Genetic classification of magmatic rocks from the Alvand plutonic complex,Hamedan, western Iran,based on zircon crystal morphology

The Alvand plutonic complex consists of gabbroic and felsic rocks, the latter can be divided into (1) porphyritic, fine-grained and mylonitic granites and (2) leucocratic granitoids. We investigated the external zircon morphology and their internal structures from all major granitoids of the pluton employing the classic Pupin method supplemented by electron microscope analyses. Zircons of gabbroic rocks are free of visible cores or inclusions and are commonly characterized by {1 0 1} pyramids and {1 0 0} prisms and show mainly zircon types P₅ and D typical for mantel-derived rocks. The zircon population from the porphyritic granite is characterized by the predominance of the pyramidal {2 1 1} and prism {1 1 0} forms and mainly composed of the subtypes S₁, S₂, S₆ and S₇ typical for peraluminous granites of crustal origin. Melt inclusions, recrystallization patches and low-CL intensity rims are typical features in these grains. Zircons from the fine-grained granites are characterized by the predominance of the pyramidal {2 1 1} and the prism face {1 1 0} and by a preponderance of the subtypes S₃, S₄, S₇ and especially S₁₂ and occasionally S₂, L₂, L₃ and L₄, typical for aluminous monzogranites and granodiorites of crustal origin. Some grains have pre-magmatic inherited domains with overgrow rims. The mylonitized granites contain zircons with {1 0 1} pyramids and {1 1 0} prisms and include subtypes G₁, P₁, P₂, S₅ whereas P₃, S₄, L₅ are rarely present, typical for I-type granites. Metamictization, radial cracks and partial overgrowths are prevalent in these zircons. Zircons from the leucocratic granitoids have well-developed magmatic oscillatory zonation and pre-magmatic zircon cores. They are characterized by {1 0 1} pyramids and {1 1 0} prisms and are mainly composed of subtypes L₅, S₅, S₁₀ and rarely P₁, P₂, S₂, S₃, S₄, S₇, G₁ typical for hybrid calc-alkaline granites.     

On the problem of transport species of tungsten by hydrothermal solutions

The solubility of pentatungstate of sodium (PTS) Na₂W₅O₁₆ · H₂O and sodium tungsten bronzes (STB) Na_0.16WO₃ in acid chloride solutions containing 0.026, 0.26, and 3.02m NaCl have been studied at 500°C, 1000 bar, given fO₂ (Co-CoO, Ni-NiO, PTS-STB buffers), and constant NaCl/HCl ratio (Ta₂O₅-Na₂Ta₄O₁₁ buffer). Depending on experimental conditions, the tungsten content in the solutions after experiments varied from 10⁻³ to 2 × 10⁻² mol/kg H₂O. Obtained data were used to calculate the formation constants of predominant tungsten complexes (VI, V): H₃W₃^VIO₁₂³⁻, W₃^VO₉³⁻, [W^VW₄^VIO₁₆]³⁻, for reactions

High pressure experimental calibration of the olivine-orthopyroxene-spinel oxygen geobarometer: implications for the oxidation state of the upper mantle

Synthetic spinel harzburgite and lherzolite assemblages were equilibrated between 1040 and 1300° C and 0.3 to 2.7 GPa, under controlled oxygen fugacity (f _{O 2}). f _{O 2} was buffered with conventional and open double-capsule techniques, using the Fe−FeO, WC-WO₂-C, Ni−NiO, and Fe₃O₄−Fe₂O₃ buffers, and graphite, olivine, and PdAg alloys as sample containers. Experiments were carried out in a piston-cylinder apparatus under fluid-excess conditions. Within the P-T-X range of the experiments, the redox ratio Fe³⁺/ΣFe in spinel is a linear function of f _{O 2} (0.02 at IW, 0.1 at WCO, 0.25 at NNO, and 0.75 at MH). It is independent of temperature at given Δlog(f _{O 2}), but decreases slightly with increasing Cr content in spinel. The Fe³⁺/ΣFe ratio falls with increasing pressure at given Δlog(f _{O 2}), consistent with a pressure correction based on partial molar volume data. At a specific temperature, degree of melting and bulk composition, the Cr/(Cr+Al) ratio of a spinel rises with increasing f _{O 2}. A linear least-squares fit to the experimental data gives the semi-empirical oxygen barometer in terms of divergence from the fayalite-magnetite-quartz (FMQ) buffer:

