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1 Department of Geological Sciences and Environmental Studies, Binghamton University, Binghamton, New York 13902, U.S.A.
2 Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, U.S.A.
3 Peter A. Rock Thermochemistry Laboratory and NEAT ORU, University of California at Davis, Davis, California 95616, U.S.A.
4 Department of Earth Sciences, University of California, Riverside, California 92521, U.S.A.
Correspondence: * E-mail: dmjenks{at}binghamton.edu
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ABSTRACT |
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 Top Abstract IntroductionMethods and analytical resultsResultsComparison of phase equilibrium...AcknowledgmentsReferences cited |
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where the entropy does not include any contributions from configurational mixing. If one includes configurational entropy contributions from cation and vacancy disorder in the triple-chain silicate and amphibole, one obtains S° and 
Hf° for Na-cjt of 919.2 J/(K·mol) and –18 417.6 kJ/mol, respectively, and S° and Hf° for Na-Mg amphibole of 650.9 J/(K·mol) and –11 919.7 kJ/mol, respectively.
Key Words: Triple-chain silicate • Na-clinojimthompsonite • thermochemistry • calorimetry
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INTRODUCTION |
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TopAbstractIntroductionMethods and analytical resultsResultsComparison of phase equilibrium...AcknowledgmentsReferences cited |
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Triple-chain silicate minerals were first discovered in a talc mine in Chester, Vermont (Veblen et al. 1977; Veblen and Burnham 1978a, 1978b). Two pure triple-chain silicates were identified, including the orthorhombic jimthompsonite [Mg10Si12O32(OH)4] and its monoclinic analogue clinojimthompsonite. Since their initial discovery, jimthompsonite, clinojimthompsonite, and related triple-chain silicates have been recognized in many localities, including California (Yau et al. 1986), Japan (Nakajima and Ribbe 1982; Akai 1982; Konishi et al. 2008), Europe (Schumacher and Czank 1987; Droop 1994; Grobéty 1996), Greenland (Konishi et al. 2007), and the Marianas trench (Akai et al. 1997). However, the Mg end-member triple-chain silicates have not been grown successfully in the laboratory. In contrast, two synthetic Na analogues to clinojimthompsonite have been synthesized, with nominal compositions of Na4Mg8Si12O32(OH)4 (Tateyama et al. 1978) and Na2Mg8Si12O30(OH)6 (Drits et al. 1974, 1976). Because of the dependability and relatively high crystallinity with which Na4Mg8Si12O32(OH)4, referred to here as Na-clinojimthompsonite (Na-cjt), can be synthesized, this study focused on this phase (Fig. 1
).
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and often occur together in experimental run products, suggesting that they form under a similar set of conditions and may share an equilibrium boundary. Although Na-cjt has not been discovered in nature, its straightforward synthesis suggests that it may form as a stable phase under some conditions. Because triple-chain silicates so closely resemble their pyroxene, amphibole, and layer silicate relatives in thin section, it seems possible that Na-cjt may have been overlooked or misidentified in natural samples. With further understanding of the stability and formation of Na-cjt, focused analysis on natural assemblages more likely to contain Na-cjt can be designed. An understanding of the thermochemistry of Na-cjt may also offer insight into the role triple-chain silicates could play in the transformation of chain to layer silicates (Veblen and Buseck 1980) or in the processes leading to the formation of triple-chain silicates as stable phases (Grobéty 1996).
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METHODS AND ANALYTICAL RESULTS |
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TopAbstractIntroductionMethods and analytical resultsResultsComparison of phase equilibrium...AcknowledgmentsReferences cited |
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Powder X-ray diffraction (XRD)
To ensure purity and crystallinity of the run products, each sample was analyzed using a Philips PW3040-MPD automated X-ray diffractometer with CuK
radiation operating at 40 kV and 20 mA with a diffracted-beam monochromator. All samples were mounted on zero-background quartz plates as a thin smear. It was thus established that each Na-cjt run product was contaminated with a small amount of Na-Mg amphibole. To quantify the percentage of Na-Mg amphibole contamination, two step-scans were measured of the combined Na-cjt run products and processed using GSAS software for Rietveld refinement (Larson and Von Dreele 2004). The average of the refinements indicates 4.38 ± 0.39 wt% Na-Mg amphibole in the Na-cjt sample used for calorimetry. The Na-Mg amphibole sample was pure.
High-temperature X-ray diffraction powder patterns were obtained using an Anton Paar HTK 10 heating stage mounted on the Philips diffractometer. Heating-stage temperatures were calibrated against the melting point of lead (327 °C). Samples were mounted on flat aluminum plates that were centered on the hot spot of the heating filament.
