Tetrahedral Rotation Research Articles

Experimental study of SiGe tetrahedral solid solution in NiCoMg talcs

In order to study SiGe substitutions, Si x -Ge 1-x talcs (0 < × < 100) were synthesized at 200 °C with various octahedral (nickel, cobalt or magnesium) cations. X-ray diffraction (XRD) reveals, in spite of different silicon and germanium cation sizes, preservation of the usual C 1 lattice symmetry group of silicon talcs for germanium talcs. An increase in the cell volume and a rotation of tetrahedra (to adjust tetrahedral and octahedral lateral sheet dimensions) are observed for SiGe talcs when the germanium content increases. Fourier transform IR (FTIR) spectroscopy reveals, with increasing germanium content, a continuous evolution of band positions towards lower frequencies, indicating a tetrahedral solid solution. According to XRD and FTIR results, germanium can easily substitute for silicon on the tetrahedral sheet of clay minerals.

Deformation of coordination polyhedra and their sheets in phyllosilicates

A statistical evaluation of crystal-structure data for 112 phyllosilicates (85 micas, 14 1:1 phyllosilicates, 13 chlorites) shows that the same principles govern the geometry of polyhedra and their sheets irrespective of the phyllosilicate subgroup. Regression relations for octahedral distortions and tetrahedral rotation as a function of interatomic distances are proposed. Multiple regressions were used to obtain generalized values for bond lengths and ionic radii for elements in different coordination. Using the relations derived here, it is possible to start with a chemical composition plus an anticipated cation ordering pattern and obtain estimates of the individual bond lengths and distortion characteristics of the crystal structure concerned. These can be translated into atomic coordinates and, ultimately, into peak intensities on diffraction patterns. The geometry of the coordination of interlayer cations in the micas shows considerable variation and the effective coordination number is seen to correlate with the tetrahedral rotation angle α. When the coordination drops to six, this angle may vary between 16° and 24°

Control of phase formation processes in glass-ceramics for medicine and technology

The control of phase separation processes in silicate glasses makes possible the control of nucleation and crystallization of base glasses. Ti(III,IV)-species influence the phase formation in SiO2–Al2O3–MgO glasses to form glass-ceramics based on ß- and α-quartz solid solutions. Additions of Na2O, K2O and F in a specific composition range and heat treatment of the glass result in an new glass-ceramic with curved micas. The structure of these crystals shows a high tetrahedral rotation. Glasses of the SiO2–Al2O3–MgO–Na2O–K2O–P2O5–F system show a double phase separation. Apatites and micas grow as a result of controlled in situ crystallization. The material can be machined and has bioactive properties. Phosphate glasses show no glass-in-glass phase separation. However, the high supersaturation is cancelled by a thermal treatment of the glass and a primary crystal is formed. Apatite crystals grow in the primary phase.

Changes in Swelling Characteristics and Structure of Na-Fluorine Micas with Ga- and Al-Substitutions

Series of Ga- and Al-Substituted Na-fluorine micas NaMg2+xLi1-x(TxSi4-x-yGeyO10)F2 and NaMg2+xLi1-x(TxGe4-x-ySiyO10)F2; x=0.0-1.0, T=Ga, Al, y=0, 1, 2, 3, were synthesized. Variations of infrared spectra, lattice constants and swelling properties were studied, and compared with those of corresponding K-series micas. Continuous changes in basal spacing (c·sinβ) with increasing Ga- and Al-contents proved that there were complete series of solid solutions between the end member micas with an exception of NaMg3(AlSi3O10)F2. Linear relations between c·sinβ or b-axis values and mean radius of tetrahedral cation were obtained for Ga- and Al-substituted Na-micas having x-value of 1.0. However, the b-axis values of Na-micas are far smaller than those of corresponding K-analogues, demonstrating that the degree of distortion in tetrahedral rotation angle α and octahedral flattening angle ψ is determined by the size of interlayer cation as well as that of tetrahedral cation. The values of α for Na-micas increased with the amounts of Ga- and Al-substitution. Na-micas lose also their swelling ability with increasing Ga- and Al-substitution. The loss of hydration property of interlayer cation results from the increase of α and the change of charge balancing, which increase the stability of interlayer structure.