A 57Fe M?ssbauer spectroscopic study of sogdianite: an example of a symmetric electric field gradient around Fe3+

Sogdianite, a double-ring silicate of composition ( \textZr_{0. 7 6} \textTi_{0. 3 8}^{4 +} \textFe_{0. 7 3}^{3 +} \textAl_0.13 )_{\Upsigma = 2} ( \square _{1. 1 5} \textNa_{0. 8 5} )_{\Upsigma = 2} \textK[\textLi ₃ \textSi _{1 2} \textO ₃₀ ] ( {\text{Zr}}_{0. 7 6} {\text{Ti}}_{0. 3 8}^{4 + } {\text{Fe}}_{0. 7 3}^{3 + } {\text{Al}}_{0.13} )_{\Upsigma = 2} \left( {\square_{ 1. 1 5} {\text{Na}}_{0. 8 5} } \right)_{\Upsigma = 2} {\text{K}}[{\text{Li}}_{ 3} {\text{Si}}_{ 1 2} {\text{O}}_{ 30} ] from Dara-i-Pioz, Tadjikistan, was studied by the combined application of ⁵⁷Fe M?ssbauer spectroscopy and electronic structure calculations. The M?ssbauer spectrum confirms published microprobe and X-ray single-crystal diffraction results that indicate that Fe³⁺ is located at the octahedral A-site and that no Fe²⁺ is present. Both the measured and calculated quadrupole splitting, ΔE _Q, for Fe³⁺ are virtually 0 mm s⁻¹. Such a value is unusually small for a silicate and it is the same as the ΔE _Q value for Fe³⁺ in structurally related sugilite. This result is traced back to the nearly regular octahedral coordination geometry corresponding to a very symmetric electric field gradient around Fe³⁺. A crystal chemical interpretation for the regular octahedral geometry and the resulting low ΔE _Q value for Fe³⁺ in the M?ssbauer spectrum of sogdianite is that structural strain is largely “taken up” by weak Li–O bonds permitting highly distorted LiO₄ tetrahedra. Weak Li–O bonding allows the edge-shared more strongly bonded Fe³⁺O₆ octahedra to remain regular in geometry. This may be a typical property for all double-ring silicates with tetrahedrally coordinated Li.     

锆石柱面中Hf、Y的配位差异性及其对晶型的控制效应

天然锆石的形态并不简单地依照PBC理论发育,它同时受到生长温度 、熔体扩散系数等物理参数的影响,以及置换Zr的杂质离子的种类和浓度等化学因素的制约 ,即杂质离子选择性地置换Zr而降低晶面的生长速度。通过对{100}和{110}柱面的半定量分 析发现,Hf4+、Y3+离子同O2-离子的成键数目在{100}与{110}生长层 上是不同的,且Hf-O的键强比Zr-O的大,而Y-O的键强比Zr-O的小。如果假定晶体与岩浆熔体并未达到真正的平衡,而是各晶面与岩浆熔体分别达到平衡,按热力学中浓度与能量变化的指数律去处理Hf和Y在{100}与{110}晶面上的配分可以得到,{100}晶面上趋于富Hf贫 Y,{110}晶面上趋于富Y贫Hf,从而导致富Hf的锆石上{100}优先发育,富Y的锆石上{110}优 先发育。     