Electron microprobe and FTIR analyses
Electron microprobe analysis (EMP) was performed on a JEOL 8900 Super-probe using wavelength-dispersive spectrometry with the ZAF correction scheme, and operating at 15 kV and either 10 or 4 nA with a beam diameter of 1 µm. Standards used were albite, periclase, and quartz, for Na, Mg, and Si, respectively. Initially, to minimize the impact of the loss of Na due to diffusion under the electron beam, counting times for Na in the sample and the standard were kept to 10 s on the peak and 3 s on the background. The same counting times were used for Mg and Si. However, further measurements indicated that Na loss was significant at 10 nA for the phases formed in this study, even with the short counting times. To remedy this, the beam current was lowered until it was found that at 4 nA there was no appreciable loss in Na counts over durations of at least 60 s, as shown in Figure 2, which is the total duration of an analysis. To retain the large sample population of the first set of analyses performed at 10 nA, the Na2O/SiO2 ratios of the first set were increased by 10% to correct for Na diffusion and bring them into agreement with those performed at 4 nA.
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. The Na-Mg amphibole was somewhat better in that it formed prismatic crystals up to 5 µm in width. The interaction volume of the electron beam generally exceeds the small size of these crystals. To overcome the difficulties of analyzing small grains, a large number of measurements were made, and any measurement with an analytical sum less than 75% for Na-cjt and 90% for the Na-Mg amphibole was discarded. These analytical totals are well within the minimum values recommended by others who have specifically looked into the analysis of fine grains (e.g., Solberg et al. 1981; Giblin et al. 1993; Jenkins and Corona 2006a). An average of the remaining 60 Na-cjt analyses gives, on the basis of 34 O atoms, a formula of Na3.68Mg8.17Si12.00(OH)4. The 34 remaining Na-Mg amphibole analyses result in the formula Na2.54Mg5.45Si8.14O22(OH)2 on the basis of 23 O atoms, as given in Table 1. Although the Si content of Na-cjt matches its theoretical value, the amphibole has a significantly higher Si content than is crystallographically feasible, which we attribute to a higher hydroxyl content in this phase, as discussed below. The compositional range of Na-cjt, defined by the 1µ uncertainties in Na2O, MgO, and SiO2 about the mean composition, is shown as the dotted rectangular area in Figure 1, while that of Na-Mg-amphibole is the solid rectangular area.
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. Both spectra show sharp OH-stretching bands above 3600 cm–1 and a broad OH-stretching region centered at about 3400 cm–1. There is a noticeable H2O-bending vibration in Na-cjt (Fig. 4a) at 1640 cm–1 that is much reduced in the Na-Mg-amphibole (Fig. 4b).
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The HRTEM images in Figure 5 show examples of characteristic CMFs in both Na-cjt and the Na-Mg amphibole. Most of the CMFs are narrow lamellae, usually half the width of a unit cell along the b-axis, often forming domains of multiple members. The CMF lamellae usually cross the entire length of an individual crystal. Na-cjt has a A'(3) of 0.891, while the Na-Mg amphibole has a A'(2) of 0.964.
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. The structure of the Na-Mg amphibole was less obvious because its composition is intermediate between Na3Mg5Si8O21(OH)3 with a C
structure and Na2Mg6Si8O22(OH)2 with P21/m. Careful examination of the SAED patterns of amphibole grains with few CMFs shows weak reflections consistent with a primitive lattice, as seen in Figure 7. Distinguishing between a monoclinic structure and that of a triclinic structure with very small (<0.5°) deviations from 90° is difficult to determine by simple measurements of reflection positions on the SAED pattern, such as looking for the small differences (~0.05 Å) that would exist between the 110 and 10 reflections in a triclinic crystal. However, one can use SAED patterns that have at least one identical reflection that can be used as an internal standard and then compare the ratios of reflections to help discern minor variations in d-spacings. For example, SAED patterns down the [110] and [10] zone axes will both contain the 001 reflection, which can be used as an internal standard. Measuring the differences in the ratios of d-spacings for symmetrically equivalent reflections normalized by a common reflection, e.g., 110/001 – 10/001, showed that these differences were statistically equivalent to zero (n = 10) and therefore consistent with monoclinic symmetry. Based on this information, we have adopted the P21/m structure for the Na-Mg-amphibole studied here.
