Magnetic behavior of trioctahedral micas with different octahedral Fe ordering

This contribution is finalized at the discussion of the magnetic structure of two samples, belonging to phlogopite–annite [sample TK, chemical composition ^IV(Si_2.76Al_1.24) ^VI(Al_0.64Mg_0.72 $ {\text{Fe}}_{1.45}^{2 + } $ Mn_0.03Ti_0.15) (K_0.96Na_0.05) O_10.67 (OH)_1.31 Cl_0.02] and polylithionite–siderophyllite joints [sample PPB, chemical composition ^IV(Si_3.14Al_0.86)^VI(Al_0.75Mg_0.01 $ {\text{Fe}}_{1.03}^{2 + } $ $ {\text{Fe}}_{1.03}^{3 + } $ Mn_0.01Ti_0.01Li_1.09) (K_0.99Na_0.01) O_10.00 (OH)_0.65F_1.35]. Samples differ for Fe ordering in octahedral sites, Fe²⁺/(Fe²⁺?+?Fe³⁺) ratio, octahedral composition, defining a different environment around Fe cations, and layer symmetry. Spin-glass behavior was detected for both samples, as evidenced by the dependency of the temperature giving the peak in the susceptibility curve from the frequency of the applied alternating current magnetic field. The crystal chemical features are associated to the different temperature at which the maximum in magnetic susceptibility is observed: 6?K in TK, where Fe is disordered in all octahedral sites, and 8?K in PPB sample, showing a smaller and more regular coordination polyhedron for Fe, which is ordered in the trans-site and in one of the two cis-sites.     

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties

Ephesite, Na(LiAl₂) [Al₂Si₂O₁₀] (OH)₂, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M₁ polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M₁ polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M₁ poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M₁ ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H _f,298.15 ⁰ =-6237372 J/mol, S _298.15 ⁰ =300.455 J/K·mol, G _298.15 ⁰ =-5851994 J/mol, and V _298.15 ⁰ =13.1468 J/bar·mol.     

Calcic amphibole equilibria and a new amphibole-plagioclase geothermometer

There is currently a dearth of reliable thermobarometers for many hornblende and plagioclase-bearing rocks such as granitoids and amphibolites. A semi-empirical thermodynamic evaluation of the available experimental data on amphibole+plagioclase assemblages leads to a new thermometer based on the Al^iv content of amphibole coexisting with plagioclase in silica saturated rocks. The principal exchange vector in amphiboles as a function of temperature in both the natural and experimental studies is \(\left( {Na\square _{ - 1} } \right)^A \left( {AlSi_{ - 1} } \right)^{T1}\) . We have analysed the data using 3 different amphibole activity models to calibrate the thermometer reactions 1. $$1. Edenite + 4 Quartz = Tremolite + Albite$$ 2. $$2. Pargasite + 4 Quartz = Hornblende + Albite.$$ The equilibrium relation for both (1) and (2) leads to the proposed new thermometer $$T = \frac{{0.677P - 48.98 + Y}}{{ - 0.0429 - 0.008314 ln K}} and K = \left( {\frac{{Si - 4}}{{8 - Si}}} \right)X_{Ab}^{Plag} ,$$ where Si is the number of atoms per formula unit in amphiboles, with P in kbar and T in K; the term Y represents plagioclase non-ideality, RTlnγ_ab, from Darken's Quadratic formalism (DQF) with Y=0 for X _ab>0.5 and Y=-8.06+25.5(1-X _ab)² for X _ab<0.5. The best fits to the data were obtained by assuming complete coupling between Al on the T1 site and Na in the A site of amphibole, and the standard deviation of residuals in the fit is ±38°C. The thermometer is robust to ferric iron recalculation procedures from electron probe data and should yield temperatures of equilibration for hornblende-plagioclase assemblages with uncertainties of around ±75° C for rocks equilibrated at temperatures in the range 500°–1100° C. The thermometer should only be used in this temperature range and for assemblages with plagioclase less calcic than An₉₂ and with amphiboles containing less than 7.8 Si atoms pfu. Good results have been attained on natural examples from greenschist to granulite facies metamorphic rocks as well as from a variety of mafic to acid intrusive and extrusive igneous rocks. Our analysis shows that the pressure dependence is poorly constrained and the equilibria are not suitable for barometry.     