The group theory of trigonal and tetrahedral molecule rotations in trigonal and tetrahedral crystal fields

The permutation symmetry groups introduced by Longuet-Higgins are employed to solve the group theory for molecules of C3v and Td symmetry rotating in crystal fields of C3v and Td symmetry. The qualitative appearances of the energy level diagrams for the groups (C3v, [Cbar]3v), (C3v, [Tbar]d) and (Td, [Cbar]3v) are deduced for the range of barrier heights from the free-rotor limits to the pinned limits, for the ground state multiplet only. The correlations between the groups derived here and the group (Td, [Tbar]d) treated by Miller and Decius are considered and the alteration in the ground state splitting pattern in going from a tetrahedral molecule in a tetrahedral field through to a trigonal molecule in a trigonal field is illustrated. The group (C3v, [Cbar]3v) is treated in detail and applied to the tunnelling states of monodeuteromethane adsorbed on the surface of graphite. The rotational Hamiltonian matrix is constructed in the pocket state formalism and diagonalized using the character table for (C3v, [Cbar]3v). The quantitative appearance of the energy level diagram for the ground librational state of CH3D on graphite is shown.

Elastic properties of the incommensurate phase of akermanite, Ca2MgSi2O7

The crystal structure of akermanite, Ca2Mg-Si2O7, consists of mixed tetrahedral sheets formed by [MgO4] tetrahedra and [Si2O7] groups interleaved along the c axis with Ca2+ ions in eight-fold coordination. Above 358 K, the structure is tetragonal \((P\bar 42_1 {\text{ }}m)\), and below it is incommensurate with modulations parallel to [110] and \([1\bar 10]\). The elastic stiffness moduli, Cij of the incommensurate phase at room temperature were measured from wave velocities in the 20–75 MHz carrier frequency range by the ultrasonic phase comparison method using optically clear synthetic single crystal plates (3×3×2 mm) oriented parallel to (100), (001), (110) and (101) planes. The Cij values (GPa) are: C11 159.40, C33 149.43, C44 30.26, C66 58.10, C12 76.58 and C13 57.80. In (010) and (001) planes, the compressional modulus, ρV2(L) from the longitudinal wave, L is considerably larger than the shear moduli, ρV2(T1, T2) both from the in-plane and perpendicular-to-plane shear waves, T1 and T2. The relatively small values of the shear moduli indicate the ease of tetrahedral rotations in response to in-plane and perpendicular-to-plane shears and may provide preconditions for structural changes involving shear-type atomic movements.

Five manganoan zinnwaldites from Japanese pegmatites.

Chemical and physical data for five manganoan zinnwaldites from Japan were analysed and were found to be high in fluorine, reflecting the crystallization under relatively high f (HF or F2) conditions. All specimens belong to 1M polytype. The role of fluorine on the formation of 1M type of mica structure was considered. Tetrahedral rotation angles α of five zinnwaldites were calculated from powder data.

Rietveld Refinement of Non-Hydrogen Atomic Positions in Kaolinite

AbstractThe structure of kaolinite (non-hydrogen atoms only) from Keokuk, Iowa, was refined in space group C1 using CuKα X-ray powder diffraction data and Rietveld refinement techniques (Rwp = 12.3%). A distance least-squares (DLS) model for the initial atomic coordinates avoided a false minimum and unrealistic results characteristic of previous Rietveld refinements of kaolinite. All Keokuk samples examined contain small amounts of dickite. The profile of the mixture was calculated using a fixed set of dickite atomic parameters and by constraining the dickite profile parameters to those refined for kaolinite. Results indicate that the individual kaolinite layer is very similar to the dickite layer; bond distances, which are similar to dickite and nacrite, are: Si-O, 1.60-1.63 Å; Al-O, 1.87-1.97 Å. The tetrahedral rotation angle is 6.9°, compared with 7.3° for dickite and 7.4° for nacrite. Previous Rietveld refinements apparently suffered from poor preferred orientation models, failure to consider the presence of dickite as a second phase, and, most importantly, refinement to a false-minimum structure. The conclusions based on the earlier refinements must therefore be reevaluated, especially regarding the kaolinite space group and hydrogen positions. Existing X-ray and electron diffraction and spectroscopic data support the presence of C-centering in kaolinite.

