High-temperature 29Si MAS NMR spectroscopy of anorthite (CaAl2Si2O8) and its P\bar 1-I\bar 1structural phase transition

We present ²⁹Si MAS NMR data for a well-ordered natural anorthite, obtained in situ at temperatures of from 25 to 500° C, which follow the changes in the aluminosilicate framework through the P $\bar 1$ -I $\bar 1$ structural phase transition. Pairs of peaks due to sites offset by approximately 1/2 [111] converge through the P $\bar 1$ phase and only four peaks are present above about 241° C. The variation of the peak positions with temperature and correlations based on structural data for the P $\bar 1$ and I $\bar 1$ phases allow assignment of all the MAS-NMR peaks to crystallographic sites. A Landau-type analysis gives an expression that relates the separation of pairs of con verging peaks to the local order parameter for the P $\bar 1$ -I $\bar 1$ transition, from which we determine its temperature dependence. Data for the best-constrained set of peak positions give for the order parameter critical exponent β = 0.27±0.04, consistent with previous results indicating that the P $\bar 1$ -I $\bar 1$ transition in pure anorthite is tricritical. No significant change in the ²⁹Si spin-lattice relaxation rate occurs across the P $\bar 1$ -I $\bar 1$ transition.     

P,T, f_{{\text{CO}}_{\text{2}} } and f_{{\text{H}}_{\text{2}} {\text{O}}} during metamorphism of calcareous sediments in the Waterville-Vassalboro area,south-central Maine

In a regional metamorphic terrain where six isograds have been mapped based on mineral reactions that are observed in metacarbonate rocks, the P-T conditions and fugacities of CO₂ and H₂O during metamorphism were quantified by calculations involving actual mineral compositions and experimental data. Pressure during metamorphism was near 3,500 bars. Metamorphic temperatures ranged from 380° C (biotite-chlorite isograd) to 520° C (diopside isograd). \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{CO}}_{\text{2}} }\) / \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) in general is higher in metacarbonate rocks below the zoisite isograd than in those above the zoisite isograd. Calculated \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) are consistent with carbonate rocks above the zoisite isograd having equilibrated during metamorphism with a bulk supercritical fluid in which \(P_{{\text{CO}}_{\text{2}} }\) + \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) = P _total. Calculations indicate that below the zoisite isograd, however, \(P_{{\text{CO}}_{\text{2}} }\) + \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) was less than P_total, and that this condition is not due to the presence of significant amounts of species other than CO₂ and H₂O in the system C-O-H-S. Calculated \(P_{{\text{CO}}_{\text{2}} }\) /( \(P_{{\text{CO}}_{\text{2}} }\) + \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) ) is low (0.06–0.32) above the zoisite isograd. The differences in conditions above and below the zoisite isograd may indicate that the formation of zoisite records the introduction of a bulk supercritical H₂O-rich fluid into the metacarbonates. The results of the study indicate that \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) are constant on a thin section scale, but that gradients in \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) existed during metamorphism on both outcrop and regional scales.     

Apsidal motion in the eclipsing binary GG Ori

High-precision WBVR photoelectric observations of the eclipsing binary GG Ori (B9.5V+B9.5V), which has an eccentric orbit (e=0.22), were carried out in 1988–2001 at the Moscow and high-altitude Tian-Shan Observatories of the Sternberg Astronomical Institute. The aim of these observations was investigation of the apsidal motion of the system. Analysis of the resulting 12-year series of observations enabled us for the first time to accurately (to within 11%) measure the rate of rotation of the orbit $\dot \omega _{obs} = 0.046 \pm 0.005^\circ /yr$ and to appreciably improve estimates of the photometric and absolute parameters. The observed value of $\dot \omega _{obs}$ is 28% higher than the theoretical prediction of $\dot \omega _{th} = \dot \omega _{cl} + \dot \omega _{rel} = 0.036 \pm 0.001^\circ /yr$ . The relativistic part of the apsidal motion in this system $\dot \omega _{rel}$ is a factor of 2.5 greater than the classical term $\dot \omega _{cl}$ due to the tidal and rotational deformations of the components. The interstellar extinction in the direction of the star (at a distance of r=425 pc) is very large (A _v =1.75 ^m ). A number of recently published results (in particular, the conclusion that the components of this eclipsing binary are young) are confirmed.     