Processes of regional metamorphism and ultrametamorphism and some problems of the geology of the deep-lying sections of folded zones

On the basis of 135 pairs of chemical analyses of coexisting hornblendes and biotites, we have established a relationship between the contents of Al^IV, Al^VI, Fe³⁺, Mg, Ti, Na, and K and the overall iron index in the hornblendes and the depth of granitoid formation. This relationship has been emphasized by the R-method of factor analysis. We have examined the strength and nature of the correlations between the elements in the hornblendes and have considered the types of Isomorphism in the amphiboles according to depth, from the viewpoint of crystal chemistry. A regular increase in the amounts of A^IV in hornblende from <0.8 to > 1.6 formula units; of (Al^VI + Fe³⁺ + Ti) from <0.5 to >1. 0 formula units; of (K + Na) from <0.35 to >0. 64 formula units; and of Group A from <0.24 to >0.51 formula units has been recorded from the near-surface granitoids to the ultra-abyssal types. Biotites In this respect display no adequately clear and reliable information.—Authors.     

Magnesiocummingtonite-P21/m: A Ca- and Mn-Poor Clino-Amphibole from New South Wales

A Ca- and Mn-poor clino-amphibole with Mg/Mg+Fe_tot+Mn (atomic ratio)=0.81 is described. The structural formula is $$Na_{0.09} (Ca_{0.19} Mg_{5.45} Fe_{1.23}^{2 + } Mn_{0.04} Fe_{0.00}^{3 + } Ti_{0.01} Al_{0.07} )_{6.99} [(Si_{7.83} Al_{0.17} )_{8.00} O_{22} /(OH)_2 ].$$ The unit-cell constants area ₀=9.49 Å,b ₀=18.00 Å,c ₀=5.30 Å, β=102.0°,V ₀=886 ų, the refractive indices α_Na=1.621, β_Na=1.632, and γ_Na=1.643. These values, when plotted against the Mg/Mg+Fe ratio, fit the extrapolations towards Mg₇[Si₈O₂₂/(OH)₂] from recently published determinative curves for the cummingtonite series. The clino-amphibole, or part of it, has space groupP2₁/m rather thanC2/m. The most magnesian cummingtonites reported thus far have Mg/Mg+Fe+Mn ratios around 0.7, but recently more magnesian Ca-poorP2₁/m clino-amphiboles have been reported. Although Ca and Mn have been claimed to stabilize cummingtonite as against anthophyllite, most magnesian cummingtonites appear to have <0.24 Ca, and <0.1 Mn per formula unit. The nomenclature of the cummingtonite series is discussed. Retaining the subdivision of the cummingtonite series at Mg/Mg+Fe=0.5, the author proposes to reviveTilley’s (1939) name magnesiocummingtonite for members with Mg/Mg+Fe >0.5. Grunerite is reserved for members with Mg/Mg+Fe <0.5. The space group,C2/m orP2₁/m, may be indicated with a suffix, if known.     

Amphiboles of a Metagabbro--Amphibolite Sequence, Hidaka Metamorphic Belt, Hokkaido

The western part of the Hidaka Metamorphic Belt, Hokkaido, consistsof primary pyroxene gabbro and lesser amounts of olivine gabbrothat have been dynamically metamorphosed to metagabbro—gabbroicamphibolite-amphibolite-epidote amphibolite during uplift andshearing about 23 m.y. ago. Textures and the presence of relic and recrystallized amphiboleand plagioclase in the same rock indicate incomplete reactionand non attainment of equilibrium during recrystallization. EPMA and bulk analyses of 165 amphiboles indicate a continuousoverall compositional range from actinolite to dark green hornblende(with 100 mg/(Mg+Fe²⁺+Fe³⁺Mn) ratios varying from 89.5 to 32.0)marked by increasing Al, Fe, Ti, and Na. A compositional gapis usually present between relic and recrystallized amphibolesin any one rock which becomes more prominent with increasingshearing. In addition to host rock chemical control, amphibole compositionis largely dependent on the An content of coexisting plagioclase.Locally epidote and sphene exert a strong influence on bothamphibole and plagioclase compositions. Amphibole Ti and Mncontents decrease with shearing and Fe enrichment of the hostrocks largely as a result of the incoming of rutile, sphene,and Fe-Ti oxides. Analysis of host rock oxidation ratio andamphibole compositions indicates that the rocks essentiallybehaved as closed systems to oxygen during metamorphism. Al^1V-Al^IV, Al^IV-Fe³⁺, and Al^IV-(Na, K)^A are the main substitutionsin the amphiboles. Within any one rock the recrystallized amphibolesare enriched in Al, Fe, Ti, and Na relative to the relice amphiboles.Increasing metamorphism results in a progressive change of amphiboles(recrystallized) to more Fe and Si (rather than Al) rich compositionsreflecting the trend towards greenschist where Fe-actinolite(+Mg chlorite) would be stable. Differentiation of the amphiboles is within the limits of SiAlreplacement and the compositional limits of the early stagereaction rim and replacement amphiboles in the host olivineand pyroxene metagabbros.     

