A TEM and RUM study of the inherent displacive flexibility of the fresnoite framework structure type

 A careful electron diffraction study has been made of the incommensurately modulated room-temperature phases of the fresnoites Ba₂TiGe₂O₈ (BTG) and Ba₂TiSi₂O₈ (BTS) and used to determine their (3+1)- and (3+2)-dimensional superspace group symmetries. The primitive primary modulation wave vectors in both materials are found to occur close to the same position in the parent Brillouin zone, near ∼0.3〈110〉 _p ^*+1/2c _p ^st . A rigid unit mode (RUM) analysis of the inherent displacive structural flexibility of the ideal fresnoite framework structure type is then carried out in an attempt to understand the significance of this particular modulation wave vector. Six zero-frequency RUM modes and two close to zero frequency quasi-RUM (Q-RUM) modes are found to exist for any modulation wave vector. These RUM modes are all primarily associated with rotations of the constituent TO₄ (T=Si or Ge) tetrahedra and TiO₅ square pyramids around in-plane i.e. perpendicular to c rotation axes. A seventh RUM mode involving rotation of the constituent rigid polyhedra around c combined with shifts in the basal plane is found but only at a very specific modulation wave vector q∼0.30〈110〉 _p ^* , in close agreement with the condensed RUM mode found in the electron diffraction study. It is the condensation of just such a RUM mode that appears to play a major role in the various incommensurately modulated structures observed in Ba₂TiGe₂O₈, Ba₂TiSi₂O₈ and Sr₂TiSi₂O₈, respectively. Received: 26 November 2001 / Accepted: 25 May 2002 Present address: Y. Tabira Materials Characterization Laboratory Mitsui Mining & Smelting Co. Ltd. 1333-2 Haraichi, Ageo, Saitama 362-0021, Japan     

X-ray powder diffraction study on the modulated high temperature forms of SiO2 tridymite between 110 and 220 °C

 The crystal structure of intermediate incommensurate tridymite was refined at 150 °C from powder data. Upon cooling from above 220 °C, the basic structure with space group symmetry C222₁ is gradually distorted from orthorhombic to monoclinic symmetry. With decreasing temperature, the monoclinic angle γ smoothly opens up to 90.3°, while a displacive modulation with temperature-dependent wavelength develops. The 3 + 1 dimensional superspace group of the incommensurate phase is C112₁(αβ0). The modulation mainly consists of two sinusoidal transverse displacement waves for the silicon atoms coupled to rotations of the rigid SiO_4/2 tetrahedra. The wave vector is r=0.1192(1)a* − 0.0043(1)b* at 150 °C. Below 150 °C tridymite discontinuously transforms to another orthorhombic phase and the modulation partially locks in at the wave vector r ₁=1/3a*. Simultaneously, an additional incommensurate modulation with r ₂= 0.0395(1)b* − 0.3882(1)c* is formed. The two-dimensional modulation does not vary significantly with the temperature. Received: 13 September 2000 / Accepted: 29 January 2001     

Potassium coordination in trioctahedral micas investigated by K-edge XANES spectroscopy

Summary Fine-grained homogeneous powder samples of thirteen trioctahedral micas, mostly intermediate members of the phlogopite – annite solid solution series, and samples close to the phlogopite, fluor-phlogopite and tetra-ferriphlogopite end members have been examined at the potassium K-edge by X-ray absorption fine structure spectroscopy. The interlayer K⁺ cation is in a coordination that is certainly lower than 12, in contrast to what is expected from the ideal hexagonal symmetry model of the mica structure, and approaches – but it does not reach – coordination 6, as it should be when the effective ligands are the three nearest outer bridging oxygens of two facing upper and lower tetrahedral sheets. The observed range of coordinations implies that only some of the three inner bridging oxygen atoms in each sheet are involved, thus leading to 6±(1 … 6) effective configurations depending on the composition of the individual mica terms. The effective coordination number was found to vary continuously with composition from 11 to 7 and to be related to the tetrahedral rotation angle (α) according to two different linear relationships for the phlogopite – annite series (Fe²⁺Mg₋₁ exchange vector, involving the octahedral sheet only) and the phlogopite – tetra-ferriphlogopite series (Fe³⁺Al₋₁ vector, involving the tetrahedral sheet), respectively. Substitutions affecting either the A cation in the interlayer or the X anion in the octahedral sheet also affect the observed trends. In particular, the latter substitution effect is best seen in two near end member phlogopites, where the fluorine to hydroxyl substitution (F⁻ (OH)⁻₋₁ exchange vector), which greatly changes the α tetrahedral rotation angle is, reflected in the experimental K XANES spectra by modifying not only the energy but also the intensities of most multiple scattering features.     