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show a steep drop in mass around 110 °C, which is probably due to water adsorbed onto the outside of the powdered sample rather than structural water relevant to the reaction. Na-cjt’s mass then steadily decreases (Fig. 8a) until a large drop at approximately 750 °C, whereas the Na-Mg amphibole’s mass is stable until an increase in the rate of weight loss approximately 200 °C before the main dehydration at 800 °C (Fig. 8b). Above 110 °C, TGA indicates a mass loss due to volatilization of water of 5.56 wt% for Na-cjt and 2.80 wt% for the Na-Mg amphibole.
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Because of the large discrepancy in the water content measurement of Na-cjt between the automated TGA and the single-step heating method, a third method was used involving incremental manual heating (for Na-cjt only). This method, referred to here as manual TGA, is similar to the second method but with incremental heating steps of 100 °C rather than one dehydration step to 900 °C. The sample was held at each temperature until the mass, measured at 15 min intervals, stabilized.
In contrast to the water loss pattern measured by automated TGA, manual TGA (Fig. 8a, circles) indicates only a slight decrease in mass (1.32%) until the primary dehydration event between 600 and 700 °C, after which the mass loss of 4.96 wt% is steady up to 1000 °C. The lower temperature of the main dehydration observed in this manual TGA heating analysis (~650 °C compared to ~750 °C) is expected based on the slower heating rates of manual heating (0.68–2.08 °C/min) compared to automated TGA (10 °C/min). The higher heating rate used in the automated TGA analyses may also be causing the continual downward slope in the TGA data above 750 °C, as the water loss does not equilibrate at each temperature. However, both techniques indicate a gradual mass loss between 110 °C and the main dehydration event, suggesting Na-cjt contains zeolitic water, possibly housed between I-beams in a site similar to the interlayer water in a layer silicate. The presence of zeolitic water is supported by the FTIR spectra as discussed below. This water would be more loosely bound than the structural water present as OH anions inside the I-beams. It is, however, considered part of the Na-cjt structure and is included in the stoichiometric formula.
The water content of Na-cjt averaged from the automated, manual, and single-step TGA measurements is 5.00 ± 0.67 wt%, after taking into account the 4.38 ± 0.39 wt% Na-Mg amphibole contamination of the Na-cjt sample. This compares favorably to Tateyama et al.’s (1978) TGA measurements of 4.1 and 3.6%, disregarding the water loss below 100 °C in their analysis. It should be noted that total water contents of 4–5 wt% H2O observed in this study and that of Tateyama et al. (1978) are above the 2.99 wt% H2O in ideal Na4Mg8Si12O32(OH)4. The average water content of the Na-Mg amphibole from automated TGA and the single-step heating analysis is 2.99 ± 0.26 wt%. This is intermediate between the values of 2.24 and 3.37 wt% H2O expected for ideal Na2Mg6Si8O22(OH)2 and Na3Mg5Si8O21(OH)3, respectively.
One can combine the electron microprobe data in Table 1 with the water contents reported above to derive the formulae of Na-cjt and Na-Mg amphibole. The nearly polymorphic nature of the triple- to double-chain reaction studied here and the overlap in their microprobe analyses (Table 1, rectangles in Fig. 1) indicate that both phases have the same composition (other than their bulk water contents), which is shown by the circle in Figure 1. Calculating the formula of Na-cjt on the basis of 34 O atoms (i.e., with four structural OH) gives the expected number of Si cations (12) and suggests that any additional water is present as H2O. This results in Na3.74Mg8.13Si12O32(OH)4·1.40H2O for Na-cjt’s formula. Calculating the formula of the Na-Mg amphibole on the basis of 23 O atoms gives, as mentioned above, a higher Si content for the double-chain backbone structure of amphibole. We have chosen instead to calculate the formula (including the 2.99 wt% H2O) on the basis of eight Si to yield Na2.49Mg5.42Si8O21.34(OH)2.66 for the Na-Mg amphibole.
Adiabatic calorimetry
Adiabatic calorimetry was performed on Na-cjt and the Na-Mg amphibole using a small-volume calorimeter designed specifically for samples of limited quantity. Samples were heated to 110 °C to remove adsorbed water before calorimetry was performed. Approximately two-thirds of a gram of each powdered sample was pressed into pellets to increase the thermal conductivity of the sample, then broken into smaller pieces to fit more easily in the calorimeter. The data are fit to functions using multiple polynomials of the type C = A0 + A1T + A2T2 + ... + AnTn smoothed at their joins to match the measured data. The experimental heat capacities below 15 K were plotted as CP/T vs. T2 to obtain the Debye-T3 coefficient. The result was used to extrapolate the measured results to 0 K. The details of this method are described in Stevens and Boerio-Goates (2004).
