A Rietveld tutorial—Mullite

2009 ◽  
Vol 24 (4) ◽  
pp. 351-361 ◽  
Author(s):  
James A. Kaduk

The crystal structure of the mullite in a commercial material was refined by the Rietveld method using laboratory X-ray powder diffraction data. In this one refinement, most of the common challenges—including variable stoichiometry (partially occupied sites), multiple impurity phases, amorphous material, constraints, restraints, correlation, anisotropic profiles, microabsorption, and contamination during grinding—are encountered and the thought processes during the refinement are described step-by-step. Interpretation of the refinements includes bulk chemical analysis, chemical composition of the mullite, assessment of the geometry, bond valence sums, the displacement coefficients, crystallite size and microstrain, comparison to similar structures to assess chemical reasonableness, and the nature of the amorphous phase.

2021 ◽  
pp. 1-6
Author(s):  
Mariana M. V. M. Souza ◽  
Alex Maza ◽  
Pablo V. Tuza

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.


2010 ◽  
Vol 25 (3) ◽  
pp. 247-252 ◽  
Author(s):  
F. Laufek ◽  
J. Návrátil

The crystal structure of skutterudite-related phase IrGe1.5Se1.5 has been refined by the Rietveld method from laboratory X-ray powder diffraction data. Refined crystallographic data for IrGe1.5Se1.5 are a=12.0890(2) Å, c=14.8796(3) Å, V=1883.23(6) Å3, space group R3 (No. 148), Z=24, and Dc=8.87 g/cm3. Its crystal structure can be derived from the ideal skutterudite structure (CoAs3), where Se and Ge atoms are ordered in layers perpendicular to the [111] direction of the original skutterudite cell. Weak distortions of the anion and cation sublattices were also observed.


Author(s):  
H. Catherine W. Skinner ◽  
Malcolm Ross ◽  
Clifford Frondel

A mineral is a naturally occurring, crystalline inorganic compound with a specific chemical composition and crystal structure. Minerals are commonly named to honor a person, to indicate the geographic area where the mineral was discovered, or to highlight some distinctive chemical, crystallographic, or physical characteristic of the substance. Each mineral sample has some obvious properties: color, shape, texture, and perhaps odor or taste. However, to determine the precise composition and crystal structure necessary to accurately identify the species, one or several of the following techniques must be employed: optical, x-ray diffraction, transmission electron microscopy and diffraction, and chemical and spectral analyses. The long history of bestowing names on minerals has provided some confusing legacies. Many mineral names end with the suffix “ite,” although not most of the common species; no standard naming practice has ever been adopted. Occasionally different names have been applied to samples of the same mineral that differ only in color or shape, but are identical to each other in chemical composition and crystal structure. These names, usually of the common rock-forming minerals, are often encountered and are therefore accepted as synonyms or as varieties of bona fide mineral species. The Fibrous Minerals list (Appendix 1) includes synonyms. A formal description of a mineral presents all the physical and chemical properties of the species. In particular, distinctive attributes that might facilitate identification are noted, and usually a chemical analysis of the first or “type” specimen on which the name was originally bestowed is included. As an example, the complete description of the mineral brucite (Mg(OH)2), as it appears in Dana’s System of Mineralogy, is presented as Appendix 3. Note the complexity of this chemically simple species and the range of information available. In the section on Habit (meaning shape or morphology) both acicular and fibrous forms are noted. The fibrous variety, which has the same composition as brucite, is commonly encountered (see Fig. 1.1D) and is known by a separate name, “nemalite.” Tables to assist in the systematic determination of a mineral species are usually based on quantitative measurements of optical properties (using either transmitted or reflected light, as appropriate) or on x-ray diffraction data.


1993 ◽  
Vol 8 (3) ◽  
pp. 175-179
Author(s):  
J. Estienne ◽  
O. Cerclier ◽  
J. J. Rosenberg

Indexed X-ray powder diffraction data are reported for two organic salts with carbon rings having two quaternary nitrogens: diazonia-6,9 dispiro [5.2.5.2] hexadecane and diazonia-6,9 dispiro [5.2.5.3] heptadecane diiodides. For these compounds, which give solid electrolytes when associated with AgI, powder diffraction diagrams calculated by the Rietveld method from single crystal structure determinations are presented and are compared to the experimental diffraction data.


1998 ◽  
Vol 54 (5) ◽  
pp. 547-557 ◽  
Author(s):  
R. L. Withers ◽  
J. G. Thompson ◽  
A. Melnitchenko ◽  
S. R. Palethorpe

The crystal structure of a new cubic cristobalite-related sodium aluminosilicate Na1.45Al1.45Si0.55O4 [P213, a = 14.553 (1) Å] has been modelled using a modulation wave approach and the model tested against X-ray powder diffraction data using the Rietveld method. Owing to there being 64 independent positional parameters and eight independent Na sites, refinement of the tetrahedral framework atom positions and Na occupancies was not possible. The framework was modelled successfully in terms of q 1 = 1\over 4〈020〉_p^*-type (p = parent) modulation waves with the requirement that the MO4 (M = Al0.725Si0.275) tetrahedra be as close to regular as possible. Na/vacancy ordering was modelled successfully in terms of q 2 = 1\over 4〈220〉_p^* modulation waves. Only the Na-atom positions were refined. The significance of this unique modulated cubic cristobalite-related structure and the possible insight it provides to understanding β-cristobalite are discussed.