Effect of network-forming cations on the oxygen isotope fractionation between silicate melts: Experimental study at 1400–1570°C

We have experimentally studied the behavior of oxygen isotope composition in silicate melts with a wide range of network-forming cations. Isotopic equilibration of the Di-An eutectic melts modified by addition of Si, Al, Ti, and Fe was carried out in a vertical tube furnace within a temperature range from 1400 to 1570°C. It was established that the value ^{10 3}Lnα between silicic and basic melts at 1400 and 1450°C systematically increases with increase of SiO₂ content, reaching ≈1‰ at 20% melt silica enrichment. The effect of the Fe₂O₃, TiO₂, and Al₂O₃ contents was studied at 1500°C. An increase in Fe₂O₃ from 5 to 20 wt % causes a 0.4‰ increase of δ¹⁸O. An increase in Ti and Al contents results in the non-linear behavior of δ¹⁸O, which decreases in the region of the highest TiO₂ (28.4%) and Al₂O₃ (29.3 %) contents. In the region of moderate Fe₂O₃, TiO₂, and Al₂O₃ contents, the values of δ¹⁸O show monotonous linear dependence on the oxide contents. Methods of estimations of oxygen isotope fractionation coefficients at T > 1400°C in the studied range of network-forming oxides are considered on the basis of experimental data. The calculation of fractionation coefficients with the use of I¹⁸O index showed that experimental values with increase of SiO₂ content deviate from calculated values by 0.3‰ for basic melts and 0.5–0.6‰ in the region of silicic melts. Similar pattern is observed during approximation of a melt by normative mineral composition. The calculation with the Garlick index leads to the systematic underestimation (on average, by 0.3‰) of 10³Lnα as compared to the experimental data. The NBO/T ratio appeared the best parameter to describe 10³Lnα in the melt-melt system, including the region of high-Fe melts. Analysis of experimental data leads us to conclude that the degree of polymerization of the melts in the studied temperature-composition region is the most important factor affecting the oxygen-isotope fractionation in the melt-melt system. Empirical index similar to the Garlick index was proposed to take into account oxygen associated with T-cations: $$I^m = (C_{Si} + aC_{Al} + bC_{Ti} + cC_{Fe^{3 + } } )/\Sigma C_i ,$$ where a, b, and c constants are empirically established coefficients: 0.75, 0. 70, and 1.75, respectively.     

Composition of hornblendes formed during the hercynian progressive metamorphism of the Aracena metamorphic belt (SW Spain)

This paper attempts to illustrate the chemical variations of metamorphic hornblendes regarding host rocks and prograde variations. Changes related to bulk chemistry (orthoamphibolites) mainly concern Si, Al, Mg, Fe_tot and Ca. The Mg, Fe²⁺ and Fe³⁺ contents of hornblendes are, however, not strictly related to host rook compositions and Mg enrichments are correlated with increasing Fe³⁺ contents in the amphiboles. Thus, variations of oxygen fugacity may control the Mg contents of the Ca amphiboles studied but this does not show clear relations with the prograde metamorphism. The most sensitive but irregular variation related to the metamorphic conditions is the prograde enrichment of the alkalis into the A vacant position and an increase of the (Na+K)_tot/Na+K+Ca ratios of the amphiboles. Increasing Ti and Al^IV contents as well as decreasing Al^VI concentrations are also, but much less evidently, related to increasing T and P. A variation trend from tschermakitic to edenitic hornblendes may be drawn using Shido's end members calculation; this tendency and the relative deficiency of Al^VI contents in the low-grade members suggests that the amphiboles studied were subjected to conditions of a low-pressure metamorphism type. Such a conclusion is in agreement with the occurrence of andalusite-cordierite/sillimanite-cordierite associations in the metapelitic rocks, and the absence of Fe-rich garnet and epidote from the orthoamphibolites of the amphibolite facies at Aracena. Comparisons with Ca amphiboles from other metamorphic areas show, in agreement with various authors, that Abukuma hornblendes are similar to those encountered in high-grade thermal aureoles and tonalitic intrusives but different from the hornblendes of Barrovian metamorphism types.     