High-temperature deformation of forsterite single crystals doped with vanadium

Creep experiments have been performed on samples from a single crystal of vanadium-doped forsterite under controlled \(p_{{\text{O}}_2 } \) conditions to investigate the effects of the addition of substitutional defects in the tetrahedral lattice sites. The addition of vanadium causes marked changes in the flow behavior of the forsterite, with a net increase in the creep rate at high \(p_{{\text{O}}_2 } \) and a new \(p_{{\text{O}}_2 } \) -dependent flow regime at low \(p_{{\text{O}}_2 } \) conditions. These observations can be interpreted as resulting from changes in the majority defect species that maintain the charge neutrality within the crystal. A climb-controlled dislocation creep model for the high-temperature deformation of vanadium-doped forsterite is proposed in which either (i) movement of uncharged jogs is rate-limited by the diffusion of silicon via a vacancy mechanism or (ii) movement of positively charged jogs is rate-limited by diffusion of oxygen via a vacancy mechanism.     

Experimental delineation of the “e” ⇌ I\bar 1 and “e” ⇌ C\bar 1 transformations in intermediate plagioclase feldspars

Approximately 125 hydrothermal annealing experiments have been carried out in an attempt to bracket the stability fields of different ordered structures within the plagioclase feldspar solid solution. Natural crystals were used for the experiments and were subjected to temperatures of ～650°C to ～1,000°C for times of up to 370 days at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =600 bars, or \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =1,200 bars. The structural states of both parent and product materials were characterised by electron diffraction, with special attention being paid to the nature of type e and type b reflections (at h+k=(2n+1), l=(2n+1) positions). Structural changes of the type C \(\bar 1\) → I \(\bar 1\) , C \(\bar 1\) → “e” structure, I \(\bar 1\) → “e” and “e” structure → I \(\bar 1\) have been followed. There are marked differences between the ordering behaviour of crystals with compositions on either side of the C \(\bar 1\) ? I \(\bar 1\) transition line. In the composition range ～ An₅₀ to ～ An₇₀ the e structure appears to have a true field of stability relative to I \(\bar 1\) ordering, and a transformation of the type I \(\bar 1\) ? e has been reversed. It is suggested that the e structure is the more stable ordered state at temperatures of ～ 800°C and below. For compositions more albite-rich than ～ An₅₀ the upper temperature limit for long range e ordering is lower than ～ 750°C, and there is no evidence for any I \(\bar 1\) ordering. The evidence for a true stability field for “e” plagioclase, which is also consistent with calorimetric data, necessitates reanalysis both of the ordering behaviour of plagioclase crystals in nature and of the equilibrium phase diagram for the albite-anorthite system. Igneous crystals with compositions of ～ An₆₅, for example, probably follow a sequence of structural states C \(\bar 1\) → I \(\bar 1\) → e during cooling. The peristerite, Bøggild and Huttenlocher miscibility gaps are clearly associated with breaks in the albite, e and I \(\bar 1\) ordering behaviour but their exact topologies will depend on the thermodynamic character of the order/disorder transformations.     

Coherent elastic energies of exsolution boundaries in peristerite and böggild intergrowths

Elastic energy calculations based upon the coherent model of Willaime and Brown [Acta Cryst. A30, 316–331 (1974)] have been carried out for some exsolution textures in peristerite and Böggild intergrowths. For peristerites it is demonstrated that substitution of K for Na moves the orientation of the exsolution lamellae from (08 \(\overline {\text{1}} \) ) to about ( \(\overline {\text{1}} \) , 21, \(\overline {\text{2}} \) ) in agreement with observations. An electron microscope study of exsolution textures in labradorite and andesine plagioclases has been carried out and information about small structural differences in these lamellar structures has been obtained from elastic energy calculations.     