High-temperature oxide-melt solution calorimetry
In the high-temperature oxide-melt drop solution calorimetry used for this study, 5 or 15 mg sample pellets, depending on the amount of material available, were dropped from room temperature into molten 2PbO·B2O3 solvent at 700 °C in a Calvet-type twin microcalorimeter. Oxygen gas was kept flowing through the system at 100 mL/min to flush out H2O evaporated from the sample. The calorimeter was calibrated by measuring the heat content of 5 and 15 mg pellets of corundum. A more detailed description of the measurement process can be found in Navrotsky (1997).
Three samples were analyzed using high-temperature oxide-melt drop solution calorimetry—the same Na-cjt and Na-Mg amphibole material used for adiabatic calorimetry, plus another Na-Mg amphibole, Na3Mg5Si8O21(OH)3, referred to as Na-cum (sodium-cummingtonite). The latter sample was included in this study to help determine the effect that variable water content has on the enthalpy of formation of Na-Mg-rich silicates. Na-cum was synthesized in a manner similar to the other phases, namely by treating a decarbonated mixture of MgO, SiO2, and Na2CO3 with 15 wt% water at 600 °C and 0.1 GPa for 186 h. These conditions were the same as those used by Maresch et al. (1991) and by Cámara et al. (2004). The synthesis product was essentially pure amphibole, via XRD analysis, with no other discernible phases, and assumed to be of ideal composition as demonstrated in previous studies (Liu et al. 1996; Cámara et al. 2004).
Experimental reversals
A series of reversal experiments was performed with a mixture of Na-cjt and Na-Mg amphibole to establish the equilibrium boundary between these two phases. This mixture is a result of a single synthesis experiment from the oxide mixture of composition Na4Mg8Si12O32(OH)4 treated in a cold-seal vessel for one week at 0.1 GPa and 600 °C with water used as the pressure medium. Direct microprobe analysis of the individual phases in this fine-grained, intimate mixture was not deemed practical. Instead, the triple- and double-chain phases in this mixture are considered to have the same compositions as the Na-cjt and Na-Mg amphibole made for calorimetry based on their identical XRD patterns, plus the temperature at which this mixture was made (600 °C) is between that used to make the Na-cjt (550 °C) and the Na-Mg-amphibole (725 °C), which are themselves isochemical (aside from their water contents). The powder XRD pattern of this mixture indicated that Na-cjt and the Na-Mg amphibole were fortuitously present in approximately equal proportions, making it an excellent starting mixture for studying the univariant boundary separating their stability fields.
For each reversal experiment, 4 to 5 mg of the starting mixture were combined with 20 wt% de-ionized water in a 10 mm long Pt capsule with an outer diameter of 1.5 mm. Some dissolution of the solids to the ambient solution is possible in these experiments; however, there was no obvious quenched amorphous material seen by optical or electron microscopy in the run products, suggesting very limited dissolution. In addition, care was taken to use the same fluid:solid ratio in each reversal experiment so that any dissolution that occurs would be consistent from one experiment to the next. Capsules were placed in cold-seal vessels for experiments at 0.1 and 0.2 GPa, internally heated gas vessels for experiments between 0.3 and 0.7 GPa, and a piston-cylinder apparatus with NaCl as the pressure medium for higher pressures. Reversal experiments were performed at conditions ranging from 0.1 to 1.0 GPa and 350 to 600 °C. At higher pressure and lower temperature (0.7 GPa and 475 °C), talc growth occurs. Experiments yielding talc could not be used to determine equilibrium conditions because it is not clear if talc is growing at the expense of Na-cjt or the Na-Mg amphibole.
Five replicate powder X-ray diffraction scans of the starting mixture and three of each run product were performed to determine the average value and standard deviation of selected peak area ratios for each sample. The stable phase at each set of conditions was determined by comparing the peak area ratios of a representative Na-cjt peak (2
= 25.2°) to an amphibole peak (2 = 26.1°) for the starting mixture and for the experimental run products. The area of each peak was found using the Philips ProFit 1.0c line profile analysis software (Philips 1996). If there was no overlap between one standard deviation of the data for the starting mixture and one standard deviation of the data for the run product, they were considered statistically different.
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RESULTS |
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TopAbstractIntroductionMethods and analytical resultsResultsComparison of phase equilibrium...AcknowledgmentsReferences cited |
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shows the individual CP measurements (open squares) and the smoothed curve used to generate the thermodynamic functions. Table 2 lists the observed heat-capacity data for both Na-cjt and the Na-Mg amphibole. The integral of the fitted polynomials was calculated to find the third-law entropy. The third-law entropy at 298.15 K measured for Na-cjt is 941.68 ± 39.69 J/(K·mol) (after accounting for the Na-Mg amphibole contamination), and the entropy measured for the Na-Mg amphibole is 622.42 ± 12.68 J/(K·mol). Because the adiabatic calorimetry does not include replicate runs of different samples, errors are estimated based on a comparison with the measurement of a reference material. The error listed above includes corrections due to the amphibole contamination in the Na-cjt sample as well as the uncertainty associated with the measurement of water content.
