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UBC Theses and Dissertations

Internally consistent thermodynamic data and phase relations in the CaO-Al₂O₃-SiO₂-H₂O system Hammerstrom, Lyle Thomas 1981

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INTERNALLY CONSISTENT THERMODYNAMIC DATA AND PHASE RELATIONS THE C a O - A l 2 0 3 - S i 0 2 - H 2 0 SYSTEM by LYLE THOMAS HAMMERSTROM B . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of G e o l o g i c a l S c i e n c e s We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October 1981 © L y l e Thomas Hammerstrom, 1981 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of G e o l o g i c a l S c i e n c e s The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date: October 16, 1981 i i A b s t r a c t I n t e r n a l l y c o n s i s t e n t thermodynamic data f o r 23 phases i n the C a O - A l 2 0 3 - S i 0 2 - H 2 0 system are determined by l i n e a r programming c o n s i s t e n t set a n a l y s i s . The c o n s i s t e n t set a n a l y s i s i s based on p u b l i s h e d experimental p e t r o l o g y data f o r e q u i l i b r i u m r e a c t i o n s i n v o l v i n g the phases i n t h i s system. I n c o n s i s t e n c i e s i n the experimental data are removed by moving four data p o i n t s beyond the maximum e r r o r a llowed by the s p e c i f i c authors or by i g n o r i n g some p o r t i o n s of the q u e s t i o n a b l e data. The phase r e l a t i o n s among the phases between 0 to 2000°C and 0 to 50,000 bars are c a l c u l a t e d u s i n g the c o n s i s t e n t thermodynamic data with the computer program PT-SYSTEM w r i t t e n by T.H. Brown and E.H. P e r k i n s of the Department of G e o l o g i c a l S c i e n c e s at the U n i v e r s i t y of B r i t i s h Columbia. The s t a b l e p o r t i o n s of the 236 s t a b l e e q u i l i b r i u m r e a c t i o n s are drawn on pressure-temperature (P-T) diagrams showing the phase r e l a t i o n s of each phase. The P-T diagrams can be used to i n t e r p r e t the p e t r o g e n e s i s of metamorphic zones c o n t a i n i n g the phases. The c o n s i s t e n t thermodynamic data i n t h i s study can be improved by u n d e r t a k i n g p e t r o l o g y experiments which w i l l s u b s t a n t i a t e and f u r t h e r d e f i n e the d a t a . Experiments i n v e s t i g a t i n g the s t a b i l i t y of p r e h n i t e , w a i r a k i t e and h e u l a n d i t e are recommended. Updating of the i n t e r n a l l y c o n s i s t e n t thermodynamic p r o p e r t i e s f o r e x i s t i n g and new phases should be c a r r i e d out f o r each a d d i t i o n a l set of experimental data by redoing the l i n e a r programming c o n s i s t e n t set a n a l y s i s on the e n t i r e experimental data s e t . The new thermodynamic p r o p e r t i e s f o r the phases c o u l d then be used t o c a l c u l a t e the new phase r e l a t i o n s . Table of Contents A b s t r a c t i i L i s t of Tables v L i s t of F i g u r e s v i Acknowledgement . . . . v i i I. INTRODUCTION .1 11 . METHOD 2 I I I . DATA 7 IV. RESULTS 23 V. CONCLUDING REMARKS 56 References 58 \ V L i s t of T a b l e s I. E q u i l i b r i u m R eactions And E x p e r i m e n t a l Data ....8 I I . Thermodynamic P r o p e r t i e s Of The Phases 9 v i L i s t of F i g u r e s F i g u r e 1 10 F i g u r e 2 11 F i g u r e 3 . 12 F i g u r e 4 13 F i g u r e 5 14 F i g u r e 6 15 F i g u r e 7 16 F i g u r e 8 . . .. 17 F i g u r e 9 25 F i g u r e 10 26 F i g u r e 11 27 F i g u r e 12 28 F i g u r e 13 29 F i g u r e 14 30 F i g u r e 15. 31 F i g u r e 16 32 F i g u r e 17 ' 33 F i g u r e 18 34 F i g u r e 19 35 F i g u r e 20 36 F i g u r e 21 37 F i g u r e 22 38 F i g u r e 23 39 F i g u r e 24 40 F i g u r e 25 41 F i g u r e 26 42 F i g u r e 27 43 F i g u r e 28 44 F i g u r e 29 . 4 5 F i g u r e 30 46 F i g u r e 31 47 F i g u r e 32 48 F i g u r e 33. 49 F i g u r e 34. . 50 F i g u r e 35 51 1 I. INTRODUCTION I n t e r n a l l y c o n s i s t e n t thermodynamic data f o r m i n e r a l phases are u s e f u l to g e o l o g i s t s , and numerous attempts to compile such data have been made. U n f o r t u n a t e l y , the m a j o r i t y of the p u b l i s h e d thermodynamic data are not t o t a l l y c o n s i s t e n t with the a v a i l a b l e experimental phase e q u i l i b r i a d a t a . The most comprehensive s t u d i e s completed are those of Robie et a l . (1978) and Helgeson et a l . (1978). Robie et a l . (1978) d e r i v e t h e i r thermodynamic p r o p e r t i e s p r i m a r i l y from c a l o r i m e t r i c d a t a , but do not t e s t a l l the p r o p e r t i e s a g a i n s t phase e q u i l i b r i a d a t a ; and, i n many cases, the c a l o r i m e t r i c and phase e q u i l i b r i a d a t a are i n c o n s i s t e n t . C a l o r i m e t r i c i n v e s t i g a t i o n s of m i n e r a l phases produce reasonably a c c u r a t e measurements of entropy, but r e s u l t i n u n c e r t a i n t i e s i n the enthalpy which lead to l a r g e e r r o r s i n computed u n i v a r i a n t e q u i l i b r i u m temperatures. Helgeson e t a l . (1978) attempt to minimize the enthalpy u n c e r t a i n t i e s by d e r i v i n g t h e i r enthalpy v a l u e s from c o m p o s i t i o n a l data and experimental phase e q u i l i b r i a data expressed as simultaneous l i n e a r e q u a t i o n s . However, they do not c o n s i d e r the e n t i r e thermodynamic system as a whole, and the r e s u l t i n g e n t h a l p y v a l u e s c o n t a i n i n c o n s i s t e n c i e s with e x p e r i m e n t a l l y measured phase e q u i l i b r i a and/or c a l o r i m e t r i c d a t a . In t h i s study there has been no attempt to approach the s c a l e of the above s t u d i e s ; r a t h e r , the emphasis has been on d e r i v i n g i n t e r n a l l y c o n s i s t e n t thermodynamic p r o p e r t i e s f o r a l i m i t e d number of phases. I n t e r n a l c o n s i s t e n c y has been main t a i n e d w i t h i n , between and among e x p e r i m e n t a l phase 2 e q u i l i b r i a data and p u b l i s h e d thermodynamic p r o p e r t i e s f o r 23 phases i n the C a O - A l 2 0 3 - S i 0 2 - H 2 0 system. The r e s u l t i n g i n t e r n a l l y c o n s i s t e n t set of thermodynamic p r o p e r t i e s f o r the phases was then used to c a l c u l a t e phase r e l a t i o n s h i p s which can be used i n the de s i g n of p e t r o l o g y experiments and i n the i n t e r p r e t a t i o n of n a t u r a l l y o c c u r r i n g metamorphic assemblages. T h i s i n t e r n a l c o n s i s t e n c y was accomplished by u s i n g the l i n e a r programming method o u t l i n e d by Gordon (1973, 1977) which a l l o w s f o r the p r o c e s s i n g of l a r g e q u a n t i t i e s of v a r i o u s k i n d s of expe r i m e n t a l data. I I . METHOD E q u i l i b r i u m r e a c t ions.among the phases can be expressed as e q u i l i b r i u m curves i n the P-T plane. In g e n e r a l , the exact l o c a t i o n of the e q u i l i b r i u m curves cannot be determined because e x p e r i m e n t a l p e t r o l o g y techniques are l i m i t e d t o d e t e c t i n g the r e l a t i v e s t a b i l i t i e s of two c o m p o s i t i o n a l l y e q u i v a l e n t phase assemblages at some e x p e r i m e n t a l l y c o n t r o l l e d p r e s s u r e and temperature. Within t h i s range of exp e r i m e n t a l u n c e r t a i n t y e q u i l i b r i u m c o n d i t i o n s must e x i s t , and f o r pure phases t h i s e q u i l i b r i u m can be expressed as a f u n c t i o n of p r e s s u r e and temperature by the e q u a t i o n : AG r (T, P) = 0 = I v i , j G°i(T,P) = E i / i , j AHf°i(298,l) - E