Reversed experimental calibration of the garnet-clinopyroxene Fe — Mg exchange thermometer

The temperature-sensitive Fe,Mg exchange equilibrium,

A Coupled Riverine-Marine Fractionation Model for Dissolved Rare Earths and Yttrium

Fractionation of yttrium (Y) and the rare earth elements (REEs) begins in riverine systems and continues in estuaries and the ocean. Models of yttrium and rare earth (YREE) distributions in seawater must therefore consider the fractionation of these elements in both marine and riverine systems. In this work we develop a coupled riverine/marine fractionation model for dissolved rare earths and yttrium, and apply this model to calculations of marine YREE fractionation for a simple two-box (riverine/marine) geochemical system. Shale-normalized YREE concentrations in seawater can be expressed in terms of fractionation factors ( _ij ) appropriate to riverine environments ( ) and seawater ( ):

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Spinel-pyroxene-garnet relationships and their dependence on Cr/Al ratio

The partitioning of Cr and Al between coexisting spinel and clinopyroxene and the dependence of spinel-cpxgarnet equilibria on Cr/Al ratio have been investigated by a combination of phase equilibrium experiments, high temperature solution calorimetry and thermodynamic calculations.The exchange equilibrium: has a measured enthalpy change for pure phases of –2,100±500 cal at 970 K and 1 atm. Experimental reversals of Cr-Al partitioning between the spinel and clinopyroxene phases yield the following partitioning relationship: where X _i ^j refers to atomic fraction of i in the octahedral sites of phase j. The compositional dependence of partitioning implies that Al-Cr mixing in spinel is nonideal with, on the symmetrical model, a W _Cr-Al ^Sp of 2,700±500 cal/gm. atom. In contrast, aluminum-chromium mixing in clinopyroxene is close to ideal.The measured stability field of knorringite (Mg₃Cr₂Si₂O₁₂) and mixing properties of garnet have been used in conjunction with our experimental data to calculate the influence of Cr/Al ratio on the important reaction: orthopyroxene+clinopyroxene+spinel=olivine+garnetThe stability field of spinel lherzolite increases by about 2.8 Kb for every increase of 0.1 in Cr/(Cr+Al) ratio up to Cr/(Cr+Al) of 0.7. The calculated stabilization is in very good agreement with the experimental results of O'Neill (1981). The partitioning relationships are such that, at the low ratios of Cr/Al (0.07) of primitive lherzolite, clinopyroxene buffers spinel composition and sharpens the spinelgarnet reaction interval from 10 Kb (little or no clinopyroxene) down to about 2 Kb in pyroxene-rich pyrolite.     

Thermodynamic modelling of non-convergent ordering in orthopyroxenes: a comparison of classical and Landau approaches

The excess Gibbs free energy due to non-convergent ordering is described by a Landau expansion in which configurational and non-configurational entropy contributions are separated:

Redox states of lithospheric and asthenospheric upper mantle

The oxidation state of lithospheric upper mantle is heterogeneous on a scale of at least four log units. Oxygen fugacities ( ) relative to the FMQ buffer using the olivine-orthopyroxene-spinel equilibrium range from about FMQ-3 to FMQ+1. Isolated samples from cratonic Archaean lithosphere may plot as low as FMQ-5. In shallow Proterozoic and Phanerozoic lithosphere, the relative is predominantly controlled by sliding Fe³⁺-Fe²⁺ equilibria. Spinel peridotite xenoliths in continental basalts follow a trend of increasing with increasing refractoriness, to a relative well above graphite stability. This suggests that any relative reduction in lithospheric upper mantle that may occur as a result of stripping lithosphere of its basaltic component is overprinted by later metasomatism and relative oxidation. With increasing pressure and depth in lithosphere, elemental carbon becomes progressively refractory and carbon-bearing equilibria more important for control. The solubility of carbon in H₂O-rich fluid (and presumably in H₂O-rich small-degree melts) under the P,T conditions of Archaean lithosphere is about an order of magnitude lower than in shallow modern lithosphere, indicating that high-pressure metasomatism may take place under carbon-saturated conditions. The maximum in deep Archaen lithosphere must be constrained by equilibria such as EMOG/D. If the marked chemical depletion and the orthopyroxene-rich nature of Archaean lithospheric xenoliths is caused by carbonatite (as opposed to komatiite) melt segregation, as suggested here, then a realistic lower limit may be given by the H₂O +C=CH₄+O₂ (C-H₂O) equilibrium. Below C –H₂O a fluid becomes CH₄ rather than CO₂-bearing and carbonatitic melt presumably unstable. The actual in deep Archaean lithosphere is then a function of the activities of CO₂ and MgCO₃. Basaltic melts are more oxidized than samples from lithospheric upper mantle. Mid-ocean ridge (MORB) and ocean-island basalts (OIB) range between FMQ-1 (N-MORB) and about FMQ +2 (OIB). The most oxidized basaltic melts are primitive island-arc basalts (IAB) that may fall above FMQ+3. If basalts are accurate probes of their mantle sources, then asthenospheric upper mantle is more oxidized than lithosphere. However, there is a wide range of processes that may alter melt relative to that of the mantle source. These include partial melting, melt segregation, shifts in Fe³⁺/Fe²⁺ melt ratios upon decompression, oxygen exchange with ambient mantle during ascent, and low-pressure volatile degassing. Degassing is not very effective in causing large-scale and uniform shifts, while the elimination of buffering equilibria during partial melting is. Upwelling graphite-bearing asthenosphere will decompress along -pressure paths approximately parallel to the graphite saturation surface, involving reduction relative to FMQ. The relative will be constrained to below the CCO equilibrium and will be a function of . Upwelling asthenosphere whose graphite content has been exhausted by partial melting, or melts that have segregated and chemically decoupled from a graphite-bearing residuum will decompress along -decompression paths controlled by continuous Fe³⁺-Fe²⁺ solid-melt equilibria. These equilibria will involve increases in relative to the graphite saturation surface and relative to FMQ. Melts that finally segregate from that source and erupt on the earth's surface may then be significantly more oxidized than their mantle sources at depth prior to partial melting. The extent of melt oxidation relative to the mantle source may be directly proportional to the depth of graphite exhaustion in the mantle source.     

Manganese thermometer for mantle peridotites

The temperature dependence of the Mn-Mg distribution between garnet and clinopyroxene, originally proposed by Carswell, was confirmed by Shimizu and Allègre (1978) using ion microprobe and electron microprobe data. High precision electron microprobe analyses of a larger set of 52 Iherzolites from S. Africa and Malaita, Solomon Islands show considerable scatter in the temperature dependence of this distribution, and correlation with the CaO content of the garnet is indicated. A new distribution coefficient is based on the reaction: $$\begin{gathered} \operatorname{Mn} _{\text{2}} \operatorname{Si} _2 \operatorname{O} _6 {\text{ + }}\operatorname{CaAl} _{2/3} \operatorname{SiO} _4 {\text{ + }}\operatorname{MgAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{Mn - pyroxene grossular pyrope}} \hfill \\ {\text{ }} \rightleftharpoons \operatorname{CaMgSi} _2 \operatorname{O} _6 {\text{ + }}2\operatorname{MnAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{ diopside spessartine}} \hfill \\ \end{gathered} $$ It was calibrated against temperature determined from two independent thermometers (Wells pyroxene and O'Neill-Wood garnet-olivine) for Iherzolitic assemblages, and shown to to be sensitive to within + 50 °C for most specimens in the range 900 °– 1,300 ° C. This distribution coefficient appears independent of pressure within the uncertainty of the available data, and has the potential to be a third independent thermometer for use in garnet Iherzolites and possibly eclogites.     