Changes in Infrared Spectra and Lattice Constants of Fluorine Micas with Ga-Substitution

The series of Ga-substituted fluorine micas, KMg2+xLi1-x(GaxSi4-x-yGeyO10)F2 and KMg2+xLi1-x(GaxGe4-x-ySiyO10)F2; x=0.0-1.0, y=0, 1, 2, 3, were synthesized and the changes in infrared spectra and lattice constants with Ga-substitution were studied. The larger flakes of mica crystals were obtained with increasing Ga- and Ge-contents. The infrared spectra of the synthesized micas varied sensitively with mica composition. An absorption band, which appeared in the range 740-705cm-1 with increasing Ga-content, is attributable to Ga-O vibration. Continuous changes of lattice constants with increasing Ga-contents proved that there were complete series of solid solutions between the end member micas. Lattice constants a and b increased linearly or almost linearly with increasing Ga-content in all series. However, c⋅sinβ (basal spacing) decreased or remained almost unchanged in the case of Ga-for-Ge substitution, while it increased linearly in the case of Ga-for-Si substitution. These complicated changes of cell dimensions were shown clearly by the plots of c⋅sinβ vs. b-dimension and explained in terms of the tetrahedral rotation angle α, the octahedral flattening angle ψ, and the change of interlayer conformation, where α and ψ show the degree of structural deformation in mica structure. It is also indicated that the degree of structural deformation increased with increasing Ga and Ge contents.

M�ssbauer effect and X-ray diffraction studies of synthetic iron bearing trioctahedral micas

Mossbauer effect, (ME) and powder X-ray diffraction, (XRD) have been used to study the relationship between cationic size, tetrahedral layer rotation, octahedral layer flattening, stability, and Mossbauer quadrupole splitting, qs, of iron bearing trioctahedral micas. Tetrahedral layer rotation accounts for much of the lattice adjustment but biotites that require an angle of rotation higher than 21 degrees are not stable. Both experimental and computational data show that qs for Fe3+ (IV) increases with increasing degree of tetrahedral layer rotation. A systematic increase of qs for Fe2+ (VI) is also observed, but this could be due to factors other than tetrahedral layer rotation.

Refinement of the Crystal Structure of Phengite-2M1

AbstractThe crystal structure of phengite-2M1 from Rio de Oro, Spanish Sahara, was refined in space group C2/c to a residual of 3.3% with 1267 independent X-ray diffraction reflections. The composition of the mica determined by electron microprobe analysis is (K0.948Na0.051Ba0.027)(Al1.510Mg0.273Fe0.144Cr0.095Ti0.010Mn0.003)2.035(Si3.253Al0.747)O10(OH)2. The cell dimensions are a = 5.2153(5), b = 9.043(2), c = 19.974(9) Å, β = 95.789(9)°, and V = 937.2(3) Å3. The substitution of Si for Al in the tetrahedral sheet and larger divalent cations for Al in the octahedra allows the amount of distortions that are generally required to alleviate tetrahedral-octahedral sheet lateral misfit in muscovite, such as tetrahedral rotation and octahedral flattening, to be reduced. The O…H vector is nearly horizontal and points slightly into the octahedral sheet where it may be involved in hydrogen bond contacts inside M(1). In contrast to previously reported refinements of all but one other phengite, no ordering of tetrahedral cations was found in the study specimen. This disorder is considered to be due to the low-pressure, high-temperature amphibolite facies environment of crystallization.

X-ray studies of defects in clays

Defects are any departures from the ideal well-ordered structure. Defects in clays can be classified in three categories: those affecting the layers themselves (cis- or transvacancies, rotation of tetrahedra, localization of the isomorphous substitutions, etc.); those specific to the interlamellar space (position of the cations and, for example, of the water molecules); and stacking faults (including a change in the nature of stacked layers). X-ray studies of clays usually involve the analysis of powder diagrams generally perturbed by a partial orientation of the particles in the powder. The paper will present a general approach to the determination of defects in clays with an indirect method of analysis. The intensities and shapes of the diffraction bands are calculated for model structures and are fitted to the experimental pattern. In such an approach the powder orientation, the shape and sizes of the coherent domains, the various backgrounds and perturbations due to the apparatus are taken into account.

