INTRODUCTION
With the increase in the amount of thermodynamic data available for common
minerals (Robie and Waldbaum, 1968; Stull and Prophet, 1971), it has become
possible to calculate chemical equilibrium in multicomponent geological environments.
Previously phase equilibria had to be measured in the laboratory using complicated
equipment, which involved considerable time and cost. The same results can be
obtained by the use of computers and available thermodynamic data. Various
approaches to tills problem have been used by Lord (1965), Smith (1965, 1966),
Helgeson (1969, 1970), Kaufman and Bernstein (1970), Skippen (i970), Griffiths
et al (1972), Grossman (1972), and Zen (1972).
Zeleznik and Gordon (1962) wrote a computer program to compute chemical
equilibrium compositions, rocket performance, and Chapman-Jouquet detonations.
This program was modified and updated by Gordon and McBride (1971) to include
incident and reflected shocks and is the basis of this study. The program was
modified to facilitate calculation of solid-vapor equilibria at a given pressure
and temperature for many types of geological systems as well as cosmic
systems. Changes were made to include fugacity coefficients of gases, molar volumes of solids
and to consider all possible species. Once the program had been modified and was
operational, test cases were run consisting of systems, which had been studied
experimentally. This study included a one-component system (SiO2), binary systems
(MgO-SiO2; MgO-H2O; CaO-SiO2;
CaO-H2O; MgO-CO2), ternary systems
(MgO-CO2-H2O;
MgO-H2O-N2), and metamorphic systems
(tremolite-H2O-CO2; tremolite-H2O).
The calculations compared favorably with the experimental results. This means that,
with reliable thermodynamic data, a considerable amount of time could be saved
in the laboratory by the use of a computer program.
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Table 1.-- List of symbols.
- ai
|
- Least squares coefficients (i = 1 to 7).
|
- aij
|
- Stotchiometric coefficient of element i of species j.
|
- boi
|
- Assigned Kg-atoms of element i per Kg of total reactant (Kg-atom)i / Kg.
|
- bi
|
- Kg-atoms of element i per Kg of mixture, (Kg-atom)i / Kg.
|
- Cp
|
- Heat capacity in calories.
|
- (Cpo)j
|
- Standard state constant pressure specific heat for species or reactant j.
|
- Gj
|
- μj / RT, dimensionless Gibbs free energy for species j.
|
- Gto
|
- Gibbs free energy at temperature T.
|
- ΔGfo
|
- Gibbs free energy of formation from reference state.
|
- Ht
|
- Heat content in kilocalories.
|
- Hj
|
- (Hot)j / RT, dimensionless enthalpy for species j.
|
- (Hto)j
|
- Enthalpy of reactant j.
|
- ΔH298o
|
- Heat of formation from reference state.
|
- L
|
- Number of chemical elements in the system.
|
- m
|
- Number of possible gaseous species.
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- N
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- Total number of possible species.
|
- nj
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- Kg-moles of species j per Kg of mixture.
|
- R
|
- Universal gas constant.
|
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Table 1.-- (Continued).
- (Sot)j
|
- Standard state entropy for species j.
|
- T
|
- Temperature in degrees Kelvin.
|
- μj
|
- Chemical potential of species j.
|
- Vj
|
- Molar volume of species j.
|
- λ
|
- Control factor used to limit size of corrections to original estimates.
|
- πi
|
- Lagrangian multiplier for chemical element i.
|
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