Partition of Ni between olivine and sulfide: equilibria with sulfide-oxide liquids

The partition of Ni between olivine and monosulfide-oxide liquid has been investigated at 1300–1395° C, =10^–8-9–10^–6.8, and =10^–2.0–10^–0.9, over the composition range 20–79 mol. % NiS. The product olivine compositions varied from Fo98 to Fo59 and from 0.06 to 3.11 wt% NiO. The metal/sulfur ratio of the sulfide-oxide liquid increases with increase in , decrease in , and increase in NiS content. The Ni/Fe exchange reaction has been perfectly reversed using natural olivine and pure forsterite as starting materials. The FeO and NiO contents of olivine from runs equilibrated at the same and form isobaric distributions with NiS content, which, to a first approximation, are dependent at constant temperature and total pressure on a variable term, –0.5 log ( / ). The Ni/Fe distribution coefficient (K _D3) exhibits only a weak decrease from 35 to 29 with increase in from the IW buffer to close to the FMQ buffer. At values higher than FMQ, the sulfide-oxide liquid has the approximate composition (Ni,Fe)₃±_xS₂K _D358. The present K _D3 vs O/(S+O) data define a trend which extrapolates to K _D320 at 10 wt% oxygen in the sulfide-oxide liquid. The compositions of olivine and Ni-Cu sulfides associated with early-magmatic basic rocks and komatiites are consistent, at 1400° C, with a value of -log ( / ) of about 7.7, which is equivalent to 0.0 wt% oxygen in the hypothesized immiscible sulfide-oxide liquid. Therefore, K _D3 would not be reduced significantly from the 30 to 35 range for sulfide-oxide liquids with low oxygen contents.     

Long-term earthquake prediction in the North Pacific seismic zone based on the time and magnitude predictable model

Earthquake recurrence intervals for large and great shallow mainshocks in 12 seismogenic sources along the North Pacific seismic zone (Alaska-Aleutians-Kamchatka-Kuril Islands) have been estimated and used for the determination of the following relations:

The crystal structure of a triclinic roscherite

Summary The crystallography of roscherite is more complicated than previously thought. Single crystal X-ray work on material from Foote Mine (California) gave triclinic symmetry. The unit cell corresponding to the one adopted for monoclinic roscherite hasa=15.921,b=11.965,c=6.741 Å, =91°04, =94°21, =89°59 1/2, space group . The least-squares refinement of the structure using 2380 non zero reflections with anisotropic temperature factors resulted in a conventional reliability factorR=0.060.The X-ray study indicates the formula while that proposed for monoclinic roscherite is The atomic arrangements of both varieties of roscherite are very similar. The lowering of symmetry is caused by the segregation of the trivalent cations into only half of the sites of a monoclinic point position. Crystallochemical considerations suggest that the symmetry of roscherite does not depend on the kind of trivalent cations occupying the 6-coordinated position, but rather by the ratio between trivalent and divalent metal ions.

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Die Kristallstruktur eines triklinen Roscherites

Zusammenfassung Die Kristallographie des Roscherites ist komplizierter als man bisher annahm. Einkristall-Röntgenuntersuchungen an Material von Foote Mine (Kalifornien) ergaben trikline Symmetrie. Die Elementarzelle, welche der für monoklinen Roscherit angenommenen entspricht, hata=15,921,b=11,965,c=6,741 Å, =91°04, =94°21, =89°59 1/2, Raumgruppe . Die Verfeinerung der Struktur mit der Methode der kleinsten Quadrate ergab unter Verwendung anisotroper Temperaturfaktoren für 2380 beobachtete Reflexe einen konventionellen ZuverlässigkeitsindexR=0,060.Die Röntgenuntersuchung weist auf die Formel , während für monoklinen Roscherit vorgeschlagen wurde. Die Atomanordnungen beider Abarten des Roscherites sind sehr ähnlich. die Symmetrieerniedrigung wird dadurch hervorgerufen, daß die dreiwertigen Kationen nur die Hälfte der Positionen einer monoklinen Punktlage besetzen. Kristallchemische Überlegungen weisen darauf hin, daß die Symmetrie nicht von der Art der dreiwertigen Kationen, welche eine 6-koordinierte Punktlage besetzen, abhängt, sondern vielmehr von dem Mengenverhältnis zwischen 3-wertigen und 2-wertigen Metallionen.