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High-temperature oxide-melt solution calorimetry
The enthalpy data necessary for calculating the enthalpy of formation of the phases relevant to this study are listed in Table 3, whereas Table 4 shows the thermodynamic cycles used for Na-cjt. Similar thermodynamic cycles were used for the amphiboles. The enthalpies of formation at 298 K for the Na-Mg amphibole and for Na-cum are –11 909.0 ± 13.62 kJ/mol and –11 932.9 ± 18.9 kJ/mol, respectively. After correcting for the Na-Mg amphibole contamination, the measured enthalpy of formation of Na-cjt is –18 436.7 ± 24.3 kJ/mol. All errors are one standard deviation of the mean and include uncertainties associated with the chemical composition, water content, and calorimetry measurement errors. For example, the error for Na-cjt, 24.3 kJ/mol, involves 23.7 kJ/mol from the solution calorimetry process alone. This includes measurement uncertainties as well as errors associated with the enthalpy of the oxides used in the thermodynamic cycle (Table 3). An additional 0.6 kJ/mol stems from the uncertainty in the concentration and associated enthalpy of formation of the contaminant Na-Mg amphibole in the Na-cjt sample. The calorimetrically measured thermodynamic values for Na-cjt and the Na-Mg amphibole are summarized in Table 5.
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lists the results of the reversal experiments conducted in this study. These are shown in Figure 10, where the curve is fitted by eye to the experimental data. It was not always possible to successfully conduct experiments in the Na-cjt side of the equilibrium boundary, as talc often formed, interfering with the reaction in the lower temperature experiments. One interesting observation that has been made in this study is that the triple-chain silicate can nucleate from the oxide starting mixture at temperatures up to 200 °C above its equilibrium boundary with amphibole. Large overstepping of a mineral stability field has been observed for other phases, such as the nucleation of clinozoisite from different starting materials well beyond its stability field relative to zoisite (see review by Poli and Schmidt 2004). In such cases, it is particularly important that the equilibrium boundary be determined with a mixture of both reactants and products, as was done here, to overcome nucleation barriers.
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-quartz from Hemingway (1987). The third method was the prediction model presented by Van Hinsberg et al. (2005b), who have determined the heat capacity contribution for structural polyhedra based on multiple linear regression analysis of 111 end-member minerals. The high-temperature heat capacity function estimated from each method was adjusted by a constant so that the estimated heat capacity at 298 K was the same as the calorimetrically measured value. The average of these three methods results in the function CP (J/K·mol) = 2061.4 – 0.0417T – 1.5 x 107T–2 – 1.4 x 104T–0.5 for Na-cjt and CP (J/K·mol) = 1431.6 – 0.0469T – 7.0 x 106T–2 – 1.1 x 104T–0.5 for the Na-Mg amphibole, both of which extrapolate to high temperatures in a reasonable manner.
The unit-cell volumes of Na-cjt and the Na-Mg amphibole were determined by Rietveld refinement of powder X-ray diffraction data. Tateyama et al.’s (1978) proposed crystal structure of Na4Mg8Si12O32(OH)4 was used as a starting model for Na-cjt. Refined cell parameters for Na-cjt are a = 10.147(1) Å, b = 27.139(3) Å, c = 5.2820(5) Å, β = 107.029(7)° with a volume of 2742.7(4) Å3 (41.86 J/bar). The refined atomic coordinates are listed and compared to those of Tateyama et al. (1978) in Table 7. Iezzi et al.’s (2004) structure for Na2Mg6Si8O22(OH)2 was used as a starting model for the Na-Mg amphibole. The measured cell parameters are a = 9.8621(7) Å, b = 18.0207(13) Å, c = 5.2819(4) Å, and β = 103.090(5)° with a volume of 914.3(1) Å3 (27.53 J/bar). The refined atomic coordinates are listed and compared to those of Iezzi et al. (2004) in Table 8. Thermal expansivities were measured in this study using the method of Jenkins and Corona (2006b). For Na-cjt, the measured thermal expansion parameter is 31.9 ± 0.2 x 10–6 K–1, and for the Na-Mg amphibole, it is 24.7 ± 0.2 x 10–6 K–1.