EPR study of chromium-doped forsterite crystals: Cr3+(M1) with associated trivalent ions Al3+ and Sc3+

Electron paramagnetic resonance (EPR) study of single crystals of forsterite co-doped with chromium and scandium has revealed, apart from the known paramagnetic centers Cr³⁺(M1) and Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2) (Ryabov in Phys Chem Miner 38:177–184, 2011), a new center Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2)–Sc³⁺ formed by a Cr³⁺ ion substituting for Mg²⁺ at the M1 structural position with a nearest-neighbor Mg²⁺ vacancy at the M2 position and a Sc³⁺ ion presumably at the nearest-neighbor M1 position. For this center, the conventional zero-field splitting parameters D and E and the principal g values have been determined as follows: D?=?33,172(29) MHz, E?=?8,482(13) MHz, g?=?[1.9808(2), 1.9778(2), 1.9739(2)]. The center has been compared with the known ion pair Cr³⁺(M1)–Al³⁺ (Bershov et al. in Phys Chem Miner 9:95–101, 1983), for which the refined EPR data have been obtained. Based on these data, the known sharp M1″ line at 13,967?cm^?1 (with the splitting of 1.8?cm^?1), observed in low-temperature luminescence spectra of chromium-doped forsterite crystals (Glynn et al. in J Lumin 48, 49:541–544, 1991), has been ascribed to the Cr³⁺(M1)–Al³⁺ center. It has been found that the concentration of the new center increases from 0 up to 4.4?×?10¹⁵?mg^?1, whereas that of the Cr³⁺(M1) and Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2) centers quickly decreases from 7.4?×?10¹⁵?mg^?1 down to 3?×?10¹⁵?mg^?1 and from 2.7?×?10¹⁵?mg^?1 down to 0.5?×?10¹⁵?mg^?1, i.e., by a factor of 2.5 and 5.4, respectively, with an increase of the Sc content from 0 up to 0.22 wt?% (at the same Cr content 0.25 wt?%) in the melt. When the Sc content exceeds that of Cr, the concentration of the new center decreases most likely due to the formation of the Sc³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2)–Sc³⁺ complex instead of the Cr³⁺(M1)– $ V_{{{\text{Mg}}^{2 + } }} $ (M2)–Sc³⁺ center. The formation of such ordered neutral complex is in agreement with the experimental results, concerning the incorporation of Sc into olivine, recently obtained by Grant and Wood (Geochim Cosmochim Acta 74:2412–2428, 2010).     

Non-ideal Mg-Fe binary mixing in cordierite: Constraints from experimental data on Mg-Fe partitioning in garnet and cordierite and a reformulation of garnet-cordierite geothermometer

The non-ideal regular Mg-Fe binary in cordierite has been derived through multivariate linear regression of the expressionRT InK_D +(P- 1)ΔVK ₁ ⁰ , 298 along with updated subfegular mixing parameter of almandine-pyrope solution (Hackler and Wood 1989; Berman 1990). The data base used for multivariate analyses consists of published experimental data (n = 177) on Mg-Fe partitioning between garnet and cordierite in theP-T range 650–1050°C and 4–12 K bar. The non-ideality can be approximated by temperature-dependent Margules parameters. The retrieved values of ΔH_<T> ^o and ΔH_<T> ^o of exchange reaction between garnet and cordierite and enthalpy and entropy of mixing of Mg-Fe cordierite were combined with recent quaternary (Fe-Mg-Ca-Mn) mixing data in garnet to obtain the geothermometric expressions to determine temperature (T Kelvin): $$\begin{gathered} T(WH) = 6832 + 0.031(P - 1) - \{ 166(X_{Mg}^{Gt} )^2 - 506(X_{Fe}^{Gt} )^2 + 680X_{Fe}^{Gt} X_{Mg}^{Gt} + 336(X_{Ca} + X_{Mn} ) \hfill \\ (X_{Mg} - X_{Fe} )^{Gt} - 3300X_{Ca}^{Gt} - 358X_{Mn}^{Gt} \} + 954(X_{Fe} - X_{Mg} )^{Crd} /1.987\ln K_D + 3.41 + 1.5X_{Ca}^{Gt} \hfill \\ + 1.23(X_{Fe} - X_{Mg} )^{Crd} \hfill \\ \end{gathered} $$ $$\begin{gathered} T(Br) = 6920 + 0.031(p - 1) - \{ 18(X_{Mg}^{Gt} )^2 - 296(X_{Fe}^{Gt} )^2 + 556X_{Fe}^{Gt} X_{Mg}^{Gt} - 6339X_{Ca}^{Gt} X_{Mg}^{Gt} \hfill \\ - 99(X_{Ca}^{Gt} )^2 + 4687X_{Ca}^{Gt} (X_{Mg} - X_{Fe}^{Gt} ) - 4269X_{Ca}^{Gt} X_{Fe}^{Gt} - 358X_{Mn}^{Gt} \} + 640(X_{Fe} - X_{Mg} )^{Crd} \hfill \\ + 1.90X_{Ca}^{Gt} (X_{Mg} - X_{Ca} )^{Gt} . \hfill \\ \end{gathered} $$      