i / i , j (T)S°i (298, 1 )• + j " I i / i , j Cp°i dT 1 298 1 - ]rivi,3 C p 0 i ( T ) " 1 d T + flvi,j V i dP (1) 298 1 1 1 3 where vi,j i s the r e a c t i o n c o e f f i c i e n t of the i t h phase i n the j t h r e a c t i o n c o n s i s t i n g of K phases, G°i(T,P) i s the apparent Gibbs f r e e energy at temperature and p r e s s u r e of the ith phase i n j o u l e s / m o l e ( J / m o l ) , AHf°i(298,1) i s the e n t h a l p y of f o r m a t i o n from the elements at 298.15 K and 1 bar of the i t h phase i n J/mol, T i s the temperature in K e l v i n s (K), S°i(298,1) i s the entropy at 298.15 K and 1 bar of i t h phase i n J/mol-K, Cp°i i s the heat c a p a c i t y at constant p r e s s u r e f o r the i t h phase i n J/mol-K, V i i s the molar volume of the i t h phase i n c u b i c c e n t i m e t e r s (cm 3=0.1J/bar) and P i s the p r e s s u r e i n b a r s . The volume c o n t r i b u t i o n to the Gibbs f r e e energy has been d i v i d e d between-, the c o n t r i b u t i o n of the s o l i d phases and the vapour phase. The volume change of the r e a c t i o n due to the s o l i d phases was assumed to be independent of temperature and p r e s s u r e . The vapour phase volume c o n t r i b u t i o n to the Gibbs f r e e energy of a r e a c t i o n was c a l c u l a t e d u s i n g a m o d i f i e d Redlich-Kwong equation as o u t l i n e d by Holloway (1977). The o r i g i n a l e q uation expressed by R e d l i c h and Kwong (1949) i s P = R«T(V-"b")- 1 - "a"[ (V 2 + nb"V)T 0- 5) ]" 1 (2) where R i s the Gas Constant (8.312 J/mol-K), "a" i s the measure of the cohesion between the molecules i n J 2(K)°- 5/bar mole, "b" i s the measure of the volume of the molecules i n J/bar-mol, P i s the p r e s s u r e i n b a r s , T i s the temperature i n K e l v i n s and V i s the molar volume i n J/bar-mol. A f t e r i a t e g r a t i o n of the 4 e q u a t i o n , the Gibbs f r e e energy of the vapour phase from 1 bar to the p r e s s u r e of i n t e r e s t can be c a l c u l a t e d . The v a l u e s of the "a" and "b" parameters used i n t h i s study were "a" = 1.279186x10 8 - (2.24141 5x10• )T "b" = 14.28062 + (6.092237x10-" )T These "a" and "b" v a l u e s were o b t a i n e d by r e g r e s s i o n of the Gibbs f r e e e n e r g i e s given i n the t a b l e s of Burnham, Holloway and Davis (1969) to the i n t e g r a t e d form of equation ( 2 ) . The r e s i d u a l s f o r the r e g r e s s i o n f i t were, i n g e n e r a l , w i t h i n 30 J/mol of the t a b u l a t e d value and, at the extreme, were l e s s than 400 J/mol. Although the r e s u l t a n t vapour p r o p e r t i e s a r e s l i g h t l y d i f f e r e n t than those g i v e n by the t a b l e s of Burnham, Holloway and Davis (1969) reasonable c o n f i d e n c e can be p l a c e d i n the r e g r e s s e d values up to 10 k i l o b a r s . Many of the diagrams which f o l l o w have been c a l c u l a t e d f o r a range up to 50 k i l o b a r s , and the c a l c u l a t e d p o s i t i o n of water-bearing r e a c t i o n s above 10 k i l o b a r s i s , t h e r e f o r e , suspect; but the diagrams do i n d i c a t e the r e l a t i o n s h i p of the v a r i o u s r e a c t i o n s to each o t h e r . The heat c a p a c i t y was expressed as a f u n c t i o n of temperature by u s i n g the M a i e r - K e l l e y p o l y n o m i a l (Anderson, 1977) which has a, b and c f i t parameters. The heat c a p a c i t y f i t parameters were not c o n s i d e r e d as v a r i a b l e s i n t h i s study because there were a c c e p t a b l e data i n t h e l i t e r a t u r e f o r most of the phases. However, i t was necessary to r e f i t heat c a p a c i t y data using the M a i e r - K e l l e y p o l y n o m i a l f o r some of the phases, and t h i s is. shown i n Table 2. 5 Using the assumptions r e g a r d i n g the volume of the s o l i d phases and the M a i e r - K e l l e y . heat c a p a c i t y equation d i s c u s s e d above, Equation (1) can be i n t e g r a t e d and r e a r r a n g e d as f o l l o w s : E i / i , j AHf ° i(298,l) - I v i , j (T) S° i ( 298 , 1 ) + E i / i , j V s , i ( P - l ) = Z v i , 3 T [ a i Q n T - l n 2 9 8 ) + bi(T-298) + c i / 2 ( T ~ 2 - 2 9 8 " 2 ) ] - L i , j [ a i ( T - 2 9 8 ) + b i / 2 ( T 2 - 2 9 8 2 ) - c i ( T " 1 - 2 9 8 " 1 ) ] " / f y i ' J V v ' i d P <3) where the v a r i a b l e s are the same as i n e q u a t i o n (1) except V v , i i s the molar volume of the ith. vapour phase i n J/bar, V s , i i s the molar volume of* the i t h s o l i d phase, and a i , b i and c i a r e f i t parameters f o r the heat c a p a c i t y e x p r e s s i o n of the i t h phase. The v a r i a b l e s on the r i g h t hand s i d e of equation (3) can be r e p l a c e d with known q u a n t i t i e s and, t h e r e f o r e , the r i g h t hand s i d e w i l l reduce to a numerical v a l u e . The v a r i a b l e s on the l e f t hand s i d e of equation (3) are the unknowns f o r t h i s study, and these can be determined u s i n g l i n e a r programming. As noted above, experimental p e t r o l o g i s t s have p r o v i d e d the p r e s s u r e s and temperatures at which the r e a c t a n t s or p r o d u c t s of a p a r t i c u l a r r e a c t i o n are s t a b l e . I f the r e a c t a n t s are s t a b l e , AGr(T,P) < 0 and the e q u a l i t y symbol i n e q u a t i o n (3) can be r e p l a c e d with a < symbol f o r t h a t p a r t i c u l a r datum p o i n t . The o p p o s i t e i s t r u e f o r a datum p o i n t at which the p r o d u c t s a r e s t a b l e ; the e q u a l i t y symbol can be r e p l a c e d by a > symbol. T h e r e f o r e , a set of experimental data f o r a r e a c t i o n can be w r i t t e n as a s e r i e s of i n e q u a l i t i e s i n the form of e q u a t i o n (3) 6 with < i n e q u a l i t i e s when the r e a c t a n t s are s t a b l e and > i n e q u a l i t i e s when the products are s t a b l e . With the l i n e a r programming approach the s o l u t i o n f o r the unknown v a r i a b l e s on the l e f t hand s i d e of e quation (3) can be determined by s i m u l t a n e o u s l y c o n s i d e r i n g a l l the i n e q u a l i t i e s r e p r e s e n t i n g each datum p o i n t i n every r e a c t i o n . The l i n e a r programming program used to s o l v e e q u a t i o n (3) i s a v a i l a b l e from the U n i v e r s i t y of B r i t i s h Columbia Computing Centre as UBC LIP, and i s a simplex l i n e a r programming a l g o r i t h m . The r e s u l t s were computed on the Centre's Amdahl 470 V/8 computer. The input matrix f o r t h i s l i n e a r programming problem c o n s i s t e d of three columns f o r each of the s o l i d phases' ent h a l p y , entropy and molar volume, two columns f o r the steam phase e n t h a l p y and entropy, and the f i n a l column was the numerical value of the r i g h t hand s i d e of e q u a t i o n ( 3 ) . The f i r s t row of the matrix was the o b j e c t i v e f u n c t i o n and s p e c i f i e d the v a r i a b l e to be o p t i m i z e d . The second to N+1 rows c o n t a i n e d the i n e q u a l i t y r e p r e s e n t a t i o n of equation (3) f o r each experimental datum p o i n t i n every e q u i l i b r i u m r e a c t i o n , where N was the number of data p o i n t s . The N+2 row through l a s t row c o n t a i n e d the e q u a l i t y e quations r e p r e s e n t i n g w e l l known thermodynamic p r o p e r t i e s of phases in the system. Because the o b j e c t i v e f u n c t i o n ( f i r s t row) can be maximized and m inimized, a range of s o l u t i o n s f o r the v a r i a b l e s was produced which i s c o n s i s t e n t with a l l of the experimental d a t a . The number of data p o i n t s that can be i n c l u