Complexation of Pb(II) by Chloride Ions in Aqueous Solutions

Lead chloride formation constants at 25°C were derived from analysis of previous spectrophotometrically generated observations of lead speciation in a variety of aqueous solutions (HClO₄–HCl and NaCl–NaClO₄ mixtures, and solutions of MgCl₂ and CaCl₂). Specific interaction theory analysis of these formation constants produced coherent estimates of (a) PbCl⁺, \textPbCl₂⁰ {\text{PbCl}}_{2}^{0} , and PbCl₃⁻ formation constants at zero ionic strength, and (b) well-defined depictions of the dependence of these formation constants on ionic strength. Accompanying examination of a recent IUPAC critical assessment of lead formation constants, in conjunction with the spectrophotometrically generated formation constants presented in this study, revealed significant differences among various subsets of the IUPAC critically selected data. It was found that these differences could be substantially reduced through reanalysis of the formation constant data of one of the subsets. The resulting revised lead chloride formation constants are in good agreement with the formation constants derived from the earlier spectrophotometrically generated data. Combining these data sets provides an improved characterization of lead chloride complexation over a wide range of ionic strengths:

Sector zoned aegirine from the Ilímaussaq alkaline intrusion,South Greenland

Sector zoned aegirine crystals occur in the interstices of peralkaline nepheline syenites in Ilímaussaq. The crystals have grass-green [001] sectors enriched in Ca and Fe²⁺ (as CaFeSi₂O₆), Mn and Zr; pale green {010} sectors enriched in Al (as NaAlSi₂O₆); blue-green {110} sectors enriched in Ti (as NaTi_0.5Fe _0.5 ²⁺ Si₂O₆); and light green {100} sectors enriched in Fe₃₊ (as NaFe³⁺ Si₂O₆).The crystals grew in the liquid with a rate that did not exceed the diffusion rate of most elements in the liquid. However. Fe³⁺ seems to have had diffusion rates lower than the crystal growth rate, and this probably caused the development of some sectors enriched in acmite and others enriched in the hedenbergite component. For Al, Ti and Zr a crystal structural control is envisaged although a recent structure-based model for sector zoning fails to explain the efficient separation of these elements into different sectors.Three more occurrences of sector zoned aegirine are noted, all from peralkaline nepheline syenites. The phenomenon is probably more widespread than hitherto realised.Contribution to the mineralogy of Ilímaussaq no. 62     

Zinc isotope fractionation under vaporization processes and in aqueous solutions

Equilibrium Zn isotope fractionation was investigated using first-principles quantum chemistry methods at the B3LYP/6-311G* level. The volume variable cluster model method was used to calculate isotope fractionation factors of sphalerite, smithsonite, calcite, anorthite, forsterite, and enstatite. The water-droplet method was used to calculate Zn isotope fractionation factors of Zn²⁺-bearing aqueous species; their reduced partition function ratio factors decreased in the order \(\left[ {{\text{Zn}}\left( {{\text{H}}_{2} {\text{O}}} \right)_{6} } \right]^{2 + } > \left[ {{\text{ZnCl}}\left( {{\text{H}}_{2} {\text{O}}} \right)_{5} } \right]^{ + } > \left[ {{\text{ZnCl}}_{2} \left( {{\text{H}}_{2} {\text{O}}} \right)_{4} } \right] > \left[ {{\text{ZnCl}}_{3} \left( {{\text{H}}_{2} {\text{O}}} \right)_{2} } \right]^{ - } > {\text{ZnCl}}_{4} ]^{2 - }\). Gaseous ZnCl₂ was also calculated for vaporization processes. Kinetic isotope fractionation of diffusional processes in a vacuum was directly calculated using formulas provided by Richter and co-workers. Our calculations show that in addition to the kinetic isotope effect of diffusional processes, equilibrium isotope fractionation also contributed nontrivially to observed Zn isotope fractionation of vaporization processes. The calculated net Zn isotope fractionation of vaporization processes was 7–7.5‰, with ZnCl₂ as the gaseous species. This matches experimental observations of the range of Zn isotope distribution of lunar samples. Therefore, vaporization processes may be the cause of the large distribution of Zn isotope signals found on the Moon. However, we cannot further distinguish the origin of such vaporization processes; it might be due either to igneous rock melting in meteorite bombardments or to a giant impact event. Furthermore, isotope fractionation between Zn-bearing aqueous species and minerals that we have provided helps explain Zn isotope data in the fields of ore deposits and petrology.     

