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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 THE C a O - A l 0 - S i 0 - H 0 SYSTEM 2  3  2  RELATIONS  2  by L Y L E THOMAS HAMMERSTROM B.Sc,  The U n i v e r s i t y  A THESIS SUBMITTED  of B r i t i s h  Columbia,  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF  SCIENCE  in  THE FACULTY OF GRADUATE Department  We  accept  of G e o l o g i c a l  this  STUDIES Sciences  t h e s i s as c o n f o r m i n g  to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA October  ©  Lyle  1975  1981  Thomas Hammerstrom,  1981  In  presenting  requirements  this  I  available  for  or  her  shall  reference  and  study.  I  extensive  my  copying  by t h e h e a d  thesis written  It for  is  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Columbia  16,  1981  thesis  gain  of of  the  British  it  freely  agree  that  for scholarly  department  understood  permission.  Sciences  October  o f my  make  further  of t h i s  financial  Geological  Date:  at the U n i v e r s i t y  Library  of t h i s  of  fulfilment  the  be g r a n t e d  without  Department  partial  that  representatives.  publication allowed  agree  for  p u r p o s e s may  in  f o r an a d v a n c e d d e g r e e  Columbia,  permission  thesis  that  or  by  his  copying or  shall  not  be  i i  Abstract  Internally the  CaO-Al 0 -Si0 -H 0 2  3  programming analysis  2  reactions  data  specific  authors  The  or  thermodynamic  portions  data  at  with  the  each phase.  petrogenesis  calculated the computer  Perkins  University  of t h e 236  stable  The  allowed  by t h e of  the  investigating  the  stability  thermodynamic  d a t a by r e d o i n g  the  consistent  of  reactions  The  are  of  properties  drawn  this  data.  prehnite, Updating  of  for existing  programming  on  relations  interpret  experiments the  stable  the  the phases.  in  out f o r each a d d i t i o n a l  the l i n e a r  to  written  Geological  Columbia.  data  define  recommended.  carried  0 t o 2000°C  p r o g r a m PT-SYSTEM  British  petrology  further  be  of  thermodynamic  undertaking  are  using  zones c o n t a i n i n g  and  should  moving  portions  d i a g r a m s c a n be u s e d  substantiate  consistent  by  of the Department  equilibrium  of m e t a m o r p h i c  by  heulandite  system.  a r e removed error  for  this  (P-T) d i a g r a m s showing t h e p h a s e P-T  consistent  improved  in  set  data  among t h e p h a s e s between  are  Brown and E.H.  The  petrology  some  linear  consistent  phases  maximum  ignoring  relations  pressure-temperature of  the  by  data.  phase  Sciences  f o r 23 p h a s e s i n  The  experimental  the  by  0 t o 50,000 b a r s  by T.H.  analysis.  involving  beyond  data  determined  i n the experimental data  points  questionable  are  set  i s b a s e d on p u b l i s h e d  Inconsistencies four  thermodynamic  system  2  consistent  equilibrium  and  consistent  can be  which  will  Experiments  wairakite the  and  internally  a n d new  s e t of  consistent  study  phases  experimental set  analysis  on  the  entire  properties new  phase  experimental  f o r the phases c o u l d relations.  data then  set.  The  be u s e d  new to  thermodynamic calculate  the  Table  Abstract L i s t of Tables L i s t of Figures Acknowledgement I. INTRODUCTION 11 . METHOD III. DATA IV. RESULTS V. CONCLUDING REMARKS References  \  of Contents  i i v vi ....vii .1 2 7 23 56 58  V  List  I. II.  of T a b l e s  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 Thermodynamic P r o p e r t i e s Of The P h a s e s  Data  ....8 9  vi  List  Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 . 30 31 32 33. 34. 35  of  Figures  .  . . ..  '  .  10 11 12 13 14 15 16 17 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51  1  I.  Internally are  useful  data  been  Helgeson  and, are  test in  in  deriving  this the  deriving limited  and  enthalpy  minimize values  a  which  et a l . (1978)  of m i n e r a l  whole,  and  with  calorimetric  there  has  been  of  within,  phases. between  but  result in et  uncertainties  by  as  data  and  simultaneous the  resulting  experimentally  entire enthalpy measured  data. no  above s t u d i e s ; r a t h e r , t h e consistent  phases  Helgeson  consider the  data  to large e r r o r s  expressed not  but  data;  phase e q u i l i b r i a  lead  do  their  data,  compositional  data  the most  equilibria  enthalpy  from  the  derive  temperatures. the  of  The  calorimetric  phase  calorimetric  as  and/or  study  number  data.  of R o b i e  from  such  c o n s i s t e n t with  e t a l . (1978)  primarily  However, t h e y  internally  maintained  those  Robie  inconsistencies  phase e q u i l i b r i a  of  are  equilibria  system  contain  In  to  phase  equations.  values  totally  majority  equilibria  equilibrium  enthalpy  thermodynamic  scale  i n the  attempt  their  the  phases  to compile  a c c u r a t e m e a s u r e m e n t s of e n t r o p y ,  univariant  experimental linear  not  phase  the  for mineral  Calorimetric investigations  uncertainties  (1978)  are  a l l the p r o p e r t i e s a g a i n s t  reasonably  computed al.  data  properties  inconsistent.  produce  Unfortunately,  et a l . (1978).  many c a s e s ,  data  numerous a t t e m p t s  s t u d i e s completed  thermodynamic not  and  experimental  comprehensive  do  made.  thermodynamic  available  and  c o n s i s t e n t thermodynamic  to g e o l o g i s t s ,  have  published  INTRODUCTION  attempt emphasis  to approach has  been  the on  thermodynamic p r o p e r t i e s f o r a  Internal and  consistency  among  has  been  experimental  phase  2  equilibria phases  data  in  internally  and p u b l i s h e d thermodynamic  the  CaO-Al 0 -Si0 -H 0 2  was t h e n  used  be  i n the  design  interpretation This  internal  programming for  2  of  to calculate  petrology  outlined large  petrology  stabilities  assemblages  at  temperature.  