Interdiffusion of NaSi—CaAl in peristerite

The ‘average’ interdiffusion coefficient ( \(\bar D\) ) for NaSi—CaAl exchange in plagioclase for the interval from An₀ to An₂₆ was estimated from experimentally determined homogenization times for peristerite exsolution lamellae. The average spacing between adjacent (unlike) lamellae is 554±77 Å. Dry heating in air at 1,100°C for 98 days produced no change in the exsolution microstructure; thus \(\bar D\) (dry)<10^?17 cm²/s. This limit is consistent with the recently reported ‘average’ \(\bar D\) (dry) values for the Huttenlocher interval (An_70–90) at this temperature. At 1.5 GPa with about 0.2 weight percent water added the ‘average’ diffusion coefficient from 1,100°C to 900°C is given by: \(\bar D\) (wet)=18 _?15 ⁺¹⁰⁸ (cm²/s) exp (?97±5 (kcal/mol)/RT), where R is the gas constant, and T is °K. This \(\bar D\) (wet) at 1,100°C is more than three orders of magnitude greater than \(\bar D\) (dry) for Na- and Ca-rich plagioclases.     

Schiller effects and exsolution in sodium-rich plagioclases

Plagioclase feldspars with mean compositions Ab_91,3Or_4,7An_4,0 and Ab_88,7An_10,1Or_1,2 have been studied by transmission electron microscopy and electron diffraction. The substructure consists of thin lamellae of albite and oligoclase. Two types of orientations of the lamellar planes were observed. The orientation of the more common type was found to change from (08 \(\bar 1\) ) to about ( \(\bar 1\) , 21, \(\bar 2\) ) as a function of the mean potassium content. The plane of the other type was found to be near ( \(\bar 7\) 12). Only the first type of lamellae produces visible Schiller colours.     

Physical conditions in faint gigahertz-peaked spectrum radio sources

Weak, compact radio sources (～100 mJy peak flux, L～1–10 pc) with their spectral peaks at about a gigahertz are studied, based on the complete sample of 46 radio sources of Snellen, drawn from high-sensitivity surveys, including the low-frequency Westerbork catalog. The physical parameters have been estimated for 14 sources: the magnetic field (H _⊥), the number density of relativistic particles (n _e), the energy of the magnetic field $(E_{H_ \bot } )$ , and the energy of relativistic particles (E _e). Ten sources have $E_{H_ \bot } \ll E_e $ , three have approximate equipartition of the energies $(E_{H_ \bot } \sim E_e )$ , and only one has $E_{H_ \bot } \gg E_e $ . The mean magnetic fields in quasars (10^?3 G) and galaxies (10^?2 G) have been estimated. The magnetic field appears to be related to the sizes of compact features as $H \sim 1/\sqrt L $ .     

Standing stock and estimated production rates of phytoplankton and zooplankton in Narragansett Bay,Rhode Island