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): $$\begin{gathered} T(WH) = 6832 + 0.031(P - 1) - \{ 166(X_{Mg}^{Gt} )^2 - 506(X_{Fe}^{Gt} )^2 + 680X_{Fe}^{Gt} X_{Mg}^{Gt} + 336(X_{Ca} + X_{Mn} ) \hfill \\ (X_{Mg} - X_{Fe} )^{Gt} - 3300X_{Ca}^{Gt} - 358X_{Mn}^{Gt} \} + 954(X_{Fe} - X_{Mg} )^{Crd} /1.987\ln K_D + 3.41 + 1.5X_{Ca}^{Gt} \hfill \\ + 1.23(X_{Fe} - X_{Mg} )^{Crd} \hfill \\ \end{gathered} $$ $$\begin{gathered} T(Br) = 6920 + 0.031(p - 1) - \{ 18(X_{Mg}^{Gt} )^2 - 296(X_{Fe}^{Gt} )^2 + 556X_{Fe}^{Gt} X_{Mg}^{Gt} - 6339X_{Ca}^{Gt} X_{Mg}^{Gt} \hfill \\ - 99(X_{Ca}^{Gt} )^2 + 4687X_{Ca}^{Gt} (X_{Mg} - X_{Fe}^{Gt} ) - 4269X_{Ca}^{Gt} X_{Fe}^{Gt} - 358X_{Mn}^{Gt} \} + 640(X_{Fe} - X_{Mg} )^{Crd} \hfill \\ + 1.90X_{Ca}^{Gt} (X_{Mg} - X_{Ca} )^{Gt} . \hfill \\ \end{gathered} $$      

Kanonaite, (Mn 0.76 3+ Al0.23Fe 0.02 3+ )[6]Al[5][O¦SiO4], a new mineral isotypic with andalusite

Kanonaite forms rare porphyroblasts up to 12mm long in a gahnite— Mg-chlorite — coronadite — quartz schist occurring near Kanona, Zambia. The composition is (microprobe analysis): SiO₂ 32.2, Al₂O₃ 33.9, Mn as Mn₂O₃ 32.2, Fe₂O₃ 0.66, ZnO 0.13, MgO 0.04, BaO 0.04, TiO₂ 0.01, CaO 0.01, PbO 0.01, CuO 0.01, total 99.21, corresponding to $$\left( {{\text{Mn}}_{{\text{0}}{\text{.76}}}^{{\text{3 + }}} {\text{Al}}_{{\text{0}}{\text{.23}}} {\text{Fe}}_{{\text{0}}{\text{.015}}}^{{\text{3 + }}} } \right)_{1.005}^{\left[ 6 \right]} {\text{AL}}_{1.00}^{\left[ 5 \right]} \left[ {{\text{O}}_{{\text{1}}{\text{.00}}} |{\text{Si}}_{{\text{0}}{\text{.99}}} {\text{O}}_{{\text{4}}{\text{.00}}} } \right]$$ The mineral is greenish black, strongly pleochroic with X(∥a) yellow green, Y(∥b) bluish green, Z(∥c) deep golden yellow, biaxial positive, with 2V = 53°(3°), α = 1.702, β = 1.730, γ = 1.823. Vickers microhardness (100 gram load) ranges between 906 and 1017kp/mm². The structure is orthorhombic, isotypic with andalusite, space group Pnnm, a = 0.7953(2), b = 0.8038(2), c = 0.5619(2) nm, V = 0.3592(1) nm³, a/b = 0.9895(3), c/b = 0.6990(3), S.G.(_x) = 3.395 g/cm³, Z = 4. The strongest X-ray powder lines are (d in nm, I, hkl):0.5669, 100, 110; 0.4590, 75, 011 and 101; 0.3577, 90, 120 and 210; 0.2827, 94, 220; 0.2517, 90, 310 and 112; 0.2212, 83, 320, 122 and 212. Comparison of the intensities of 373 observed X-ray reflections with those calculated for several models of Mn³⁺-distribution indicates octahedral coordination of all or most of the manganese present. Interpretation of magnetic measurements (μ_eff = 3.15B.M. per Mn atom at 25 ° C) indirectly supports octahedral coordination of Mn³⁺. The name of the mineral is for Kanona, a town near the type locality. The name is proposed for the end member Mn^{3+ [6]}Al^[5][O¦SiO₄] and for members of the solid-solution series towards andalusite with octahedral Mn³⁺>Al. The presently described mineral may be referred to as aluminian kanonaite.     