d e d i n the matrix i s ' dependent on 7 the s p e c i f i c l i m i t s of the program used and the c a p a c i t y of the computer. I l l . DATA The experimental phase e q u i l i b r i a data used i n t h i s study are l i s t e d i n Table 1 along with the source and the e x p e r i m e n t a l e r r o r which was a p p l i e d f o r each set of data i n t h i s study. There were 178 i n d i v i d u a l e x p e r i m e n t a l data p o i n t s expressed i n the form of equation (3) i n the f i n a l matrix of the l i n e a r programming problem matrix of 226 rows by 60 columns. The i n i t i a l thermodynamic p r o p e r t i e s which c o n s t r a i n e d and formed the b a s i s of the c o n s i s t e n t set were the e n t h a l p i e s and e n t r o p i e s of alpha and beta q u a r t z , corundum, w o l l a s t o n i t e , steam and the molar volumes of the s o l i d phases. Because l i n e a r programming permits a range of p o s s i b l e s o l u t i o n s between the maxima and minima f o r each v a r i a b l e , there are a l a r g e number of c o n s i s t e n t s e t s that can be produced from the same -experimental d a t a . For the v a r i a b l e v a l u e s which c o u l d not be e s t i m a t e d by a sum of the oxides or s i m i l a r scheme, or be found i n the l i t e r a t u r e , the v a l u e s were s e l e c t e d by t a k i n g the m i d - p o i n t v a l u e i n the maximum-minimum range. The r e s u l t a n t c o n s i s t e n t set of thermodynamic p r o p e r t i e s of the phases and t h e i r symbols are l i s t e d i n Table 2. The e q u i l i b r i u m curves f o r each r e a c t i o n i n T a b l e 1, which were c a l c u l a t e d u s i n g the thermodynamic p r o p e r t i e s l i s t e d i n Table 2, are shown with the b r a c k e t i n g data p o i n t s i n F i g u r e s 1 through 8. The e q u i l i b r i u m c u rves were c a l c u l a t e d u s i n g a TABLE 1. E q u i l i b r i u m r e a c t i o n s and e x p e r i m e n t a l d a t a used E q u i l i b r i u m R e a c t i o n 1. g r o s s u l a r + q u a r t z = a n o r t h i t e + 2 w o l l a s t o n l t e 2. 2 g r o s s u l a r = 3 w o l l a s t o n l t e + g e h l e n l t e + a n o r t h i t e 3. 3 a n o r t h i t e * g r o s s u l a r + 2 k y a n l t e + q u a r t z 4. g r o s s u l a r + corundum = g e h l e n l t e + a n o r t h i t e 5. 4 z o l s l t e + q u a r t z = 5 a n o r t h i t e + g r o s s u l a r + 2 H i O 6. 2 z o l s l t e . + s l l l l m a n l t e + q u a r t z = 4 a n o r t h i t e + H»0 7. 6 z o l s l t e = 6 a n o r t h i t e + 2 g r o s s u l a r + corundum + 3 H 8. 4 l a w s o n l t e = 2 z o l s l t e + k y a n l t e + q u a r t z + 7 H i O 9. l a w s o n l t e = a n o r t h i t e + H»0 10. l a w s o n l t e + 2 q u a r t z = w a l r a k l t e 11. l a u m o n t l t e = l a w s o n l t e + 2 q u a r t z + 2 H?0 12. l a u m o n t l t e = w a l r a k l t e + 2 H i O 13. s t e l l e r l t e = l a u m o n t l t e + 3 q u a r t z + 3 H*0 14. w a l r a k l t e = a n o r t h i t e + 2 q u a r t z + 2 H,0 15. h e u l a n d l t e = l a u m o n t l t e + 3 q u a r t z + 2 H i O 16. 5 p r e h n l t e = 2 z o l s l t e + 2 g r o s s u l a r + 3 q u a r t z + 4 H i 17. m a r g a r l t e = a n o r t h i t e + corundum + H i O 18. m a r g a r l t e + q u a r t z = a n o r t h i t e + k y a n l t e / s 1 1 1 I m a n l t e + 19. k y a n l t e = s l l l l m a n l t e 20. a n d a l u s l t e = s l l l l m a n l t e 21. k y a n l t e = a n d a l u s l t e 22. Ca-Al p y r o x e n e = corundum + g e h l e n l t e + a n o r t h i t e 23. Ca-Al p yroxene = g r o s s u l a r + corundum 24. Ca-Al p yroxene + g r o s s u l a r = a n o r t h i t e + g e h l e n l t e l i n e a r programming c o n s i s t e n t se t a n a l y s i s Source of Data E r r o r A p p l l e d T°C P b a r s B o e t t c h e r (1970) +5 ±50 Newton (1966) ±10 ±400 Huckenholz et a l . (1975) ±5 ± 2 % Wlndom and B o e t t c h e r (1976) + 10 ±300 Huckenholz et a l . (1975) ±5 + 2% H a r l y a and Kennedy (1968) ±5 ±1000 Henson et a l . (1975) +5 ±1000 Huckenholz e t a l . (1975) ±5 ± 2 % B o e t t c h e r (1970) ±5 ±50 Newton ( 1965) ±5 ±100 B o e t t c h e r (1970) ±5 ±50 Newton and Kennedy (1963) + 10 ±1000 Newton ( 1966) + 10. ±400 Newton ( 1965) ±5 + 100 + 10 ±1000 B o e t t c h e r (1970) +5 ±100 Newton and Kennedy (1963) + 10 ±1000 Cra w f o r d and F y f e (1965) + 10 ± 5 % L l o u (197 1) +5 ±50 L1ou (1971) +5 ±50 L1ou (1971) +5 ±50 L l o u (1971a) +5 ±50 L l o u (1970) +5 ±50 Thompson (1970) ±10 +50 L1ou (1971b) ±5 ±50 C h a t t e r j e e (1974) ±5 ±100 S t o r r e and N l t s c h (1974) ±10 +5% S t o r r e and N l t s c h (1974) + 10 ± 5 % R i c h a r d s o n et a l . (1969) +5 ±100 Newton ( 1969) + 10 ±1000 Holdaway (1971) ±5 ± 1 .5% Newton ( 1966) ±15 ± 5 % R i c h a r d s o n et a l . (1969) ±5 ±100 Holdaway ( 1971) +5 ± 1 .5% Hays (1967) + 10 ±1000 Hays (1967) ±10 ±1000 Hays ( 1967) ±10 ±1000 TABLE 2. Thermodynamic properties of the phases determined by linear programming consistent set analysis of the experimental phase e q u i l i b r i a data l i s t e d In Table 1. Phase Formula Symbol H°f(. ... 0 S°(. . 1 8 i 0 Cp Parameters Molar Volume (J/mol) (J/mol-K) a b c (cm1 ) alpha-quartz S10, aOZ -910647. b 41 . 338b 66 . 953 b 0. 0053780b -2305284. b 23. ,348b beta-quartz S10. pOZ -909434. b 42 . 769b 66 . 953 b 0. 0053780b -2305284. ,b 23. ,720b corundum Al .Oi CO -1675700. c 50. 92 c 113. 4776n 0. 0136884n -3428987. n 25, ,575c wol1astonlte CaSIOi WO - 1635220. c 82 . 01 c 111. 462 g 0. 0150624g -2727968. g 39. .93 c kyanlte Al,S10» KY -2591770. a 83 . 76 a 172 . 1583c 0. 0291791c -5306697. c 44 . ,09 c anda1 us 1te Al.S10» AD -2587570. a 92 . 965e 173. 7506c- O. 0253580c -5291258. , c 51 , . 53 c s1111 man 1te Al.S10» SI -2584370. a 96 . 856e 164 . 4293c 0. 0335876c -4608576, , c 49, .9 c grossular Ca j A1 .S1J 0 1 I GR -6645044. a 255. 5 c 435 . 2063f 0. .07 11807f - 1 1429839, . f 125, .3 c a n orthlte CaAl,S1.0. AN -4232833. a 201 . 02 a 266 . 4560c 0. ,0599580c -6535409. . c 100, .79 c gehlen1te Ca.Al»S10. GE -3986326. a 209 . 8 c 279 . 0217t 0. ,0251397t -8288805, , t 90, .24 c Ca-Al pyroxene CaAl.510. CA-AL P -3298127. a 146 . 44 g 221 . 8132p 0. 0344461p -6500660. P 63, .5 g steam H.O H.O -241818. c 188 . ,715c 30. 5432d 0. 0102926d 0, ,d zo1s1te Ca.AliS1i0 •.(OH) ZO -6901151. a 295. 851u 413. 881 u 0, .1521302U - 10075072, . u 135 .9 g 1awsonlte CaAl.S1.0. (OH). H.O LW -4867586. a 230. 036u 378 . 100 u O. 0710330U - 1 1 189760. . u 101 . 32 c prehn1te Ca.Al.S1iO io(OH), PR - 6 2 1 4 2 3 4 . a 279. .0 a 4 0 6 . 015 u 0 . 1 2 5 4 7 8 0 U - 1 0 4 6 8 3 6 8 . u 1 4 0 . 33 g margar 1 te CaAl(AliS1 ,0> o)(0H). MA -6244 154 . a 263 . 634u 426 . 057 u 0. ,1011273U -12652416, . u 129 . 587a 1 aumont 1 te CaAlJ 51.0i .-4H.0 LM -7251991 . a 485. . 762q 515. 4685g 0. .1860624g -6874310 • g 207 . 55 g wa1rak1te CaAl.SI .0. .•2H.0 WR -6658887 . a 385 . 175q 420. 0732g 0. .1860624g -6874310 • g 190 . 33 h heu1 and 1te CaAl.SI rO. . -6H.0 HE - 10560141. a 742 . 58 r 8 11. 721 k 0 ,2021920k -13790464 .k 317 .1411 s te11er1te CaAl.SI.0i . • 7H.0 ST - 10854900. a 791 . 57 s 859 . 419 k 0, .2021920k -13790464 .k 328 .7 j d1aspore A100H DI -999342. m 35. . 25 1m 60. 3751g 0 .0175728g 0 • g 17 .76 g kaol1n1te Al.SI.0.(OH). KA -4121352. m 203 . , 129m 304 . 4695g 0 .1221727g -9003965 • g 99 . 52 g pyrophy111te Al.SI.Oio(OH). PY -5640529. m 239 , 405m 332 . 3433g 0 .1640713g -7230782 • g 126 .6 g (a)Thls study,consistent set r e s u l t . (b)Berman,R.(1982) (c)Roble et al.(1978).3 parameter f i t of Cp data. (d ) S t u l l and Prophet (1971),2 parameter f i t of Cp data (e)Thls study,S°AD,S°Si calculated from S"KYby maintaining AS°r values for KY=AD and KY= S I from Helgeson et al.(1978) (f)Krupka et al.(1979). (g)Helgeson et a1.