Manganocummingtonite from the mesoproterozoic,Sausar fold belt,central India

Manganocummingtonite occurs with spessartine, quartz and pyrolusite in the Chikmara area, Sausar fold belt, central India. Its composition is [Ca_0.3–0.35(Mg_3.3–3.5Mn_1.6–1.8Fe²⁺ _1.4–1.5)(Si_{7.931–7.997}Al^iv _{0.003–0.069})O₂₂(OH_1.5–2.0F_0.0–0.5)] being fairly rich in Ca, which is indicative of metamorphic temperature in the amphibolite facies. The garnet contains 77.5% spessartine, 13% almandine and minor andradite, grossular and pyrope components. Unusually, there is no carbonate, pyroxene, pyroxmangite, rhodonite, magnetite or hematite. The available Al in the rock stabilized garnet and this mineral incorporated minor Fe³⁺ present in the rock as andradite component. The manganocummingtonite-garnet pairs developed at ～600°C during amphibolite facies metamorphism in low $X_{CO_2 } $ system, stabilized with $X_{Mn/(Mn + Fe^{2 + } + Mg)} $ = 0.25 to 0.28 in the amphibole and 0.85 in the garnet and formed under unusually low fO ₂ conditions for the Sausar region, near channelized fluids which deposited quartz may have controlled the fO ₂ .     

The compositional variation of synthetic sodic amphiboles at high and ultra-high pressures

Sodic amphiboles in high pressure and ultra-high pressure (UHP) metamorphic rocks are complex solid solutions in the system Na₂O–MgO–Al₂O₃–SiO₂–H₂O (NMASH) whose compositions vary with pressure and temperature. We conducted piston-cylinder experiments at 20–30?kbar and 700–800?°C to investigate the stability and compositional variations of sodic amphiboles, based on the reaction glaucophane=2jadeite+talc, by using the starting assemblage of natural glaucophane, talc and quartz, with synthetic jadeite. A close approach to equilibrium was achieved by performing compositional reversals, by evaluating compositional changes with time, and by suppressing the formation of Na-phyllosilicates. STEM observations show that the abundance of wide-chain structures in the synthetic amphiboles is low. An important feature of sodic amphibole in the NMASH system is that the assemblage jadeite–talc?±?quartz does not fix its composition at glaucophane. This is because other amphibole species such as cummingtonite (Cm), nyböite (Nyb), Al–Na-cummingtonite (Al–Na-Cm) and sodium anthophyllite (Na-Anth) are also buffered via the model reactions: 3cummingtonite?+?4quartz?+?4H₂O=7talc, nyböite?+?3quartz=3jadeite?+?talc, 3Al–Na-cummingtonite + 11quartz + 2H₂O=6jadeite + 5talc, and 3 sodium anthophyllite?+?13quartz?+?4H₂O=3 jadeite + 7talc. We observed that at all pressures and temperatures investigated, the compositions of newly grown amphiboles deviate significantly from stoichiometric glaucophane due to varying substitutions of Al^IV for Si, Mg on the M(4) site, and Na on the A-site. The deviation can be described chiefly by two compositional vectors: [Na^AAl^IV]<=>[□^ASi] (edenite) toward nyböite, and [Na^(M4)Al^VI]<=>[Mg^(M4)Mg^VI] toward cummingtonite. The extent of nyböite and cummingtonite substitution increases with temperature and decreases with pressure in the experiments. Similar compositional variations occur in sodic amphiboles from UHP rocks. The experimentally calibrated compositional changes therefore may prove useful for thermobarometric applications.     