Geochemistry, Geochronology and Lu-Hf Isotopes of Peraluminous Granitic Porphyry from the Walegen Au Deposit, West Qinling Terrane

Walegen Au deposit is closely correlated with granitic intrusions of Triassic age, which are composed of granite and quartz porphyries. Both granite porphyry and quartz porphyry consist of quartz, feldspar and muscovite as primary minerals. Weakly peraluminous granite porphyry(A/CNK=1.10–1.15) is enriched in LREE, depleted in HREE with Nb-Ta-Ti anomalies, and displays subduction-related geochemistry. Quartz porphyry is strongly peraluminous(A/CNK=1.64–2.81) with highly evolved components, characterized by lower TiO_2, REE contents, Mg~#, K/Rb, Nb/Ta, Zr/Hf ratios and higher Rb/Sr ratios than the granite porphyry. REE patterns of quartz porphyry exhibit lanthanide tetrad effect, resulting from mineral fractionation or participation of fluids with enriched F and Cl. LAICP-MS zircon U-Pb dating indicates quartz porphyry formed at 233±3 Ma. The ages of relict zircons from Triassic magmatic rocks match well with the detrital zircons from regional area. In addition, ε_(Hf)(t) values of Triassic magmatic zircons from the granite and quartz porphyries are -14.2 to -9.1(with an exception of +4.1) and -10.8 to -8.6 respectively, indicating a crustal-dominant source. Regionally, numerous Middle Triassic granitoids were previously reported to be formed under the consumption of Paleotethyan Ocean. These facts indicate that the granitic porphyries from Walegen Au deposit may have been formed in the processes of the closing of Paleotethyan Ocean, which could correlate with the arc-related magmatism in the Kunlun orogen to the west and the Qinling orogen to the east.     

Fluid–rock interaction at a carbonatite-gneiss contact, Alnö, Sweden

We evaluate balanced metasomatic reactions and model coupled reactive and isotopic transport at a carbonatite-gneiss contact at Alnö, Sweden. We interpret structurally channelled fluid flow along the carbonatite-gneiss contact at ～640°C. This caused (1) metasomatism of the gneiss, by the reaction: ${\hbox{biotite} + \hbox{quartz} + \hbox{oligoclase} + \hbox{K}_{2} \hbox{O} +\,\hbox{Na}_{2}\hbox{O} \pm \hbox{CaO} \pm \hbox{MgO} \pm \hbox{FeO} = \hbox{albite} + \hbox{K-feldspar} + \hbox{arfvedsonite} + \hbox{aegirene-}\hbox{augite} + \hbox{H}_{2} \hbox{O} + \hbox{SiO}_{2}}We evaluate balanced metasomatic reactions and model coupled reactive and isotopic transport at a carbonatite-gneiss contact at Aln?, Sweden. We interpret structurally channelled fluid flow along the carbonatite-gneiss contact at ∼640°C. This caused (1) metasomatism of the gneiss, by the reaction: , (2) metasomatism of carbonatite by the reaction: calcite + SiO₂ = wollastonite + CO₂, and (3) isotopic homogenization of the metasomatised region. We suggest that reactive weakening caused the metasomatised region to widen and that the metasomatic reactions are chemically (and possibly mechanically) coupled. Spatial separation of reaction and isotope fronts in the carbonatite conforms to a chromatographic model which assumes local calcite–fluid equilibrium, yields a timescale of 10²–10⁴ years for fluid–rock interaction and confirms that chemical transport towards the carbonatite interior was mainly by diffusion. We conclude that most silicate phases present in the studied carbonatite were acquired by corrosion and assimilation of ijolite, as a reactive by-product of this process and by metasomatism. The carbonatite was thus a relatively pure calcite–H₂O−CO₂–salt melt or fluid.     