(1978). (h)L1ou (1970). (1)Breck (1974). (j)L1ou (1971a). (k)calculated by assuming ACpr=0 for ST=LM+3QZ+3H,0(z)(=zeol1te,a=47.6976,b=0.,c=0..Helgeson et al.1978)and ST=HE+H.O(z). (m)values of Helgeson et a).( 1978) adjusted for CO H°f and S ° used In th i s study. (n)Dltmars and Douglas (1971) (p)Thompson et a1.( 1978). (q)Thls s tudy, 1 n 111 a 1 estimate from S°WR = SllLM-2S,lH20(z)(58.9944 J/mol-K , Helgeson et al.1978) and 2 S " L M = S"Leonhardite (=922.153 J/mol -K,He 1 geson et al.1978) + S°H2OW. (r)Th1s study , 1 n 1 11 a 1 estimate from S°HE = S°LM+3S°«0Z + 2S°H20(z) (s)Thts study. I n i t i a l estimate from S"ST = S ° L M + 3S °«OZ+3S ° H 2 O U ) (t )Pankratz and Kelley ( 1964) 3 parameter f i t of Cp data (u)Perklns et al.(1980) 10 400 600 800 1000 1200 1400 TEMPERATURE (deg. C) F i g u r e 1. P-T diagram of the e q u i l i b r i u m c u r v e s of the f o u r anhydrous r e a c t i o n s ; (1) 2KY+GR+cQZ = 3AN D = S (2) GR+0QZ = 2WO+AN W = A (3) CO+GR=GE+AN <> = <=> (4) 2GR=GE+AN+3WO V = A i n the system C a O - A l 2 0 3 - S i 0 2 - H 2 0 f o r which e x p e r i m e n t a l data i s a v a i l a b l e (see Tabl e 1). The ex p e r i m e n t a l d a t a p o i n t s used i n the l i n e a r programming c o n s i s t e n t s et a n a l y s i s a r e i n d i c a t e d by the symbols f o l l o w i n g the l i s t e d r e a c t i o n s . The c u r v e s are c a l c u l a t e d u s i n g the i n t e r n a l l y c o n s i s t e n t thermodynamic data i n Ta b l e 2. The number "1" datum p o i n t on the diagram has been moved 700 bars below the maximum e r r o r l i m i t g i v e n by H a r i y a and Kennedy (1968). 400 500 600 700 800 TEMPERATURE (deg. C) F i g u r e 2. P-T diagram of the e q u i l i b r i u m c u r v e s of the t h r e e a l u m i n o s i l i c a t e r e a c t i o n s ; (1) KY = AD S • • (2) SI » AD V = A (3) .KY « SI V = A Refer t o the c a p t i o n of F i g u r e 1 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 12 400 600 800 1000 1200 1400 TEMPERATURE (deg. C) F i g u r e 3. P-T diagram of the e q u i l i b r i u m c u r v e s of the four z o i s i t e - b e a r i n g r e a c t i o n s ; (1) 4LW=2ZO+KY+aQZ + 7H 20 0 = 0 (2) <,QZ + SI+2ZO=H 20 V = A (3) 4ZO+^QZ=GR+5AN+2H20 V = A (4) 6ZO=CO+2GR+6AN + 3H ?0 S = D The number "2" datum p o i n t on the diagram has been moved 1000 bars below the maximum e r r o r l i m i t g i v e n by Newton and Kennedy (1963). R e f e r t o the c a p t i o n of F i g u r e 1 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 13 •i. 0 100 200 300 400 500 TEMPERATURE (deg. C) F i g u r e 4. P-T diagram of the e q u i l i b r i u m c u r v e s of z e o l i t e r e a c t i o n s ; (1) HE=3DQZ+LM+2H 20 X = + (2) ST=3oQZ+LM+3H20 <> = • (3) WR=2cQZ+AN+2H20 A = V The number "3" datum p o i n t on the diagram has been moved to a temperature 5°C l e s s than the maximum e r r o r l i m i t and the number "4" datum p o i n t has been moved to a temperature 5°C g r e a t e r than the maximum e r r o r l i m i t g i v e n by L i o u (1970). R e f e r t o the c a p t i o n of F i g u r e 1 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 14 TEMPERATURE ( d e g . C) F i g u r e 5. P-T diagram of the e q u i l i b r i u m c u r v e s of the t h r e e r e a c t i o n s ; (1) LM=2cQZ+LW+2H20 A = V (2) WR=LW+2aQZ 0 = S (3) LW=AN+2H?0 . 0 = ° R e f e r to the c a p t i o n of F i g u r e 1 f o r d e t a i l s o f the c o n s t r u c t i o n of the diagram. 15 400 450 500 550 600 650 700 TEMPERATURE (deg. C) F i g u r e 6. P-T diagram of the e q u i l i b r i u m c u r v e s of the m a r g a r i t e - b e a r i n g r e a c t i o n s ; (1) MA=C0+AN+H20 0 = • (2) MA+oQZ=H?0+AD/KY+AN V = A Re f e r to the c a p t i o n of F i g u r e 1 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 16 i i i i i 1 1 1 1 i r 360 380 400 420 440 460 TEMPERATURE (deg. C) F i g u r e 7. P-T diagram of the e q u i l i b r i u m c u r v e s of the p r e h n i t e - b e a r i n g r e a c t i o n ; (1) 5PR=4H20+2ZO+2GR+3cQZ A = V Refer to the c a p t i o n of F i g u r e 1 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 17 1100 1200 1300 1400 1500 1600 1700 1800 1900 TEMPERATURE ( d e g . C) F i g u r e 8. P-T diagram of the e q u i l i b r i u m c u r v e s of the Ca-Al p y r o x e n e - b e a r i n g r e a c t i o n s ; (1) GR+2CO=3CA-AL P 0 = • (2) GR+3CA-AL P=2GE+2AN + = * (3) 3CA-AL P=GE+AN+C0 V = A Ref e r t o the c a p t i o n of F i g u r e 1 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 18 F o r t r a n computer program, PT-SYSTEM, w r i t t e n by T.H. Brown and E.H. P e r k i n s of the Department of G e o l o g i c a l S c i e n c e s , U.B.C. T h i s program was a l s o used to c a l c u l a t e a l l the s t a b l e e q u i l i b r i u m r e a c t i o n s among the phases l i s t e d i n T a b l e 2. Maintenance of i n t e r n a l c o n s i s t e n c y with a l l of the experimental . data and p r e v i o u s l y p u b l i s h e d thermodynamic p r o p e r t i e s was not p o s s i b l e . T h e r e f o r e , i t was n e c e s s a r y to make reasonable temperature or p r e s s u r e adjustments f o r some of the data p o i n t s beyond the maximum e r r o r l i m i t s l i s t e d i n T a b l e 1. The f o l l o w i n g a l t e r a t i o n s were the only e x c e p t i o n s to the p u b l i s h e d thermodynamic p r o p e r t i e s and the e x p e r i m e n t a l data of T a b l e 1. In F i g u r e 1, data p o i n t 1 was moved 700 bars below the maximum e r r o r l i m i t s t a t e d by H a r i y a and Kennedy (1968) f o r the r e a c t i o n 3AN= 2KY+GR+QZ, so t h a t the r e s u l t i n g • k y a n i t e e n t h a l p y made the assemblage of corundum p l u s q u a r t z m e t a s t a b l e . C o n s i s t e n c y was a l s o maintained with a l l the other data and r e s u l t e d i n an a l u m i n o s i 1 i c a t e t r i p l e p o i n t p o s i t i o n of 490°C and 3700 bars c o r r e s p o n d i n g to Helgeson et a l . (1978), (see F i g u r e 2 ) . The e xperimental data on the g r o s s u l a r to a n o r t h i t e r e a c t i o n i n F i g u r e 1 d i d not permit the use of the e n t r o p i e s of both g r o s s u l a r and a n o r t h i t e as r e p o r t e d by Robie et a l . (1978), which were based on recent c a l o r i m e t r i c d a t a . The c o n s i s t e n t set a n a l y s i s allowed the use of the Robie et a l . (1978) g r o s s u l a r entropy of 255.5±0.51 J/mol-K, but r e q u i r e d an a n o r t h i t e entropy of 201 .02 J/mol-K and not t h e i r r e p o r t e d entropy of 199.6±0.3 J/mol-K. 19 The z o i s i t e - b e a r i n g r e a c t i o n s shown i n F i g u r e 3 are a l l c o n s i s t e n t with the z o i s i t e entropy of 295.851 J/mol-K determined by Perki n s et a l . (1980). However, i n or d e r t o main t a i n c o n s i s t e n c y between the experimental data and the lawso n i t e entropy 230.036 J/mol-K of P e r k i n s et a l . (1980), i t was necessary to move datum p o i n t 2 i n F i g u r e 3 to a p r e s s u r e one k i l o b a r l e s s than the e r r o r allowed by Newton and Kennedy (1963) f o r t h e i r p i s t o n - c y l i n d e r experiment. The r e a c t i o n s r e l a t i n g the z e o l i t e s to l a w s o n i t e , a n o r t h i t e , alpha quartz and steam are shown i n F i g u r e s 4 and 5. There was a major i n c o n s i s t e n c y with r e a c t i o n s i n v o l v i n g w a i r a k i t e when the p u b l i s h e d data of L i o u (1970, 1971) were used i n t h e i r e n t i r e t y . With no c o n s t r a i n t s imposed on the H f ° , S° and V f o r w a i r a k i t e , the c o n s i s t e n t set a n a l y s i s a l l o w e d w a i r a k i t e a maximum molar volume of 182.679 cm 3 which was much l e s s than the molar volume of 190.33 cm 3 c a l c u l