Crystal Structure of Cronstedtite-2H2

AbstractThe crystal structure of a magnesian cronstedtite-2H2 from Pribram, Czechoslovakia, was refined in space group C1 to a residual of 5.4% with 1832 independent reflections. Tetrahedral ordering between Fe3+ and Si is judged to be complete on the basis of electron density maps, the first confirmation of such ordering in a layer silicate. Octahedral cations are disordered on the M sites. Mean T-O bond lengths do not confirm the tetrahedral ordering, perhaps due to tetrahedral distortion in order to relieve the extreme corrugation of the sheet that would arise from ordering of such different size cations.In the initial stages of refinement the structure of the crystal under study could not be described adequately on the basis of a single 2H2 polytype. The structure contains two kinds of 2H2 domains that appear shifted by b/3 relative to one another due to a mistake in the interlayer stacking sequence. This mistake of zero shift (the normal 2H2 polytype consists of alternating —b/3 and +b/3 shifts) affects only the tetrahedral sheets. It creates adjacent enantiomorphic domains of 2H2 packets such that domains with small Si tetrahedra sit above larger Fe3+-rich tetrahedra and vice versa. This mechanism to relieve strain may indeed be the cause of the stacking mistakes. A third kind of domain contains regions in which the sense of tetrahedral rotation is reversed, giving rise to split basal oxygens on electron density maps. This multiple domain model best explains extra atomic positions observed on Fourier maps, lack of streaking of k ≠ 3n reflections, and possible nonintegral “satellitic” reflections observed on Weissenberg films.

Structure refinement of an 1M‐lepidolite

AbstractThe structure of an 1M‐lepidolite from Wakefield (Canada) has been investigated by X‐ray diffraction structure analysis. The refined atomic coordinates and occupation factors indicate an ordered distribution of the octahedrally coordinated cations. The structure has the space group C 2. The tetrahedra do not show any remarkable ordering of their central cations. Octahedral flattening is characterized by a mean octahedral angle of 58.66°. The tetrahedral rotation angle is equal to 5.9°.

Synthesis and the crystal structure of a manganoan fluoromica, K(Mg2.44Mn0.24)Si3.82Mn0.18)O10F2.

Synthesis of a manganoan fluoromica KMg3(Si3.5Mn0.5)O10F2 with Mn in fourfold coordination was tried, utilizing mixtures of KF, MgF2, MgO, SiO2 and MnC2O4 for the starting materials. Mica crystals were obtained below 1150°C after crystallization of manganoan chondrodite (Mg, Mn)5Si2O8(OH, F)2. The X-ray structure analysis revealed that the crystal has a structure of the 1 M mica with cell dimensions of a=5.285(1), b=9.157(1), c=10.190(2)A and β=99.97(2)°, and a chemical composition corresponding to K(Mg2.44Mn0.24)(Si3.82Mn0.18)O10F2. The structure refinement was carried out with the full-matrix least-squares procedure to the final R value of 0.043 for 1131 observed reflections. The (Si, Mn)–Oapical distance is 1.616A and the mean (Si, Mn)–Obasal distance is 1.638A. The mean (Si, Mn)–O distance of 1.632A is longer than the literature value of 1.625A for the mean Si–O distance in the SiO4 tetrahedra by 0.007A, supporting the conclusion that Mn atoms substituted a part of Si4+ ions at the tetrahedral sites in the present experiment. The mean octahedral cation-anion distances are 2.071A for M(1) octahedra and 2.070A for M(2). The tetrahedral rotation angle is 1.73°, and the octahedral flattening angles are 58.4° for M(1) octahedra and 58.3° for M(2).

Crystal structure and thermal expansion of α-quartz SiO2 at low temperatures

The crystal structure of α-SiO2 (low quartz) has been refined at 296, 78, and 13 K from time-of-flight neutron powder diffraction data. The major effect of temperature from 296 to 78 K is a nearly rigid body rotation of the SiO4 tetrahedra. Below 78 K, tetrahedral rotation is substantially reduced giving rise to a much smaller thermal expansion. A comparison of the volume dependence of the Si-O-Si angle, the rotation angle for SiO4 tetrahedra and the c/a ratio suggests that the mechanism for expansion may be changing from tetrahedral rotation to tetrahedral distortion at the lowest temperatures. The inverse linear relation between the mean Si-O bond distance and −sec(Si-O-Si) which has been observed for silica minerals at both ambient and high-temperature conditions appears to be consistent with the structural variations that occur at low temperatures.