Heat-capacity measurements and absolute entropy of ɛ-Mg2PO4OH

The low-temperature heat capacity of -Mg₂PO₄OH was measured between 10 and 400 K by adiabatic calorimetry. No phase transition was observed over this temperature range. A relative enthalpy increment of 22,119 J mol^–1 and an absolute entropy value of 127.13±0.25 J mol^–1 K^–1 at 298.15 K are derived from the results. The low-temperature heat-capacity data are compared with the DSC data obtained from 143 K to 775 K and show marginal differences in the common temperature range. The latter data are fitted by the polynomial

Spatial relationships of multivariate data

Spatial factor analysis (SFA) is a multivariate method that determines linear combinations of variables with maximum autocorrelation at a given lag. This is achieved by deriving estimates of auto-/cross-correlations of the variables and calculating the corresponding eigenvectors of the covariance quotient matrix. A two-point spatial factor analysis model derives factors by the formation of transition matrixU comparing auto-/cross-correlations at lag 0,R ₀, with those at a specified lag d,R _d, expressed asU _d=R ₀ ^–1 R_d. The matrixU _d can be decomposed into its spectral components which represent the spatial factors. The technique has been extended to include three points of reference. Spatial factors can be derived from the relationship:

Fractionation of carbon and oxygen isotopes and magnesium between coexisting metamorphic calcite and dolomite

Fractionations of carbon and oxygen isotopes and magnesium between coexisting dolomite and calcite have been determined for marbles and calcareous schists of a wide variety of metamorphic environments from Vermont and the Grenville Province of Ontario. Concordant equilibrium fractionations are given by 83% of the samples. Calibration of the isotopic thermometers using the Mg-calcite solvus thermometer gave in the temperature range: 650°>T°>100°C $$ \begin{gathered} 1,000\ln \alpha _{D - Ct}^{O^{18} } = 0.45 (10^6 T^{ - 2} ) - 0.40 \hfill \\ 1,000\ln \alpha _{D - Ct}^{O^{18} } = 0.18 (10^6 T^{ - 2} ) + 0.17. \hfill \\ \end{gathered} $$ These isotopic fractionation expressions differ significantly from the experimentally derived relations, including the dolomite-Mg-calcite C¹³ partial exchange experiments of this study. Temperature ranges obtained for the metamorphic zones of Vermont are: chlorite zone, 210° to 295° C; biotite zone, 255° to 400° C; staurolite-kyanite zone, 110° to 550° C. In amphibolite-facies rocks the quenched partition relations can be complex. The temperature of quench or recrystallization may be as large as 400° C below the inferred metamorphic maximum. Oxygen isotope disequilibrium in high grade rocks, particularly from the Chester dome area, Vermont, is characterized by large negative δO _D ¹⁸ –δO _Ct ¹⁸ values. The size of the equilibrium exchange system for carbon and oxygen isotopes and magnesium is small, less than a few inches across the inferred relict bedding. This is attributed to the lack of a mobile pore fluid except in systems undergoing decarbonation. C¹³/C¹² ratios in Grenville and Vermont marbles and O¹⁸/O¹⁶ ratios in Grenville and greenschist-facies Vermont carbonates span the range of ancient limestones. Staurolite-kyanite zone calcareous schists and marbles from the Chester dome area, Vermont are depleted in O¹⁸(δO¹⁸=12 to 20‰) due to equilibrium or disequilibrium decarbonation and some partial exchange. Extrapolation of the dolomite-calcite fractionation expressions to 20° C indicates that dolomite is enriched in O¹⁸ by about 4.9‰ and in C¹³ by about 2.4‰.     