a t e d from c r y s t a l l o g r a p h i c data of L i o u (1970). The r e a c t i o n t h a t l i m i t e d the w a i r a k i t e molar volume to 182.679 cm 3 was LM=WR+H20, and L i o u (1971) r e p o r t e d d i f f i c u l t y i n o b t a i n i n g t r u s t w o r t h y r e s u l t s f o r t h i s e q u i l i b r i u m . P o s s i b l y d u r i n g the quenching phase of the experiment the amount of z e o l i t i c water i n the chan n e l s of the c r y s t a l l a t t i c e of laumontite was changing and c o u l d have made d e t e c t i o n of l a u m o n t i t e - w a i r a k i t e r e v e r s a l s d i f f i c u l t . T h e r e f o r e , the L i o u (1971) data f o r LM=WR+H20 was not used i n t h i s study. The data f o r the w a i r a k i t e breakdown to a n o r t h i t e , alpha q u a r t z and steam (Liou,1970) r e s t r i c t e d the r e s u l t i n g w a i r a k i t e molar volume to 187.17 cm 3 which, a g a i n , was l e s s than 20 190.33 cm 3. L i o u ' s d e s c r i p t i o n of the r e s u l t s of the experiment s t a t e s t h a t determining the d i r e c t i o n of the r e a c t i o n at l e s s than 2000 bars was d i f f i c u l t , and, t h e r e f o r e , a l l data f o r t h a t r e a c t i o n at l e s s than 2000 bars were d i s r e g a r d e d i n t h i s s t udy. The only anomalies remaining are shown i n F i g u r e 4 where datum p o i n t 3 was moved to a temperature 5°C l e s s than the e r r o r allowed by L i o u , and datum p o i n t 4 was moved to a temperature 5°C g r e a t e r than the e r r o r allowed by L i o u . The r e s u l t of these a l t e r a t i o n s was a set of data which would accept a molar volume of 190.33 cm 3 f o r w a i r a k i t e . A l l data f o r the remaining r e a c t i o n s i n F i g u r e s 4 and 5 were not a l t e r e d from the r e p o r t e d experimental v a l u e s . The data f o r the r e a c t i o n of h e u l a n d i t e to l a u m o n t i t e , q u a r t z and steam (Thompson, 1970) c o n s i s t e d of one r e v e r s a l a t 130±10°C and 2000 bars and were based on weight changes of s i n g l e c r y s t a l s of q u a r t z . These data were used and r e s u l t e d i n an entropy of 742.58 J/mol-K f o r h e u l a n d i t e which gave i t a reasonable s t a b i l i t y f i e l d with r e s p e c t to the other z e o l i t e s . N i t s c h (1968) r e p o r t e d a r e v e r s a l f o r the r e a c t i o n h e u l a n d i t e t o l a w s o n i t e , q u a r t z and steam at <200°C and 7000 b a r s . The r e v e r s a l f o r that r e a c t i o n f o r c e d the entropy of h e u l a n d i t e t o be <400 J/mol-K, because a l a r g e r entropy r e s u l t e d i n h e u l a n d i t e being s t a b l e with r e s p e c t t o a l l the z e o l i t e s . T h e r e f o r e the N i t s c h (1968) data were i n c o n s i s t e n t with other experiments and f i e l d r e l a t i o n s and were d i s r e g a r d e d i n t h i s study. The e n t r o p i e s of laumontite and w a i r a k i t e were based on the Helgeson et a l . (1978) scheme f o r e s t i m a t i n g the entropy of 21 z e o l i t i c water. Use of the estimated z e o l i t i c water entropy and the entropy of l e o n h a r d i t e given by Helgeson et a l . (1978) r e s u l t e d i n a laumontite entropy estimate of 490.674 J/mol-K, which was c l o s e to the c o n s i s t e n t s et a n a l y s i s r e s u l t (see Table 2 ) . An estimated w a i r a k i t e entropy of 372.685 J/mol-K, which was. w i t h i n 12.5 J/mol-K of the c o n s i s t e n t set a n a l y s i s entropy, was c a l c u l a t e d from the laumontite entropy e s t i m a t e and the z e o l i t i c water estimate (see Table 2 ) . The e n t r o p i e s of s t e l l e r i t e and h e u l a n d i t e were estimated by a s i m i l a r scheme with the a d d i t i o n of qua r t z to the r e a c t i o n s which made the p r e d i c t e d v a l u e s l e s s c e r t a i n . The h e u l a n d i t e entropy used i n the c o n s i s t e n t set a n a l y s i s was 10.0 J/mol-K g r e a t e r than t h a t p r e d i c t e d by the z e o l i t e water scheme. The s t e l l e r i t e entropy used i n t h i s study was c a l c u l a t e d from the z e o l i t e water scheme. The m a r g a r i t e - b e a r i n g r e a c t i o n s of F i g u r e 6 were c a l c u l a t e d u s i n g u n a l t e r e d e x p e r i m e n t a l data from v a r i o u s authors (see Table 1). S t o r r e and N i t s c h (1974) a l s o r e p o r t e d e x p e r i m e n t a l data f o r the r e a c t i o n m a r garite p l u s q u a r t z t o z o i s i t e , k y a n i t e and steam. These data suggested a much st e e p e r n e g a t i v e s l o p e f o r the e q u i l i b r i u m curve than the thermodynamic p r o p e r t i e s of P e r k i n s et a l . (1980) p e r m i t t e d , and t h e r e f o r e , the e x p e r i m e n t a l data were not used. The d i s c r e p e n c y c o u l d be due to impure n a t u r a l m a r g a r i t e being used as the s t a r t i n g m a t e r i a l f o r the experiment. The p r e h n i t e r e a c t i o n data i n F i g u r e 7 was taken from L i o u (1971b) and r e s u l t e d i n a maximum p r e h n i t e entropy of 279.0 J/mol-K from the c o n s i s t e n t s et a n a l y s i s . The exp e r i m e n t a l data 22 were not a l t e r e d from the maximum e r r o r l i m i t s a l l o w e d by L i o u . The entropy r e s u l t was 13.75 J/mol-K l e s s than the p u b l i s h e d p r e h n i t e entropy of 292.75 J/mol-K of Pe r k i n s et a l . (1980). To o b t a i n a 292.75 J/mol-K entropy from the exp e r i m e n t a l data would r e q u i r e a shallower n e g a t i v e slope f o r the e q u i l i b r i u m curve than that shown i n F i g u r e 7. I t c o u l d be done by a p p l y i n g 20°C e r r o r l i m i t s to the data, but that l a r g e an a l t e r a t i o n i s not c o n s i s t e n t with the o b j e c t i v e s of u s i n g c o n s i s t e n t s e t a n a l y s i s and l i n e a r programming to check the v a l i d i t y of e x p e r i m e n t a l r e s u l t s with respect to thermodynamic data. L i o u (1971b) a l s o r e p o r t e d experimental data f o r the metastable r e a c t i o n PR=AN+WO+.H20 which f u r t h e r r e s t r i c t e d the p r e h n i t e entropy t o 264.77 J/mol-K, and t h i s data was d i s r e g a r d e d because of a 28 J/mol-K entropy c o n t r a d i c t i o n with the P e r k i n s et a l . (1980) c a l o r i m e t r i c r e s u l t s . The entropy d i f f e r e n c e s were s i g n i f i c a n t because the l a r g e r the p r e h n i t e entropy, the s m a l l e r the s t a b i l i t y f i e l d f o r p r e h n i t e . T h i s i s d i s c u s s e d f u r t h e r below. The Ca-Al pyroxene-bearing r e a c t i o n s i n F i g u r e 8 were based on the data of Hays (1967) which were not a l t e r e d . These d a t a were given l i b e r a l e r r o r l i m i t s when i n t e r p o l a t e d from Hays' diagrams and, t h e r e f o r e , do not d e l i m i t the r e s u l t a n t p r o p e r t i e s very w e l l . 