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With 1 Figure     

The dependence of the Fe2+-Mg cation-partitioning between olivine and basaltic liquid on pressure,temperature and composition

The equilibrium partitioning of Fe²⁺ and Mg between olivine and liquid along a liquid line of descent has been determined for a calc-alkaline system, ranging in composition from picritic to andesitic. Experiments were conducted between 1000–1450° C and 1 bar to 30 kbar. Within the compositional range investigated and , the compositional dependence of the Fe²⁺ and Mg partitioning is a function of the Mg-content of the liquid. The Mg-content of the liquid correlates strongly with temperature. The variation of the Fe²⁺ and Mg partitioning were therefore evaluated individualy as functions of composition and temperature alone. The composition dependence of the cation-partitioning coefficients (Kd) is given by the following two equations:

The graphite-COH fluid equilibrium in P,T, f_{O_2 } space

The oxygen fugacity ( ) of a C-O-H fluid in equilibrium with graphite has been determined in the range 10–30 kbar by equilibrating solid -buffer assemblages in graphite capsules containing C-O-H fluid. By using different buffers (Fe_xO-Fe₃O₄, Ni-NiO, Co-CoO, Mo-MoO₂), the of the graphite-saturated fluid is bracketed within a narrow range. This technique produces a calibration for the imposed on a sample contained within a graphite capsule. To achieve a thermodynamically-invariant system at fixed P and T, the was imposed on the system with an external buffer and the double-capsule technique. The experiments were performed in solid-media, high pressure apparatus with 19 mm tale-pyrex assemblies. A series of experiments at 10, 15, 20, 25, and 30 kbar, 800–1600° C, with imposed by the Fe₂O₃-Fe₃O₄-H₂O equilibrium were conducted. The experimental results have been fitted to the following equation:

Maximum entropy and shear strain of shear zone

The principle of maximum entropy can be used to determine the shear strain in natural shear zones. When the margin of a shear zone is assumed, the principle leads to the truncated exponential distribution of the shear strain. Ifx is the distance remote from the shear zone center, which possesses the maximum shear strain, the shear strain (x) is given by

An experimental study of Fe-Mg partitioning between olivine and orthopyroxene at 1173, 1273 and 1423 K and 1.6 GPa

The partitioning of Mg and Fe²⁺ between coexisting olivines and orthopyroxenes in the system MgO-FeO-SiO₂ has been investigated experimentally at 1173, 1273, 1423 K and 1.6 GPa over the whole range of Mg/Fe ratios. The use of barium borosilicate as a flux to promote grain growth, and the identification by back-scattered electron imaging of resulting growth rims suitable for analysis by electron microprobe, results in coexisting olivine and orthopyroxenene compositions determined to a precision of±0.003 to 0.004 in molar Fe/(Mg+Fe). Quasi-reversal experiments were performed starting with Mg-rich olivine and Fe-rich orthopyroxene (low K_D) and vice versa (high K_D), which produced indistinguishable results. The distribution coefficient, K_D, depends on composition and on temperature, but near Fe/(Mg+Fe)=0.1 (i.e. mantle compositions) these effects cancel out, and K_D is insensitive to temperature. The results agree well with previous experimental investigations, and constrain the thermodynamic mixing properties of Mg-Fe olivine solid solutions to show small near-symmetric deviations from ideality, with between 2000 and 8000 J/mol. Multiple non-linear least squares regression of all data gave a best fit with (implying 5450 J/mol at 1 bar) and , but the two W _G parameters are so highly correlated with each other that our data are almost equally well fit with , as obtained by Wiser and Wood. This value implies , apparently independent of temperature. Our experimental results are not compatible with the assessment of olivine-orthopyroxene equilibria of Sack and Ghiorso.     