Synthesis,crystallographic data,solubility and electrokinetic properties of meta-zeunerite,meta-kirchheimerite and nickel-uranylarsenate

{M[UO₂¦AsO₄]₂ · nH₂O} with M=Cu²⁺, Co²⁺, Ni²⁺ has been synthesized from reagent grade chemicals and by ion exchange of trögerite {HUO₂AsO₄ · 4 H₂O}. Synthetic meta-zeunerite (M=Cu²⁺), meta-kirchheimerite (M=Co²⁺) and nickel-uranylarsenate are all tetragonal. The cell parameters determined from Guinier-Hägg diffraction data for {Cu[UO₂¦AsO₄]₂ · 8 H₂O} are a=b=7.10 Å and c=17.42 Å, with Z=2 and the measured density 3.70 g cm^?3. The cell parameters for {Co[UO₂¦AsO₄]₂ · 7 H₂O} and {Ni[UO²¦AsO⁴]² · 7 H₂O} are a=b=20.25 Å and c=17.20 Å, with Z=16 and the measured density 3.82 and 3.74 g cm^?3, respectively. The solubility products for synthetic Cu-, Co- and Ni-uranylarsenate at 25° C are 10^?49.20, 10^?45.34 and 10^?45.10, respectively. The zeta-potential remains negative between pH=2 and pH=9 and is strongly affected by the presence of different cations.     

Magnesiochloritoid: Compressibility and high pressure structure refinement

The response of magnesiochloritoid to pressure has been studied by single crystal X-ray diffraction in a diamond anvil cell, using crystals with composition Mg_1.3Fe_0.7Al₄Si₂O₁₀(OH)₄. The unit cell parameters decrease from a = 9.434 (3), b = 5.452 (2), c = 18.136 (5) Å, β = 101.42° (2) (1 bar pressure) to a = 9.370 (7), b = 5.419 (5), c = 17.88 (1) Å, β = 101.5° (1) (42 kbar pressure), following a slightly anisotropic compression pattern (linear compressibilities parallel to unit cell edges: β _a = 1.85, β _b = 1.74, β_c = 3.05 × 10^?4 kbar^?1) with a bulk modulus of 1480 kbar. Perpendicular to c, the most compressible direction, the crystal structure (space group C2/c) consists of two kinds of alternating octahedral layers connected via isolated SiO₄ tetrahedra. With increasing pressure the slightly wavy layer [Mg_1.3Fe_0.7AlO₂(OH)₄] tends to flatten. Furthermore, the octahedra in this layer, with all cations underbonded, are more compressible than the octahedra in the (A1₃O₈) layer with slightly overbonded aluminum. Comparison between high-pressure and high-temperature data yields the following equations: $$\begin{gathered} a_{P,T} = 9.434{\text{ }}{\AA} - 174 \cdot 10^{ - 5} {\text{ }}{\AA}{\text{kb}}^{{\text{ - 1}}} \cdot P \hfill \\ {\text{ }} + 9 \cdot 10^{ - 5} {\text{ }}{\AA}^\circ C^{ - 1} \cdot (T - 25^\circ C) \hfill \\ b_{P,T} = 5.452{\text{ }}{\AA} - 95 \cdot 10^{ - 5} {\text{ }}{\AA}{\text{kb}}^{{\text{ - 1}}} \cdot P \hfill \\ {\text{ }} + 5 \cdot 65 \cdot 10^{ - 5} {\text{ }}{\AA}^\circ C^{ - 1} \cdot (T - 25^\circ C) \hfill \\ c_{P,T} = 18.136{\text{ }}{\AA} - 549 \cdot 10^{ - 5} {\text{ }}{\AA}{\text{kb}}^{{\text{ - 1}}} \cdot P \hfill \\ {\text{ }} + 16 \cdot 2^{ - 5} {\text{ }}{\AA}^\circ C^{ - 1} \cdot (T - 25^\circ C) \hfill \\ \end{gathered} $$ with P in kbar and T in °C. These equations indicate that the unit cell and bond geometry of magnesiochloritoid at formation conditions do not differ greatly from those at the outcrop conditions, e.g. the calculated unitcell volume is 917.3 ų at P = 16 kbar and T=500 °C, whereas the observed volume at room conditions is 914.4 ų. In addition, they show that the specific gravity increases from formation at depth to outcrop at surface conditions.     