23 IV. RESULTS A f t e r d etermining the i n t e r n a l l y c o n s i s t e n t thermodynamic p r o p e r t i e s f o r the 23 phases i n the C a O - A l 2 0 3 - S i 0 2 - H 2 0 system, i t was p o s s i b l e to c a l c u l a t e the s t a b l e e q u i l i b r i u m r e a c t i o n s u s i n g the computer program PT-SYSTEM. With 23 phases a simple b i n o m i a l expansion determined t h a t there were 33,649 p o s s i b l e r e a c t i o n s among the phases, but t h a t only about 20,000 of those were a c t u a l r e a c t i o n s because some were repeated degenerate r e a c t i o n s . With about 20,000 a c t u a l r e a c t i o n s to c o n s i d e r computer f i l e space and e x e c u t i o n run time became a c o n s t r a i n t at v a r i o u s stages of the PT-SYSTEM program. T h e r e f o r e , a l l polymorphic phases ( is-quartz, a n d a l u s i t e and s i l l i m a n i t e ) and Ca-Al pyroxene were omitted from the c a l c u l a t i o n s , and t h i s l e f t 19 phases g i v i n g 11,628 p o s s i b l e r e a c t i o n s . The program then e l i m i n a t e d the repeated degenerate r e a c t i o n s l e a v i n g about 7400 a c t u a l equations and f u r t h e r reduced t h i s number by c o m p i l i n g an e x c l u s i o n l i s t f o r metastable assemblages. For example, the program determined t h a t the assemblage corundum p l u s q u a r t z i s metastable i n t h i s system, and, t h e r e f o r e , each time t h a t assemblage o c c u r r e d i n a r e a c t i o n the program a u t o m a t i c a l l y e l i m i n a t e d the r e a c t i o n from f u r t h e r c a l c u l a t i o n s . The program r e q u i r e d fewer than f i f t e e n minutes of c e n t r a l p r o c e s s i n g u n i t time on an Amdahl 470 V-8 computer to compute a l l of the r e a c t i o n s among the phases, to e l i m i n a t e metastable r e a c t i o n s , and to p l o t and l a b e l s t a b l e r e a c t i o n s . The . r e s u l t i n g s t a b l e r e a c t i o n s c o n t a i n i n g the polymorph of an omitted phase were d u p l i c a t e d and t e s t e d f o r s t a b i l i t y with r e s p e c t to the e x i s t i n g 24 r e a c t i o n s . The Ca-Al pyroxene r e a c t i o n s were c a l c u l a t e d by o m i t t i n g a l l of the low temperature phases and s p e c i f y i n g t h a t o n l y Ca-Al pyroxene r e a c t i o n s were to be c o n s i d e r e d i n the c a l c u l a t i o n s . A f t e r a l l metastable r e a c t i o n s were e l i m i n a t e d , t h e r e were only 236 s t a b l e e q u i l i b r i u m r e a c t i o n s from 0 to 50 k i l o b a r s and 0 to 2000°C c a l c u l a t e d u s i n g the i n t e r n a l l y c o n s i s t e n t thermodynamic p r o p e r t i e s in Table 2. There was no c o n s i d e r a t i o n of the e f f e c t s of m e l t i n g on the phases, and, t h e r e f o r e , even though the e q u i l i b r i u m . r e a c t i o n s are c a l c u l a t e d to 2000°C, many of the phases would have melted be f o r e that temperature was a t t a i n e d . I t must be emphasized t h a t the s t a b l e r e a c t i o n s and t h e i r l o c a t i o n s i n the P-T plane are v a l i d only f o r the thermodynamic p r o p e r t i e s i n Table 2. D i f f e r e n t thermodynamic p r o p e r t i e s would r e s u l t in d i f f e r e n t P-T l o c a t i o n s f o r the e q u i l i b r i u m r e a c t i o n s and, undoubtedly, d i f f e r e n t s t a b l e r e a c t i o n s . A l s o these s t a b l e r e a c t i o n s were c a l c u l a t e d among only 23 phases i n the system, and any other phase in the system not c o n s i d e r e d here c o u l d render some of these s t a b l e r e a c t i o n s m e t a s t a b l e . As an example, at the lower temperatures h y d r o g r o s s u l a r c o u l d be s t a b l e with re s p e c t to- g r o s s u l a r f o r some of the e q u i l i b r i u m r e a c t i o n s . The 236 s t a b l e e q u i l i b r i u m r e a c t i o n s i n the system a r e shown i n F i g u r e s 9 through 34 and every r e a c t i o n i s l a b e l l e d at l e a s t once i n the s e r i e s of f i g u r e s . Each f i g u r e was drawn t o show a l l of the r e a c t i o n s that i n v o l v e a s p e c i f i c phase; f o r example, a l l of the r e a c t i o n s i n v o l v i n g w a i r a k i t e are shown i n 25 400 800 1200 1600 2000 TEMPERATURE (deg. C) F i g u r e 9. P-T diagram of the phase r e l a t i o n s i n t h e system C a O - A l 2 0 3 - S i 0 2 - H 2 0 f o r the anhydrous phases l i s t e d i n T a b l e 2. The s t a b l e r e a c t i o n s between the phases have been c a l c u l a t e d u s i n g the i n t e r n a l l y c o n s i s t e n t thermodynamic p r o p e r t i e s i n Tab l e 2. The s t a b l e r e a c t i o n s were determined, c a l c u l a t e d and drawn u s i n g the computer program PT-SYSTEM, written- by T.H. Brown and E.H. P e r k i n s of the Dept. of G e o l o g i c a l S c i e n c e s , U.B.C. In t h i s and the f o l l o w i n g f i g u r e s a l l of t h e s t a b l e r e a c t i o n s c o n t a i n i n g a s p e c i f i c phase or phases a r e drawn on one diagram. Not every s t a b l e r e a c t i o n i s l a b e l l e d on each diagram, but every r e a c t i o n i s l a b e l l e d at l e a s t once on one of the f o l l o w i n g diagrams. 26 1100 1200 1300 1400 1500 1600 1700 . 1800 1900 TEMPERATURE (deg. C) F i g u r e 10. P-T diagram f o r the s t a b l e r e a c t i o n s c o n t a i n i n g the phase Ca-Al pyroxene. Refer to the c a p t i o n of F i g u r e .9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 27 TEMPERATURE (deg. C) F i g u r e 11. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phases s t e l l e r i t e and h e u l a n d i t e . Refer t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the d i a g r a m . The dashed l i n e b e g i n n i n g at 180°C and 1 bar on t h i s diagram r e p r e s e n t s the two phase boundary f o r water. 28 TEMPERATURE (deg. C) F i g u r e 1.2. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase l a u m o n t i t e . Refer to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. The dashed l i n e b e g i n n i n g at 200°C and 1 bar on t h i s diagram r e p r e s e n t s the two phase boundary f o r water and i t i s a l s o p r e s e n t on s e v e r a l of the f o l l o w i n g diagrams. 29 180 200 220 240 260 280 300 T E M P E R A T U R E (deg. C ) F i g u r e 13. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase l a u m o n t i t e which are not l a b e l l e d i n F i g u r e 12. R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 30. 0 100 200 300 400 500 600 700 TEMPERATURE (deg. C) F i g u r e 14. P-T diagram of the r e a c t i o n LM=2aQZ+LW+2H.20 showing the s t a b l e and m e t a s t a b l e p o r t i o n s of the e q u i l i b r i u m curve which i s a contin u o u s l o o p . The e q u i l i b r i u m c u r v e was c a l c u l a t e d using the thermodynamic p r o p e r t i e s i n T a b l e 2 f o r the phases i n the r e a c t i o n . 31 TEMPERATURE (deg. C) F i g u r e 15. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase w a i r a k i t e . Refer t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. I I I I I I 2400 H 160 180 200 220 240 260 280 300 TEMPERATURE (deg. C) F i g u r e 16. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase w a i r a k i t e which are not l a b e l l e d i n F i g u r e 15. R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 33 TEMPERATURE (deg. C) F i g u r e 17. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase l a w s o n i t e . Refer to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 34 TEMPERATURE (deg. C) F i g u r e 18. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase l a w s o n i t e from 0-400°C and 0-8000 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 35 0 400 800 1200 1600 2000 TEMPERATURE (deg. C) F i g u r e 1 9 . P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase z o i s i t e . R e fer t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 3 6 J I I L 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1100 1 2 0 0 TEMPERATURE (deg. C) F i g u r e 20. P-T diagram of the r e a c t i o n 5WO+2ZO=H20+3GR+2,9QZ showing the s t a b l e and metastable p o r t i o n s of the e q u i l i b r i u m c u r v e . The e q u i l i b r i u m curve was c a l c u l a t e d u s i n g the thermodynamic p r o p e r t i e s i n Table 2 f o r the phases i n the r e a c t i o n . The e q u i l i b r i u m curve goes t o h i g h e r t e m p e r a t u r e s a t low p r e s s u r e s which i s unusual behaviour f o r w a t e r - b e a r i n g r e a c t i o n s . 