2002 ◽  
Vol 17 (5) ◽  
pp. 1112-1117 ◽  
Author(s):  
M. Avdeev ◽  
M. P. Seabra ◽  
V. M. Ferreira

The crystal structure of microwave dielectric ceramics in the (1 − x)La(Mg0.5Ti0.5)O3 (LMT)–xBaTiO3 (BT) (0 ≤ x ≤ 0.9) system has been refined by Rietveld method using x-ray powder diffraction data. LMT and BT were found to form a solid solution in the whole compositional range. The increase of BaTiO3 content results in the following sequence of structure transformations of those solid solutions: P21/n (a−a−c+, B-site ordered) → Pbnm (a−a−c+) → I4/mcm (a0a0c−) → Pm3m (a0a0a0). These structural changes are related to the disappearance of B-site cation ordering (x > 0.1), in-phase tilting (x > 0.3), and antiphase tilting (x > 0.5), respectively.


2004 ◽  
Vol 36 (1) ◽  
pp. 121 ◽  
Author(s):  
V. Psycharis ◽  
V. Perdikatsis ◽  
G. Christidis

Synthetic zeolites have been produced from a variety of natural silica-rich rocks including volcanic glasses, such as perlite and pumice. The Zeolite studied in this work has been synthesized from perlite and expanded perlite fines. Detailed powder X-ray diffraction studies determined it as Zeolite A. In early studies the structure of Zeolite-Α was described with a cubic cell with a=12.3 A and space group Pm-3m. However the observation of the (531) reflection indicates that a F lattice with a larger cell of 24.60 A gives a more accurate description. Two end products were studied on the basis of the degree of crystallization of the parent gels to zeolite A . One end product was characterized by total conversion of the incipient gel to zeolite A with high degree of crystallinity, whereas in the second a substantial amount of the original gel did not crystallize out and zeolite A coexisted with amorphous material. The former resulted from gels with S1O2/AI2O3 molar ratio 2:1 and 5 hours reaction time and the latter from gels with SÌO2/AI2O3 molar ratio of 2.5:1 and 3 hours reaction time. The X-ray powder diffraction data recorded from the former sample were used for the analysis of the crystal structure of zeolite A and the final model was refined by the Rietveld method.


2019 ◽  
Vol 289 ◽  
pp. 59-64
Author(s):  
Vasyl Stotskyi ◽  
Svitlana Pukas ◽  
Roman E. Gladyshevskii

The crystal structure of the new ternary aluminide Sc1.33Pd3Al8was refined by the Rietveld method from X-ray powder diffraction data. It crystallizes with a Gd1.33Pt3Al8-type structure:hR51-14.00,R-3m,a= 4.29142(4),c= 38.1638(4) Å,RB= 0.0344. The main feature of the structure is the statistical distribution of Sc atoms and Al3triangles within atomic layers of composition Sc2Al3(Sc0.67Al within the translation unit here), which is likely to correspond to stacking disorder of ordered layers. During the final cycles of the refinement, the occupancies of the corresponding sites were fixed at occ. = 2/3 for Sc in Wyckoff position 6cand occ. = 1/3 for Al in 18h. The unit cell of Sc1.33Pd3Al8contains six Sc0.67Al layers, nine Pd and eighteen Al atom layers along the crystallographic direction [001]. Together with the structure types Tb0.67PdAl3, Y2Co3Ga9, Sc0.67Fe2Si5, Er4Pt9Al24, Yb0.67Ni2Al6, and ErNi3Al9, the structure type Gd1.33Pt3Al8forms a family of intergrowth structures built up of three kinds of similar monoatomic layer.


2011 ◽  
Vol 66 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Nancy Frenzel ◽  
Elisabeth Irran ◽  
Martin Lerch ◽  
Alexandra Buchsteiner

A new compound of the composition Nb0.84N was prepared by ammonolysis of NbO2 at 1100 °C. The crystal structure refinement was performed by the Rietveld method using X-ray and neutron powder diffraction data. Nb0.84N crystallizes in the trigonal space group R3m (no. 166) with the lattice parameters a = 298.5(2) and c = 2384.3(4) pm. The niobium atoms form a close packing with a layer sequence which can be described by the Jagodzinski symbol hhc. The nitrogen atoms fill all octahedral voids. Along [001] a sequence of two layers of trigonal NbN6 prisms and one layer of NbN6 octahedra is formed. The nitrogen positions are fully occupied, the niobium positions only partially. Nb0.84N is part of a family of crystal structures between the anti-NiAs and the NaCl type consisting of close-packed metal layers with varying stacking sequences


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