equilibrium  plane.  curves  techniques of  two  the  linear  1977) w h i c h  allows  various  kinds  cannot  exist,  expressed  the  be d e t e r m i n e d  of  to  detecting  controlled  of and  as  a  pressure  experimental f o r pure function  exact  because  compositionally equivalent  c o n d i t i o n s must  the phase and  uncertainty phases  this  of p r e s s u r e and  by t h e e q u a t i o n :  = 0 = Ivi,j  G°i(T,P) = E i / i , j  E i / i , j (T)S°i (298, 1 )• +  j"Ii/i,j  AHf°i(298,l) Cp°i dT  298 1  ]rivi,3 298  assemblages.  general,  are limited  range  be  In  experimentally  1  -  i n the  t h e p h a s e s c a n be e x p r e s s e d a s  this  can  temperature  -  some  Within  equilibrium  of  which can  METHOD  i n t h e P-T  of the e q u i l i b r i u m  relative  (1973,  f o r the  and  by u s i n g  quantities  r e a c t ions.among  curves  experimental  experiments  by G o r d o n  resulting  data.  Equilibrium  location  relationships  o c c u r r i n g metamorphic  II.  equilibrium  phase  The  f o r 23  properties  c o n s i s t e n c y was a c c o m p l i s h e d method  experimental  of  naturally  the processing of  AG r ( T , P)  system.  2  c o n s i s t e n t s e t o f thermodynamic  phases used  3  properties  1  Cp i(T)" dT 0  1  +  flvi,j 1 1  V i dP  (1)  3  where vi,j jth  reaction  Gibbs in  i s the r e a c t i o n  free  coefficient  consisting  energy at temperature  the  J/mol,  T  elements  at  and  at  298.15 K and  and  1 bar of  the  The  ( c m = 0 . 1 J / b a r ) and  vapour  phase.  The  solid  phases  was  pressure.  The  energy  contribution  assumed  ith  phase  of  i t h phase is  in the  i n J / m o l - K , Cp°i  is  the  in  the  ith  phase  i t h phase  t o be volume  reaction  free  energy  of t h e s o l i d the  in cubic  independent  has  phases  reaction  due  been  and  the  to  the  of t e m p e r a t u r e  contribution  was  calculated  e q u a t i o n as o u t l i n e d  by H o l l o w a y  original  a  phase  apparent  S°i(298,1)  for  to the Gibbs  volume c h a n g e o f  vapour of  Redlich-Kwong  the  the  P i s the p r e s s u r e i n b a r s .  3  between-,  The  volume  volume c o n t r i b u t i o n  divided  free  molar  (K),  i t h phase  J/mol-K,  centimeters  1 bar of the  in Kelvins  at constant p r e s s u r e  is  i s the  p r e s s u r e of the  the heat c a p a c i t y Vi  in  i s the e n t h a l p y of f o r m a t i o n  298.15 K  i s the temperature  entropy  i t h phase  of K phases, G°i(T,P)  j o u l e s / m o l e ( J / m o l ) , AHf°i(298,1)  from  of the  e q u a t i o n e x p r e s s e d by R e d l i c h  to  the  using  a  and  Gibbs  modified  (1977). and  Kwong  (1949)  is  P = R«T(V-"b")-  where R of is  the  i s t h e Gas  - " a " [ ( V + b " V ) T - ) ]"  1  2  Constant  c o h e s i o n between  0  5  (2)  1  (8.312 J / m o l - K ) ,  "a" i s the  the m o l e c u l e s i n J (K)°- /bar 2  measure mole,  5  t h e m e a s u r e o f t h e volume of t h e m o l e c u l e s i n J / b a r - m o l ,  the p r e s s u r e i n b a r s , the  n  molar  volume  T  in  i s the temperature J/bar-mol.  After  in Kelvins  and  iategration  P is V  of  "b"  is the  4  equation,  the Gibbs  to  the  pressure  the  " a " and  "b"  14.28062 +  (6.092237x10-" )T  (1969)  to  for  30  of  J/mol 400  Holloway  the  the the  J/mol.  slightly  values  and  obtained  i n the  integrated  Although  Davis  the  than  form  f i t  and,  calculated  kilobars  those  to  10  The  heat  capacity study  by 1977)  capacity phases,  the  data and  in the  by  the  was  can of  water-bearing  using  the a,  b and  However,  as  in Table  in the  are  placed  in  t o 50  kilobars,  r e a c t i o n s above indicate  other. function  of  polynomial The  variables  necessary  2.  less  diagrams  f i t parameters.  c o n s i d e r e d as  i t was  within  the  a  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 i s . shown  be  Maier-Kelley c  The  Burnham,  t h e d i a g r a m s do  expressed  and  properties  t a b l e s of  Many  t h e r e were a c c e p t a b l e d a t a  this  of  the  (2).  e x t r e m e , were  confidence  but  of  general,  v a r i o u s r e a c t i o n s to each  w h i c h has  phases.  equation  f o r a r a n g e up  of  f i t p a r a m e t e r s were not  because of  the  values  were  vapour  kilobars.  position  capacity  temperature (Anderson,  of  at  given  i s , therefore, suspect;  relationship  1 bar  Burnham, H o l l o w a y  of  resultant  f o l l o w have been c a l c u l a t e d the  The  regression  were,  (1969) r e a s o n a b l e up  by  t a b l e s of  tabulated value  regressed values  most  were  regression  different  study  from  (2.24141 5x10• )T  energies given  residuals  the  in this  =  "b"  vapour phase calculated.  "b"  Davis  10  be  8  free  and  can  p a r a m e t e r s used -  the  1.279186x10  Gibbs  which  interest  of  =  " a " and  the  of  energy  "a"  These  than  free  in  literature to  refit  f o r some o f  heat this for heat the  5  Using phases  the assumptions  and  the  M a i e r - K e l l e y . heat  above, E q u a t i o n  Ei/i,j  (1) c a n  be  -  Li,j[ai(T-298) y i  'J  V  where t h e v a r i a b l e s the  molar  v  ' i  are  be  and  The  for  will  these As  side can  noted  p r e s s u r e s and a particular  replaced  the  be  as  the  determined  above,  are  the  equality set  a series  for  follows:  of  =  ci/2(T~ -298" )] 2  2  ) - ci(T" -298" ) ] 1  phase  p h a s e , and capacity  right  1  and,  the  of e q u a t i o n  are  the i t h (3)  right  variables  can hand  on  study,  have p r o v i d e d  r e a c t a n t s or p r o d u c t s  I f the symbol  r e a c t a n t s are in equation  for that p a r t i c u l a r  datum  experimental inequalities  replaced data i n the  by  (3) c a n  point.  