A comment on “Calcic amphibole equilibria and a new amphibole — plagioclase geothermometer” by J.D. Blundy and T.J.B. Holland (Contrib Mineral Petrol (1990) 104: 208–224)

Conclusions The calibration by Blundy and Holland is not a calibration of the reaction albite + tremolite = edenite + 4quartz, because the Al^IV content of amphiboles is a combined result of substitutions.The requirements for a calibration of any of these substitutions are: (1) an amphibole-activity model unequivocally accounting for each substitution and (2) a data-set, wherein all amphiboles are buffered by the same assemblages.     

Sapphirine II

The crystal structure of aP2₁/a polymorph of sapphirine (a=11.286(3),b=14.438(2),c=9.957(2) Å, β=125.4(2) °) of composition [Mg_3.7Fe _0.1 ²⁺ Al_4.1- Fe _0.1 ³⁺ ]^IV[Si_1.8Al_4.2]^IVO₂₀ was refined using structure factors determined by both neutron and x-ray diffraction methods to conventionalR factors of 0.067 and 0.031. respectively, forF _obs>2σ. The results of the two refinements agree reasonably well, but a half-normal probability plot (Abrahams, 1974) comparing the two data sets indicates that the pooled standard deviations of the atomic coordinates have been underestimated by a factor of two. The structure of sapphirine, solved initially by Moore (1969), consists of cubic closest packed oxygens with octahedral and predominantly tetrahedral layers alternately stacked along [100]. The layer in which 70% of the octahedral sites are occupied has an Mg-Al distribution characterized by Mg-rich octahedra sharing edges mainly with Al-rich octahedra. Mean octahedral bond lengths correlate well with Al occupancy determined by neutron site refinement if the relative number of shared octahedral edges is taken into account (see Table 1). The predominantly tetrahedral layer has 10% of the octahedral sites occupied by Al and 30% of the tetrahedral sites occupied by Al-Si in the ratio 2.33∶1. There are single chains of Al-Si tetrahedra parallel toz with corner-sharing wing tetrahedra (T5 andT6) on either side in the (100) plane. The meanT-O distance is highly correlated with Al occupancy, X_Al, as determined from the neutron site refinement: $$\langle T - O\rangle = 1.656 + 0.105X_{Al} (r^2 = 0.995).$$ Details of the neutron refinement are summarized below.     

Garnet-clinopyroxene geothermometer

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al₂O₃-Na₂O-SiO₂ is as follows: $$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K _D are given by the following equations $$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$ (mole fractions in garnet) $$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO₃, Fe = FeSiO₃, Ca = CaSiO₃, Al = (Al₂O₃-Na₂O)] K _D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe²⁺+Fe³⁺.     

Distribution of Al between coexisting micas in metamorphic rocks from the Central Alps

In 61 pairs of coexisting biotites and muscovites from the Central Alps total Al scatters considerably, but in both series a gradual increase is noticed with increasing metamorphic grade. The ratio Al _Mu ^tot /Al _Bi ^tot remains virtually constant (1.61 average for greenschist facies, 1.57 for amphibolite facies). Tetrahedral Al varies little in biotites and increases in muscovites-phengites with rising metamorphic grade; accordingly the ratio Al _Mu ^IV /Al _Bi ^IV increases slightly with grade. Far the best control of metamorphism is evidenced by octahedral Al. In the muscovite series, and still more pronounced in the biotite series, Al^VI increases with increasing metamorphic grade. Consequently 1 $$K_D = \frac{{Al_{Mu}^{VI} }}{{Al_{Bl}^{VI} }}$$ decreases from 14 to 3. A map (Fig. 6) representing the regional distribution of the K_D values locates a 100 km long and 23 km broad central zone with low K_D. The outline of this central core almost coincides with the isograds anorthite-diopside-calcite and labradorite-pyroxene-hornblende of the Tertiary regional metamorphism; with some deviations this core also agrees with the zone in which phenomena of partial anatexis are observed. The K_D values of micas from anateotic pegmatites agree with those of associated gneisses and schists. The study demonstrates that in the course of progressive regional metamorphism equilibrium has been approached to an unexpected extent and that the two micas coexisted in a strict sense.     

