The mystery of birefringent garnet: is the symmetry lower than cubic?

2013 ◽  
Vol 28 (4) ◽  
pp. 281-288 ◽  
Author(s):  
Sytle M. Antao
Keyword(s):  
Crystal Structure ◽  
Phase Transitions ◽  
Rietveld Method ◽  
Chemical Formula ◽  
X Ray Diffraction ◽  
X Ray ◽  
Garnet Phase ◽  
Cubic Phases ◽  
General Chemical ◽  
Monochromatic Synchrotron

The cause of birefringence in several garnet-group minerals with general chemical formula, [8]X3[6]Y2[4]Z3[4]O12, which was observed over 100 years ago, is unknown, although many different reasons were proposed, including symmetry lower than cubic. In this study, electron microprobe analyses (EMPA) were obtained for a Ti-rich andradite, ideally Ca3(Fe23+)Si3O12, from Magnet Cove, Arkansas, USA, and the results show that the sample is inhomogeneous with two distinct compositions. The crystal structure was refined by the Rietveld method, cubic space group $Ia\overline 3 d$, and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data, which shows a mixture of three distinct cubic phases that are intergrown together and cause birefringence because of strain arising from small structural mismatch. This mixture of three cubic phases was not observed by any other experimental technique. These results have many implications, including garnet phase transitions from cubic to lower symmetry in the mantle, which has important geophysical consequences.

scholarly journals Crystal Chemistry of Six Grossular Garnet Samples from Different Well-Known Localities

Minerals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 767
Author(s):  
Sytle M. Antao
Keyword(s):  
Ionic Radius ◽  
Rietveld Method ◽  
Cubic Phase ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cubic Phases ◽  
Backscattered Electron ◽  
Grossular Garnet ◽  
Elemental Maps ◽  
Monochromatic Synchrotron

Two isotropic grossular (ideally Ca3Al2Si3O12) samples from (1) Canada and (2) Tanzania, three optically anisotropic grossular samples (3, 4, 5) from Mexico, and one (6) anisotropic sample from Italy were studied. The crystal structure of the six samples was refined in the cubic space group Ia3¯d, using monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data and the Rietveld method. The compositions of the samples were obtained from electron microprobe analyses (EPMA). The HRPXRD traces show a single cubic phase for two isotropic samples, whereas the four anisotropic samples contain two different cubic phases that were also resolved using X-ray elemental line scans, backscattered electron (BSE) images, and elemental maps. Structural mismatch from two cubic phases intergrown in the birefringent samples gives rise to strain-induced optical anisotropy. Considering the garnet general formula, [8]X3[6]Y2[4]Z3[4]O12, the results of this study show that with increasing unit-cell parameter, the Y-O distance increases linearly and rather steeply, the average <X-O> distance increases just slightly in response to substitution mainly on the Y site, while the Z-O distance remains nearly constant. The X and Z sites in grossular contain Ca and Si atoms, respectively; both sites show insignificant substitutions by other atoms, which is supported by a constant Z-O distance and only a slight increase in the average <X-O> distance. The main cation exchange is realized in the Y site, where Fe3+ (ionic radius = 0.645 Å) replaces Al3+ (ionic radius = 0.545 Å), so the Y-O distance increases the most.

X-ray powder diffraction data of LaNi0.5Ti0.45Co0.05O3, LaNi0.45Co0.05Ti0.5O3, and LaNi0.5Ti0.5O3 perovskites

2021 ◽  
pp. 1-6
Author(s):  
Mariana M. V. M. Souza ◽  
Alex Maza ◽  
Pablo V. Tuza
Keyword(s):  
Crystal Structure ◽  
Rietveld Method ◽  
Pechini Method ◽  
Powder Diffraction Data ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Modified Pechini Method ◽  
Scanning Electron

In the present work, LaNi0.5Ti0.45Co0.05O3, LaNi0.45Co0.05Ti0.5O3, and LaNi0.5Ti0.5O3 perovskites were synthesized by the modified Pechini method. These materials were characterized using X-ray fluorescence, scanning electron microscopy, and powder X-ray diffraction coupled to the Rietveld method. The crystal structure of these materials is orthorhombic, with space group Pbnm (No 62). The unit-cell parameters are a = 5.535(5) Å, b = 5.527(3) Å, c = 7.819(7) Å, V = 239.2(3) Å3, for the LaNi0.5Ti0.45Co0.05O3, a = 5.538(6) Å, b = 5.528(4) Å, c = 7.825(10) Å, V = 239.5(4) Å3, for the LaNi0.45Co0.05Ti0.5O3, and a = 5.540(2) Å, b = 5.5334(15) Å, c = 7.834(3) Å, V = 240.2(1) Å3, for the LaNi0.5Ti0.5O3.