Structure variation with octahedral cation substitution in the system of germanate micas, KMg3-xMnxGe3AlO10F2.

Structure variation with octahedral cation substitution in manganoan germanate micas KMg3−xMnxGe3AlO10F2 has been examined by refining the structures of two specimens with Mg/Mn ratios of about 1/0.3 and 1/2. The crystals are monoclinic with the space group C2⁄m. The cell dimensions are a=5.435(1), b=9.413(2), c=10.458(3) A and β=100.03(3)° in the Mg-rich specimen and a=5.489(1), b=9.509(1), c=10.462(3) A and β=100.12(2)° in the Mn-rich one. The stuctures were refined with the full-matrix least-squares procedure to the final R values of 0.039 for 1528 observed reflection data of the Mg-rich specimen and 0.050 for 1413 reflection data of the other. The mean Ge,Al-O distance in (Ge,Al)O4 tetrahedra is 1.746 A in the former specimen, while 1.749 A in the latter. Octahedral cations are randomly distributed over the two independent octahedral sites in each specimen. The tetrahedral rotation angles are 14.9° and 13.2° in the Mg-rich and Mn-rich ones, respectively. The thickness of the octahedral sheet increases approximately linearly with the degree of octahedral substitution and that of the tetrahedral sheet remains almost constant, while the interlayer thickness shows a discontinuous change.

Rotated and extended model structures in amphiboles and pyroxenes

SummaryThe model for the amphibole and pyroxene structures based on close-packed oxygen layers introduced by Thompson is investigated systematically. It is shown that different features of it can best be understood in terms of three different symbolisms: the O and S rotations of tetrahedra; the A,B, C stacking notation for close-packed layers; and the c, h notation for the relationship of close-packed layers to their neighbours. The possible stacking arrangements and their space-groups are derived systematically. Relationships between the close-packed, fully rotated, model and the extended chain model are discussed, and some important drawbacks in the former model are pointed out, especially in connection with real amphibole structures.

X-ray and infrared investigations of a synthetic dioctahedral vermiculite saturated with alkali and alkaline earth cations

AbstractA synthetic dioctahedral vermiculite was saturated with Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr and Ba, and examined by X-ray diffraction and infrared spectroscopy under various dehydration conditions. Cations which were larger than the ditrigonal hole (Cs, Rb, Ba) increased the b-dimension by forcing the oxygen triads open. With small cations the b-dimension decreased as a function of the residual water content rather than of cation size. The OH stretching vibration did not change in position, probably due to the inclined orientation of OH groups. The cations perturbed the lattice vibrations when they caused a change in the tetrahedral rotation angle, i.e. in b-dimension. With the small cations Be, Li and Mg, librations below 450 cm−1 shifted towards higher frequencies indicating cation migration into the empty octahedral sites.

Hydroxyl Orientations in 2:1 Phyllosilicates

AbstractThe hydroxyl orientations in 31 dioctahedral and trioctahedral 2:1 phyllosilicate structures have been determined by electrostatic energy calculations. These structures included micas, brittle micas, and other related minerals exhibiting ordered as well as disordered cation distributions. The dioctahedral micas and brittle micas were examined with and without the interlayer cation. A range of orientations from 1.3° to 183.3° (the angle ρ between the O-H and (001) measured with respect to the M1 site) were found. The orientations for the dioctahedral structures represent a continuum of values whereas the trioctahedral species exhibit two possible orientations separated by an energy barrier. One orientation is near 90° the other is near 180°. The latter orientation results from a concentration of charge on the interlayer (IC) and tetrahedral (T) sites at the expense of the octahedral (M) sites. A multiple regression analysis of all 31 structures, using as predictors the a and b cell parameters, d001, and the charges for T, IC, M1, and M2 sites, was performed. This analysis indicated that the important factors are the charges for IC, T, and M2 sites. When treated as a separate group, one finds the same factors for the dioctahedral structures. The trioctahedral orientations are determined by the charge on the M2 site and the amount of tetrahedral rotation. Using these two predictor equations, the value of ρ can be estimated with a standard deviation of 4.7° and 2.9° for the dioctahedral and trioctahedral cases, respectively.