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COMPARISON OF PHASE EQUILIBRIUM AND CALORIMETRIC DATA |
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TopAbstractIntroductionMethods and analytical resultsResultsComparison of phase equilibrium...AcknowledgmentsReferences cited |
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 | (1) |
where G, H, S, CP, and V are the Gibbs free energy, enthalpy, entropy, heat capacity, and volume change of the reaction, respectively, 
H2O is the moles of water exchanged in the reaction, fH2OP,T is the fugacity of H2O at the pressure and temperature (P,T) under investigation, and R is the gas constant. Fugacity data and the CP function of H2O are those reported by Holland and Powell (1998). The thermal expansion and bulk modulus values are used in the evaluation of
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using the equations in Holland and Powell (1998).
The calculated equilibrium boundary for the reaction:
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is shown in Figure 11 as the dotted curve, alongside the bracketing experimental reversal data from this study. Clearly, there is a discrepancy between the experimental and calculated equilibrium conditions. Not only is the calculated curve several hundred degrees Celsius higher than the measured data, but it shows no maximum at which it begins to bend back toward lower temperatures with increasing pressure. Discrepancies in the location of a reaction boundary determined experimentally vs. that calculated from calorimetric data have been observed before, as, for example, in the case of tremolite, where the calculated dehydration boundary lies some 200–400 °C above the experimental boundary (Graham et al. 1989).
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errors to the enthalpy of formation of Na-cjt and the entropy of Na-Mg amphibole, while subtracting 95% of the 1 errors to the entropy of Na-cjt and the enthalpy of formation of the Na-Mg amphibole. This results in enthalpy of formation and third-law entropy values of –18 413.6 kJ/mol and 904.1 J/(K·mol), respectively, for Na-cjt, and –11 922.0 kJ/mol and 634.5 J/(K·mol) for the Na-Mg amphibole, as summarized in Table 5. The calculated boundary based on these data are shown as the dashed curve in Figure 11. Unfortunately this boundary does not bend back to match the higher-pressure data. It was considered critical to fit the lower pressure data, especially at 0.2 GPa, because it was the samples made at this pressure whose chemical composition and water content were measured.
The shape of the equilibrium boundary as measured through experimental reversals is distinctive, and yet the calorimetrically measured data cannot match it. Both sets of data were carefully and systematically determined, and neither can be discounted in favor of the other. A strongly back-bending reaction boundary as observed here could be the result of a large change in either the chemical composition or the water content of one phase relative to the other. To test this hypothesis, we treated ~100 mg portions of these samples at the maximum pressures investigated here (1.0 GPa) and at the conditions of the equilibrium boundary (425 °C) using the same water content used in the reversal experiments (20 wt%) for one week durations. Electron microprobe analyses of these treated samples are listed in Table 1 and show there is very little change in their compositions that might arise, for example, from the preferential incongruent dissolution of one phase relative to the other. The water contents of these samples were assessed by manual TGA, showing Na-cjt (4.2 ± 0.5 wt% H2O) to be essentially unchanged while Na-Mg amphibole’s water content (4.0 ± 0.5 wt% H2O) may have increased. Gain of water by Na-Mg amphibole relative to Na-cjt will not, however, give the back-bending nature of this boundary for any reasonable choice of thermodynamic values for structural or zeolitic water. One would need to reduce the thermodynamic activity of a given amphibole component by over two orders of magnitude to match the experimental reversal data at 1 GPa that, though feasible, seems unlikely.
The simplest explanation for the shape of this curve is to allow Na-cjt to take in variable amounts of zeolitic water with changes in pressure. The water content of Na-cjt has historically been questionable (Tateyama et al. 1978; Welch et al. 1992), and the measurements undertaken in this study support the idea that Na-cjt has a bulk water content beyond the nominal four structural OH groups. The FTIR spectra indicate that at least some of this is present as molecular water (Fig. 4a). The continuous weight loss of Na-cjt during automated TGA also suggests a wide range of water contents with variable retention in the structure (Fig. 8a). Other Mg-rich silicates exhibit this behavior as well. For example, aspidolite [NaMg3(AlSi3)O10(OH)2] has long been known to have variable hydration states (Carman 1974), and even talc [Mg3Si4O10(OH)2] can incorporate interlayer water with increasing pressure leading to the 10 Å phase (Bauer and Sclar 1981; Pawley and Wood 1995), which is probably variable in its interlayer water content (Phillips et al. 2007). Only a small change in Na-cjt’s water content is necessary to significantly alter the equilibrium conditions of this boundary. In this study, we present a thermodynamic analysis where Na-cjt takes in variable water relative to Na-Mg amphibole. It is likely that both phases change in their water contents, but until more information is available, particularly involving in situ measurements at P and T, we will assume only Na-cjt changes its water content.