Structure of Carbonated Hydroxyapatite Based on Rietveld Method

2008 ◽  
Vol 368-372 ◽  
pp. 1187-1189
Author(s):  
Xu Ran ◽  
Jun Guo Ran ◽  
Li Gou ◽  
Ji Yong Chen ◽  
Jiao Min Luo
Keyword(s):  
Crystal Structure ◽  
Sintering Temperature ◽  
Rietveld Method ◽  
Rietveld Analysis ◽  
Structure Parameters ◽  
X Ray Diffraction ◽  
Carbonated Hydroxyapatite ◽  
X Ray ◽  
Quantitative Results ◽  
Distortion Index

The crystalline structures of B-type carbonated hydroxyapatite (CHA) powders sintered at 700, 900 and 1100°C, respectively, were studied by Rietveld analysis of powder X-ray diffraction (XRD) data. A series of structure parameters, including lattice parameters (a and c), bond length and the distortion index of PO4 tetrahedron (Dind) were calculated by Rietveld method to characterize the fine structure of CHA. The broadening effect of XRD reflections was separated to calculate the micro-strain and crystalline size. The results showed that CHA become more stable with the increase of sintering temperature, but the CO3 2- is almost lost at temperature of 1100°C. The quantitative results about crystal structure of CHA based on crystalline structure simulated by Rietveld method are obtained.

scholarly journals Thermal evolution of the crystal structure and phase transitions of KNbO 3

2018 ◽  
Vol 5 (6) ◽  
pp. 180368 ◽  
Author(s):  
S. L. Skjærvø ◽  
K. Høydalsvik ◽  
A. B. Blichfeld ◽  
M.-A. Einarsrud ◽  
T. Grande
Keyword(s):  
Crystal Structure ◽  
Phase Transitions ◽  
Thermal Evolution ◽  
Dynamical Instability ◽  
X Ray Diffraction ◽  
Two Phase ◽  
X Ray ◽  
Cell Parameters ◽  
First Order ◽  
Heating And Cooling

The thermal evolution of the crystal structure and phase transitions of KNbO 3 were investigated by high-temperature powder X-ray diffraction and Rietveld refinement of the diffraction data. Two phase transitions from orthorhombic ( Amm 2) to tetragonal ( P 4 mm ) and from tetragonal to cubic ( P m 3 ¯ m ) were confirmed, both on heating and cooling. Both phase transitions are first order based on the observed hysteresis. The mixed displacive and order–disorder nature of the tetragonal to cubic transition is argued based on symmetry and apparent divergence of the atomic positions from pseudo-cubic values. The transition between the orthorhombic and tetragonal phase shows no temperature-dependence for atomic positions and only thermal expansion of the unit cell parameters and is thus discussed in relation to a lattice dynamical instability.

Al analogue of chayesite from a lamproite of Cancarix, SE Spain, and its crystal structure

2020 ◽  
Vol 196 (3) ◽  
pp. 193-198
Author(s):  
Natalia V. Zubkova ◽  
Nikita V. Chukanov ◽  
Christof Schäfer ◽  
Konstantin V. Van ◽  
Igor V. Pekov ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Diffraction Data ◽  
Empirical Formula ◽  
Structure Refinement ◽  
Crystal Chemical ◽  
Chemical Formula ◽  
Crystal Chemical Formula ◽  
X Ray Diffraction ◽  
Se Spain ◽  
X Ray

Al analogue of chayesite (with Al > Fe3+) was found in a lamproite from Cancarix, SE Spain. The mineral forms green thick-tabular crystals up to 0.4 mm across in cavities. The empirical formula derived from EMP measurements and calculated on the basis of 17 Mg + Fe + Al + Si apfu is (K0.75 Na0.20 Ca0.11)Mg3.04 Fe0.99 Al1.18 Si11.80 O30. The crystal structure was determined from single crystal X-ray diffraction data ( R = 2.38%). The mineral is hexagonal, space group P 6/ mcc, a = 10.09199(12), c = 14.35079(19) Å, V = 1265.78(3) Å3, Z = 2. Fe is predominantly divalent. Al is mainly distributed between the octahedral A site and the tetrahedral T 2 site. The crystal chemical formula derived from the structure refinement is C (K0.73 Na0.16 Ca0.11)B (Na0.02)4 A(Mg0.42 Al0.29 Fe0.29)2 T 2(Mg0.71 Fe0.16 Al0.13)3 T 1(Si0.985 Al0.015)12 O30.