a  >  for a reaction form  the of  stable, be The  a datum p o i n t a t w h i c h t h e p r o d u c t s be  the  programming.  petrologists  at which the  ci  unknowns f o r t h i s  using linear  equality  e x p r e s s i o n of  The  Vv,i  in J/bar, V s , i i s  t h e r e f o r e , the  value.  stable.  (1) e x c e p t  a i , b i and  hand s i d e  (3) a r e  symbol can of  2  +  in equation  ith. vapour  experimental  temperatures  true  a  same as  heat  of e q u a t i o n  and  is  Therefore, written  solid  <3)  to a numerical  w i t h a < symbol  opposite stable;  on  reaction  AGr(T,P) < 0  2  known q u a n t i t i e s  reduce  hand  + bi(T-298)  ith solid  the  variables  replaced with  left  r e a r r a n g e d as  + bi/2(T -298  volume o f t h e  parameters  side  the  d P  the  the m o l a r volume of* t h e  phase.  of  capacity equation discussed  i n t e g r a t e d and  T[aiQnT-ln298)  " /f  fit  volume  A H f ° i ( 2 9 8 , l ) - I v i , j (T) S° i ( 298 , 1 ) + E i / i , j V s , i ( P - l ) Zvi,3  is  r e g a r d i n g the  are  symbol. can  of e q u a t i o n  be (3)  6  with  <  inequalities  inequalities  when t h e  programming  approach  the  left  hand  e a c h datum p o i n t  is  the of  reactants are  in every  reaction.  the  UBC  LIP,  algorithm.  The  r e s u l t s were computed  V/8  input  consisted  of  enthalpy,  matrix  three  numerical first  row  of  the  variable  was  can  be  the  British  on  >  linear  by  representing  equation  Columbia  linear the  on  determined  solve  simplex  the  (3)  Computing  programming  Centre's  Amdahl  thermodynamic objective range of  of  data  solutions with  data  that  second  for all  can  be  the of  can  of  470  equation  t o N+1  N+2  in the  be  and  i n the  phases' the  the  (3).  The  specified contained  (3)  for  reaction,  row  matrix  N  last  well  row  known  Because  the  minimized,  produced data.  each  where  through  system.  steam  was  rows  m a x i m i z e d and was  problem  column  function  experimental  included  for  representing  variables the  columns  equation  The  phases  row)  solid  equilibrium  equations  (first  side  of  the  final  objective The  of  of  the  points.  properties  function  points  the  in every  equality  consistent  and  optimized.  programming  v o l u m e , two  r i g h t hand  was  datum p o i n t  the  each  representation  number  contained  the  linear  for  molar  matrix  inequality  this  entropy,  of  t o be  experimental  and  and  value  for  columns  entropy  phase e n t h a l p y  the  a  and  computer. The  the  is  With  inequalities  of  as  stable  unknown v a r i a b l e s  program used to  University  and  the  (3)  all  from t h e  for  equation  considering  are  stable.  solution  l i n e a r programming  available  Centre  the  products  side  simultaneously  The  when  The  a  which  is  number  of  i s ' dependent  on  7  the  specific  limits  of  the  program used  and  the c a p a c i t y of  the  computer.  Ill.  The are  experimental  listed  error  in Table  which  was  phase e q u i l i b r i a  1 along applied  T h e r e were  178  individual  the  of  equation  form  programming initial the  thermodynamic of  entropies  of  s t e a m and  maxima and  data.  For  sum  the  minima  are  the  beta  oxides the  or  equilibrium  calculated  Table  2,  are 8.  experimental  in t h i s  study.  final  matrix  by  60  of  the  the  in  linear  columns.  The formed  enthalpies  and  q u a r t z , corundum, w o l l a s t o n i t e , solid  phases.  there are from  scheme,  the  or  selected  range.  by  The the  Because  solutions  v a l u e s which c o u l d not  p r o p e r t i e s of  linear  between  the  a l a r g e number  of  same - e x p e r i m e n t a l be be  estimated found  t a k i n g the resultant  p h a s e s and  by  in  a  the  mid-point consistent  their  symbols  2. curves  using  shown w i t h The  the  study  points expressed  were  produced  were  this  w h i c h c o n s t r a i n e d and  set  the  similar  values  in Table  data  rows  f o r each v a r i a b l e , be  and  in  s e t of d a t a  a r a n g e of p o s s i b l e  variable  were  through  226  used  source  the  properties  and  thermodynamic  listed The  in  of  i n t h e maximum-minimum of  each  (3)  s e t s t h a t can  literature,  set  for  consistent  alpha  permits  consistent  value  the  t h e m o l a r v o l u m e s of  programming  of  the  with  data  experimental  problem matrix  basis  DATA  the the  equilibrium  f o r each  reaction  in Table  1,  which  thermodynamic p r o p e r t i e s l i s t e d b r a c k e t i n g data curves  were  points  in Figures  calculated  using  in 1 a  TABLE  1.  Equilibrium  reactions  Equilibrium  1. g r o s s u l a r  + quartz  and e x p e r i m e n t a l  linear  used  = anorthite  + 2  wollastonlte  2 grossular  = 3 wollastonlte  3.  3 anorthite  * grossular  4.  grossular  + corundum  + gehlenlte  5.  4 zolslte  + quartz  6.  2 zolslte. + sllllmanlte  + quartz  7.  6 zolslte  + 2 grossular  + 2 kyanlte  = gehlenlte  = 5 anorthite  = 6 anorthite  +  +  +  anorthite  quartz  anorthite  + grossular  + 2 HiO  = 4 anorthite  + H»0  + corundum  + 3 H  4 lawsonlte = 2 z o l s l t e + kyanlte + quartz + 7 H i O l a w s o n l t e = a n o r t h i t e + H»0 lawsonlte + 2 quartz = walraklte 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 laumontlte = walraklte + 2 HiO 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 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 heulandlte = laumontlte + 3 quartz + 2 HiO 5 prehnlte = 2 z o l s l t e + 2 grossular + 3 quartz + 4 Hi 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 19. k y a n l t e = s l l l l m a n l t e 20. 21.  andaluslte = sllllmanlte kyanlte = andaluslte  22. 23. 24.  Ca-Al Ca-Al Ca-Al  programming  c o n s i s t e n t set  + kyanlte/s111Imanlte  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 p y r o x e n e = g r o s s u l a r + corundum pyroxene + grossular = anorthite + gehlenlte  +  B o e t t c h e r (1970) Newton ( 1 9 6 6 ) Huckenholz e t a l . (1975) Wlndom a n d B o e t t c h e r ( 1 9 7 6 ) Huckenholz e t a l . (1975) H a r l y a and Kennedy (1968) Henson e t a l . (1975) H u c k e n h o l z e t a l . (1975) B o e t t c h e r (1970) Newton ( 1965) B o e t t c h e r (1970) Newton a n d K e n n e d y ( 1 9 6 3 ) Newton ( 1966) Newton ( 1965) B o e t t c h e r (1970) Newton a n d K e n n e d y C r a w f o r d and F y f e L l o u (197 1) L1ou (1971) L1ou (1971) L l o u (1971a) L l o u (1970) Thompson ( 1 9 7 0 ) L1ou (1971b) Chatterjee (1974) S t o r r e and N l t s c h S t o r r e and N l t s c h Richardson et a l . N e w t o n ( 1969) Holdaway (1971) Newton ( 1966) Richardson et a l . H o l d a w a y ( 1971) Hays (1967) Hays (1967) H a y s ( 1967)  analysis  Error T°C  Source of Data  Reaction  2.  8. 9. 10. 11. 12. 13. 14. 15. 16. 17.  data  (1963) (1965)  (1974) (1974) (1969)  (1969)  +5 ±10 ±5 + 10 ±5 ±5 +5 ±5 ±5 ±5 ±5 + 10 + 10. ±5 + 10 +5 + 10 + 10 +5 +5 +5 +5 +5 ±10 ±5 ±5 ±10 + 10 +5 + 10 ±5 ±15 ±5 +5 + 10 ±10 ±10  Applled P bars ±50 ±400 ±2% ±300 + 2% ±1000 ±1000 ±2% ±50 ±100 ±50 ±1000 ±400 + 100 ±1000 ±100 ±1000 ±5% ±50 ±50 ±50 ±50 ±50 +50 ±50 ±100 +5% ±5% ±100 ±1000 ± 1 .5% ±5% ±100 ± 1 .5% ±1000 ±1000 ±1000  TABLE 2. Thermodynamic p r o p e r t i e s of the phases determined by l i n e a r programming c o n s i s t e n t 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 alpha-quartz beta-quartz corundum wol1astonlte kyanlte anda1 us 1te s1111 man 1te grossular anorthlte gehlen1te Ca-Al pyroxene steam zo1s1te 1awsonlte prehn1te margar 1 t e 1 aumont 1 t e wa1rak1te heu1 and 1te s te11er1te d1aspore kaol1n1te pyrophy111te  Formula S10, S10. Al .Oi CaSIOi Al,S10» Al.S10» Al.S10» Ca j A1 .S1J 0 1 I CaAl,S1.0. Ca.Al»S10. CaAl.510. H.O C a . A l i S 1 i 0 •.(OH) H.O CaAl.S1.0. (OH). Ca.Al.S1iO io(OH), C a A l ( A l i S 1 ,0> o)(0H). C a A l J 51.0i .-4H.0 C a A l . S I .0. .•2H.0 C a A l . S I rO. . -6H.0 C a A l . S I . 0 i . • 7H.0 A100H Al.SI.0.(OH). Al.SI.Oio(OH).  Symbol  S°(. . i 0 (J/mol-K) 41 .338b 42 .769b 50. 92 c 82 .01 c 83 .76 a 92 .965e 96 .856e 255. 5 c 201 ..02 a c 209 .8 .44 g 146 . 188 . ,715c 295. 851u 230. 036u 279..0 a  H°f(. ... 0 (J/mol) -910647. b -909434. b -1675700. c - 1635220.c -2591770. a -2587570. a -2584370. a -6645044. a -4232833. a -3986326. a -3298127. a  18  aOZ pOZ CO WO KY AD SI GR AN GE CA-AL P -241818. c H.O -6901151. a ZO -4867586. a LW -6214234 . a PR - 6 2 4 4 154 . a MA -7251991 .a LM -6658887 .a WR - 10560141. a HE - 10854900. a ST -999342. m DI -4121352. m KA -5640529. m PY  a 66 .953 b 66 .953 b 113. 4776n 111. 462 g 172 .1583c 173. 7506c164 .4293c 435 .2063f 266 .4560c 279 .0217t 221 .8132p 30. 5432d 413. 881 u 378 . 100 u 4 0 6 . 015 u 426 . 057 u 515. 4685g 420. 0732g 8 11.721 k 859 .419 k 60. 3751g 304 .4 6 9 5 g 332 . 3433g  263 . 6 3 4 u  485.. 762q 385 . . 175q .58 r 742 . 791 ..57 s 35. . 25 1m , 129m 203 . 239 , 405m  set analysis  Cp Parameters b c -2305284. b 0.0053780b 0.0053780b -2305284.,b -3428987. n 0.0136884n -2727968. g 0.0150624g -5306697. c 0.0291791c O. 0253580c -5291258., c 0. 0335876c -4608576,, c 0..07 11807f - 1 1429839,. f 0.,0599580c -6535409.. c 0.,0251397t -8288805,, t 0. 0344461p -6500660. P 0. 0102926d 0,,d - 10075072,. u 0,.1521302U O. 0 7 1 0 3 3 0 U - 1 1 189760.. u - 10468368 . u 0 .1254780U - 1 2 6 5 2 4 1 6 ,. u 0.,1011273U -6874310 • g 0..1860624g 0..1860624g -6874310 • g - 1 3 7 9 0 4 6 4 .k 0 ,2021920k -13790464 .k 0,.2021920k 0 .0175728g 0•g -9003965 • g 0 .1221727g 0 .1640713g -7230782 • g  Molar Volume (cm ) 23. ,348b 23. ,720b 25, ,575c 39. .93 c 44 . ,09 c 51 . , 53 c 49, .9 c 125,.3 c 100,.79 c 90, .24 c 63, .5 g 1  135 .9  g 101 . 32 c 1 4 0 . 33 g 129 . 587a 207 . 55 g 190 . 33 h 317 .1411  328 .7 j 17 .76 g 99 . 52 g 126 .6 g  ( a ) T h l s s t u d y , c o n s i s t e n t s e t r e s u l t . (b)Berman,R.(1982) ( c ) R o b l e et a l . ( 1 9 7 8 ) . 3 parameter f i t of Cp d a t a . ( d ) S t u l l and Prophet (1971),2 parameter f i t of Cp data ( e ) T h l s study,S°AD,S°Si c a l c u l a t e d from S"KYby m a i n t a i n i n g AS°r v a l u e s f o r KY=AD and K Y = S I from Helgeson et a l . ( 1 9 7 8 ) ( f ) K r u p k a et a l . ( 1 9 7 9 ) . (g)Helgeson e t a1.(1978). (h)L1ou (1970). (1)Breck (1974). ( j ) L 1 o u (1971a). ( k ) c a l c u l a t e d by assuming ACpr=0 f o r ST=LM+3QZ+3H,0(z)(=zeol1te,a=47.6976,b=0.,c=0..Helgeson e t al.1978)and ST=HE+H.O(z). (m)values of Helgeson e t a).( 1978) a d j u s t e d f o r CO H°f and S ° used In t h i s study. (n)Dltmars and Douglas (1971) (p)Thompson e t a1.( 1978). ( q ) T h l s s tudy, 1 n 111 a 1 estimate from S°WR = S LM-2S H20(z)(58.9944 J/mol-K , Helgeson e t al.1978) and 2 S " L M = S"Leonhardite (=922.153 J/mol -K,He 1 geson et al.1978) + S°H OW. (r)Th1s study , 1 n 1 11 a 1 e s t i m a t e from S°HE = S°LM+3S°«0Z + 2S°H 0(z) ( s ) T h t s study. I n i t i a l e s t i m a t e from S"ST = S ° L M + 3S °«OZ+3S ° H O U ) (t )Pankratz and K e l l e y ( 1964) 3 parameter f i t of Cp d a t a (u)Perklns et al.(1980) ll  2  2  2  ,l  10  400  600  800  1000  1200  1400  TEMPERATURE ( d e g . C ) Figure 1. P-T d i a g r a m o f t h e e q u i l i b r i u m c u r v e s o f t h e 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 t h e system C a O - A l 0 - S i 0 - H 0 f o r which e x p e r i m e n t a l d a t a i s available ( s e e T a b l e 1). The e x p e r i m e n t a l d a t a p o i n t s u s e d i n t h e l i n e a r programming c o n s i s t e n t s e t a n a l y s i s a r e i n d i c a t e d by the symbols following the l i s t e d reactions. The c u r v e s a r e 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 T a b l e 2. The number "1" datum p o i n t on t h e d i a g r a m h a s been moved 700 b a r s below t h e maximum e r r o r l i m i t g i v e n b y H a r i y a a n d Kennedy ( 1 9 6 8 ) . 