A possible relation between the masses of black holes in galactic nuclei and the parameters of the host galaxies

Data on about forty virialized galaxy clusters with bright central galaxies, for which both the galactic velocity dispersion (?? _gal) and the stellar velocity dispersion in the brightest galaxies (??*) are measured, have been used to obtain several approximate relations between ?? _gal, ??*, the absolute B magnitude of the brightest central galaxyM _B ^BCG , and the mass of the central massive black holeM _BH: $\begin{gathered} \log \sigma _* = (0.12 \pm 0.14)\log \sigma _{gal} + (2.1 \pm 0.4), \hfill \\ \log \sigma _* = - (0.15 \pm 0.02)M_B^{BCG} + (0.85 \pm 0.5), \hfill \\ \log M_{BH} = 0.51\log \sigma _{gal} + 7.28. \hfill \\ \end{gathered} $ . These relations can be used to derive crude estimates ofMBH in the nuclei of the brightest galaxies using the parameters of the both host galaxies and the host galaxy clusters. The last relation above confirms earlier suggestions of a quadratic relation between the masses of the coronas of the host systems and the masses their central objects: M _hg ^halo ?? M _cent ² . The relations obtained are consistent with the common evolution of subsystems with different scales and masses formed in the process of hierarchical clustering.     

Crystal chemistry of Fe3+-bearing (Mg,Fe)SiO3 perovskite: a single-crystal X-ray diffraction study

Magnesium silicate perovskite is the predominant phase in the Earth’s lower mantle, and it is well known that incorporation of iron has a strong effect on its crystal structure and physical properties. To constrain the crystal chemistry of (Mg, Fe)SiO₃ perovskite more accurately, we synthesized single crystals of Mg_0.946(17)Fe_0.056(12)Si_0.997(16)O₃ perovskite at 26 GPa and 2,073 K using a multianvil press and investigated its crystal structure, oxidation state and iron-site occupancy using single-crystal X-ray diffraction and energy-domain Synchrotron Mössbauer Source spectroscopy. Single-crystal refinements indicate that all iron (Fe²⁺ and Fe³⁺) substitutes on the A-site only, where \( {\text{Fe}}^{ 3+ } /\Upsigma {\text{Fe}}\sim 20\,\% \) based on Mössbauer spectroscopy. Charge balance likely occurs through a small number of cation vacancies on either the A- or the B-site. The octahedral tilt angle (Φ) calculated for our sample from the refined atomic coordinates is 20.3°, which is 2° higher than the value calculated from the unit-cell parameters (a = 4.7877 Å, b = 4.9480 Å, c = 6.915 Å) which assumes undistorted octahedra. A compilation of all available single-crystal data (atomic coordinates) for (Mg, Fe)(Si, Al)O₃ perovskite from the literature shows a smooth increase of Φ with composition that is independent of the nature of cation substitution (e.g., \( {\text{Mg}}^{ 2+ } - {\text{Fe}}^{ 2+ } \) or \( {\text{Mg}}^{ 2+ } {\text{Si}}^{ 4+ } - {\text{Fe}}^{ 3+ } {\text{Al}}^{ 3+ } \) substitution mechanism), contrary to previous observations based on unit-cell parameter calculations.     

Distribution of Mg and Fe in cummingtonite-hornblende and cummingtonite-actinolite pairs from metamorphic assemblages

The atomic fractions Mg/(Mg + Fe) and the Mg-Fe distribution coefficient $$K_{{\text{D}}{\text{.Mg - Fe}}}^{{\text{Ca - am - Cum}}} \left( { = \tfrac{{[{\text{Mg/Fe]}}_{{\text{Ca - am}}} }}{{{\text{[Mg/Fe]}}_{{\text{Cum}}} }}} \right)$$ are calculated for 31 metamorphic cummingtonite-hornblende pairs. Data on 21 pairs are taken from the litterature, and new electron microprobe analyses and structural formulae are presented of nine pairs from Tydal, Sör-Tröndelag, Norway, and of one pair from Cooma, N.S.W., Australia (cf. Kisch, 1969). The electron microprobe methods used are described, particularly the use of mineral standards, and the variation of the mass absorption in substitution series. The hornblendes from the Tydal pairs are markedly pargasitic in composition, and contain minor proportions of the cummingtonite “molecule”. The Mg-Fe distributions in the cummingtonite-hornblende pairs — as plotted on a [Mg/(Mg + Fe)]_Ca-am vs. [Mg/(Mg + Fe)]_Cum diagram (Fig. 3) — differ significantly from the Mg-Fe distribution curve for cummingtonite-actinolite pairs from Quebec (Mueller, 1961). Whereas the actinolites have markedly higher Mg/Fe ratios than the co-existing cummingtonites (K _D.Mg-Fe ^Ca-am-Cum ≈ 1.5–2.0), the cummingtonite-hornblende pairs diverge towards lower values from the distribution coefficient. In most of the metamorphic cummingtonite-hornblende pairs — including the nine pairs from Tydal — the Mg/Fe ratio of the hornblende is lower than in the co-existing cummingtonite, i.e K _D.Mg-Fe ^Ca-am-Cum <1. A relation appears to exist between the Mg-Fe distribution and the Al content of the calcic amphibole phase. This is believed to be due to the non-random distribution of Al^Y among the octahedral lattice sites: in hornblende Al^VI enters the M ₁+M₃ positions, in which Mg is preferred over Fe, rather than M ₂, in which Fe is preferred (Ghose, 1965). Since the cummingtonites remain Al-poor, the over-all Mg/Fe ratio in the hornblende is reduced relative to the co-existing cummingtonite as a result. The variations of the Mg-Fe distribution in the cummingtonite-hornblende pairs can also be related directly to the presence and composition of the plagioclase and other Al-rich phases in the metamorphic mineral assemblage. In any range of Mg/Fe ratios, the cummingtonite-hornblende pairs associated with oligoclase have lower distribution coefficients (0.61–0.81; 12 pairs) than those associated with calcic plagioclase or plagioclase-free assemblages (0.97 to 1.89; 6 pairs); the pairs associated with andesine have intermediate Mg-Fe distributions (0.74–1.15; 6 pairs).     