Seasonal changes in phytoplankton biomass and production, total zooplankton biomass, and biomass and potential production rates of the two dominant copepods, Acartia hudsonica (formerly called Acartia clausi) and Acartia tonsa are described for several stations in Narragansett Bay, R.I. Plankton in the bay behaved as a single population with simultaneous changes occurring at the upper bay (Station 5) and the lower bay (Station 1). Phytoplankton biomass was higher in the upper bay ( \(\bar x\) =16.95 mg chl a·m^?3) than in the lower bay ( \(\bar x\) =6.37 mg chl a·m^?3) and these 0269 0101 V differences in biomass were reflected in the phytoplankton production rates. The zooplankton, which was dominated by A. hudsonica in the spring and early summer and A. tonsa during summer and fall, showed no such consistent differences between the stations. Mean A. hudsonica biomass (St 1, \(\bar x\) ;=82.7 mg dry wt·m^?3; St 5, _ \(\bar x\) ;=95.2 mg dry wt·m^?3) exceeded that of A. tonsa (St 1, \(\bar x\) ;=56.7 mg dry wt·m^?3; St 5, \(\bar x\) ;=60.0 mg dry wt·m^?3). Potential production rates of the two Acartia 0269 0101 V spp. were strongly temperature dependent. Despite the higher biomass levels of A. hudsonica, low temperatures resulted in lower potential production rates ( \(\bar x\) ; St 1=7.25 mg C·m^?3 day^?1; \(\bar x\) ; St 5=10.77mg C·m^?3 day^?1) and biomass doubling times of up to 9.6 days. Potential production rates of A. tonsa at summer temperatures were high ( \(\bar x\) ; St 1=19.0 mg C·m^?3 day^?1; \(\bar x\) ; St 5=22.9 mg C·m^?3 day^?1) and biomass doubling times were generally less than one day.     

Fitting matrix-valued variogram models by simultaneous diagonalization (Part I: Theory)

Suppose that ¯(x₁),...,¯Z(x_n). are observations of vector-valued random function ¯(x). In the isotropic situation, the sample variogram γ^*(h) for a given lag h is $$\bar \gamma ^ * (h) = \frac{1}{{2N(h)}}\mathop \sum \limits_{s(h)} (\overline Z (x_1 ) - \overline Z (x_1 )) \overline {(Z} (x_1 ) - \overline Z (x_1 ))^T $$ where s(h) is a set of paired points with distance h and N(h) is the number of pairs in s(h).. For a selection of lags h₁, h₂, .... h_k such that N (h₁) > O. we obtain a ktuple of (semi) positive definite matrices $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ . We want to determine an orthonormal matrix B which simultaneously diagonalizes the $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ or nearly diagonalizes them in the sense that the sum of squares of offdiagonal elements is small compared to the sum of squares of diagonal elements. If such a B exists, we linearly transform $\overline Z (x)$ by $\overline Y (x) = B\overline Z (x)$ . Then, the resulting vector function $\overline Y (x)$ has less spatial correlation among its components than $\overline Z (x)$ does. The components of $\overline Y (x)$ with little contribution to the variogram structure may be dropped, and small crossvariograms fitted by straightlines. Variogram models obtained by this scheme preserve the negative definiteness property of variograms (in the matrix-valued function sense). A simplified analysis and computation in cokriging can be carried out. The principles of this scheme arc presented in this paper.     

A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).     

Local distortion of the spodumene structure around isolated cations using E.P.R. and the superposition model

The superposition model is used to attempt to explain the EPR spectrum of Fe³⁺ in spodumene (LiAlSi₂O₆). Two different models for the distortion of the local environment of Fe³⁺ are considered. If the local structure around Fe³⁺ is distorted toward that of its isomorphic compound LiFeSi₂O₆, it is possible to obtain an agreement between experimental data and calculated constants, only if it is considered that the values of \(\bar B_2\) are different for the two non equivalent oxygens O₁ and O₂. A second model of local distortion of the structure, based on crystal chemical considerations, is proposed. With this model, it is possible to explain the EPR spectrum with a single value of \(\bar B_2\) . It is seen that the local arrangement around isolated Fe³⁺ in spodumene may be different from that in LiAlSi₂O₆.     

Intergrowth of pyroxene and pyroxenoid; chain periodicity faults in pyroxene

Intergrowth of clinopyroxenes (augite, A) and pyroxenoids (Fe-rhodonite and pyroxferroite, Pxo) was observed by transmission electron microscopy. The following orientation relationship was found: (001)_Pxo is parallel to \((1\mathop {\bar 1}\limits^ + \bar 1)_{\text{A}}\) and \([1\bar 10]_{Pxo}\) is parallel to [011]_A. This relationship can be explained by similarities of the structures of clinopyroxenes and pyroxenoids. It contradicts a suggestion based on structural arguments of Koto et al. (1976). Chain periodicity faults parallel to \((1\mathop {\bar 1}\limits^ + \bar 1)\) are also observed in pure clinopyroxenes.     

