Accurate Determination of Unit-Cell Parameters using Conventional X-Ray Powder Diffractometry

1991 ◽  
Vol 35 (A) ◽  
pp. 431-438
Author(s):  
Hideo Toraya ◽  
William Parrish

AbstractA procedure for the accurate determination of unit-cell parameters using conventional Xray powder diffractometry is described. Two important factors in the procedure are: 1) the use of high-resolution-type diffractometer, which can suppress the axial beam divergence and thus gives nearly symmetric diffraction profiles in the low 2θ region and 2) the use of a new algorithm for systematic peak shift correction during the least-squares determination of unit-cell parameters of a sample with an internal standard [Toraya & Kitamura (1990). J. Appl. Cryst. 23 , 282-285]. The procedure has been tested by measuring successively the unit-cell parameter of W, CeO2, and Si in three mixtures, Si+W, W+CeO2, and CeO2+Si: the unit-cell parameter of W, which was first determined by using NIST SRM 640b Si powder as an internal standard reference material, was used as a standard reference value to determine the unit-cell parameter of CeO; in the next W+CeO2 mixture, and so on. The difference between the end value of observed Si unit-cell parameters and the starting value of 5.430940(35) Å were just 1 to 5 p.p.m. High accuracy is attainable in measuring the uni-cell parameters even with the conventional powder diffractometry provided with the nearly symmetric diffraction profile and the algorithm for peak shift correction used in the present study.

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.


1994 ◽  
Vol 9 (4) ◽  
pp. 272-279 ◽  
Author(s):  
H. Toraya ◽  
T. Ochiai

The accuracy of the unit-cell parameters refined by using the whole-powder-pattern decomposition method is discussed. Powders of W, ZnO, TiO2, BaTiO3 Mg2SiO4, Al2SiO5 (+α-SiO2), and monoclinic ZrO2 were used as test samples. Two internal standard reference materials of Si and CeO2 and two types of powder diffractometers were used for data collections. The systematic peak-shift was corrected by determining the unit-cell parameters and the error function simultaneously during the whole-pattern-fitting. The estimated standard deviations for sample means ranged from <10 ppm (10−6) in cubic symmetry to 20∼50 ppm in monoclinic symmetry. These analyses could be carried out almost automatically in a computation time of less than l min for each sample on a workstation. The use of symmetric experimental profiles, obtained by the suppression of axial divergence, is very effective and of essential importance for improving the accuracy of unit-cell parameters.


1987 ◽  
Vol 2 (4) ◽  
pp. 225-226
Author(s):  
Peter Bayliss ◽  
Slade St. J. Warne

AbstractMagnesium-chlorophoenicite may be differentiated from the Mn-analogue chlorophoenicite, because for magnesium-chlorophoenicite at 7Å, whereas for chlorophoenicite.In a review of the literature for the Mineral Powder Diffraction File by Bayliss et al. (1980), powder X-ray diffraction data could not be found of the mineral species magnesium-chlorophoenicite, (Mg,Mn)3Zn2(AsO4)(OH,O)6. Dunn (1981) states that the powder X-ray diffraction data of magnesium-chlorophoenicite is essentially identical to that of chlorophoenicite (Mn analogue) and confirms that the minerals are isostructural.With the crystal structure parameters determined by Moore (1968) for a Harvard University specimen from New Jersey of chlorophoenicite, a powder X-ray diffraction pattern was calculated with the programme of Langhof, Physikalische Chemie Institute, Darmstadt. The calculated pattern was used to correct and complete the indexing of the powder X-ray diffraction data of chlorophoenicite specimen ROM M15667 from Franklin, Sussex County, New Jersey, U.S.A. by the Royal Ontario Museum (PDF 25-1159). With the correctly indexed data of ROM M15667, the unitcell parameters were refined by least-squares analysis and are listed in Table 1.The most magnesium-rich magnesium-chlorophoenicite found in the literature is a description of Harvard University specimen 92803 from Franklin, Sussex County, New Jersey, U.S.A. by Dunn (1981), where Mg is slightly greater than Mn. A 114.6 mm Debye-Schemer film taken of HU92803 with Cu radiation and a Ni filter (CuKα = 1.5418Å) was obtained from Dr. P. Dunn and measured visually. The unit-cell parameters, which were refined by least-squares analysis starting from the unit-cell parameters of PDF 25-1159 in space group C2/m(#12), are listed in Table 1, and give F28 = 4.1(0.050,136) by the method of Smith & Snyder (1979).The hkl, dcalulated, dobserved and relative intensities (I/I1) of HU92803 are presented in Table 2. With the atomic positions and temperature factors of chlorophoenicite determined by Moore (1968), the Mn atomic positions occupied by 50% Mg and 50% Mn, and the unit-cell parameters of HU92803, a powder X-ray diffraction pattern was calculated and Icalculated is recorded in Table 2. A third powder X-ray diffraction pattern was calculated with the Mn atomic positions fully occupied by Mg. Because the atomic scattering factor of Mn is more than twice greater than Mg, chlorophoenicite may be differentiated from magnesium-chlorophoenicite based upon the calculated intensities of the first three reflections given in Table 3.Although the a, c and β unit-cell parameters of chlorphoenicite are similar to those of magnesium-chlorphoenicite, the b unit-cell parameter of chlorophoenicite is significantly greater than that of magnesium-chlorophoenicite (Table 1). The b unit-cell parameter represents the 0–0 distance of the Mn octahedra (Moore, 1968). Since the size of Mn is greater than that of Mg, chlorophoenicite may be differentiated from magnesium-chlorophoenicite based upon the b unit-cell parameter given in Table 1.American Museum of Natural History (New York, N.Y., U.S.A.) specimen 28942 from Sterling Hill, Ogdensburg, New Jersey is composed of willemite, haidingerite and magnesian chlorophoenicite. A spectrographic analysis of the magnesian chlorophoenicite shows As, Mg, Mn and Zn. Powder X-ray diffraction data (PDF 34-190) of the magnesian chlorophoenicite was collected by diffractometer with Cu radiation and a graphite 0002 monochromator (Kα1 = 1.5405) at a scanning speed of 0.125° 2θ per minute. The unit-cell parameters, which were refined by leastsquares analysis starting from the unit-cell parameters of PDF 25-1159, are given in Table 1. Specimen AM 28942 is called chlorophoenicite, because of its large b unit-cell parameter (Table 1), and the I/I1 of 25 for reflection 001 and of 50 for reflection 201 compared to the Icalculated in Table 3.


1983 ◽  
Vol 47 (343) ◽  
pp. 221-227 ◽  
Author(s):  
R. J. Gilkes ◽  
B. Palmer

AbstractUnit-cell parameters of synthesized members of the crandallite (a = 7.007 Å, c = 16.216 Å)-goyazite (a = 7.013 Å, c = 16.650 Å) series vary linearly with composition between end-members. Most members of the series consist of 0.1 μm platy crystals, but crandallite also contains some larger (1–5 µm) tapered crystals elongated along the c axis.With increasing Sr substitution the dehydroxylation temperature decreases from c. 475 °C for crandallite to 420 °C at 20 mole % Sr, and then increases to 440 °C for goyazite. Partial dehydroxylation of crandallite is accompanied by contraction of the c unit cell parameter and expansion of a, thereby retaining an unaltered unit cell volume. The much greater sensitivity of c to both Sr substitution and dehydroxylation may be due to the rigidity of continuous sheets of Al(OH)4O2 octahedra which are parallel to the (001) plane in these minerals.


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.


2002 ◽  
Vol 17 (4) ◽  
pp. 295-300 ◽  
Author(s):  
Nichole Wonderling ◽  
Else Breval ◽  
Joseph P. Dougherty

The change in the orthorhombic structure of PbZrO3 was studied as a function of the La substitution for Pb and Ti substitution for Zr. Two types of changes can occur: (1) a change in the atom coordinates toward the positions for a perfect cubic perovskite lattice; and (2) a change of orthorhombic unit cell parameters so that ao, bo, and co exactly fit with the cubic cell parameter ac. Therefore, ao=ac√2, bo=ac.2√2, and co=ac.2, where ao, bo, and co are the orthorhombic cell parameters, and ac is the cubic cell parameter. Substitution of Pb by La in the orthorhombic PLZT leads to both a change in atom coordinates and a change in unit cell parameters toward the perfect cubic structure, especially for La≥4. Substitution of Zr by Ti in the orthorhombic PLZT leads to similar atom coordinate changes, but the unit cell parameters do not change. The composition 0/92.5/7.5 contains a major tetragonal phase and a minor orthorhombic phase. There are only small differences in the orthorhombic structure between the A and the B composition of PLZT. The A composition has a structure closer to the cubic structure than the B composition.


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.


1996 ◽  
Vol 11 (1) ◽  
pp. 31-34 ◽  
Author(s):  
Nicole M. L. N. P. Closset ◽  
René H. E. van Doorn ◽  
Henk Kruidhof ◽  
Jaap Boeijsma

The crystal structure of La1−xSrxCoO3−δ (0≤x≤0.6) has been studied, using powder X-Ray diffraction. The crystal structure shows a transition from rhombohedral distorted perovskite for LaCoO3−δ into cubic perovskite for La0.4Sr0.6CoO3−δ. The cubic unit cell parameter is ac=3.8342(1) Å for La0.4Sr0.6CoO3−δ, the space group probably being Pm3m. Using a hexagonal setting, the cell parameters for La0.5Sr0.5CoO3−δ, are a=5.4300(3) Å, c=13.2516(10) Å; a=5.4375(1) Å, c=13.2313(4) Å for La0.6Sr0.4CoO3−δ; a=5.4437(1) Å, c=13.2085(5) Å for La0.7Sr0.3CoO3−δ; a=5.4497(2) Å, c=13.1781(6) Å for La0.8Sr0.2CoO3−δ and a=5.4445(2) Å, c=13.0936(6) Å for LaCoO3−δ with the space group probably being R3c.


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