The thermodynamic values of Na-cjt are dependent on its molar mass and, therefore, on its water content. This relationship can be treated through modeling of the phase as a solid solution between the hydrous and anhydrous end-members, as has been done, for example, with cordierite (e.g., Newton and Wood 1979; Carey and Navrotsky 1992). However, there is not enough H2O-solubility data in this study to make this analysis possible. Instead, a simple mathematical function was used to express the change in water content of Na-cjt with variation in pressure, as well as that of the change in the three principal thermodynamic variables (enthalpy, entropy, and volume) with variation in water content, needed to fit the experimental data.
Van Hinsberg et al. (2005a) have established the thermodynamic properties of interstitial or free water (called "H2O free") in a crystalline substance through their mineral polyhedra regression analysis. Their value for the volume change per mole of water in the structure, 1.46 J/bar, was used here to adjust the molar volume of Na-cjt with varying water contents. Their component polyhedra values were also used to determine the contribution of free H2O to Na-cjt’s entropy and enthalpy by the following equations:
 | (2) |
 | (3) |
where SNa,cjt° and Hf,Na,cjt° are values measured in this study. The enthalpy for free H2O in the structures of Na-Mg amphibole and Na-cum were calculated using equations similar to that of Equation 3, and the results for Na-cjt, Na-Mg amphibole, and Na-cum were averaged. For the entropy of free H2O, only the result from Equation 2 was used because there are only two measured entropy values from this study, which was not considered enough to provide a meaningful average. This resulted in a sH2O and a hH2O for free water in Na-cjt of 43.4 J/(K·mol) sH2O and –295.5 kJ/mol H2O, respectively.
These values were used for expressing the change in Na-cjt’s thermodynamic values with water content in the following equations:
 | (4) |
 | (5) |
 | (6) |
where H2O,rxn is the moles of H2O released in the reaction of Na-cjt to Na-Mg amphibole.
The value 1.40 is from reaction 1; it is considered accurate for the measured thermodynamic values because the samples used for calorimetry are the same as those used for chemical analysis, including measurement of the water content. Equations 4–6 can be simplified to:
 | (7) |
 | (8) |
 | (9) |
where H2O,Na-cjt is the total moles of water (including structural OH) in Na-cjt. These expressions were used to calculate the amount of water released in reaction 1 necessary to fit within the measured experimental reversal brackets or half brackets at each pressure. It was found that the variation in the total water content of Na-cjt can be expressed by the equation:
 | (10) |
with pressure (P) in GPa (Fig. 12). This corresponds to a change in the amount of water in Na-cjt varying from 4.9 to 7.6 wt% from 0.1 to 1 GPa. Equation 10 is considered reasonable up to approximately 1.6 GPa; because Na-cjt forms at lower pressures, this range should be sufficient for analysis of its stability over a wide range of geological conditions.
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shows the equilibrium boundary between Na-cjt and the Na-Mg amphibole using the 298 K and 1 bar thermodynamic values for both phases corrected by 95% of their standard deviation, water content varying as per Equation 10, and variations in the enthalpy of formation, entropy, and volume of Na-cjt with water content given by Equations 7–9. With this method, it is possible to fit all of the brackets and half-brackets determined through experimental reversals with minimal variation of water content in Na-cjt. We can also carry out this thermodynamic analysis including configurational mixing terms to the entropy of Na-cjt and Na-Mg amphibole. Our primary source of information on cation disorder is the microprobe analyses, supplemented where possible by site-occupancy refinements and with FTIR spectroscopy.
For Na-cjt, the microprobe analysis indicates that there are more than enough Mg (8.13) atoms to occupy the eight M1 through M4 octahedral sites. The remaining 0.13 Mg are assigned, along with 1.87 Na, to the two smaller Na2 sites, which have an average Na-O distance of 2.35 Å compared to 2.70 Å for the NaA site (based on the crystallographic data of Tateyama et al. 1978). This leaves 1.87 Na and 0.13 vacancies at the two NaA sites, or 94% occupancy by Na. This is in close agreement with a site occupancy of 90% deduced from the X-ray diffraction Rietveld refinements, as discussed below. Yet another estimate of the Na occupancy at the NaA site comes from the FTIR spectrum of Na-cjt in the OH-stretching region (Fig. 4a). Figure 4a shows the presence of two distinct absorption bands at 3728 and 3678 cm–1. By analogy with amphiboles (e.g., Robert et al. 1989; Hawthorne et al. 1997; Melzer et al. 2000; Cámara et al. 2004; Iezzi et al. 2004), the 3728 cm–1 band is assigned to the vibration of an O-H dipole bonded to three Mg cations and directed toward an NaA site (analogous to the amphibole A site) occupied by Na, whereas the 3678 cm–1 band is an O-H vibration directed toward a vacant NaA site. A simple ratio of the band intensities (integrated areas) indicates Na occupancy at the NaA site to be 75%. This is much less than the 90–94% occupancy deduced from the other methods. Until the source of this discrepancy is resolved, we will use the average of the microprobe and Rietveld refinements, giving 92% Na and 8% vacancies at the two NaA sites. Combining the configurational entropy of Na and Mg mixing at the Na2 sites [4.0 J/(K·mol)] with the (average) Na and vacancy mixing at the NaA sites [4.6 J/(K·mol)] results in a total configurational entropy of 8.6 J/(K·mol).
