Algorithm and program for precise determination of unit-cell parameters of single crystal taking into account the sample eccentricity

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.

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Monoclinic-to-orthorhombic phase transition in Cu2(AsO4)(OH) olivenite at high temperature: strain and mode decomposition analyses

Mineralogical Magazine ◽

10.1180/minmag.2017.081.048 ◽

2018 ◽

Vol 82 (2) ◽

pp. 347-365 ◽

Cited By ~ 2

Author(s):

Serena C. Tarantino ◽

Michele Zema ◽

Athos M. Callegari ◽

Massimo Boiocchi ◽

Michael A. Carpenter

Keyword(s):

Phase Transition ◽

High Temperature ◽

Single Crystal ◽

Volume Expansion ◽

Monoclinic Phase ◽

Orthorhombic Phase ◽

Unit Cell ◽

The Other ◽

Unit Cell Parameters ◽

Cell Parameters

ABSTRACTA natural olivenite single crystal was submitted to in situ high-temperature single-crystal X-ray diffraction from room temperature (RT) to 500°C. Unit-cell parameters were measured at regular intervals of 25°C, and complete datasets collected at T = 25, 50, 100, 150, 200, 250, 300, 400 and 500°C. Evolution of unit-cell parameters and structure refinements indicates that olivenite undergoes a structural phase transition from P21/n to Pnnm at ~200°C, and eventually becomes isostructural with the other members of the olivenite-mineral group. Volume expansion with temperature is larger in the monoclinic phase – where it follows a non-linear trend – than in the orthorhombic one. Axial and volume expansion coefficients of the orthorhombic olivenite phase are positive and linear and similar to those of the other Cu-bearing member of the mineral family, namely libethenite, but rather different from those of the Zn-analogue arsenate adamite.Distortion of Cu polyhedra is quite high in the olivenite monoclinic phase at RT and goes towards a relative regularization with increasing T until the phase transition occurs. In the orthorhombic phase, no significant variation of the polyhedral distortion parameters is observed with increasing temperature, and maximum expansion is along the b direction and governed by corner-sharing. Landau potential provides a good representation of the macroscopic changes associated with the phase transition, coupling between the strains and the order parameter is responsible for the nearly tricritical character of the transition.

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The crystal structure of alstonite, BaCa(CO3)2: an extraordinary example of ‘hidden’ complex twinning in large single crystals

Mineralogical Magazine ◽

10.1180/mgm.2020.61 ◽

2020 ◽

Vol 84 (5) ◽

pp. 699-704

Author(s):

Luca Bindi ◽

Andrew C. Roberts ◽

Cristian Biagioni

Keyword(s):

Crystal Structure ◽

Single Crystals ◽

Structure Determination ◽

Unit Cell ◽

Crystal Structure Determination ◽

Unit Cell Parameters ◽

Space Group ◽

Cell Parameters ◽

Structure Determinations

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.

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Layer stacking disorder in Mg-Fe chlorites based on powder X-ray diffraction data

American Mineralogist ◽

10.2138/am-2020-6982 ◽

2020 ◽

Vol 105 (3) ◽

pp. 353-362

Author(s):

Katarzyna Luberda-Durnaś ◽

Marek Szczerba ◽

Małgorzata Lempart ◽

Zuzanna Ciesielska ◽

Arkadiusz Derkowski

Keyword(s):

Accurate Determination ◽

Unit Cell ◽

Powder Xrd ◽

X Ray Diffraction ◽

Unit Cell Parameters ◽

Xrd Pattern ◽

X Ray ◽

Cell Parameters ◽

Layer Stacking

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.

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Redefinition of satimolite

Mineralogical Magazine ◽

10.1180/minmag.2017.081.081 ◽

2018 ◽

Vol 82 (5) ◽

pp. 1033-1047 ◽

Cited By ~ 2

Author(s):

Igor V. Pekov ◽

Natalia V. Zubkova ◽

Dmitry A. Ksenofontov ◽

Nikita V. Chukanov ◽

Vasiliy O. Yapaskurt ◽

...