Low-temperature crystal structure of RS-thiocamphor

2004 ◽  
Vol 219 (9) ◽  
Author(s):  
E. Louise R. Robins ◽  
Michela Brunelli ◽  
Asiloé J. Mora ◽  
Andrew N. Fitch
Keyword(s):  
Crystal Structure ◽  
Phase Transitions ◽  
Low Temperature ◽  
Room Temperature ◽  
Cubic Phase ◽  
X Ray Diffraction ◽  
Orthorhombic Space Group ◽  
Two Phase ◽  
X Ray ◽  
Low Temperature Crystal Structure

AbstractDSC and high-resolution powder X-ray diffraction measurements in the range 295 K–100 K show that RS-thiocamphor undergoes two phase transitions. The first, at around 260 K on cooling, is from the room-temperature body-centred-cubic phase to a short-lived intermediate. At 258 K the low-temperature form starts to appear. The crystal structure of the latter is orthorhombic, space group

X-ray Diffraction Study of the Crystal Structure of the Tl Ternary Chalcogenides Tl2x In2(1−x)Se2, x = 0.2, 0.3,...0.9

1998 ◽  
Vol 54 (4) ◽  
pp. 358-364 ◽  
Author(s):  
K. G. Hatzisymeon ◽  
S. C. Kokkou ◽  
A. N. Anagnostopoulos ◽  
P. I. Rentzeperis
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Rietveld Method ◽  
Direct Methods ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
Single Crystal Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
Volume Decrease

A series of thallium ternary chalcogenides with the composition Tl2x In2(1−x)Se2, x = 0.2, 0.3,...0.9, have been studied by X-ray powder and, for some of them, single-crystal diffraction. They are tetragonal, space group I4/mcm, Z = 4, and isostructural with the binary semiconductor TlSe. Their crystal structures have been solved by direct methods and refined by the Rietveld method to a precision which is satisfactorily comparable to single-crystal results. As x is changed from x = 0.2 to x = 0.9 the unit-cell parameters and volume decrease or increase following Kurnakov's law, which is valid for solid solutions. Refined positional parameters of Se, In—Se and Tl—Se bond lengths vary with x also according to the same law. The distribution of In and Tl cations in 4(a) and 4(b) sites depends on the stoichiometry x and the crystals are composed of [In3+Se2]_{\infty}^- chains along the c axis in which InSe4 tetrahedra share edges; the chains are interconnected with Tl+(In+) ions.

Crystal structure and powder X-ray diffraction data for new Tb3CuAl3Ge2 compound

2015 ◽  
Vol 30 (1) ◽  
pp. 63-66 ◽  
Author(s):  
Chao Zeng ◽  
Guoqiang Lin ◽  
Weijing Zeng ◽  
Wei He
Keyword(s):  
Crystal Structure ◽  
Rietveld Refinement ◽  
Diffraction Data ◽  
Rietveld Method ◽  
Unit Cell ◽  
Type Structure ◽  
X Ray Diffraction ◽  
Quaternary Compound ◽  
Space Group ◽  
X Ray

The crystal structure of new Tb3CuAl3Ge2 quaternary compound was studied by the Rietveld method from powder X-ray diffraction (XRD) data. The Tb3CuAl3Ge2 compound crystallized in the hexagonal Y3NiAl3Ge2-type structure with space group P-62m (no. 189) and lattice parameters a = 7.0041(2) Å, c = 4.1775(1) Å, V = 177.48 Å3. There is only one formula in each unit cell, Z = 1, and the density of Tb3CuAl3Ge2 is ρx = 7.1696 g cm−3. The reliability factors characterizing the Rietveld refinement results are Rp = 6.43%, Rwp = 8.65%, RB = 4.81%, and RF = 4.09%, respectively. The powder XRD data of Tb3CuAl3Ge2 were presented and the reliability of indexation is F30 = 120.9(0.0073, 34).

scholarly journals On the crystal structure of the ordered vacancy compound Cu3In5Te9

2019 ◽  
Vol 65 (4 Jul-Aug) ◽  
pp. 360 ◽  
Author(s):  
G. E. Delgado ◽  
C. Rincón ◽  
G. Marroquin
Keyword(s):  
Crystal Structure ◽  
Diffraction Data ◽  
Rietveld Method ◽  
Structural Models ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
Space Group ◽  
X Ray ◽  
Cell Parameters

The crystal structure of the ordered vacancy compound (OVC) Cu3In5Te9 was analyzed using powder X-ray diffraction data. Several structural models were derived from the structure of the Cu-poor Cu-In-Se compound b-Cu0.39In1.2Se2 by permuting the cations in the available site positions. The refinement of the best model by the Rietveld method in the tetragonal space group P2c (Nº 112), with unit cell parameters a = 6.1852(2) Å, c = 12.3633(9) Å, V = 472.98(4) Å3, led to Rp = 7.1 %, Rwp = 8.5 %, Rexp = 6.4 %, S = 1.3 for 162 independent reflections. This model has the following Wyckoff site atomic distribution: Cu1 in 2e (0,0,0); In1 in 2f (½,½,0), In2 in 2d (0,½,¼); Cu2-In3 in 2b (½,0,¼); in 2a (0,0,¼); Te in 8n (x,y,z).

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