The effect of coherency stress on the mechanism of the reaction albite+K+⇌K-feldspar+Na+ and on the mechanical state of the resulting feldspar

Coherency stress and coherency strain energy generated by Na⁺?K⁺ ion exchange in alkali feldspars are calculated using an isotropic model, and deformation of single crystals of alkali feldspars exposed to molten alkali chlorides at \(P_{H_2 O} \) < 1 bar is described. Coherency stress in alkali feldspars can reach 10–20 kb. When it is large, partial relaxation by fracture and/or plastic deformation takes place under anhydrous conditions, but temporary build-up of stress is unavoidable even under hydrothermal conditions. Because of coherency strain energy, a thin layer of an end-member alkali feldspar produced by cation exchange on a grain of the other end-member alkali feldspar would be unstable with respect to dissolution. Therefore, under hydrothermal conditions one end-member alkali feldspar replaces the other by dissolution and precipitation. The mechanism of the reaction $$Na_x K_{1 - x} AlSi_3 O_{8_{(feld.)} } + yK^ + \rightleftharpoons Na_{x - y} K_{1 + y - x} AlSi_3 O_{8_{(feld.)} } + yNa^ + $$ is primarily controlled by \(P_{H_2 O} \) and by ΔK/(Na + K), the difference between the equilibrium value and the initial value of the atomic K/(Na + K) ratio of the feldspar. When ¦ΔK/(Na + K)¦ is small, the reaction proceeds by cation exchange. When ¦ΔK/(Na + K)¦ is large, cation exchange still occurs if \(P_{H_2 O} \) is very low, but under hydrothermal conditions replacement by dissolution and precipitation occurs.     

Interaction of B(OH)_3^0 and HCO_3^ - in Seawater: Formation of B(OH)_2 CO_3^ -

Boron is known to interact with a wide variety of protonated ligands(HL) creating complexes of the form B(OH)₂L^-.Investigation of the interaction of boric acid and bicarbonate in aqueoussolution can be interpreted in terms of the equilibrium $B(OH)_3^0 + HCO_3^ - \rightleftharpoons B(OH)_2 CO_3^ - + H_2 O$ The formation constant for this reaction at 25 °C and 0.7 molkg^-1 ionic strength is $K_{BC} = \left[ {B(OH)_2 CO_3^ - } \right]\left[ {B(OH)_3^0 } \right]^{ - 1} \left[ {HCO_3^ - } \right]^{ - 1} = 2.6 \pm 1.7$ where brackets represent the total concentration of each indicatedspecies. This formation constant indicates that theB(OH)₂ $CO_3^ - $ concentration inseawater at 25 °C is on the order of 2 μmol kg^-1. Dueto the presence of B(OH)₂ $CO_3^ - $ , theboric acid dissociation constant ( $K\prime _B $ ) in natural seawaterdiffers from $K\prime _B $ determined in the absence of bicarbonate byapproximately 0.5%. Similarly, the dissociation constants of carbonicacid and bicarbonate in natural seawater differ from dissociation constantsdetermined in the absence of boric acid by about 0.1%. Thesedifferences, although small, are systematic and exert observable influenceson equilibrium predictions relating CO₂ fugacity, pH, totalcarbon and alkalinity in seawater.     