3.7 F i g u r e 21. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase z o i s i t e from 0-1200 0C and 20,000-50,000 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 38 TEMPERATURE (deg. C) F i g u r e 22. P-T diagram of the s t a b l e r e a c t i o n s < c o n t a i n i n g the phase z o i s i t e from 0-500°C and 0-10,000 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 39 F i g u r e 23. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase z o i s i t e from 900-1900 0C and 10,000-28,000 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of t h e diagram. 40 TEMPERATURE ( d e g . C) F i g u r e 24. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase p r e h n i t e . Refer to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 41 i i I i i i i i r 200 220 240 260 280 TEMPERATURE (deg. C) F i g u r e 25. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase p r e h n i t e from 200-300°C and 1000-4000 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 42 TEMPERATURE (deg. C) F i g u r e 26. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase p r e h n i t e from 0-200°C and 0-1500 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 43 360 380 400 420 440 TEMPERATURE (deg. C) F i g u r e 27. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g ^ t h e phase p r e h n i t e from 350-450°C and 0-1000 b a r s . T h i s f i g u r e shows a r e p e a t e d i n v a r i a n t p o i n t . Refer t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the d i a g r a m . 44-40 80 120 160 200 2 4 0 TEMPERATURE (deg. C) F i g u r e 28. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phases p r e h n i t e and m a r g a r i t e from 0-250°C and 0-900 b a r s . R e f e r to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of t h e c o n s t r u c t i o n of the diagram. 45 0 100 200 300 400 500 600 700 TEMPERATURE (deg. C) F i g u r e 29. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase m a r g a r i t e . Refer to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 46 i I i i i 1 1 1 r 200 220 240 260 280 TEMPERATURE (deg. C) F i g u r e 30. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase m a r g a r i t e from 200-300°C and 1000-2500 b a r s . R e f e r to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 47 0 40 80 120 160 200 240 TEMPERATURE (deg. C) F i g u r e 31. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase m a r g a r i t e from 0-250°C and 0-2000 b a r s . R e f e r to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 48 260 280 300 320 340 360 380 400 TEMPERATURE (deg. C) F i g u r e 32. P-T diagram of the s t a b l e r e a c t i o n s c o n t a i n i n g the phase m a r g a r i t e from 250-400°C and 0-9000 b a r s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. 49 TEMPERATURE (deg. C) F i g u r e 33. P-T diagram of the s t a b l e r e a c t i o n s p r e t a i n i n g t o the alumina h y d r o x y l phases. Refer t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. .50 Q < 200 220 240 260 280 300 320 340 360 TEMPERATURE (deg. C) F i g u r e 34. P-T diagram of the s t a b l e r e a c t i o n s p r e t a i n i n g t o the alumina h y d r o x y l phases from 150-375°C and 0-350 b a r s . Refer to the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the. c o n s t r u c t i o n of the diagram. 51 0 100 2 0 0 300 4 0 0 5 0 0 TEMPERATURE (deg. C) F i g u r e 35. P-T diagram of the s t a b i l i t y b o u n d a r i e s f o r the phases s t e l l e r i t e , h e u l a n d i t e , l a u m o n t i t e , w a i r k i t e , p r e h n i t e and l a w s o n i t e taken from the p r e c e d i n g f i g u r e s . R e f e r t o the c a p t i o n of F i g u r e 9 f o r d e t a i l s of the c o n s t r u c t i o n of the diagram. The arrows are p o s s i b l e P-T paths f o r the m i n e r a l assemblages observed w i t h i n c r e a s i n g depth of b u r i a l by the above a u t h o r s . f .52 F i g u r e 15. T h e r e f o r e , some of the i n v a r i a n t p o i n t s i n each diagram can be incomplete. For example, w a i r a k i t e - a b s e n t e q u i l i b r i a r e a c t i o n s f o r a l l of the i n v a r i a n t p o i n t s i n F i g u r e 15 do not appear i n th a t f i g u r e . However, the m i s s i n g r e a c t i o n at each i n v a r i a n t p o i n t can be determined by i d e n t i f y i n g one of the other phases about the i n v a r i a n t p o i n t and by r e f e r e n c i n g the f i g u r e showing t h a t phase. The r e f e r e n c e d f i g u r e w i l l c o n t a i n the i n v a r i a n t p o i n t and the w a i r a k i t e - a b s e n t r e a c t i o n . T h i s g r a p h i c a l p r e s e n t a t i o n was chosen because of the l a r g e number of s t a b l e r e a c t i o n s . The f i g u r e s of s t a b l e r e a c t i o n s are s e l f - e x p l a n a t o r y , and, t h e r e f o r e , only s p e c i f i c p o i n t s of i n t e r e s t w i l l be c o v e r e d . The s t a b i l i t y f i e l d of p r e h n i t e shown i n F i g u r e 24 i s q u e s t i o n a b l e because of the entropy d i s c r e p a n c i e s between P e r k i n s et a l . (1980) and the experimental data of L i o u (1971b) as d i s c u s s e d i n the DATA s e c t i o n . The p r e h n i t e s t a b i l i t y f i e l d shown i n F i g u r e 24 was c a l c u l a t e d using a p r e h n i t e e n t r o p y of 279.0 J/mol-K (see Table 2) which r e s u l t e d i n a maximum p r e s s u r e of 7740 bars at 320°C. The P e r k i n s et a l . (1980) entropy of 292.75 J/mol-K r e s u l t e d i n a maximum pr e s s u r e of 6800 bars a t 305°C, whereas a 264.77 J/mol-K entropy c o r r e s p o n d i n g t o both of the experiments of L i o u (1971b) r e s u l t e d i n a maximum p r e s s u r e of 9350 bars at 347°C. The maximum temperature f o r p r e h n i t e between 440°C and 450°C a t 1000 bars was very s i m i l a r f o r a l l th r e e e n t r o p i e s . The g r e a t e s t e f f e c t of the d i f f e r e n t p r e h n i t e e n t r o p i e s was on the e q u i l i b r i u m curve of the r e a c t i o n 2PR=LW+GR+eQZ, the slope of which i n c r e a s e d as the p r e h n i t e 53 entropy i n c r e a s e d . The entropy of 292.75 J/mol-K r e s u l t e d i n a 0°C i n t e r c e p t f o r the curve at 964 b a r s , whereas a 264.77 J/mol-K entropy r e s u l t e d i n a 0°C i n t e r c e p t at 9032 bars. T h e r e f o r e the t r u e h i g h p r e s s u r e s t a b i l i t y l i m i t of p r e h n i t e may be a p p r e c i a b l y d i f f e r e n t than that l i m i t d e p i c t e d i n F i g u r e 24, p a r t i c u l a r l y at lower temperatures. The p r e h n i t e - b e a r i n g r e a c t i o n shown i n F i g u r e 27 i n v o l v i n g the phases p r e h n i t e , z o i s i t e , g r o s s u l a r , a l p h a q u a r t z , a n o r t h i t e and steam had a repeated i n v a r i a n t p o i n t o c c u r r i n g a t 392°C, 130 bars and a t 420°C, 590 ba r s . Repeated i n v a r i a n t p o i n t s a l s o o c c u r r e d i n other f i g u r e s p a r t i c u l a r l y near the b o i l i n g curve of water. The f i g u r e s show only the s t a b l e p o r t i o n s of the e q u i l i b r i a curves of r e a c t i o n s and do not show the metastable p o r t i o n s . I f these f i g u r e s are to be used t o a i d i n the de s i g n of experiments, i t i s a l s o u s e f u l f o r the experimentor t o understand the behaviour of the metastable e x t e n s i o n . T h i s i s i l l u s t r a t e d by three s e l e c t e d examples of metastable e x t e n s i o n s which e x h i b i t e d unusual behaviour and which c o u l d p r e s e n t d i f f i c u l t i e s i n the i n t e r p r e t a t i o n of the e x p e