Determination of unit-cell parameters of single crystals from rotation patterns

1974 ◽  
Vol 7 (2) ◽  
pp. 291-292 ◽  
Author(s):  
S. Popović
2020 ◽  
Vol 84 (5) ◽  
pp. 699-704
Author(s):  
Luca Bindi ◽  
Andrew C. Roberts ◽  
Cristian Biagioni

AbstractAlstonite, BaCa(CO3)2, is a mineral described almost two centuries ago. It is widespread in Nature and forms magnificent cm-sized crystals. Notwithstanding, its crystal structure was still unknown. Here, we report the crystal-structure determination of the mineral and discuss it in relationship to other polymorphs of BaCa(CO3)2. Alstonite is trigonal, space group P31m, with unit-cell parameters a = 17.4360(6), c = 6.1295(2) Å, V = 1613.80(9) Å3 and Z = 12. The crystal structure was solved and refined to R1 = 0.0727 on the basis of 4515 reflections with Fo > 4σ(Fo) and 195 refined parameters. Alstonite is formed by the alternation, along c, of Ba-dominant and Ca-dominant layers, separated by CO3 groups parallel to {0001}. The main take-home message is to show that not all structure determinations of minerals/compounds can be solved routinely. Some crystals, even large ones displaying excellent diffraction quality, can be twinned in complex ways, thus making their study a crystallographic challenge.


2021 ◽  
Vol 62 (5) ◽  
Author(s):  
П.C. Серебренникова ◽  
В.Ю. Комаров ◽  
А.С. Сухих ◽  
С.А. Громилов

2020 ◽  
Vol 105 (3) ◽  
pp. 353-362
Author(s):  
Katarzyna Luberda-Durnaś ◽  
Marek Szczerba ◽  
Małgorzata Lempart ◽  
Zuzanna Ciesielska ◽  
Arkadiusz Derkowski

Abstract The primary aim of this study was the accurate determination of unit-cell parameters and description of disorder in chlorites with semi-random stacking using common X-ray diffraction (XRD) data for bulk powder samples. In the case of ordered chlorite structures, comprehensive crystallographic information can be obtained based on powder XRD data. Problems arise for samples with semi-random stacking, where due to strong broadening of hkl peaks with k ≠ 3n, the determination of unit-cell parameters is demanding. In this study a complete set of information about the stacking sequences in chlorite structures was determined based on XRD pattern simulation, which included determining a fraction of layers shifted by ±1/3b, interstratification with different polytypes and 2:1 layer rotations. A carefully selected series of pure Mg-Fe tri-trioctahedral chlorites with iron content in the range from 0.1 to 3.9 atoms per half formula unit cell was used in the study. In addition, powder XRD patterns were carefully investigated for the broadening of the odd-number basal reflections to determine interstratification of 14 and 7 Å layers. These type of interstratifications were finally not found in any of the samples. This result was also confirmed by the XRD pattern simulations, assuming interstratification with R0 ordering. Based on h0l XRD reflections, all the studied chlorites were found to be the IIbb polytype with a monoclinic-shaped unit cell (β ≈ 97°). For three samples, the hkl reflections with k ≠ 3n were partially resolvable; therefore, a conventional indexing procedure was applied. Two of the chlorites were found to have a monoclinic cell (with α, γ = 90°). Nevertheless, among all the samples, the more general triclinic (pseudomonoclinic) crystal system with symmetry C1 was assumed, to calculate unit-cell parameters using Le Bail fitting. A detailed study of semi-random stacking sequences shows that simple consideration of the proportion of IIb-2 and IIb-4/6 polytypes, assuming equal content of IIb-4 and IIb-6, is not sufficient to fully model the stacking structure in chlorites. Several, more general, possible models were therefore considered. In the first approach, a parameter describing a shift into one of the ±1/3b directions (thus, the proportion of IIb-4 and IIb-6 polytypes) was refined. In the second approach, for samples with slightly distinguishable hkl reflections with k ≠ 3n, some kind of segregation of individual polytypes (IIb-2/4/6) was considered. In the third approach, a model with rotations of 2:1 layers about 0°, 120°, 240° was shown to have the lowest number of parameters to be optimized and therefore give the most reliable fits. In all of the studied samples, interstratification of different polytypes was revealed with the fraction of polytypes being different than IIbb ranging from 5 to 19%, as confirmed by fitting of h0l XRD reflections.