Transmission electron microscopy of experimentally deformed chalcopyrite single crystals

Two crystals of natural chalcopyrite, CuFeS₂, experimentally deformed at 200° C have been studied by means of transmission electron microscopy (TEM). The activated glide planes are (001) and {112}. The dislocations in (001) have the Burgers vector [110] and a predominating edge character. They are split into two colinear partials b=1/2[110] and can cross split into {112}. The dislocations in {112} consist of straight segments along low index lattice lines. They are often arranged in dipoles generating trails of loops. Few dislocations with b=1/2[ \(\overline {11} \) 1] and [1 \(\bar 1\) 0] are present and dislocations with b=[0 \(\bar 2\) 1] occur in low angle subgrain boundaries. From weak beam contrasts it is presumed that most of the dislocations gliding in {112} have b=1/2〈3 \(\overline {11} \) 〉. They are dissociated into up to four partials. Microtwins and different types of stacking faults in {112} also occur. Models of the dissociation of dislocations are discussed.     

The order-disorder transition in gallium analogue of albite,NaGaSi3O8

The order-disorder transformation in NaGaSi₃O₈ was studied at \(P_{H_2 O} \approx 100\) bar using a hydrous sodium gallium silicate gel and synthetic Ga-albites of various degrees of order as initial materials. The structural state of the gallium albites was determined by the angle separation in X-ray powder patterns of 131 and 1 \(\bar 3\) 1, and of \(\bar 2\) 04 and 060 peaks. The direction of order-disorder transformations was found to change sharply at 938 (±3)°C. This indicates a first order phase transition in NaGaSi₃O₈ as in albite, of which it is the structural analogue.     

Redox state of the upper mantle

The oxygen fugacity condition of equilibration has been carefully determined from a spinel lherzolite from Mongolia, olivine xenocrysts from chrome pyrope-bearing peridotite nodules from kimberlites of Yakutia, and basaltic samples from ocean floor, iron arcs and the continental areas. These indicate that the spinel lherzolites occurring within alkali basalts from Mongolia, equilibrated under an \(f_{O_2 } \) condition similar to that of WM buffer. The diamond and chrome pyrope-bearing peridotites from the kimberlite pipes equilibrated between IW and WM buffers. Some of the ilmenite-bearing peridotite crystallized under \(f_{O_2 } \) conditions similar to that between WM and QFM buffers and chondrites equilibrated below the QFI buffer. It is concluded that during geochemical processes in the upper mantle the \(f_{O_2 } \) conditions vary broadly, and are similar to that between FMQ and IW buffers. There is a dramatic change in the composition of the kimberlitic fluid, which is CH₄-bearing at an early stage, but is in equilibrium with H₂O and CO₂ at a later stage. This is related to mass transfer of fluids from the lower part of the mantle with a low oxidation state to the upper part having a higher \(f_{O_2 } \) condition.     

A note on the significance of the assemblage calcite-quartz-plagioclase-paragonite-graphite

The biotite zone assemblage: calcite-quartz-plagioclase (An₂₅)-phengite-paragonite-chlorite-graphite, is developed at the contact between a carbonate and a pelite from British Columbia. Thermochemical data for the equilibrium paragonite+calcite+2 quartz=albite+ anorthite+CO₂+H₂O yields: $$\log f{\text{H}}_{\text{2}} {\text{O}} + \log f{\text{CO}}_{\text{2}} = 5.76 + 0.117 \times 10^{ - 3} (P - 1)$$ for a temperature of 700°K and a plagioclase composition of An₂₅. By combining this equation with equations describing equilibria between graphite and gas species in the system C-H-O, the following partial pressures: \(P{\text{H}}_2 {\text{O}} = 2572{\text{b, }}P{\text{CO}}_2 = 3162{\text{b, }}P{\text{H}}_2 = 2.5{\text{b, }}P{\text{CH}}_4 = 52.5{\text{b, }}P{\text{CO}} = 11.0{\text{b}}\) are obtained for \(f{\text{O}}_2 = 10^{ - 26}\) . If total pressure equals fluid pressure, then the total pressure during metamorphism was approximately 6 kb. The total fluid pressure calculated is extremely sensitive to the value of \(f{\text{O}}_2\) chosen.