2  3  2  2  400  500  600  700  TEMPERATURE (deg.  800  C)  Figure 2. P-T d i a g r a m of t h e e q u i l i b r i u m c u r v e s aluminosilicate reactions; ( 1 ) KY = AD S• • (2) S I » AD V = A (3) .KY « SI V = A 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 t h e of the d i a g r a m .  of  the  three  construction  12  400  600  800  1000  1200  1400  TEMPERATURE ( d e g . C ) F i g u r e 3. P-T d i a g r a m o f t h e e q u i l i b r i u m c u r v e s of the four zoisite-bearing reactions; (1) 4LW=2ZO+KY+aQZ + 7 H 0 0 = 0 (2) <,QZ + SI+2ZO=H 0 V=A (3) 4ZO+^QZ=GR+5AN+2H 0 V = A (4) 6ZO=CO+2GR+6AN + 3 H 0 S = D The number "2" datum p o i n t on t h e d i a g r a m h a s b e e n moved 1000 b a r s b e l o w t h e maximum e r r o r l i m i t g i v e n by Newton and Kennedy (1963). Refer t o the c a p t i o n of Figure 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. 2  2  2  ?  13  •i.  0  100  200  TEMPERATURE  300  400  500  ( d e g . C)  F i g u r e 4. P-T d i a g r a m o f t h e e q u i l i b r i u m curves of zeolite reactions; (1) H E = 3 D Q Z + L M + 2 H 0 X=+ (2) ST=3oQZ+LM+3H 0 <> = • (3) WR=2cQZ+AN+2H 0 A=V The number "3" datum p o i n t on t h e d i a g r a m h a s b e e n moved t o a t e m p e r a t u r e 5°C l e s s t h a n t h e maximum e r r o r l i m i t a n d t h e number "4" datum p o i n t h a s b e e n moved t o a t e m p e r a t u r e 5 ° C g r e a t e r t h a n t h e maximum e r r o r l i m i t g i v e n by L i o u (1970). Refer to the caption of Figure 1 for details of t h e c o n s t r u c t i o n o f t h e diagram. 2  2  2  14  T E M P E R A T U R E ( d e g . C) F i g u r e 5. P-T d i a g r a m o f t h e e q u i l i b r i u m c u r v e s o f t h e three reactions; (1) LM=2cQZ+LW+2H 0 A = V (2) WR=LW+2aQZ 0 = S (3) LW=AN+2H 0 . 0 = ° 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 o f t h e c o n s t r u c t i o n of t h e d i a g r a m . 2  ?  15  400  450  500  550  600  650  700  TEMPERATURE (deg. C) Figure 6. P-T d i a g r a m of the e q u i l i b r i u m curves of the margarite-bearing reactions; (1) MA=C0+AN+H 0 0 = • (2) MA+oQZ=H 0+AD/KY+AN V= A 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 t h e c o n s t r u c t i o n of t h e diagram. 2  ?  16  i  i  360  i  380  i  i  1  400  1  1  420  1 440  i  r  460  TEMPERATURE ( d e g . C ) F i g u r e 7. P-T diagram of prehnite-bearing reaction; (1) 5PR=4H 0+2ZO+2GR+3cQZ R e f e r to t h e c a p t i o n of F i g u r e of t h e d i a g r a m . 2  the  equilibrium  A=V 1 for details  curves  of  the  of t h e c o n s t r u c t i o n  17  1100  1200  1300  1400  1500  1600  1700  1800  1900  TEMPERATURE ( d e g . C ) Figure 8. P-T d i a g r a m o f t h e e q u i l i b r i u m pyroxene-bearing reactions; (1) GR+2CO=3CA-AL P 0= • (2) GR+3CA-AL P=2GE+2AN + = * (3) 3CA-AL P=GE+AN+C0 V = A Refer t o the caption of Figure 1 f o r d e t a i l s of t h e d i a g r a m .  curves  of the Ca-Al  of the construction  18  Fortran E.H.  computer  Perkins  This  of  program  equilibrium  program, the  was  properties  of  was  The  temperature  thermodynamic  limits  the  of  the  thermodynamic  i t was  only  2.  necessary  to  f o r some  of  listed  in Table  exceptions  to  experimental  the  data  of  1.  maximum  error  reaction  3AN= 2KY+GR+QZ, so  made  the  resulted  in  grossular anorthite entropy  of  of  1 d i d not  H a r i y a and  to  on  with  plus all  entropy of  on  permit  the  of  use  of  199.6±0.3 J/mol-K.  J/mol-K  metastable.  other  data  and  of  490°C  a l . (1978),  (see  grossular to a n o r t h i t e  use  of  the  data.  the  entropies  The  Robie  J/mol-K, and  the  enthalpy  r e p o r t e d by R o b i e e t a l .  255.5±0.51  201 .02  quartz  et  the  (1968) f o r  point position  the  the  below  •kyanite  the  Helgeson  data  bars  Kennedy  recent c a l o r i m e t r i c  allowed  700  resulting  corundum  a n o r t h i t e as  based  entropy  moved  t h a t the  experimental  in Figure  analysis  was  s t a t e d by  corresponding The  were  1  aluminosi1icate triple  g r o s s u l a r and  which  point  also maintained  an  2).  reaction  limit  was  3700 b a r s  Figure  1, d a t a  assemblage  Consistency  set  and  stable  a l l  adjustments  p r o p e r t i e s and  Figure  both  Therefore,  were t h e  the  with  published  maximum e r r o r  following alterations  Brown  in Table  consistency  or p r e s s u r e  the  all  phases l i s t e d  possible.  In  and  calculate  previously  p o i n t s beyond  published Table  and  T.H.  of G e o l o g i c a l S c i e n c e s , U.B.C.  to  internal  not  make r e a s o n a b l e  1.  used  r e a c t i o n s among t h e  experimental . data  data  Department  also  Maintenance  the  PT-SYSTEM, w r i t t e n by  not  but  of  (1978),  consistent  e t a l . (1978) required  their  an  reported  19  The  zoisite-bearing  consistent  with  determined  by  maintain  the z o i s i t e Perkins  consistency  lawsonite  entropy  was  necessary  one  kilobar  There  a  wairakite in and  V  than  the error  relating  quartz  major  wairakite  a  less  t h e molar  the  volume  data  of L i o u  molar  volume  the  equilibrium.  experiment crystal  made  lattice  theLiou  this  study.  alpha  quartz  wairakite  of  (1970).  reactions (1970,  and  molar  involving  1971) were  3  3  w h i c h was much  that  and  phase  could  reversals 2  f o r t h e w a i r a k i t e breakdown restricted 3  results of  i n thechannels of  f o r LM=WR+H 0 was  volume t o 187.17 c m  limited 2  was c h a n g i n g  (Liou,1970)  from  was LM=WR+H 0, a n d  the quenching water  S°  allowed  calculated  3  used  on t h e H f ° ,  i n obtaining trustworthy  laumontite-wairakite  steam  cm  t o 182.679 cm  of laumontite  The d a t a  lawsonite,  i n F i g u r e s 4 a n d 5.  The r e a c t i o n  of z e o l i t i c  (1971) d a t a  pressure  set analysis  190.33  Possibly during  t h e amount  detection  Therefore,  with  of L i o u  of  (1971) r e p o r t e d d i f f i c u l t y  a  to  maximum m o l a r volume o f 182.679 c m  Liou  the  zeolites  the consistent  wairakite  this  and t h e  by Newton a n d K e n n e d y  a n d steam a r e shown  the  for  allowed  to  W i t h no c o n s t r a i n t s i m p o s e d  f o r wairakite,  crystallographic  i n order t o  data  2 i nFigure 3  inconsistency  entirety.  than  However,  J/mol-K  experiment.  when t h e p u b l i s h e d d a t a  their  295.851  the experimental  piston-cylinder  alpha  3 are a l l  230.036 J/mol-K o f P e r k i n s e t a l . ( 1 9 8 0 ) , i t  less  anorthite,  i n Figure  of  a l . (1980).  between  reactions  was  et  shown  entropy  t o move datum p o i n t  (1963) f o r t h e i r The  reactions  which, a g a i n ,  have  difficult.  not  used  in  toanorthite, the  resulting  was l e s s  than  20  190.33 c m .  Liou's description  3  states than  that  2000 b a r s  reaction The  was  at less  3  allowed  was  than  to  alterations  was  190.33  cm  reactions  The quartz  the e r r o r  for  3  data  steam  entropy  reasonable  reaction  (Thompson, and  of q u a r t z .  of  742.58  stability  of  were  quartz  for that  being  stable  Nitsch  (1968) d a t a  These data  J/mol-K  field  and  with  steam  reaction  with  relations The  Helgeson  on  temperature  the  from  of  these volume  remaining  the r e p o r t e d  to  were u s e d  f o r h e u l a n d i t e which gave respect to the  other  f o r the r e a c t i o n  at  <200°C  entropy  inconsistent  a n d were d i s r e g a r d e d  a l . (1978)  scheme  changes  with  and  zeolites.  heulandite to  heulandite  resulted  in this  The to  in heulandite Therefore the  experiments  and  study.  and w a i r a k i t e were b a s e d for  i t a  7000 b a r s .  of  other  of  and r e s u l t e d i n  respect to a l l the z e o l i t e s . were  laumontite,  weight  f o r c e d the entropy  e n t r o p i e s of l a u m o n t i t e et  the error  a molar  for  heulandite  based  be <400 J/mol-K, b e c a u s e a l a r g e r  field  datum  1970) c o n s i s t e d o f one r e v e r s a l a t  (1968) r e p o r t e d a r e v e r s a l  lawsonite,  where  The r e s u l t  A l l data  that study.  a  w h i c h would a c c e p t  wairakite.  f o r the  crystals  reversal  by L i o u .  for  than  to  less  in this 4  5°C l e s s  at  values.  and  Nitsch  allowed  a s e t of data  130±10°C a n d 2000 b a r s  an  temperature  i n F i g u r e s 4 and 5 were n o t a l t e r e d  experimental  single  in Figure  by L i o u , and datum p o i n t 4 was moved than  experiment  of the r e a c t i o n  were d i s r e g a r d e d  a r e shown  a  of the  and, t h e r e f o r e , a l l d a t a  2000 b a r s  remaining  moved  greater  of  the d i r e c t i o n  difficult,  only anomalies  point  5°C  determining  of the r e s u l t s  on t h e  e s t i m a t i n g the entropy  of  21  zeolitic the  water.  entropy  resulted which  K,  was  given  laumontite  entropy  a  close 2).  to  zeolitic  with  water  used  by  in this The  using  less  were  the z e o l i t e  to  f o r the r e a c t i o n  and  steam.  used.  natural margarite  J/mol-  being  The  e s t i m a t e and entropies  by a s i m i l a r  reactions  scheme. from  data  which  the z e o l i t e  than  The used  from  than  6 were  t h e thermodynamic  that  scheme.  calculated (see  experimental  to zoisite,  a much s t e e p e r  the  entropy  authors  reported  plus quartz  scheme  used i n  water  various  of  made  The s t e l l e r i t e  (1974) a l s o  suggested  curve  2).  r e a c t i o n s of F i g u r e  margarite  These data  not  o f 372.685  The h e u l a n d i t e e n t r o p y  water  e t a l . (1980) p e r m i t t e d ,  were  result  was 10.0 J/mol-K g r e a t e r  S t o r r e and N i t s c h  data  Perkins  the  was c a l c u l a t e d  the e q u i l i b r i u m  a l . (1978)  analysis  entropy  estimated  certain.  margarite-bearing  1).  et  o f 490.674 J/mol-K,  set  (see Table  of q u a r t z  study  estimate  the laumontite  unaltered experimental  Table  data  from  consistent set analysis  predicted  Helgeson  e n t r o p y and  12.5 J/mol-K o f t h e c o n s i s t e n t s e t a n a l y s i s  estimate  values  by  water  wairakite entropy  heulandite  the a d d i t i o n  zeolitic  consistent  An e s t i m a t e d  and  predicted  for  the  was c a l c u l a t e d  stellerite  the  leonhardite  w h i c h was. w i t h i n  entropy, the  of  in  (see T a b l e  Use o f t h e e s t i m a t e d  kyanite  negative  slope  properties  of  and t h e r e f o r e , t h e e x p e r i m e n t a l  d i s c r e p e n c y c o u l d be due t o i m p u r e as the s t a r t i n g  material  f o r the  experiment. The  prehnite  reaction  (1971b) a n d r e s u l t e d J/mol-K  from  in a  data  in Figure  maximum  7 was t a k e n  prehnite  the c o n s i s t e n t s e t a n a l y s i s .  entropy  from of  The e x p e r i m e n t a l  Liou 279.0 data  22  were The  not a l t e r e d entropy  prehnite obtain  result  entropy  a  that  error  was 13.75 J/mol-K  linear  results  the data,  2  J/mol-K,  and  because  larger  The on  Ca-Al  the data  were g i v e n  very  well.  this  curve  I t c o u l d be done by a p p l y i n g  20°C  slope  check  the v a l i d i t y data.  for  data  of experimental  Liou  (1971b)  the metastable the p r e h n i t e  The e n t r o p y  the Perkins differences  the prehnite  entropy,  et were  the  limits  reaction  o f a 28  significant smaller  interpolated the r e s u l t a n t  These from  the  below.  r e a c t i o n s i n F i g u r e 8 were  t h e r e f o r e , do n o t d e l i m i t  to  a l . (1980)  This i sdiscussed further  when  also  entropy  (1967) w h i c h were n o t a l t e r e d .  error  i s not  analysis  was d i s r e g a r d e d b e c a u s e  with  pyroxene-bearing o f Hays  To  for the equilibrium  for prehnite.  liberal  d i a g r a m s and,  e t a l . (1980).  would  restricted  contradiction  results.  field  published  data  data  further  calorimetric  stability  the  by L i o u .  b u t t h a t l a r g e an a l t e r a t i o n  to  experimental  the  than  the experimental  r e s p e c t t o thermodynamic  J/mol-K e n t r o p y  allowed  the o b j e c t i v e s of using c o n s i s t e n t s e t  PR=AN+WO+.H 0 w h i c h 264.77  7.  programming  with  reported  to  with  less  from  negative  shown i n F i g u r e  limits  limits  o f 292.75 J/mol-K o f P e r k i n s  shallower  consistent and  t h e maximum e r r o r  a 292.75 J/mol-K e n t r o p y  require than  from  based data Hays'  properties  23  IV.  After  determining  properties it  was  using  the i n t e r n a l l y  f o r t h e 23 p h a s e s  possible  t h e computer  program  reactions  among t h e p h a s e s ,  reactions. computer at  file  eliminated actual  program  eliminated required t i m e on an reactions and  about  11,628 p o s s i b l e  further  in  that  this  occurred  in  the r e a c t i o n fewer  than  Amdahl among  t o p l o t and  a  program. and  reactions.  470 V-8  label stable  reactions  containing  duplicated  and  tested  the  number  reactions.  for stability  For  example,  each  compute  of  that  automatically The  a l l  program unit  of  the  reactions,  .resulting  stable  an o m i t t e d p h a s e  with respect  an  quartz i s time  metastable The  7400  the  of c e n t r a l p r o c e s s i n g  to eliminate  polymorph  then  about  corundum p l u s  to  left  by c o m p i l i n g  the program  computer  the phases,  leaving  and  this  program  calculations.  minutes  a l l  sillimanite)  therefore,  further  fifteen  constraint  Therefore,  The  assemblages.  reaction  from  those  consider  t h e c a l c u l a t i o n s , and  and,  simple possible  to  r u n time became a  the assemblage  system,  a  20,000 o f  reactions  reduced t h i s  for metastable  reactions  were r e p e a t e d d e g e n e r a t e  (is-quartz, a n d a l u s i t e  determined  assemblage  actual  PT-SYSTEM  system,  2  were 33,649  the repeated degenerate r e a c t i o n s  list  metastable  only  20,000  execution  2  equilibrium  there  some  the  e q u a t i o n s and  exclusion  but t h a t  3  W i t h 23 p h a s e s  that  were o m i t t e d f r o m  giving  2  because  s p a c e and  phases  pyroxene  19 p h a s e s  about  s t a g e s of  polymorphic Ca-Al  reactions With  various  determined  thermodynamic  CaO-Al 0 -Si0 -H 0  PT-SYSTEM.  expansion  actual  i n the  consistent  to c a l c u l a t e the s t a b l e  binomial  were  RESULTS  were  to the e x i s t i n g  24  reactions. omitting only  The  Ca-Al  all  Ca-Al  of  pyroxene  the  pyroxene  low  reactions  temperature  reactions  were  were  calculated  p h a s e s and to  be  specifying  considered  by that  in  the  there  were  kilobars  and  calculations. After only 0  236  a l l metastable  stable  to  of  the  the  the  must  locations  thermodynamic  reactions.  not  23  phases  i n the  As  hydrogrossular  could  shown least  be  stable  in Figures  show a l l o f  system,  an  equilibrium  236  once  stable  the  example, a l l of  and  any  stable valid  P-T  at  2 0 0 0 ° C , many  other  only  for  the  phase  the  stable  in the  stable  to-  the  for  calculated  lower  respect  and  thermodynamic  different  these  was  reactions  locations  were  even  temperature  Different  some o f  with  consideration  among system  reactions  temperatures grossular  for  reactions. equilibrium 34  s e r i e s of  reactions the  2.  reactions  example,  9 through  i n the  that  are  consistent  therefore,  undoubtedly,  render  stable  and,  the  different  and,  here could  metastable.  The  in  Table  no  c a l c u l a t e d to  plane  in  reactions these  are  that  P-T  50  internally  phases,  emphasized  the  0 to  T h e r e was  before  result  Also  the  the  the  melted  properties  considered  some of  be  in  would  equilibrium  only  on  from  2.  equilibrium.reactions  It  properties  using  in Table  p h a s e s w o u l d have  attained. their  properties  were e l i m i n a t e d ,  reactions  calculated  e f f e c t s of m e l t i n g  though of  equilibrium  2000°C  thermodynamic  reactions  that  reactions  and  reactions every  figures. involve involving  i n the  reaction Each a  system  are  is labelled  at  f i g u r e was  specific wairakite  drawn  phase; are  shown  to for in  25  400  800  1200  1600  2000  TEMPERATURE ( d e g . C) Figure 9. P-T diagram of the phase r e l a t i o n s i n t h e s y s t e m C a O - A l 0 - S i 0 - H 0 f o r the anhydrous phases l i s t e d i n T a b l e 2. The stable reactions between the phases have been c a l c u l a t e d using the internally consistent thermodynamic properties in Table 2. The s t a b l e r e a c t i o n s were d e t e r m i n e d , c a l c u l a t e d a n d drawn u s i n g t h e c o m p u t e r program PT-SYSTEM, writtenby 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 Sciences, U.B.C. I n t h i s and t h e f o l l o w i n g figures a l l of the stable 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 p h a s e o r p h a s e s a r e d r a w n on one diagram. Not e v e r y 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 e a c h d i a g r a m , but every reaction i s l a b e l l e d at l e a s t o n c e on o n e o f t h e f o l l o w i n g diagrams. 2  3  2  2  26  1100  1200  1300  1400  1500  1600  1700 . 1800  1900  TEMPERATURE ( d e g . C ) F i g u r e 10. P-T d i a g r a m f o r t h e s t a b l e r e a c t i o n s phase C a - A l pyroxene. Refer to the caption of 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 d i a g r a m .  containing Figure .9  the for  27  TEMPERATURE  (deg.  