On the least-squares fit of small and great circles to spherically projected orientation data

Given the direction cosines a _i ^′ = (a ₁ ⁱ , a ₂ ⁱ , a ₃ ⁱ )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x₁, x₂, x₃, x₄)for the angular radius x₄,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking x_j+1 = x_j + Δxwhere x_j is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.     

Thermodynamic mixing properties of Mg(Al,Cr)2O4 spinel crystalline solution at high temperatures and pressures

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies. Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, and . The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: , P expressed in bars, T in K, G _m ^ex and W _G,i ^Sp in joules/mol. Temperature-dependence of G _m ^ex is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 , and changes barely with pressure. Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.     

Rate Equations and an Ion-pair Mechanism for Batch Dissolution of Gypsum: Repositioning the Shrinking Object Model at the Core of Hydrodynamic Modelling

Recent improvements to experiments and modelling of batch dissolution in a turbulent reactor, based upon the shrinking object model, are extended to middle loadings of gypsum, that is, in the region between low and high loadings, which lead, respectively, to high under-saturation or saturation with a great excess of solid left undissolved. Dissolved calcium sulphate concentration was monitored by change in electrical conductivity. This investigation uses an improved, ion-pair model for CaSO ₄ ⁰ to allow for the presence of calcium or sulphate added as common ions. The study demonstrates that the full dissolution curve for 5.82 mM loadings of 106-μm particles of gypsum (~1.00 g L^?1) in de-ionised water barely changed in the presence of either 4.64 or 8.09 mM calcium chloride, or 4.39 mM sodium sulphate. However, this masked a doubling of dissolution rate imposed by comparable increases in ionic strength from sodium chloride. The results are consistent with the ion pair, CaSO ₄ ⁰ , being the key species in the rate-determining step of the back-reaction, and perhaps all salt dissolutions, including calcium carbonate. In this case, the rate equation is as follows: \( {\frac{{{\text{d}}c}}{{{\text{d}}t}}} = \frac{S}{V} \cdot (k_{1} - k_{2}^{\prime } \cdot [{\text{CaSO}}_{ 4}^{0} ]) \), where k ₁ and k ₂′ are rate constants. The reported observations are interpreted as effects of ionic strength and common ion concentrations upon the formation equilibrium for the ion pair. This rate equation readily transforms mathematically to one involving the product of [Ca²⁺] and [SO₄ ^2?] in the back-reaction. The parallel of this with the well-known PWP equation used in calcium carbonate dissolution is discussed, with the CaHCO₃ ⁺ ion pair of the equation being replaced by that of CaCO ₃ ⁰ . Meanwhile, the earlier use of the product, [Ca²⁺]^½ × [CO₃ ^2?]^½, in the back-reaction term of another dissolution rate equation for calcite is shown to be incorrect. Finally, it is argued that the shrinking object model should be repositioned as a logical derivative of the hydrodynamical approach to dissolution.