Structured diffuse scattering, displacive flexibility and polymorphism in Ba-hexacelsian

 The results of a temperature-dependent electron diffraction study of the low frequency modes of distortion of Ba-hexacelsian and their relationship to the α-β polymorphic phase transition therein are presented. Cs- and Rb-doped Ba-hexacelsian specimens are also investigated. An extremely strong and characteristic diffuse intensity distribution in the form of polarized sheets of diffuse intensity perpendicular to the <1 1 0> directions is found for the high temperature polymorph and the doped specimens. The diffuse distribution appears to result from coupled tetrahedral rotation of <1 1 0> columns of corner-connected (Al,Si)O₄ tetrahedra about the [0 0 1] axis (uncorrelated from column to column as a result of the positioning of the rotation axes). Received: 25 January 1999 / Revised, accepted: 13 July 1999     

Thermal expansion and dehydroxylation of phengite micas

Phengite samples (2M ₁ and 3T politypes) and a synthetic end-member muscovite specimen were studied by in situ high-temperature synchrotron radiation X-ray diffraction. The measured volume thermal expansion of 2M ₁ phengite (<α _V> ≈ 36.6 × 10⁻⁶ K⁻¹) was systematically greater than <α _V> of the 3T polytype (≈33.3 × 10⁻⁶ K⁻¹). A positive linear correlation between the average thermal expansion on (001) plane and the mean tetrahedral rotation angle at ambient condition is proposed on the ground of new measurements and literature data. Dehydroxylation processes were observed in 2M ₁, starting at 1,000 K in 3T at 800 and 945 K in synthetic muscovite. Rietveld refinements allowed a determination of structural variations upon heating of phengite samples and their dehydroxylate phases. The phengite structure expands by regularizing the tetrahedral sheet and by reducing the bond length differences between the outer and inner coordination shell of the interlayer site. The dehydroxylate phase derived from 2M ₁ is characterized by fivefold polyhedra in the low temperature form as a consequence of two OH groups reacting to form H₂O + O (residual). The dehydroxylate exhibits an increase of the cation–cation distances along the M–Or–M bonds with respect to low-temperature phengite structures. For the 3T phase, we were unable to achieve completion of dehydroxylation. The refined structural model of the dehydroxylate phase shows two hydroxyl sites, but at a short distance from one another. This result suggests that the dehydroxylation reaction did not proceed to completion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Direct observation of anti-phase domain structure in omphacite

Single crystal electron diffraction patterns of an omphacite (CaNa, Mg²⁺, Fe²⁺, Al³⁺, Fe³⁺)Si₂O₆ from a glaucophane schist facies (type C) eclogite, Tiburon Peninsula, California show weak reflections violating the C2/c space group. Transmission electron microscopy with dark field imaging, using h+k = even reflections reveal no special features, while dark field viewing through certain superstructure reflections violating the C2/c space group (h k l, with h+k = odd and h 0 l with h and/or l odd) reveal anti-phase domains, 100 to 3000 Å in width. Diffraction contrast experiments show that these domains are related by a displacement vector R=1/2[110]. This displacement vector explains the origin of the domains in terms of ordering of various cations in the octahedral (M1 type) and polyhedral (M2 type) sites without any changes in the tetrahedral silicate chains.     