Thermodynamic properties of andradite and application to skarn with coexisting andradite and hedenbergite

The enthalpy of formation of andradite (Ca₃Fe₂Si₃O₁₂) has been estimated as-5,769.700 (±5) kJ/mol from a consideration of the calorimetric data on entropy (316.4 J/mol K) and of the experimental phaseequilibrium data on the reactions: 1 $$\begin{gathered} 9/2 CaFeSi_2 O_6 + O_2 = 3/2 Ca_3 Fe_2 Si_3 O_{12} + 1/2 Fe_3 O_4 + 9/2 SiO_2 (a) \hfill \\ Hedenbergite andradite magnetite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 4 CaFeSi_2 O_6 + 2 CaSiO_3 + O_2 = 2 Ca_3 Fe_2 Si_3 O_{12} + 4 SiO_2 (b) \hfill \\ Hedenbergite wollastonite andradite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 18 CaSiO_3 + 4 Fe_3 O_4 + O_2 = 6Ca_3 Fe_2 Si_3 O_{12} (c) \hfill \\ Wollastonite magnetite andradite \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} Ca_3 Fe_2 Si_3 O_{12} = 3 CaSiO_3 + Fe_2 O_3 . (d) \hfill \\ Andradite pseudowollastonite hematite \hfill \\ \end{gathered} $$ and $$log f_{O_2 } = E + A + B/T + D(P - 1)/T + C log f_{O_2 } .$$ Oxygen-barometric scales are presented as follows: $$\begin{gathered} E = 12.51; D = 0.078; \hfill \\ A = 3 log X_{Ad} - 4.5 log X_{Hd} ; C = 0; \hfill \\ B = - 27,576 - 1,007(1 - X_{Ad} )^2 - 1,476(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite (Ad)-hedenbergite (Hd)-magnetite-quartz: $$\begin{gathered} E = 13.98; D = 0.0081; \hfill \\ A = 4 log(X_{Ad} / X_{Hd} ); C = 0; \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-quartz: 1 $$\begin{gathered} E = 13.98;{\text{ }}D = 0.0081; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 0;}} \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-calcitequartz: 1 $$\begin{gathered} E = - 1.69;{\text{ }}D = - 0.199; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 2;}} \hfill \\ B = - 20,441 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-calcite: 1 $$\begin{gathered} E = - 17.36;{\text{ }}D = - 0.403; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 4;}} \hfill \\ B = - 11,720 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 \hfill \\ \end{gathered} $$ The oxygen fugacity of formation of those skarns where andradite and hedenbergite assemblage is typical can be calculated by using the above equations. The oxygen fugacity of formation of this kind of skarn ranges between carbon dioxide/graphite and hematite/magnetite buffers. It increases from the inside zones to the outside zones, and appears to decrease with the ore-types in the order Cu, Pb?Zn, Fe, Mo, W(Sn) ore deposits.     

High-temperature creep and kinetic decomposition of Ni2SiO4

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

An experimental study of the diffusion of oxygen in quartz and albite using an overgrowth technique

Diffusion rates of¹⁸O tracer in quartz ( c, 1 Kb H₂O) and Amelia albite ( 001, 2 Kb H₂O) have been measured, using Secondary Ion Mass Spectrometry (SIMS). A new technique involving hydrothermal deposition of labelled materials has removed the possibility of pressure solution-reprecipitation processes adversely affecting the experiments. Reported diffusion constants are:-quartz ( c), ,Q=98±7 KJ mol^–1 (600–825° C, 1 Kb); Amelia albite ( 001), ,Q=85±7 KJ mol^–1, (400–600° C, 2 Kb). Measured quartz¹⁸O diffusivities decrease discontinuously at the- transition, reflecting strong structural influences. The reported albite data agree with previously recorded studies, but-quartz data indicate significantly lower activation energies. Possible causes of this discrepancy, and some geological consequences, are noted.     

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:

Analysis of seismic intensities observed in Israel

Macroseismic data of earthquakes felt in Israel and also recorded instrumentally are analyzed. The analysis yields the following empirical relations: