This was the first system to involve condensed oxides. A singular matrix was encountered on the first run. It was found empirically that in order for the program to work, a slight excess of O2 was required (0.00001 moles). This is because a slight excess of some gas must be present in order for the system to converge (Gordon and McBride, 1971). The method of selecting the most stable phase of a condensed species worked well for beta-quartz and beta-cristobalite. Difficulty was encountered at the phase transition from beta-quartz to Si0a liquid at 6000 bars. This problem was solved by substituting the molar volume of silica glass (Robie and Waldbaum, 1968) for the molar volume of SiO2 liquid.

Thermodynamic data were available for most of the condensed phases of SiO2 beyond their transition T at one bar except for alpha-quartz. Thermodynamic data for alpha-quartz were extrapolated up to 1000 K by using the method described in the thermodynamic data section. Alpha and beta-quartz require different molar volumes. Gradually increasing the value of the molar volume for beta-quartz affected the beta-quartz/beta-cristobalite transition, shifting it to a higher P. The molar volume for beta-quartz was held constant and the value of the molar volume for alpha-quartz was lowered gradually until results were obtained which agreed with Tuttle (1953). The values finally used in the computations were 0.54076 cal/bar for alpha-quartz and 0.54226 cal/bar for beta-quartz. The results are plotted in Figure 2. According to the calculations, alpha-quartz is not as stable at

higher P and T as the experimental results of Tuttle. However, this problem could be due to the nature of the alpha-beta quartz transition, which appears to be second order as indicated by Klement and Cohen (l968). If this is the case, then the program will not handle a second order transition. In the computed system, beta-tridymite becomes meta-stable with respect to beta-cristobalite at 1000 bars. Tuttle (l953) found that beta-tridymite is the stable polymorph to 3000 bars. This difference could be due to inaccuracy of the molar volume value for beta-tridymite, which is greater than the value for beta-cristobalite given in Robie and Waldbaum (1968). The Systems CaO-SiO2 and MgO-SiO2 The systems CaO-SiO2 and MgO-SiO2 were chosen to study a binary system consisting of solid phases only. The MgO-SiO2 system was studied in order to determine whether it was necessary for the gas phase of the condensed species to be present. An excess amount of O2 was included in the calculations. In order to simplify the procedure, only three starting compositions were considered: equal amounts of Mg2SiO4-MgSiO3, MgSiO3-SiO2, and Mg2SiO4-SiO2, all over a T range of 573^o-1973^o K and at one bar. A singular matrix was encountered in each case. For the Mg2SiO4-MgSiO3 system, all the condensed species of SiO2 were then omitted from the system, and satisfactory results were obtained. The solid and liquid phases of Mg2SiO4 were omitted from the MgSiO3-SiO2 system in order to achieve satisfactory results. The omission, of condensed phases did not circumvent this problem for the system MgO-SiO2.

In studying the iterative process, it was found that the singular matrix occurred at the Mg2SiO4-MgSiO3 starting composition because after Mg2SiO4, was added to the system, SiO2 was added next instead of MgSiO3. To circumvent this problem the procedure of adding a condensed species was changed (see modifications to the program section) so that the program added the condensed species with the second lowest free energy. Up to this point, thermodynamic data for MgSiO3 had been taken from Robie and Waldbaum (1968). The data of Stull and Prophet (1971) for MgSiO3 were substituted, where ΔH^o₂₉₈ is one kilocalorie less than that given by Robie and Waldbaum (1968). With these two changes, it became possible to obtain results in the Mg2SiO4-MgSiO3 and MgSiO3-SiO2 systems without omitting any species. The addition of subroutine MOLEWT made it possible to study the entire MgO-SiO2 system at 0.5 mole intervals over a T range of 573^o-1973^o K (Fig. 3) in one run. There are some discrepancies between the calculations, experiments (Bowen and Anderson, 1914; Barth, 1962) and calculations of others (Griffiths et al. , 1972). The present program does not consider solid or liquid solutions. Figure 3 does not show the incongruent melting point, a field of MgSiO3 - liquid, or a field of Mg2SiO3 - liquid. The program can be modified at some future date to consider solid and liquid solutions. The methods used to study the MgO-SiO2 system were also used to study the CaO-SiO2 system. However, the original thermodynamic data did not contain any calcium species so data for condensed calcium species were added. A singular matrix was encountered in the first run. The

results of the MgO-SiO2 system indicated that the absence of gas data for the calcium compounds was not the problem. Thermodynamic data for calcium gas were appended and favorable results were obtained. As with the MgO-SiO2 system, there is a problem with condensed species. But again the alternative method for selecting the condensed species solved the problem. The CaO-SiO2 system was then studied at 0.05 mole intervals over a T range of 573^o - 1773^o K (Fig. 4). There were no liquid data available for these species. The computed equilibria are in good agreement with sub-solidus equilibria presented by Phillips and Muan (1959).

Thermodynamic data for magnesite to 1100^o K were taken from Robie and Waldbaum (1968). The data were extrapolated to 1600^o K using the method described in the thermodynamic data section. A sample problem was run with the mole fraction of MgO ranging from O.1 to 0.9 over a T range of 500^o to 1600^o K at 100° intervals at 1, 500, 1000, 2000 and 3000 bars to determine the T at which magnesite decomposes to periclase and vapor (Fig. 5). Once the general range was found for each P, smaller T intervals were used until the exact T was found. These transition points were:

These results were compared with those of Walter (1963). Walter does not give the exact transition T at these P(except for 1000 bars), but

there appears to be a difference of ±24^o between his results and those obtained in this study. The difference could be due to several factors, namely error in extrapolating the magnesite data, experimental error, error in interpretation of Walter's graph, or an excess of O2 in the system In this problem a minimum of 0.003 mole percent of excess O2 ensures that the program works. It was found that by using a greater excess of O2, the change from magnesite to periclase is more gradual. This is because

the addition of O2 makes the system ternary rather than binary. However, the change still occurred at about the same T. A 0.00001 mole excess of O2 was used in studying the MgO-CO2-H2O system at a later date resulting in a sharper change from magnesite to periclase.

Harker and Tuttle (1955) studied the dissociation of calcite, dolomite and magnesite. Their curve was drawn through the interval between the occurrence of periclase and magnesite over a wider transition range then that obtained in this study.

This system has been studied by Bowen and Tuttle (1949), Roy et al. (1953), MacDonald (1955), Roy and Roy (1957), Fyfe (1958). Barnes and Ernst (1963), and Weber and Roy (1965). Their techniques vary according to the type of equipment used. MacDonald's (1955) results are from a theoretical study.

Data for brucite to 1000^o K are taken from Stull and Prophet (1971). The original run used equal amounts of MgO and H2O as the initial composition with a 0.003 mole excess of O2. The amount of O2 was reduced to 0.00001 moles to determine the effect on the zone of interaction between brucite and periclase. In both cases, the transition was a sharp break rather then the gradual transition encountered in the CaO-H2O and MgO-CO2 systems.

Equilibria were studied at 1, 500, 1000, 2000 and 3000 bars over a T range of 400^o - 1000^o K. The results (Fig. 6) were compared with published data. The transition from brucite to periclase is particularly T sensitive at P above 1 KB. Experimental data are not available above 3 KB.

Computed equilibria compare favorably with that of Kennedy (1956). MacDonald (1955) and Kennedy note that the equilibria may be dependent on the grain size of reactants. The computed results are consistent with those obtained by Fyfe (1958) at 500 bars. Fyfe found that brucite is stable to about 835^o at 500 bars whereas the program places the curve at 825^o. Barnes and Ernst (1963), Weber and Roy (1965), and Roy and Roy (1957) found that brucite persists to a T higher then that determined in this study.

The effect of decreasing the P_H2O at constant total P was determined. Barnes and Ernst (1963) studied this system using NaOH to decrease the activity of water present. They studied the stability of brucite in the NaOH-MgO-H2O system. By varying the amount of NaOH present, they could obtain different ratios of NaOH to H20 in the vapor phase.
In this study, N2 was used instead of NaOH to lower the fugacity of H20. At first, one part MgO was used with 10 and 15 parts N2 and 10 and 5 parts of H20. However this resulted in a large T interval (±20^o ) over which periclase and brucite existed together. By increasing the amounts of N2 and H20 three-fold, the interval was reduced to ±6^o . After it was found that this method was sucessful, 16.32 moles of H2O and 3.68 moles of N2 was used to compare with Barnes and Ernst results at 12.5 molal NaOH solution (Fig. 6).
Using pure H20, there is a ±8^o difference between Barnes and Ernst results and those of this study while there is a ±25^o difference using a 12.5 molal NaOH solution. Both Barnes and Ernst results and this study indicate that as the mole fraction of H2O in the vapor decreases, brucite becomes less stable at high P. The thermodynamic data for brucite can be refined by comparing computed equilibria with experimental equilibria, such as those obtained by Barnes and Ernst (1963).

This system was studied using methods outlined for the systems MgO-H2O and MgO-CO2. Thermodynamic data for portlandite to 700^o K were from Robie and Waldbaum (1968) and extrapolated to 1600^o K for the first run. The system was run from 500^o to 2000^o K and at 1, 500, 1000, 2000

and 3000 bars. It was found that at 2000 and 3000 bars; portlandite was stable up to 1600^o K. The data were then extrapolated to 2000^o K and the problem was run again (Fig. 7). It was found that portlandite dissociated at the following T and P:

The problem of excess 02 was again encountered. Phase transitions were narrowest when the least quantity of excess 02 (0.00001 moles) is present.

This program considers only sub-solidus equilibria. The results of this study are compared with those of Majumdar and Roy (1956). Majumdar and Roy plot the dehydration of portlandite to a vapor + Ca0 phase from 3000 psi to 40000 psi. They found that at 1000 bars, portlandite dissociates at 913^o K whereas computed equilibria requires that portlandite dissociates at 1378^o K. A discrepancy of this magnitude occurs over the entire P range investigated. This could be related to either the value of the molar volume and/or methhods of extrapolation. If the molar volume is incorrect, the difference should increase with increasing P, because the free energy contribution equals VAP, so as AP increases VAP increases. If the method of extrapolation is in error, the effect of P on the difference can not be evaluated. If the method of extrapolation is inaccurate, then the same difference should have occurred in the MgO-H2O and MgO-CO2 systems. The results from these two systems indicate the method of extrapolation is fairly accurate. If both the

molar volume value and method of extrapolation are correct, then the difference could be due to the fact that portlandite melts at 1000 bars as indicated by Wyllie and Tuttle (1959). But until better thermodynamic data becomes available for portlandite, no definite explanation can be provided.

This system was studied to determine if the results of Boyd (1959) could be duplicated. The reaction studied here is shown in the following equation:

Data for tremolite were available from Robie and Waldbaum (1969) to 1100^o K. Additional data were extrapolated to 1400^o K using the method described in the thermodynamic data section. The problem was run over a T range of 500 - 2000^o K at 1, 500, 1000, 1500 and 2000 bars using a mixture of one part tremolite and 20 parts H2O. An excess of 0.00001 mole fraction of 02 was used to insure that the problem would reach equilibria. The large excess of H20 was used in order to decrease the zone of transition from tremolite to its constituents to one degree rather then a larger T range as experienced in previous systems (i.e.: CaO-H2O and MgO-CO2). The results are plotted in Figure 8 and compared with Boyd's (1959) results.

The three-degree transition range at 1000 bars is uncertain because the program encountered a singular matrix at that point. This range conceivably could be reduced to one degree with more accurate data.

The results of this study indicate that as total pressure is

increased to 500 bars, tremolite becomes more stable with respect to vapor - diopside - enstatite - quartz than at lower P. Above 500 bars, the upper stability T of tremolite increases more gradually and it is possible that the dehydration curve passes through a T maximum at P above 2000 bars. But until more accurate thermodynamic data become available, it is difficult to determine the real relationship at higher P. The results of this study do not compare favorably with those of Boyd (1959). There is a 46^o difference at 500 bars, 70^o difference at

1000 bars, 90^o difference at 1500 bars and 101^o difference at 2000 bars. The same difference between computed equilibria and experimental equilibria occurred in the CaO-H2O system. The difference in this system could be due to the same problem. In studying the tremolite - calcite - quartz reaction a 100^o difference between the computed results and the experimental results of Skippen (1971) occurred. In that system, it was noted that the difference could be due to the ΔH^o₂₉₈ value used for diopside or tremolite. The results of these two systems indicate that some serious consideration should be given to the validity of the tremolite and/or diopside thermodynamic data.

Regardless of the difference in the results of this study with those of Skippen (1971) or Boyd (1959), it is apparent that tremolite will form from diopside - water - enstatite - quartz or dissociate to these phases as indicated by these two workers. This problem took less then one minute to run on a CDC 6400 computer, a remarkably short time when compared with the 56 days required for experimental investigation of one P-T point (cf. Skippen (1971)).

This reaction was studied in order to compare the results with those of Skippen (l971). The method used by Skippen was to react calcite, quartz and tremolite with a gas phase consisting initially of pure water. There was a discrepancy between his results and those of Metz and Winkler (1964) and Metz (l966). Skippen concluded that the difference was due to the way equilibrium was approached from a fluid phase along the zone of undetectable reaction. The balanced equation for the reaction is:

This type of relation is important in the study of some metamorphic processes.

This problem was run at 2000 bars over a T interval of 600^o to 800^o K. The first run involved reactants in the proportions specified by the above equation. But this did not work very well so the amounts of H2O and CO2 were increased. A problem was encountered in choosing the proper amounts of H20 and CO2. If the amount of CO2 and H2O is increased to a 20:1 ratio of gas to solid, the program encounters a singular matrix. The best results were obtained if one part diopside and H2O were used while CO2 increased from one paart to 20 parts or if one par CO2 was used while H2O increased from one part to 20 parts. A zone of interaction was encountered between the diopside and tremolite reaction. As the amount of gas (H2O or CO2) increased, the width of the zone decreased. Figure 9 is a T-gas composition diagram illustrating the stability field of tremolite - calcite - quartz in the presence of CO2 and H2O.

The computed equilibria are similar to those obtained by Skippen (1971) but occur at T, which are about 100^o lower. This may be due to uncertainty in the value of ΔH^o₂₉₈ for diopside, which was taken from Kracek et al. (1953) as suggested by Griffiths et al. (1972). The phase boundary in Figure 9 diverges from Skippen's results near both 1.0 and 0 mole fraction CO2. If there is 100% CO2 present, i.e. no H2O, tremolite cannot exist. If no CO2 is present then calcite cannot exist. Skippen's phase boundaries should project to the horizontal axis at 0 and 1.0 mole fraction

CO2. Figure 9 shows that as the amount of CO2 in the gas increases from 0 to 80 mole percent, the stability field of tremolite expands with respect to that of diopside. However, from 80 to 100 mole percent CO2 the situation reverses, and the stability field of diopside expands at the expense of tremolite.

The phases encountered in this system were vapor (H2O and CO2), brucite (Mg(OH)2), periclase (MgO), and magnesite(MgC03)- The thermodynamic data for brucite used in this study are taken from Stull and Prophet (1971). The problem was run at 400^o, 500^o, and 580^o C, 1000 bars, and O.1 mole fraction intervals. An excess of 0.003 moles of 02 was included in the first run to insure that the problem would work. However, the field boundaries of the solid phases were affected. The magnesite-brucite-periclase field was closer to the CO2-H2O join than expected. The amount of excess O2 was reduced to 0.00001 moles resulting in the boundaries intersecting the MgO-CO2 and MgO-H2O joins at MgCO2 and Mg(OH)2. A 1 bar comparative run was made, but a large number of points encountered a singular matrix. More detailed sections were run at 0.02 mole fractions across the field boundaries in order to plot their exact position.

At 500^o and 580^o (Figures 10 and 11) there are four fields: vapor-magnesite, periclase-brucite-magnesite, vapor-magnesite-brucite, and vapor-brucite. The vapor phase consists of varying amounts of H2O and CO2.

The results of this study indicate that magnesite is more stable

than periclase or brucite in the presence of H2O or CO2 as the mole percent of MgO decreases from 50%. The boundary between the vapor-brucite and vapor-magnesite-brucite field moves towards the MgO-H2O join as T decreases from 580^o to 500^o C. The vapor-brucite field disappears below 400^o C (Fig. 12). This system was studied at 600^o C and 1 Kb but only two fields exist because brucite dissociates( see MgO-H2O system).

This problem was compared with the results of Walters et al. (1962).

who studied the system at 1000 bars. They plotted two ternary diagrams of the system, 635^o C < T < 630^o C and T < 600^o C. At T < 600^o C, they found the same 3 phase fields and indicate the presence of a vapor field along the H2O-CO2 join. But in this study, a vapor field only existed on the H2O-CO2 join. This discrepancy exists because solute solubility in the vapor is assumed to be zero in the program. Walter et al. (1962) found that brucite dissociates between 635^o C and 630^o C so the brucite-vapor field persisted to 630^o C instead of 587^o C as found in the present

study. The difference between the transition T for brucite in Walters et al. (1962) work, and that of this study could be due to experimental error in their work or the thermodynamic data may be in error. The difference is small enough to indicate that the methods used in this study are fairly accurate.

This site built and hosted for free by FreeWebs.com. Click here to get your own free website.