Heat capacities of Tschermak substituted Fe-biotite

Six members of the annite–siderophyllite join were synthesized in a three step process – crystallization of biotite from gels, decomposition of the fine-grained biotite under oxidizing conditions and resynthesis of Fe-Al biotite with planned compositions from these products – producing biotite crystals with thicknesses of up to 10 μm. The biotite was characterized by microprobe, electron microscopy and X-ray diffraction. Heat capacities of these biotites were measured with a DSC (differential scanning calorimeter) over the temperature range 143 to 623 K. Using a least-squares technique, the data were fitted to a c_p-polynomial, c _p =k ₀+k ₁ T ^−0.5+ k ₂ T ⁻²+k ₃ T ⁻³. In the temperature range 143 to 250 K, heat capacities of the different annite–siderophyllite members decrease linearly with increasing Al content. At higher temperatures, however, the c_p-polynomial of biotites with intermediate composition (except Ann₇₉Sid₂₁) exhibit a steeper slope than those of other biotites. This produces positive excess heat capacities in the annite–siderophyllite join at higher temperatures. The activity-composition data of the same binary derived from phase equilibrium experiments (Benisek et al. 1996) and the data of this study suggest two compositional regions along this join, with different extent of deviation from ideality. One at X _Sid < 0.3, characterized by a small deviation, one at X _Sid > 0.3 showing a higher nonideality, resulting in a discontinuity visible at this composition. Powder IR-spectra of these solid solutions were measured with a FTIR-spectrometer and used to calculate heat capacities according to the vibrational model of Kieffer (1979). The comparison of the vibrational function with the c_p-polynomials shows that the vibrational function reproduces well the DSC-data of the siderophyllite-poor and -rich members, but deviates for intermediate compositions, where the excess heats of mixing occur. With increasing Tschermak vector, the tetrahedral rotation angle α increases from 0 to 13° for annite to siderophyllite, respectively. At the composition of the discontinuity, this rotation angle α reaches a value of ∼8^∘. The processing of ∼300 chemical data of natural biotites indicates that over 90% of them have a tetrahedral rotation angle that lies between 7 and 9°. It would appear that biotites with these structural characteristics are most stable. Received: 27 August 1998 / Accepted: 10 November 1998     

The Possible Topologic structure Types of Orthopyroxene with Space Group P21ca

The possible topologic structure types of orthopyroxene with space group P21ca comprise four kinds of tetrahedral chains and four kinds of octahedral sites.all of which are non-equivalent in symmetry,In these structure types,the skew of the octahedral layers has a sequence of --,There are sixteen possible combination forms for the rotation type of tetradral chain.Twelve of them violate Thompson ‘s sparity rule and the remainder constitutes two pairs.In each pair,the two polar forms show a relationship of anti-orientation for their polar a-axes.Thus,there are only two possible different topologic structure types for P21ca-orthopyroxene.The ratios of O-rotated and S-rotated tetrahedral chains for these two structure types are 3:1 and 1:3,respectively,In the view S-rotated tetrahedral chains for these two structure types are 3:1 and 1:3,respectively,In the view of crystallochemical principle,the most likely form is the one with a ratio of 3:1,and its constitutions of two stacks of I-beam,which are non-equivalent both in symmetry and in topology,are and the configurations of the two types of M2 sites are P.P and P.N,respectively,A complementary twinning on(100) would be formed between the anti-oriented structure pairs,and their twin boundary is exactly equivalent to the inversion boundary,Moreover,it is possible that the ordered structure would appear when the atom ratio of Mg:Fe is equal to 3:1 as well as to 1：1。     

Rigid unit modes and dynamic disorder: SiO2 cristobalite and quartz

The high temperature (β) phases of SiO₂ cristobalite and quartz are studied by performing molecular dynamics simulations using a model which allows easy analysis of tetrahedral motions. The dynamic nature of the disordered high-temperature phase of cristobalite is attributed to rigid unit mode (RUM) excitations, and it is found that the entire spectrum of RUMs is responsible for the disorder. Comparisons of the results of β-cristobalite with those of β-quartz lead to the conclusion that framework structures with high degrees of geometric flexibility, and hence many RUMs, are free to deform through cooperative tetrahedral rotations even in the limit of extremely large tetrahedral stiffnesses. Received: 10 March 1998 / Revised, accepted 15 January 1999     