2014 ◽  
Vol 70 (4) ◽  
pp. 1115-1123 ◽  
Author(s):  
Christian G. Frankaer ◽  
Olga V. Moroz ◽  
Johan P. Turkenburg ◽  
Stein I. Aspmo ◽  
Majbritt Thymark ◽  
...  

A microcrystalline suspension ofBacillus lentussubtilisin (Savinase) produced during industrial large-scale production was analysed by X-ray powder diffraction (XRPD) and X-ray single-crystal diffraction (MX). XRPD established that the bulk microcrystal sample representative of the entire production suspension corresponded to space groupP212121, with unit-cell parametersa= 47.65,b= 62.43,c= 75.74 Å, equivalent to those for a known orthorhombic crystal form (PDB entry 1ndq). MX using synchrotron beamlines at the Diamond Light Source with beam dimensions of 20 × 20 µm was subsequently used to study the largest crystals present in the suspension, with diffraction data being collected from two single crystals (∼20 × 20 × 60 µm) to resolutions of 1.40 and 1.57 Å, respectively. Both structures also belonged to space groupP212121, but were quite distinct from the dominant form identified by XRPD, with unit-cell parametersa= 53.04,b = 57.55,c= 71.37 Å anda= 52.72,b= 57.13,c= 65.86 Å, respectively, and refined toR= 10.8% andRfree= 15.5% and toR= 14.1% andRfree= 18.0%, respectively. They are also different from any of the forms previously reported in the PDB. A controlled crystallization experiment with a highly purified Savinase sample allowed the growth of single crystals of the form identified by XRPD; their structure was solved and refined to a resolution of 1.17 Å with anRof 9.2% and anRfreeof 11.8%. Thus, there are at least three polymorphs present in the production suspension, albeit with the 1ndq-like microcrystals predominating. It is shown how the two techniques can provide invaluable and complementary information for such a production suspension and it is proposed that XRPD provides an excellent quality-control tool for such suspensions.


2013 ◽  
Vol 28 (3) ◽  
pp. 194-199 ◽  
Author(s):  
James A. Kaduk ◽  
Thomas N. Blanton

A sample of cellulose II, prepared by deacetylation of cellulose acetate, has permitted more precise determination of the unit-cell parameters by the Rietveld method. Cellulose II is monoclinic, with space group P21c-axis unique (or P1121) (No. 4) and refined unit-cell parameters a = 8.076(13), b = 9.144(10), c = 10.386(20) Å, γ = 117.00(8)°, and V = 683.5(18) Å3. A density functional geometry optimization using these fixed unit-cell parameters has resulted in an improved structural model for cellulose II. A powder pattern calculated from this new model has been submitted to the ICDD for inclusion in future releases of the Powder Diffraction File.


1992 ◽  
Vol 25 (2) ◽  
pp. 294-308 ◽  
Author(s):  
P. D. Carr ◽  
D. W. J. Cruickshank ◽  
M. M. Harding

A method is described whereby the unit cell of a crystal and its orientation can be determined from a single Laue diffraction pattern (in transmission). The axial ratios and interaxial angles can be determined precisely, but the absolute scaling of the cell depends upon the accuracy with which the minimum wavelength for the experiment is known. Several examples are given.


1983 ◽  
Vol 16 (1) ◽  
pp. 99-102 ◽  
Author(s):  
O. S. Mayall

The f.c.c. + tetragonal two-phase region of the Cu–Ni–Zn system has been delineated, and unit-cell parameters along the boundaries determined. Apparently anomalous parameter measurements prevented the determination of the tie lines. A pattern of diffraction broadening from the tetragonal phase common to both the two-phase and single-phase regions was related to the variation in lattice spacing of the tetragonal phase along the boundary. Reasons for this broadening are discussed.


1998 ◽  
Vol 13 (1) ◽  
pp. 22-31
Author(s):  
Ludo K. Frevel

Combining the exhaustive indexing of triclinic powder diffraction patterns with a crystallographic determination of unit cell parameters from pinacoid and prism reflections yields unit cell parameters with realistic limits of error. Additionally a referee method has been developed by which the six reciprocal cell parameters of a triclinic phase are determined by solving an exhaustive set of linear simultaneous equations in six unknowns.


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