An experimental study of Ti and Zr partitioning among zircon, rutile, and granitic melt

In order to evaluate the effect of trace and minor elements (e.g., P, Y, and the REEs) on the high-temperature solubility of Ti in zircon (zrc), we conducted 31 experiments on a series of synthetic and natural granitic compositions [enriched in TiO₂ and ZrO₂; Al/(Na + K) molar ~1.2] at a pressure of 10 kbar and temperatures of ~1,400 to 1,200 °C. Thirty of the experiments produced zircon-saturated glasses, of which 22 are also saturated in rutile (rt). In seven experiments, quenched glasses coexist with quartz (qtz). SiO₂ contents of the quenched liquids range from 68.5 to 82.3 wt% (volatile free), and water concentrations are 0.4–7.0 wt%. TiO₂ contents of the rutile-saturated quenched melts are positively correlated with run temperature. Glass ZrO₂ concentrations (0.2–1.2 wt%; volatile free) also show a broad positive correlation with run temperature and, at a given T, are strongly correlated with the parameter (Na + K + 2Ca)/(Si·Al) (all in cation fractions). Mole fraction of ZrO₂ in rutile $ \left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) $ in the quartz-saturated runs coupled with other 10-kbar qtz-saturated experimental data from the literature (total temperature range of ~1,400 to 675 °C) yields the following temperature-dependent expression: $ {\text{ln}}\left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) + {\text{ln}}\left( {a_{{{\text{SiO}}_{2} }} } \right) = 2.638(149) - 9969(190)/T({\text{K}}) $ , where silica activity $ a_{{{\text{SiO}}_{2} }} $ in either the coexisting silica polymorph or a silica-undersaturated melt is referenced to α-quartz at the P and T of each experiment and the best-fit coefficients and their uncertainties (values in parentheses) reflect uncertainties in T and $ \mathop X\nolimits_{{{\text{ZrO}}_{2} }}^{\text{rt}} $ . NanoSIMS measurements of Ti in zircon overgrowths in the experiments yield values of ~100 to 800 ppm; Ti concentrations in zircon are positively correlated with temperature. Coupled with values for $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ for each experiment, zircon Ti concentrations (ppm) can be related to temperature over the range of ~1,400 to 1,200 °C by the expression: $ \ln \left( {\text{Ti ppm}} \right)^{\text{zrc}} + \ln \left( {a_{{{\text{SiO}}_{2} }} } \right) - \ln \left( {a_{{{\text{TiO}}_{2} }} } \right) = 13.84\left( {71} \right) - 12590\left( {1124} \right)/T\left( {\text{K}} \right) $ . After accounting for differences in $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ , Ti contents of zircon from experiments run with bulk compositions based on the natural granite overlap with the concentrations measured on zircon from experiments using the synthetic bulk compositions. Coupled with data from the literature, this suggests that at T ≥ 1,100 °C, natural levels of minor and trace elements in “granitic” melts do not appear to influence the solubility of Ti in zircon. Whether this is true at magmatic temperatures of crustal hydrous silica-rich liquids (e.g., 800–700 °C) remains to be demonstrated. Finally, measured $ D_{\text{Ti}}^{{{\text{zrc}}/{\text{melt}}}} $ values (calculated on a weight basis) from the experiments presented here are 0.007–0.01, relatively independent of temperature, and broadly consistent with values determined from natural zircon and silica-rich glass pairs.