The role of CO2 in the genesis of olivine melilitite

The nature of the near-liquidus phases for a mantle-derived olivine melilitite composition have been determined at high pressure under dry conditions and with various water contents. Olivine and clinopyroxene occur on or near the liquidus and there are no conditions where orthopyroxene crystallizes in equilibrium with the olivine melilitite. We have determined the effect on the liquidus temperature and liquidus phases of substituting CO₂ for H₂O on a mole for mole basis at 30 kb, using olivine melilitite + 20 wt% H₂O at = 0 and = (CO₂)/(H₂+CO₂) (mole fraction) = 0.25, 0.5, 0.75 and 1.0 (i.e. olivine melilitite + 38 wt% CO₂). Experiments were buffered by the MH or NNO buffers. At 30 kb, CO₂ is only slightly less soluble than water for <0.5 as judged by the slight increase in liquidus temperature on mole-for-mole substitution of CO₂ for H₂O and at 30 kb, 1200° C, = = 0.5 the olivine melilitite contains 8.8 wt% H₂O and 21 wt% CO₂ in solution. For 1 the CO₂ saturated liquidus is depressed 70 ° C below the anhydrous liquidus and the magma dissolves approx. 17% CO₂ at 30kb, 1400 ° C, 1, 0. Infrared spectra of quenched glasses have absorption bands characteristic of CO ₃ ⁼ and OH- molecules and no evidence for HCO ₃ ^- . The effect of CO ₃ ⁼ molecules dissolved in the olivine melilitite at high pressure is to suppress the near-liquidus crystallization of olivine and clinopyroxene and bring orthopyroxene and garnet on to the liquidus. We infer that olivine melilitite magmas may be derived by equilibrium partial melting (<5%) of pyrolite at 30 kb, 1150–1200 ° C, provided that both H₂O and CO₂ are present in the source region in minor amounts. Preferred conditions are 0< <0.5, 0.5< <1, and at low oxygen fugacities (相似文献   

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.     

The influence of disordered,non-equilibrium dolomites on the Mg-solubility in calcite in the system CaCO3-MgCO3

The influence of different degrees of disorder of dolomites on the solubility of MgCO₃ in calcite has been studied under isothermal and isobaric conditions. At 900° C, 4kb and 1000° C, 5 and 7kb, varied smoothly as function of the particular structural and cationic disorder of coexisting dolomite. Higher degrees of disorder of dolomite, estimated by the d _00.6/d _11.0 values and the peak height ratio I _01.5/I_00.6, lead to greater solubility of MgCO₃ in calcite. The run time for all experiments was 96 h, much longer than in previous work. The influence of disorder of dolomite on appears to be larger than that of temperature, as shown by the large range of (0.12–0.30) in calcite at 900° C 4 kb, found in this study. The state of order of dolomite seems to control the solubility limits in this system, and may explain discrepancies found in previous experimental work.     

Systematic study of liquidas phase relations in olivine melilitite +H2O +CO2 at high pressures and petrogenesis of an olivine melilitite magma

Near-liquidus phase relationships of a spinel lherzolite-bearing olivine melilitite from Tasmania were investigated over a P, T range with varying , , and . At 30 kb under MH-buffered conditions, systematic changes of liquidus phases occur with increasing ( = CO₂/CO₂ +H₂O+olivine melilitite). Olivine is the liquidus phase in the presence of H₂O alone and is joined by clinopyroxene at low . Increasing eliminates olivine and clinopyroxene becomes the only liquidus phase. Further addition of CO₂ brings garnet+orthopyroxene onto the liquidus together with clinopyroxene, which disappears with even higher CO₂. The same systematic changes appear to hold at higher and lower pressures also, only that the phase boundaries are shifted to different . The field with olivine- +clinopyroxene becomes stable to higher with lower pressure and approaches most closely the field with garnet+orthopyroxene+clinopyroxene at about 27 kb, 1160 °C, 0.08 and 0.2 (i.e., 6–7% CO₂+ 7–8% H₂O). Olivine does not coexist with garnet+orthopyroxene+clinopyroxene under these MH-buffered conditions. Lower oxygen fugacities do not increase the stability of olivine to higher and do not change the phase relationships and liquidus temperatures drastically. Thus, it is inferred that olivine melilitite 2927 originates as a 5% melt (inferred from K_{2 O} and P₂O₅ content) from a pyrolite source at about 27kb, 1160 dg with about 6–7% CO₂ and 7–8% H₂O dissolved in the melt. The highly undersaturated character of the melt and the inability to find olivine together with garnet and orthopyroxene on the liquidus (in spite of the close approach of the respective liquidus fields) can be explained by reaction relationships of olivine and clinopyroxene with orthopyroxene, garnet and melt in the presence of CO₂.     

