination is the prediction of a crystal structure without the use of experimental information relevant to that particular structure. This process, called crystal structure prediction CSP), would allow one to announce a crystal structure before any confirmation by chemical synthesis or discovery in nature. The outcome of CSP is the prediction of the atomic coordinates of the structural model, together with the space group and cell constant specifications. The relation of CSP with powder diffraction relies on the fact that a powder pattern can be calculated using this outcome, which could further be used to identify a real compound not yet characterized. 

If Miller indices can be assigned to the various reflections in the powder pattern, it becomes possible to determine the cell constants. This assignment is readily achieved for cubic crystal systems with a simple relationship between the diffraction angles and lattice parameters. 

Powder diffraction patterns can be indexed to determine cell constants in simple crystal systems. 

Bragg s equation gives an easy way to understand XRPD. Powder X-ray diffraction data collected on crystalline samples gives information about peak intensities and peak positions. Peak intensities are determined by the contents of unit cells, and peak positions are closely related to the cell constants. Interplanar spacing is a function of Miller indices and cell constants. Therefore, if the cell constants are known for a crystalline compound, peak positions corresponding to Miller indices can be obtained from the Bragg s equation the wavelength. A, is machine-specific. The determination of cell parameters in structure determination of XRPD pattern is a reverse process to find cell constants from peak positions. Here, note that the cell constants for a unit cell are not affected by the contents in the unit cell. The contents in the unit cell have effects on the peak intensities. 

Characterization of Samples. Powder diffraction patterns of the samples were obtained with a Philips diffractometer using monochromated high-intensity CuKai radiation (X = 1.5405A). For qualitative identification of the phases present, the patterns were taken from 12° < 20 <72° with a scan rate of 1° 20/min and a chart speed of 30 in/hr. The scan rate used to obtain x-ray patterns for precision cell constant determination was 0.25° 20/min with a chart speed of 30 in/hr. Cell parameters were determined by a least-squares refinement of the reflections. 

Knowing the unit cell constants and the orientation of the crystal in the x-ray beam, each spot or reflection observed in the diffraction pattern can be defined using the Miller indices corresponding to the set of lattice planes that produced the reflection. There is a reciprocal relationship between the diffraction angle and the spacing between the lattice planes df, in the crystal. Thus, crystals with larger unit cells, such as proteins, will produce a more dense diffraction pattern than that of salt crystals or other small molecules with much smaller unit cells. 

The compound Cs2[Pt(CN)4]Cl0.3 prepared by either method above forms fine, needlelike crystals which are metallic bronze in color. X-Ray diffraction data on both crystals yield identical cell constants and indicate the unit cell to be body-centered tetragonal11 a = 13.176(2) A, c = 5.718(1) A, and V = 992.7 A.3 Experimental confirmation of the calculated density of 3.889 g/cm3 was not possible for lack of a suitable solvent. 

---