Keyword(s):

Crystal Structure ◽

Single Crystal ◽

Rietveld Method ◽

Three Dimensional ◽

Direct Methods ◽

Salt Dome ◽

Unit Cell ◽

Unit Cell Parameters ◽

Cell Parameters ◽

Octahedral Clusters

ABSTRACTThe borate mineral satimolite, which was first described in 1969 and remained poorly-studied until now, has been re-investigated (electron microprobe analysis, single-crystal and powder X-ray diffraction studies, crystal-structure determination, infrared spectroscopy) and redefined based on the novel data obtained for the holotype material from the Satimola salt dome and a recently found sample from the Chelkar salt dome, both in North Caspian Region, Western Kazakhstan. The revised idealized formula of satimolite is KNa2(Al5Mg2)[B12O18(OH)12](OH)6Cl4·4H2O (Z = 3). The mineral is trigonal, space group R$\bar{3}$m, unit-cell parameters are: a = 15.1431(8), c = 14.4558(14) Å and V = 2870.8(4) Å3 (Satimola) and a = 15.1406(4), c = 14.3794(9) Å and V = 2854.7(2) Å3 (Chelkar). The crystal system and unit-cell parameters are quite different from those reported previously. The crystal structure of the sample from Chelkar was solved based on single-crystal data (direct methods, R = 0.0814) and the structure of the holotype from Satimola was refined on a powder sample by the Rietveld method (Rp = 0.0563, Rwp = 0.0761 and Rall = 0.0667). The structure of satimolite is unique for minerals. It contains 12-membered borate rings [B12O18(OH)12] in which BO3 triangles alternate with BO2(OH)2 tetrahedra sharing common vertices, and octahedral clusters [M7O6(OH)18] with M = Al5Mg2 in the ideal case, with sharing of corners between rings and clusters to form a three-dimensional heteropolyhedral framework. Each borate ring is connected with six octahedral clusters: three under the ring and three over the ring. Large ellipsoidal cages in the framework host Na and K cations, Cl anions and H2O molecules.

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The determination of unit-cell parameters from Laue diffraction patterns using their gnomonic projections

Journal of Applied Crystallography ◽

10.1107/s0021889891012803 ◽

1992 ◽

Vol 25 (2) ◽

pp. 294-308 ◽

Cited By ~ 5

Author(s):

P. D. Carr ◽

D. W. J. Cruickshank ◽

M. M. Harding

Keyword(s):

Diffraction Pattern ◽

Unit Cell ◽

Unit Cell Parameters ◽

Laue Diffraction ◽

Cell Parameters ◽

The Absolute ◽

Diffraction Patterns

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.

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The f.c.c.+tetragonal two-phase region of the Cu–Ni–Zn system

Journal of Applied Crystallography ◽

10.1107/s0021889883010018 ◽

1983 ◽

Vol 16 (1) ◽

pp. 99-102 ◽

Cited By ~ 2

Author(s):

O. S. Mayall

Keyword(s):

Tetragonal Phase ◽

Lattice Spacing ◽

Single Phase ◽

Phase Region ◽

Unit Cell ◽

Unit Cell Parameters ◽

Two Phase ◽

Cell Parameters ◽

Tie Lines

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.

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Waimirite-(Y), orthorhombic YF3, a new mineral from the Pitinga mine, Presidente Figueiredo, Amazonas, Brazil and from Jabal Tawlah, Saudi Arabia: description and crystal structure

Mineralogical Magazine ◽

10.1180/minmag.2015.079.3.18 ◽

2015 ◽

Vol 79 (3) ◽

pp. 767-780 ◽

Cited By ~ 4

Author(s):

Daniel Atencio ◽

Artur C. Bastos Neto ◽

Vitor P. Pereira ◽

José T. M. M. Ferron ◽

M. Hoshino ◽

...