Antigorite-ophicarbonates: Phase relations in a portion of the system CaO-MgO-SiO2-H2O-CO2

The occurrence of critical assemblages among antigorite, diopside, tremolite, forsterite, talc, calcite, dolomite and magnesite in progressively metamorphosed ophicarbonate rocks, together with experimental data, permits the construction of phase diagrams in terms of the variables P, T, and composition of a binary CO₂-H₂O fluid. Equilibrium constants are given for the 30 equilibria that describe all relations among the above phases. Ophicalcite, ophidolomite, and ophimagnesite assemblages occupy partially overlapping fields in the diagram. The upper temperature limit of ophicalcite rocks lies below that of ophidolomite and ophimagnesite. The fluid phase in ophicarbonate rocks has 0.8$$ " align="middle" border="0"> , and there are indications that during their progressive metamorphism is approximately equal to P _total.     

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.     

A regional gradient in the composition of metamorphic fluids in pelitic schist,Pecos Baldy,New Mexico

Two metamorphic isograds cut across graphitic schist near Pecos Baldy, New Mexico. The southern isograd marks the first coexistence of staurolite with biotite, whereas the northern isograd marks the first coexistence of andalusite with biotite. The isograds do not record changes in temperature or pressure. Instead, they record a regional gradient in the composition of the metamorphic fluid phase. Ortega Quartzite, which contains primary hematite, lies immediately north of the graphitic schist. Mineral compositions within the schist change gradually toward the quartzite, reflecting gradients in and . The chemical potential gradients, locally as high as 72 cal/m in and 9 cal/m in , controlled the positions of the two mapped isograds. The staurolite-biotite isograd records where fell below 0.80, at near 10^–23 bars; the andalusite-biotite isograd records where fell below 0.25, at near 10^–22 bars. Dehydration and oxidation were coupled by graphite-fluid equilibrium.The chemical potential gradients apparently formed during metamorphism, as graphite in schist reacted with hematite in quartzite. Local oxidation of graphite formed CO₂ which triggered dehydration reactions along the schistquartzite contact. This process created a C-O-H fluid which infiltrated into overlying rocks. Upward infiltration, local fluid-rock equilibration and additional infiltration proceeded until the composition of the infiltrating fluid evolved to that in equilibrium with the infiltrated rock. This point occurs very close to the staurolite-biotite isograd. Pelitic rocks structurally above this isograd show no petrographic evidence of infiltration, even though calculations indicate that volumetric fluid/rock ratios may have exceeded 15 and thin, rare calc-silicate beds show extensive K-metasomatism and quartz veining.     

An almandine garnet isograd in the Rogers Pass area,British Columbia: The nature of the reaction and an estimation of the physical conditions during its formation

In the Rogers Pass area of British Columbia the almandine garnet isograd results from a reaction of the form: 5.31 ferroan-dolomite+8.75 paragonite+4.80 pyrrhotite+3.57 albite+16.83 quartz+1.97 O₂=1.00 garnet+16.44 andesine+1.53 chlorite+2.40 S₂+1.90 H₂O+10.62 CO₂. The coefficients of this reaction are quite sensitive to the Mn content of ferroan-dolomite.Experimental data applied to mineral compositions present at the isograd, permits calculation of two intersecting P, T equilibrium curves. P=29088–39.583 T is obtained for the sub-system paragonite-margarite (solid-solution), plagioclase, quartz, ferroan-dolomite, and P=28.247 T–14126 is obtained for the sub-system epidote, quartz, garnet, plagioclase. These equations yield P=3898 bars and T=638° K (365° C). These values are consistent with the FeS content of sphalerite in the assemblage pyrite, pyrrhotite, sphalerite and with other estimates for the area.At these values of P and T the composition of the fluid phase in equilibrium with graphite in the system C-O-H-S during the formation of garnet is estimated as: bars, bars, bars, bars, bars, bars, bars, bars, , bars, bars.     

Devolatilization equilibria in graphite-pyrite-pyrrhotite bearing pelites with application to magma-pelite interaction

The proportions of species in a C-O-H-S fluid in equilibrium with graphite, pyrite and pyrrhotite were calculated for a range of pressure, temperature and conditions, using the equilibrium constants and mass balance method, for ideal and non-ideal mixing in the fluid. Under typical metamorphic conditions, H₂O, CO₂, CH₄ and H₂S are the principal fluid species with H₂S favored by higher temperatures, lower pressures and lower conditions. The dominance of H₂S in the fluid at high temperatures leads to values of becoming significantly less than 1, and causes hydrous minerals to dehydrate at lower temperatures than the case when . The production of H₂S-bearing fluids provides a mechanism for the selective transfer of sulfur from a graphite-pyrite-pyrrhotite bearing pelite into a pluton via a fluid phase, without requiring wholesale melting and assimilation of rocks. Such a process is feasible if a magma is intruded by stoping, which allows a significant volume of pelite country rock to be raised rapidly to temperatures approaching that of the magma. H₂S-bearing fluids produced from graphite-pyrite-pyrrhotite pelites (due either to magmatic intrusion or regional metamorphism) may also mobilize ore-forming metals as sulfide complexes.     

The volatile component of quaternary ignimbrite magmas from the North Island,New Zealand

Ignimbrites from the central North Island consist mainly of glass or its devitrified product (70–95%); their phenocryst mineralogy is varied and includes plag., hyp., ti-mag., ilm., aug., hblende, biot., san., qtz, ol., with accessory apatite, zircon and pyrrhotite. The Fe-Mg minerals can be used to divide the ignimbrites into four groups with hyp.+aug. reflecting high quench temperatures and biot.+hblende +hyp.+aug., low quench temperatures. Oxygen fugacities lie above the QMF buffer curve and even in ignimbrites with low crystal contents the solid phases apparently buffered fO₂. Some ignimbrites contain the assemblage actinolite, gedrite, magnetite and hematite, reflecting post-eruption oxidation. The mineralogy also allows estimation of using pyrrhotite and thence , . The assemblage biotite-sanidine can be used to estimate and thence . Water fugacity is calculated in a variety of ways using both biotite and hornblende as well as the combining reaction . It is high and approaches P _total in most ignimbrites (~4kb) but is lower in unwelded pumice breccias. Comparison of temperature estimates using mineral geothermometers for the various phenocryst phases suggests that the ignimbrite magmas showed temperature differences of 60–100 °C and pressure differences of several kilobars. Individual magma chambers therefore, would have extended over several kilometres vertically. The chemical potential of water may have been constant through the magma.     

A case study of the amount and distribution of heat and fluid during metamorphism

The volume of fluid and amount of heat involved in a portion of a metamorphic event around three synmetamorphic granitic stocks has been quantitatively estimated using mineral composition and modal data from carbonate rocks. Values of volumetric fluid-rock ratios range, with respect to a reference zoisite isograd, from 0.001 to 0.434. Amounts of heat involved range from –25 to 134 cal/cm³ rock. Contours of constant fluid-rock ratio and of constant amount of heat are generally concentric about the granitic stocks indicating that the stocks are foci of high heat and fluid fluxes during metamorphism. In addition, contours of fluid-rock ratios and amount of heat outline NE-SW-trending channelways of high fluid and heat fluxes that alternate with regions of lower fluid and heat fluxes. The NE-SW-trending vertical bedding and schistosity in the area — of premetamorphic origin — probably constrained fluid and heat transfer to occur preferentially in NE-SW directions. Large values of heat involved in metamorphism are strongly correlated with large fluid-rock ratios, suggesting that fluids are an important carrier of heat during metamorphism. Configurations of mapped isograds in the area mimic the patterns of contours of constant fluid-rock ratio and of heat content, indicating that configurations of isograds may contain useful information about regional patterns of heat and fluid transfer during metamorphism.Notation T Last temperature recorded by metacarbonate rocks (°C) - P Lithostatic pressure (bars) - Pi Partial pressure of component i (bars) - of last fluid in equilibrium with carbonate rocks during metamorphism - R 1.987 cal/bar-degree - K _s Activity constant for an assemblage of solid mineral phases - In Natural logarithm - c _v Volumetric heat capacity (cal/cm³-degree) - Q Heat added to or subtracted from a rock during metamorphism in the zoisite zone (kcal/100 cm³ rock; cal/cm³ rock) - Q{ibrxn} Heat added to or subtracted from a rock due to mineral reactions during metamorphism in the zoisite zone (kcal/100 cm³ rock; cal/cm³ rock) - Std. Dev. Standard Deviation - Average of fluid in equilibrium with carbonate rocks during their metamorphism in the zoisite zone - of fluid in equilibrium with carbonate rocks at the zoisite isograd - T Temperature at the zoisite isograd (°C) - X _i,j Mole fraction of component i in phase j - H _i Molar enthalpy of reaction i at 0 bars pressure - ¯V _i Change of molar volume due to reaction _ii - _i Measure of progress of reaction i - V Change in rock volume due to fluid-rock reactions - iV Initial rock volume before metamorphism within the zoisite zone - ¯V _s,i Change in molar volume of solid minerals due to reaction i Component notation an CaAl₂Si₂O₈ Phase notation Pl Plagioclase - Am Amphibole - Cc Calcite - Qz Quartz - Di Diopside - Zo Zoisite - Ga Garnet - Bi Biotite - Kf Microcline - Mu Muscovite     

Phase equilibria involving humite minerals in impure dolomitic limestones

The natural occurrence of critical assemblages among the phases clinohumite, chondrodite, norbergite, tremolite, forsterite, brucite, periclase, diopside, calcite and dolomite, together with experimental and thermochemical data, permits the calculation of phase equilibria governing the stability of the humite group minerals in impure dolomitic limestones. The phase relations are described by 29 divariant (OH-F) continuous reactions, and 11 univariant discontinuous reactions. The equilibrium conditions for these reactions have been calculated and plotted in isobaricT-X(OH-F) andT- phase diagrams. Continuous reactions govern the compositions of (OH-F) solid solutions and the consequent movement of three-phase triangles on the chemographic diagram. Discontinuous reactions result in the appearance or disappearance of a distinct phase assemblage. The pure OH-humite minerals are metastable relative to forsterite+brucite. With increasing fluorine content, clinohumite, followed in turn by chondrodite and norbergite, becomes stable. The stability fields for the individual humite minerals expand to more CO₂-rich fluid compositions with increasing fluorine content and decreasing total pressure. At 1,000 bars, clinohumite can contain a maximum of 58 mole percent fluorine before reacting discontinuously to form chondrodite (X _F=0.61) and forsterite. The stability field for clinohumite+calcite is restricted to fluids with <0.40. At temperatures less than 700°C, the minimum fluorine mole fractions required to stabilize chondrodite and norbergite are 0.31 and 0.62 respectively. At the same conditions, chondrodite can contain a maximum of approximately 85 mole % F. The calculated phase equilibrium boundaries, the range of stable humite compositions and the compositions of coexisting (OH-F) phases are in good overall agreement with natural assemblages. Owing to steepdT/d slopes for several of the humite continuous reactions, the F/(F+OH) ratio of a given humite mineral is a useful indicator of the CO₂/H₂O ratio of the fluid phase.     

The origin of the high-K latites from Camp Creek,Arizona: constraints from experiments with variable fO2 and a_{{\text{H}}_{\text{2}} {\text{O}}}

Near-liquidus melting experiments were performed on a high-K latite at fO₂'s ranging from iron-wustite-graphite (IWG) to nickel-nickel oxide (NNO) in the presence of a C-O-H fluid phase. Clinopyroxene is a liquidus phase under all conditions. At IWG , the liquidus at 10 kb is about 1,150° C but is depressed to 1,025° C at NNO and . Phlogopite and apatite are near-liquidus phases, with apatite crystallizing first at pressures below 10 kb. Phlogopite is a liquidus phase only at NNO and high . Under all conditions the high-K latites show a large crystallization interval with phlogopite becoming the dominant crystalline phase with decreasing temperature. Increasing fO₂ affects phlogopite crystallization but the liquidus temperature is essentially a function of . The chemical compositions of the near-liquidus phases support formation of the high-K latites under oxidizing conditions (NNO or higher) and high . It is concluded from the temperature of the H₂O-saturated liquidus at 10 kb, the groundmass: crystal ratio and presence of chilled latite margins around some xenoliths that the Camp Creek high-K latite magma passed thru the lower crust at temperatures of 1,000° C or more.     

P total,P_{H_2 O} and the occurrence of cummingtonite in volcanic rocks

The phenocryst assemblage of cummingtonite, orthopyroxene, quartz, titanomagnetite and ilmenite in rhyolites of New Zealand has been used to calculate P _total and . The values of P _total and depend strongly upon whether an ideal mixing, or an ordered, model is used for the solid-solutions, but in both cases P _total.The rhyolite magma contained over 9 per cent water (by weight) when the cummingtonite phenocrysts precipitated, and possibly as much as 12 per cent, so that it is surprising that one of these rhyolites is a coherent lava. The calculated values of P _total and are very sensitive to uncertainty in both the composition of the solid-solutions and temperature. Calculations show that >0.7–0.8 P _total for cummingtonite to precipitate in rhyolites, and that iron-rich olivine and cummingtonite could only exist in rhyolites over a small temperature range at a pressure near 5 kilobars. Hornblende phenocrysts co-existing with fayalitic olivine in rhyolites accordingly have a very low activity of Mg₇Si₈O₂₂(OH)₂.     

Die Reaktion Phlogopit + Calcit + Quarz = Tremolit + Kalifeldspat + H2O + C2O

Hydrothermal experiments with mixtures of synthetic minerals have shown the reversibility of the reaction 5 phlogopite + 6 calcite + 24 quartz = 3 tremolite + 5 K-feldspar + 2 H₂O + 6 CO₂. In an isobaric T – diagram the equilibrium curve reaches a maximum at = 0,75. The P, T-values for this maximum are: 2 kb-523°; 4 kb-585°; 6 kb-625°; P±5%, T±10° C. These results give a first approximation of the P, T conditions responsible for a similar mineral reaction which has been recorded from natural metamorphic assemblages.

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Herrn Prof. H. G. F. Winkler danke ich für anregende Diskussionen, desgleichen Herrn Dr. D. Puhan für wichtige Hinweise und Mitteilung seiner exp. Daten. Herrn Prof. V. Trommsdorff und Herrn P. H. Thompson bin ich für petrographische Angaben zu Dank verpflichtet. Der Aufbau der Hydrothermalanlage und die Finanzierung der laufenden Untersuchungen wurde aus den Mitteln des Fonds zur Förderung der wissenschaftlichen Forschung ermöglicht. Für diese Unterstützung gilt daher mein besonderer Dank.     

Solubility of CO2 in olivine melilitite at high pressures and role of CO2 in the earth's upper mantle

The positions of the liquidi and the near-liquidus phases of olivine-melilitite+CO₂ have been determined under MH-buffered and furnace-buffered conditions up to 40 kb. It is found that CO₂ alone lowers the liquidus compared to dry conditions, yet its influence is minor compared to H₂O. The major role of CO₂ is to favour the growth of orthopyroxene and garnet over that of olivine at least at high pressures. CO₂-contents of glasses from experiments just above the liquidus (MH-buffered) were determined as 5.1 % at 10kb; 7.5 % at 20kb, 9.3 % at 30kb and 10–11 % (estimated) at 40 kb. Experiments on (pyrolite –40 % olivine)+H₂O+CO₂ show that CO₂ occurs under mantle conditions as carbonate under subsolidus conditions and dissolved in a melt above the solidus. At 30kb, the solidus lies between 1,000 ° C and 1,050 ° C for vapour-saturated conditions, at and at .     

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.     

Fe2+-Mg2+ partition between coexisting cordierite and garnet — a discussion of the experimental data

The partition of iron and magnesium between cordierite and garnet depends on as well as temperature. The apparently conflicting experimental data on the values of K _D may be reconciled by considering the pertaining during the different experiments.     

A re-examination of the role of hydrogen in Al−Si interdiffusion in feldspars

Recent experimental studies have shown that the rates of Al–Si order-disorder and interdiffusion in alkali feldspars at high pressures under dry conditions increase dramatically in the approximate pressure range 7–14 kb, depending on temperature and feldspar composition (Goldsmith 1987, 1988). Enhancement of Al–Si interdiffusion rates is ascribed to the involvement of hydrogen, but the species of hydrogen involved is undetermined.A simple kinetic analysis of the data of Goldsmith (1987) on disordering of dry albite at 800°–950° C and 6–24 kb in the solid media press is consistent with the NaCl pressure cell acting as a proton donor by enhancing dissociation of water in the pressure medium, generating a high in the experimental environment. The rate constant for disordering of albite is found to increase linearly with the estimated experimental and with the density of aqueous salt solution, implicating H⁺ as the rate-enhancing species.Further experimental studies confirm the importance of . At 16 kb and 850° C, dry albite in sealed Pt capsules in a NaCl cell containing tantalum powder (which reduces H₂O to H₂) remains highly ordered over the same time that complete disordering would occur in the absence of Ta. H₂ cannot therefore be the rate-enhancing species. At 1 kb and 850° C, the extent of Al–Si disorder in albite in direct contact with various NaCl–H₂O solutions increases from partially disordered for pure H₂O to completely disordered for saturated aqueous NaCl solution, giving strong support to the proton model. SIMS scanning ion imaging of albite run products demonstrates conclusively that solution-reprecipitation is not responsible for enhanced disordering rates.Results of disordering experiments in the solid media apparatus cannot be duplicated in Ar gas media internally-heated pressure vessels, even with the same experimental configuration around the albite-bearing capsules, due to the different proton-buffering capacities of the solid and gas media apparatus.     

Aenigmatite,sodic pyroxene,arfvedsonite and associated minerals in syenites from Morotu,Sakhalin

Aenigmatite, sodic pyroxene and arfvedsonite occur as interstitial minerals in metaluminous to weakly peralkaline syenite patches in alkali dolerite, Morotu, Sakhalin. Aenigmatite is zoned from Ca, Al, Fe³⁺-rich cores to Ti, Na, Mn, Si-rich rims reflecting the main substitutions Fe²⁺Ti⁴⁺Fe³⁺, NaSiCaAl and Mn²⁺Fe²⁺. Aenigmatite replaces aegirine and ilmenite supporting the existence of a no-oxide field in — T space. In one case aenigmatite has apparently formed by reaction between ilmenite and arfvedsonite. Titanian aegirine (up to 3.0 wt% TiO₂) and Fe-chlorite may replace aenigmatite. Sodic pyroxene occurs as zoned crystals with cores of aegirine-augite rimmed by aegirine and in turn by pale green aegirine containing 93 mol% NaFe³⁺Si₂O₆. Additional substitution of the type NaAlCaFe²⁺ is indicated by significant amounts (up to 6 mol%) of NaAlSi₂O₆. Arfvedsonite is zoned with rims enriched in Na, Fe and depleted in Ca which parallels the variation of these elements in the sodic pyroxenes.The high peralkalinity of the residual liquid from which the mafic phases formed resulted from the early crystallization of microperthite (which makes up the bulk of the syenites) leading to an increase in the Na₂O/(Na₂O+K₂O) and (Na₂O+K₂O)/Al₂O₃ ratios of the remaining interstitial liquid which is also enriched in Ti, Fe, and Mn. Bulk composition of the melt, , temperature and volatile content were all important variables in determining the composition and stability of the peralkaline silicates. in the residual liquid appears to have been buffered by arfvedsonite-aegirine and later by the arfvedsonite-aenigmatite and aenigmatite-aegirine equilibria under conditions of a no-oxide field. An increase in , above that of the alkali buffer reactions, is inferred by an increase of Ti and Mn in aenigmatite rims. The latest postmagmatic vapour crystallization stage of the syenites is marked by extremely low which may have been facilitated by exsolution of a gas phase. Low is supported by the replacement of aenigmatite by titanian aegirine, and the formation of rare Ti-rich garnet with a very low (Ti⁴⁺+Fe³⁺)/(Ti+Fe) ratio of 0.51, associated with leucoxene alteration of ilmenite.