Transformations of the stuffed cristobalites, K2MSiO4, M=Mg, Zn, Co, Cd, with temperature and composition

The effects of composition and of temperature on the orthorhombic, Pca2 ₁ to cubic, F4ˉ3m transition of the stuffed cristobalite structure are reported. A distorton index which measures the departure of the orthorhombic unit cell from a metrically cubic cell shows that at room temperature, distortion increases in the progression K₂CdSiO₄ <K₂MgSiO₄ <K₂ZnSiO₄≈K₂CoSiO₄. High temperature X-ray powder measurements document an apparently discontinuous transition to a structure of F4ˉ3m symmetry. Differential scanning calorimetry shows a sharp, reversible, first order transition to the high temperature phase at about 500–600 °C for these compounds. Measured transformation enthalpies in the range of 7 to 16 J/g correlate roughly with the distortion index. The transformation involves tetrahedral rotation to an orientationally disordered cubic structure which retains an ordered M²⁺/Si distribution. Received: 8 November 1996 / Revised, accepted: 14 October 1997     

Comparative compressibility and equation of state of orthorhombic and tetragonal edingtonite

The high-pressure (HP) behaviour of a natural orthorhombic and tetragonal edingtonite from Ice River, Canada, has been investigated using in situ single-crystal X-ray diffraction. The two isothermal equations of state up to 6.74(5) GPa were determined. V₀, K_T0 and K refined with a third-order Birch–Murnaghan equation of state (BM-EoS) are: V₀ = 598.70(7) ų, K_T0 = 59(1) GPa and K=3.9(4) for orthorhombic edingtonite and V₀ = 600.9(2) ų, K_T0 = 59(1) GPa and K=4.2(5) for tetragonal edingtonite. The experiments were conducted with nominally hydrous pressure penetrating transmitting medium. No overhydration effect was observed within the pressure range investigated. At high-pressures the main deformation mechanism is represented by cooperative rotation of the secondary building unit (SBU).Si/Al distribution slightly influences the elastic behaviour of the tetrahedral framework: the SBU bulk moduli are 125(8) GPa and 111(4) GPa for orthorhombic and tetragonal edingtonite, respectively. Extra-framework contents of both zeolites show an interesting behaviour under HP conditions: the split Ba2 site at P >2.85 GPa is completely empty; only the position Ba1 is occupied. Electronic Supplementary Material. Supplementary material to this paper (Observed and calculated structure factors) is available in electronic form at Electronic Supplementary Material Supplementary material is available in the online version of this article at     

Pressure-induced phase transition in synthetic trioctahedral Rb-mica

 The crystal structure of a synthetic Rb analog of tetra-ferri-annite (Rb–TFA) 1M with the composition Rb_0.99Fe²⁺ _3.03(Fe³⁺ _1.04 Si_2.96)O_10.0(OH)_2.0 was determined by the single-crystal X-ray diffraction method. The structure is homooctahedral (space group C2/m) with M1 and M2 occupied by divalent iron. Its unit cell is larger than that of the common potassium trioctahedral mica, and similar lateral dimensions of the tetrahedral and octahedral sheets allow a small tetrahedral rotation angle α=2.23(6)°. Structure refinements at 0.0001, 1.76, 2.81, 4.75, and 7.2 GPa indicate that in some respects the Rb–TFA behaves like all other micas when pressure increases: the octahedra are more compressible than the tetrahedra and the interlayer is four times more compressible than the 2:1 layer. However, there is a peculiar behavior of the tetrahedral rotation angle α: at lower pressures (0.0001, 1.76, 2.81 GPa), it has positive values that increase with pressure [from 2.23(6)° to 6.3(4)°] as in other micas, but negative values −7.5(5)° and −8.5(9)° appear at higher pressures, 4.75 and 7.2 GPa, respectively. This structural evidence, together with electrostatic energy calculations, shows that Rb–TFA has a Franzini A-type 2:1 layer up to at least 2.81 GPa that at higher pressure yields to a Franzini B-type layer, as shown by the refinements at 4.75 and 7.2 GPa. The inversion of the α angle is interpreted as a consequence of an isosymmetric displacive phase transition from A-type to B-type structure between 2.81 and 4.75 GPa. The compressibility of the Rb–TFA was also investigated by single-crystal X-ray diffraction up to a maximum pressure of 10 GPa. The lattice parameters reveal a sharp discontinuity between 3.36 and 3.84 GPa, which was associated with the phase transition from Franzini-A to Franzini-B structure. Received: 21 October 2002 / Accepted: 25 February 2003     

Early Palaeozoic sub-arc chromitite-bearing peridotite in the Kudi ophiolite on the westernmost Tibetan Plateau

ABSTRACT

A chromite deposit was discovered in the Kudi ophiolite in the Palaeozoic western Kunlun orogenic belt. Chromite forms elongated (<2 m in width) and banded chromitite bodies (<0.1 m in width for each band) in dunite and podiform chromitite bodies (<1.5 m in width) in harzburgite. Dunite is classified into two types. Type I dunite hosting massive and banded chromitites shows low Fo in olivine (88.1–90.9), moderate Cr^# [=Cr/(Cr + Al), 0.47–0.56] in chromite, and a positively sloped primitive mantle-normalized platinum group elements (PGE) pattern, suggesting that it is a cumulate of a mafic melt. Harzburgite and type II dunite show olivine with high Fo (>91.1) and chromite with moderate to high Cr^# (0.44–0.61), and flat to negatively sloped primitive mantle-normalized PGE patterns, indicating that they are residual mantle peridotite after partial melting. Chromite in all three types of chromitites has relatively uniform moderate values Cr^# ranging from 0.43 to 0.56. Massive chromitite contains euhedral chromite with high TiO₂ (0.40–0.43 wt.%) and has a positively sloped primitive mantle-normalized PGE pattern, suggesting that it represents a cumulate of a melt. Rocks containing disseminated and banded chromite show overall low total PGE, < 117 ppb, and a negatively sloped primitive mantle-normalized PGE pattern. Chromite grains in these two types of occurrences are irregular in shape and enclose olivine grains, suggesting that chromite formed later than olivine. We suggest that chromite-oversaturated melt penetrated into the pre-existing dunite and crystallized chromite. The oxygen fugacity (fO₂ values of chromitites and peridotites are high, ranging from FMQ+0.8 (0.8 logarithmic unit above the fayalite-magnetite-quartz buffer) to FMQ+2.3 for chromitites and from FMQ+0.9 to FMQ+2.8 for peridotites (dunite and harzburgite). The mineral compositions and high fO₂ values as well as estimated parental magma compositions of the chromitites suggest that the Kudi ophiolite formed in a sub-arc setting.     

Characterization of the chemical structures of natural and synthetic aluminosilicate gels and sols by infrared spectroscopy

Infrared spectra in the 300–1400 cm^?1 region indicate that the non-crystalline products of interaction between hydroxyaluminium species and orthosilicic acid in dilute aqueous solutions of pH < 5 differ markedly in structure from those formed in near-neutral and alkaline solutions of pH > 6. The compound formed in acid solution has an infrared spectrum similar to imogolite, and is termed proto-imogolite; like imogolite, it contains orthosilicate groups and 6-coordinated aluminium, and has an ideal Si:Al ratio of around 0.5, but it can incorporate some excess alumina or silica and it does not have the regular tubular structure of imogolite. Compounds formed in alkaline solutions that are not too dilute have infrared spectra resembling the feldspathoid group of minerals and are termed hydrous feldspathoids. They incorporate a condensed tetrahedral framework with an Si:Al ratio greater than one, but can also contain 6-coordinated aluminium.Natural allophanes of the proto-imogolite and hydrous feldspathoid types exist. The allophane of weathered pumice, however, contains a condensed silicate anion that incorporates little tetrahedral aluminium. Proto-imogolite forms stable sols at pH < 5 and must play an important role in the transport of aluminium in acidic natural waters containing dissolved silica.     

An electron diffraction study of the polymorphs of siO2-tridymite

The results of a detailed TEM study of the low frequency modes of distortion of high temperature SiO₂-tridymite and their relationship to the extensive structural polymorphism of tridymite are presented. It is found that low energy modes of distortion of the ideal tridymite tetrahedral framework structure give rise to a strong and extremely characteristic diffuse intensity distribution (which can be broken into two component types) for the two highest temperature polymorphs of tridymite. Experimental results strongly suggest that this observed diffuse distribution is not a result of irreversible beam damage but is rather an intrinsic property of the ideal tridymite tetrahedral framework structure. The diffuse intensity distribution is closely related to the lower temperature polymorphs of tridymite — in particular, the primary modulation wave-vectors of these low temperature polymorphs always fall on the higher temperature diffuse distribution. The first type of diffuse distribution appears to result from coupled tetrahedral edge rotation of 〈110〉 columns of corner-connected SiO₄ tetrahedra (uncorrelated from column to column as a result of the tetrahedral connectivity of the ideal tridymite framework structure). The real space structural origin of the second curved type of diffuse distribution, however, remains unclear.     

Rigid unit modes at high pressure: an explorative study of a fibrous zeolite-like framework with EDI topology

We report a comparative study on the high pressure (HP) structural behaviour of a fibrous zeolite (with EDI topology) on the basis of rigid unit modes (RUM) modelling and previously published single-crystal X-ray diffraction. HP single-crystal diffraction data lead to a more precise determination of the elastic parameters (axial and volume compressibilities) useful to define the equation-of-state under isothermal conditions, and the structural refinements are useful to describe the main deformation mechanisms of the Si/Al framework and extra-framework content at high pressure. The RUM modelling is applied to simulate the compressive behaviour of the framework, under hydrostatic and non-hydrostatic conditions, using a minimum number of parameters, and to describe the deformation mechanism intuitively in terms of the rotations of the SiO₄ polyhedra. The local and global P-induced deformation mechanisms of the Si/Al framework observed in experiment (channel ellipticity, SBU rotation) are well reproduced by RUM modelling. The simulation of uniaxial compression (non-hydrostatic conditions) shows an interesting result on the structural behaviour. This comparative study tests the reliability of the RUM modelling in open-framework silicates with a complicated crystal structure.Electronic Supplementary Material: Supplementary material to this paper is available in electronic form at     

Comparison of the surface structure of the tetrahedral sheets of muscovite and phlogopite by AFM

 The surface structure of the tetrahedral sheet of dioctahedral mica muscovite was compared to that of the tetrahedral sheet of trioctahedral mica phlogopite using atomic force microscopy (AFM). AFM revealed distinct structural differences between the tetrahedral sheet surfaces of the two micas. The hexagonal ring in the AFM image of muscovite elongates in the [3 1 0] direction, and the groove runs perpendicular to the [3 1 0] direction. On the phlogopite surface, the hexagonal ring contracts slightly in the a axis direction, but the groove is not apparent. These results were consistent with the bulk structure data of the two micas determined by X-ray diffraction (XRD). The degree of surface relaxation was much larger in muscovite than in phlogopite. In muscovite, the interlayer K reduces the amount of tetrahedral rotation that actually occurs, since the interlayer K is too large for its hexagonal hole after full tetrahedral rotation. Thus, it is naturally expected that muscovite will show more tetrahedral rotation after removal of the interlayer K. It is also expected that muscovite will show more tilting of SiO₄ tetrahedra after cleaving, since an attractive force between the hydrogen in the OH group and the lower basal oxygen should be in operation, due to the decreased distance between them following interlayer K removal. Received: 14 March 2000 / Accepted: 29 July 2000     

Chemical composition of soil vermiculite clays as related to their genesis

Chemical and mineralogical analyses of the clay fraction of eleven soils containing a large amount of vermiculite clay and representing a wide range of parent materials revealed that two types of vermiculite clays exist: (1) An aluminous type in which Al³⁺ substitutes for Si⁴⁺ in tetrahedral positions in the same order of magnitude as in the coarse grained vermiculites and micas, and with Al³⁺ as the dominant octahedral ion. (2) A silicious type in which only Si⁴⁺ occupies the tetrahedral positions, and with Fe³⁺ and Mg²⁺ as the dominant octahedral ions. The aluminous vermiculite clay was found to occur in soils derived from acid igneous rocks and is usally associated with mica, whereas the silicious type was found to occur in soils derived from basic igneous rocks which do not contain mica. Because of this close association of these two types to their parent material, it was concluded that the aluminous vermiculite is a product of alteration of mica whereas the silicious type is a product of synthesis from primary oxides of silica, alumina, iron, and magnesium. Both types of vermiculite clays tend to be dioctahedral in contrast to the trioctahedral nature of the coarse-grained vermiculite.     

First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation (10³lnα). Based on the density functional theory, we investigated how the average Ca–O bond length and the reduced partition function ratios (10³lnβ) and 10³lnα of ⁴⁴Ca/⁴⁰Ca in forsterite (Fo) are affected by its Ca concentration. Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 Å with the Ca/(Ca + Mg) varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64. However, outside this narrow range, i.e., Ca/(Ca + Mg) is lower than 1/64 or higher than 1/8, Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant. Because the 10³lnβ is negatively correlated with Ca–O bond length, the 10³lnβ significantly increases with decreasing Ca/(Ca + Mg) when 1/64 < Ca/(Ca + Mg) < 2/16. As a consequence, the 10³lnα between forsterite and other minerals also strongly depend on the Ca content in forsterite. Combining previous studies with our results, the heavier Ca isotopes enrichment sequence in minerals is: forsterite > orthopyroxene > clinopyroxene > calcite ≈ diopside > dolomite > aragonite. Olivine and pyroxenes are enriched in heavier Ca isotope compared to carbonates. The 10³lnα between forsterite with a Ca/(Ca + Mg) of 1/64 and clinopyroxene (Ca/Mg = 1/1, i.e., diopside) is up to ~ 0.64‰ at 1200 K. The large 10³lnα_Fo-diopside relative to the current analytical precision for Ca isotope measurements suggests that the dependence of 10³lnα_Fo-diopside on temperature can be used as a thermometer, similar to the one based on the 10³lnα of ⁴⁴Ca/⁴⁰Ca between orthopyroxene and diopside. These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.

     

Crystal chemistry and OH defect concentrations in spodumene from different granitic pegmatites

Thirty spodumene samples of distinct paragenetic types (primary magmatic, secondary after petalite and hydrothermal) from variety of granitic pegmatites were characterized by electron microprobe, polarized FTIR spectroscopy and Mössbauer spectroscopy. The FTIR spectra of OH (weak sharp pleochroic bands at 3,425, 3,410, 3,395 cm⁻¹ and in the 3,500–3,470 spectral region) are strongly polarized with maximum absorption parallel to n_γ. The majority of OH dipoles are presumably generated by a partial replacement of O2 oxygen atoms with an orientation pointing above the Li vacancy site. The separation of the bands probably resulted from a replacement of the coordinating Al by Fe and Si by Al. Homogeneous spodumene mostly close to its ideal formula LiAlSi₂O₆ shows Fe (0.00–0.10 apfu as Fe³⁺; Fe³⁺ >> Fe²⁺) and Na (0.00–0.04 apfu) as the only minor cations and Fe³⁺Al₋₁ substitution up to 10 mol% of the LiFe³⁺Si₂O₆ component. Hydrogen concentrations (from 0.1 up to <5 ppm H₂O by weight) vary as a function of genetic type with the highest amounts in high-temperature magmatic spodumene. Differences among particular genetic types of spodumene are related to maximum solubility of OH in spodumene structure at given P–T conditions and at actual chemical composition of spodumene. OH defect concentrations in spodumene follow a trend, LT/LP pyroxenes containing lower hydrogen contents compared to HT/HP ones. The hydrogen contents in particular genetic types of spodumene and their decrease with decreasing T and P are consistent with petrologic models of the pegmatite (sub)types formations.