For the Na-Mg amphibole, the microprobe analysis indicates that there is more than enough Mg (5.42) for the five M1 through M3 sites, leaving 0.42 Mg and 1.58 Na to occupy the two M4 sites. This leaves 0.91 Na atoms at the amphibole A site, or 91% occupancy with 9% vacancy. This is lower than the full occupancy (no vacancies) deduced from Rietveld refinement (Table 8). There is a very weak band in the FTIR spectra of the Na-Mg amphibole (Fig. 4b) at 3678 cm–1, corresponding to OH next to a vacant A site as in Na-cjt (vertical dashed line). Its integrated-area intensity relative to the two bands at 3715 and 3740 cm–1, assigned to OH next to filled A sites, amounts to 1–3% vacancy depending on the choice of background and peak width. The average Na occupancy at the A site based on three independent measurements (microprobe, Rietveld refinement, FTIR spectrum) is 96%. Finally, the extra H in this P21/m amphibole is assumed to reside in a crystallographically well-defined location by analogy with the C amphibole studied by Cámara et al. (2004). Random mixing of 2.66 H and 0.34 vacancies over these three sites will contribute an additional 8.8 J/(K·mol). Combining the configurational mixing of Na and Mg mixing on the M4 sites [8.5 J/(K·mol)], Na and vacancy mixing on the A site [1.3 J/(K·mol)], and H and vacancy mixing on three H sites [8.8 J/(K·mol)], gives a total of 18.6 J/(K·mol).
We can apply these configurational entropy contributions to the third-law entropies of Na-cjt and Na-Mg amphibole and then repeat the same thermodynamic analysis that was done above. When this is done, one can get agreement between the calorimetric and experimental reversal data at 0.2 GPa by adjusting the calorimetric data by only 78% of the 1 uncertainties. This gives an enthalpy of formation and third-law entropy for Na-cjt of –18417.6 kJ/mol and 919.2 J/(K·mol), respectively, whereas for Na-Mg amphibole these values are –11919.7 kJ/mol and 650.9 J/(K·mol), respectively, as summarized in Table 5. The variation in the total water content of Na-cjt needed to get agreement with the experimental reversals at the other pressures is expressed by an equation that is slightly different from Equation 10, namely:
 | (11) |
Combining calorimetrically measured data with experimental reversals provides critical insight into the complexity of Na-cjt’s thermochemistry. Using the calorimetrically measured values alone and assuming that the composition of Na-cjt is constant produces a reaction boundary that is inconsistent with the experiments. The experimental reversals suggest that a compositional change occurs along the univariant boundary. Microprobe analyses do not indicate any obvious change in the bulk composition of the phases between low (0.2 GPa) and high (1.0 GPa) pressures (Table 1). We therefore propose that the reaction boundary is being controlled by changes in the water content of the triple-chain silicate, or at least a greater rate of change than in the double-chain silicate, with variation in the ambient water pressure. It will most likely require in situ measurements of the water contents of Na-cjt and its Na-Mg amphibole breakdown product to confirm this hypothesis, which is beyond the scope of the present study. Regardless of the extent to which the water content of these phases varies with pressure, we suggest that the 298 K, 1 bar thermodynamic data presented here (Table 5) may be used to evaluate possible geological settings in which Na-Mg-rich triple-chain silicates occur in nature. This will be the subject of an upcoming manuscript.
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ACKNOWLEDGMENTS |
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TopAbstractIntroductionMethods and analytical resultsResultsComparison of phase equilibrium...AcknowledgmentsReferences cited |
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Footnotes |
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MANUSCRIPT RECEIVED March 21, 2008; MANUSCRIPT ACCEPTED May 4, 2009
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REFERENCES CITED |
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