r i m e n t a l r e s u l t s . For example, i n the r e a c t i o n 2pQZ+3GR+H20=220+5WO, which i s shown i n F i g u r e 1 9 , water i s on the low temperature s i d e of the e q u i l i b r i u m c u r v e . When the metastable e x t e n s i o n of the cur v e was c a l c u l a t e d ( F i g u r e 20), the curve a c t u a l l y went t o a h i g h e r temperature as the pre s s u r e approached 1 b a r , which i s the op p o s i t e of t h a t normally expected i n r e a c t i o n s i n v o l v i n g a gas phase. For the r e a c t i o n s LM=2cQZ+2LW+2H20 ( F i g u r e 14) and 54 ST=LM+3GQZ+3H 20 ( F i g u r e 4) s t a b l e and metastable p o r t i o n s of the e q u i l i b r i u m curves formed continuous l o o p s . These t h r e e examples i l l u s t r a t e t h a t assumptions about the behaviour of an e q u i l i b r i u m curve should not be made u s i n g only the s t a b l e p o r t i o n of the curve, because i t can be very m i s l e a d i n g . I t i s recommended t h a t the e n t i r e e q u i l i b r i u m curve f o r a r e a c t i o n be c a l c u l a t e d t o show i t s true behaviour, p a r t i c u l a r l y i f the r e s u l t i s going to be used i n the design of experiments. F i e l d o b s e r v a t i o n s of the v a r i o u s m i n e r a l s c o n t a i n e d i n the metamorphic zones of an area can be used i n c o n j u n c t i o n w i t h F i g u r e s 9 through 34 to determine the area's p e t r o g e n e s i s . Because the f i g u r e s were c a l c u l a t e d from i n t e r n a l l y c o n s i s t e n t thermodynamic p r o p e r t i e s , the p r e s s u r e and temperature c o n d i t i o n s of the metamorphic events can be i n t e r p r e t e d w i t h some c o n f i d e n c e . In F i g u r e 35 the phase boundaries f o r the Ca-z e o l i t e s , p r e h n i t e and l a w s o n i t e are shown. These phases d e l i n e a t e the P-T c o n d i t i o n s of s u b - g r e e n s c h i s t metamorphism, and the f i g u r e i l l u s t r a t e s some of the observed s t r a t i g r a p h i c z o n a t i o n s as given by L i o u (1971). He r e p o r t e d the g e n e r a l i z e d sequence of occurrence f o r Ca-bearing phases with i n c r e a s i n g depth of b u r i a l to be s t e l l e r i t e , h e u l a n d i t e , l a u m o n t i t e , w a i r a k i t e and p r e h n i t e which i s s u b s t a n t i a t e d by the s t a b i l i t y f i e l d s f o r those phases in F i g u r e 35. The s t r a t i g r a p h i c sequence f o r the Tanzawa Mountains i n Japan r e p o r t e d by S e k i e t a l . (1969) a l s o f o l l o w e d the above g e n e r a l i z e d sequence. The New Zealand sequence of h e u l a n d i t e , laumontite and p r e h n i t e r e p o r t e d by Coombs et a l . (1959) and shown on F i g u r e 35 appears 55 to have been formed at a l e s s e r geothermal g r a d i e n t and a g r e a t e r depth of b u r i a l than the Japanese sequence. I t can be deduced from F i g u r e 35 that the prescence of la w s o n i t e w i t h the other phases p r o v i d e s a maximum temperature l i m i t f o r the metamorphism at these low p r e s s u r e s . A l l of the f i g u r e s can be used i n the above manner to i n t e r p r e t the metamorphic zones observed i n f i e l d r e l a t i o n s h i p s . ' These P-T diagrams are a l s o u s e f u l when i n t e r p r e t i n g the phases observed i n hand and t h i n - s e c t i o n specimens. With c a r e f u l o b s e r v a t i o n of the specimen, the r e a c t a n t phases and the product phases can be determined as w e l l as whether the r e a c t i o n was prograde or r e t r o g r a d e . The s p e c i f i c r e a c t i o n observed between the phases can then be l o c a t e d i n the f i g u r e s , and a P-T regime f o r the specimen determined. Knowing the approximate p o s i t i o n of the p r e d i c t e d e q u i l i b r i u m curve, the e x p e r i m e n t a l p e t r o l o g i s t can a v o i d the e f f o r t of s e a r c h i n g f o r the same i n f o r m a t i o n e m p i r i c a l l y . As d e s c r i b e d i n the DATA s e c t i o n , the thermodynamic p r o p e r t i e s f o r the phases given i n Table 2 are based on exp e r i m e n t a l data from which the i n c o n s i s t e n t data were removed i n order t o o b t a i n a c o n s i s t e n t set of p r o p e r t i e s . The thermodynamic p r o p e r t i e s r e s u l t i n g from the c o n s i s t e n t s et a n a l y s i s performed i n t h i s study can be r e f i n e d by r e p e a t i n g the experiments which r e s u l t e d i n i n c o n s i s t e n t data and by unde r t a k i n g new experiments. These new experiments s h o u l d be s e l e c t e d to o b t a i n data t h a t w i l l f u r t h e r r e f i n e the thermodynamic p r o p e r t i e s of the phases. . 56 The f o l l o w i n g proposed experiments are some examples of those necessary to r e f i n e the thermodynamic p r o p e r t i e s . The two experiments 5PR=4H20+2ZO+2GR+3cQZ and 2PR=LW+GR+oQZ ( F i g u r e 24), which d e l i n e a t e the s t a b i l i t y boundaries of p r e h n i t e would p r o v i d e a b e t t e r e s timate f o r the entropy of p r e h n i t e . The thermodynamic p r o p e r t i e s of w a i r a k i t e can be improved by completing the experiments WR=AN+2aQZ+2H20 and 5WR=MA+2ZO+12cQZ+8H20 ( F i g u r e 15), which d e l i n e a t e the h i g h temperature boundary f o r w a i r a k i t e . Because the thermodynamic p r o p e r t i e s of h e u l a n d i t e were based on only one r e v e r s a l of the r e a c t i o n HE=LM+3aQZ+2H20, exp e r i m e n t a l data from t h i s r e a c t i o n and 3HE=LM+2ST+3cQZ can p r o v i d e b e t t e r e s t i m a t e s of the p r o p e r t i e s of h e u l a n d i t e . V. CONCLUDING REMARKS The i n t e r n a l l y c o n s i s t e n t set of thermodynamic p r o p e r t i e s given i n Tabl e 2 should not be viewed as the f i n a l and a b s o l u t e set of p r o p e r t i e s that can or w i l l be generated by the method o u t l i n e d i n t h i s study. When new experimental data i n v o l v i n g any of the phases i n Table 2 become a v a i l a b l e , these data can be added to the e x i s t i n g l i n e a r programming c o n s i s t e n t s et a n a l y s i s data and a l l of the data r e t e s t e d f o r i n t e r n a l c o n s i s t e n c y . The e q u i l i b r i a data f o r any new r e a c t i o n can c o n t a i n phases not l i s t e d i n Table 2, and thermodynamic p r o p e r t i e s f o r these new phases which are c o n s i s t e n t w i t h the thermodynamic p r o p e r t i e s of a l l phases can a l s o then be determined. By t h i s p r o c e s s the number of phases f o r which i n t e r n a l l y c o n s i s t e n t thermodynamic 57 p r o p e r t i e s are known can be i n c r e a s e d . Every new item of experimental data has the p o t e n t i a l t o f u r t h e r d e l i m i t the thermodynamic maxima-minima ranges of the p r o p e r t i e s of one or s e v e r a l of the phases and, u l t i m a t e l y , t o change the p r e d i c t e d phase r e l a t i o n s h i p s . For t h i s reason i t i s e s s e n t i a l t h a t a l l of the experimental data, o l d and new, be i n c l u d e d i n the c o n s i s t e n t set a n a l y s i s c a l c u l a t i o n and t h a t the new data i s not simply "tacked on" to the e x i s t i n g thermodynamic p r o p e r t i e s . T h i s process of updating the thermodynamic data s e t and c a l c u l a t i n g new phase r e l a t i o n s h i p s can be completed i n a r e l a t i v e l y s h o r t p e r i o d of time because of the power and e f f i c i e n c y of the l i n e a r programming method and the PT-SYSTEM computer program. 58 REFERENCES Anderson, G.M. 1977. 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