Keyword(s):

Crystal Structure ◽

Saudi Arabia ◽

Single Crystal ◽

Electron Microprobe ◽

Empirical Formula ◽

Unit Cell ◽

New Mineral ◽

Charge Balance ◽

Unit Cell Parameters ◽

Cell Parameters

AbstractWaimirite-(Y) (IMA 2013-108), orthorhombic YF3, occurs associated with halloysite, in hydrothermal veins (up to 30 mm thick) cross-cutting the albite-enriched facies of the A-type Madeira granite (∼1820 Ma), at the Pitinga mine, Presidente Figueiredo Co., Amazonas State, Brazil. Minerals in the granite are 'K-feldspar', albite, quartz, riebeckite, 'biotite', muscovite, cryolite, zircon, polylithionite, cassiterite, pyrochlore-group minerals, 'columbite', thorite, native lead, hematite, galena, fluorite, xenotime-(Y), gagarinite-(Y), fluocerite-(Ce), genthelvite–helvite, topaz, 'illite', kaolinite and 'chlorite'. The mineral occurs as massive aggregates of platy crystals up to ∼1 μm in size. Forms are not determined, but synthetic YF3 displays pinacoids, prisms and bipyramids. Colour: pale pink. Streak: white. Lustre: non-metallic. Transparent to translucent. Density (calc.) = 5.586 g/cm3 using the empirical formula. Waimirite-(Y) is biaxial, mean n = 1.54–1.56. The chemical composition is (average of 24 wavelength dispersive spectroscopy mode electron microprobe analyses, O calculated for charge balance): F 29.27, Ca 0.83, Y 37.25, La 0.19, Ce 0.30, Pr 0.15, Nd 0.65, Sm 0.74, Gd 1.86, Tb 0.78, Dy 8.06, Ho 1.85, Er 6.38, Tm 1.00, Yb 5.52, Lu 0.65, O (2.05), total (97.53) wt.%. The empirical formula (based on 1 cation) is (Y0.69Dy0.08Er0.06Yb0.05Ca0.03Gd0.02Ho0.02Nd0.01Sm0.01Tb0.01Tm0.01Lu0.01)Σ1.00[F2.54〈0.25O0.21]Σ3.00. Orthorhombic, Pnma, a = 6.386(1), b = 6.877(1), c = 4.401(1) Å, V = 193.28(7) Å3, Z = 4 (powder data). Powder X-ray diffraction (XRD) data [d in Å (I) (hkl)]: 3.707 (26) (011), 3.623 (78) (101), 3.438 (99) (020), 3.205 (100) (111), 2.894 (59) (210), 1.937 (33) (131), 1.916 (24) (301), 1.862 (27) (230). The name is for the Waimiri-Atroari Indian people of Roraima and Amazonas. A second occurrence of waimirite-(Y) is described from the hydrothermally altered quartz-rich microgranite at Jabal Tawlah, Saudi Arabia. Electron microprobe analyses gave the empirical formula (Y0.79Dy0.08Er0.05Gd0.03Ho0.02Tb0.01Tm0.01Yb0.01)Σ1.00[F2.85O0.08〈0.07]Σ3.00. The crystal structure was determined with a single crystal from Saudi Arabia. Unit-cell parameters refined from single-crystal XRD data are a = 6.38270(12), b = 6.86727(12), c = 4.39168(8) Å, V = 192.495(6) Å3, Z = 4. The refinement converged to R1 = 0.0173 and wR2 = 0.0388 for 193 independent reflections. Waimirite-(Y) is isomorphous with synthetic SmF3, HoF3 and YbF3. The Y atom forms a 9-coordinated YF9 tricapped trigonal prism in the crystal structure. The substitution of Y for Dy, as well as for other lanthanoids, causes no notable deviations in the crystallographic values, such as unit-cell parameters and interatomic distances, from those of pure YF3.

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Systematic crystallographic refinement of triclinic unit cells

Powder Diffraction ◽

10.1017/s0885715600009714 ◽

1998 ◽

Vol 13 (1) ◽

pp. 22-31

Author(s):

Ludo K. Frevel

Keyword(s):

Powder Diffraction ◽

Unit Cell ◽

Simultaneous Equations ◽

Unit Cell Parameters ◽

Cell Parameters ◽

Triclinic Phase ◽

Unit Cells ◽

Diffraction Patterns ◽

Limits Of Error

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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