C)  Figure 11. P-T d i a g r a m o f 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 t h e p h a s e s s t e l l e r i t e and heulandite. Refer to the caption of Figure 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 this diagram r e p r e s e n t s t h e two p h a s e b o u n d a r y f o r w a t e r .  28  TEMPERATURE ( d e g .  C)  Figure 1.2. P-T d i a g r a m o f 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 t h e phase l a u m o n t i t e . 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 details of the c o n s t r u c t i o n of the diagram. The d a s h e d l i n e beginning a t 200°C and 1 b a r on t h i s diagram represents 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 o f t h e f o l l o w i n g diagrams.  29  180  200  220  240  TEMPERATURE  260  (deg.  280  300  C)  F i g u r e 13. P-T d i a g r a m o f 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 the phase l a u m o n t i t e w h i c h a r e n o t l a b e l l e d i n F i g u r e 12. 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.  30.  0  100  200  300  400  500  600  700  TEMPERATURE (deg. C ) F i g u r e 14. P-T d i a g r a m o f t h e r e a c t i o n LM=2aQZ+LW+2H. 0 s h o w i n g the stable and m e t a s t a b l e portions of the e q u i l i b r i u m curve which i s a continuous loop. The e q u i l i b r i u m curve was c a l c u l a t e d using t h e thermodynamic p r o p e r t i e s i n T a b l e 2 f o r t h e phases i n the r e a c t i o n . 2  31  TEMPERATURE ( d e g . C) Figure 15. P-T d i a g r a m 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 t h e phase w a i r a k i t e . R e f e r t o the c a p t i o n of F i g u r e 9 for details of t h e c o n s t r u c t i o n o f t h e d i a g r a m .  I  I  I  I  I  I  180  200  220  240  260  280  2400 H  160  300  TEMPERATURE ( d e g . C) Figure 16. P-T d i a g r a m 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 t h e p h a s e w a i r a k i t e w h i c h a r e not l a b e l l e d i n F i g u r e 15. Refer to the caption of F i g u r e 9 f o r d e t a i l s o f t h e c o n s t r u c t i o n o f t h e diagram.  33  TEMPERATURE ( d e g . C ) F i g u r e 17. P-T d i a g r a m 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 the phase lawsonite. 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 t h e c o n s t r u c t i o n o f t h e d i a g r a m .  34  TEMPERATURE ( d e g . C) F i g u r e 18. P-T d i a g r a m o f 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 phase lawsonite from 0-400°C and 0-8000 b a r s . Refer to 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 construction of diagram.  the the the  35  0  400  800  1200  1600  2000  TEMPERATURE ( d e g . C ) Figure 1 9 . P-T d i a g r a m 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 phase z o i s i t e . 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 the c o n s t r u c t i o n of the diagram.  the of  36  600  J  I  I  L  700  800  900  1000  TEMPERATURE  1100  1200  (deg. C)  Figure 20. P-T d i a g r a m o f t h e r e a c t i o n 5WO+2ZO=H 0+3GR+2,9QZ showing t h e 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 equilibrium curve. The equilibrium curve was calculated 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 reaction. The e q u i l i b r i u m c u r v e g o e s 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 water-bearing react ions. 2  3.7  Figure 21. phase z o i s i t e the caption diagram.  P-T d i a g r a m o f 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 t h e f r o m 0 - 1 2 0 0 C and 20,000-50,000 b a r s . Refer to 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 t h e 0  38  TEMPERATURE ( d e g .  C)  F i g u r e 22. P-T d i a g r a m o f 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 the phase zoisite from 0-500°C and 0-10,000 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 details of the construction of the diagram.  39  Figure 23. phase z o i s i t e the caption diagram.  P-T d i a g r a m 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 t h e f r o m 9 0 0 - 1 9 0 0 C a n d 10,000-28,000 b a r s . Refer to 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 o f t h e 0  40  TEMPERATURE ( d e g . C) F i g u r e 24. P-T phase p r e h n i t e . the c o n s t r u c t i o n  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 R e f e r t o t h e 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 o f of t h e d i a g r a m .  41  i  200  i  I  220  i  i  240  i  i  260  i  r  280  TEMPERATURE ( d e g . C)  Figure 25. P-T d i a g r a m o f 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 t h e p h a s e p r e h n i t e f r o m 2 0 0 - 3 0 0 ° C and 1000-4000 b a r s . Refer to the caption of Figure 9 for details of the c o n s t r u c t i o n of t h e diagram.  42  TEMPERATURE ( d e g .  C)  F i g u r e 26. P-T d i a g r a m o f 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 phase prehnite from 0-200°C and 0-1500 b a r s . Refer to 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 construction of diagram.  the the the  43  360  380  400  420  440  TEMPERATURE ( d e g . C ) Figure 27. P-T d i a g r a m of t h e s t a b l e r e a c t i o n s containing^the phase p r e h n i t e from 350-450°C and 0-1000 b a r s . This figure shows a repeated invariant point. Refer t o t h e 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 o f t h e d i a g r a m .  44-  40  80  120  160  200  240  TEMPERATURE ( d e g . C) F i g u r e 28. P-T d i a g r a m o f 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 the phases prehnite and margarite from 0-250°C a n d 0-900 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 t h e c o n s t r u c t i o n of t h e d i a g r a m .  45  0  100  200  300  400  500  600  700  TEMPERATURE ( d e g . C) F i g u r e 29. P-T d i a g r a m o f 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 the phase margarite. R e f e r t o t h e 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 o f t h e c o n s t r u c t i o n of t h e d i a g r a m .  46  i  200  I  i  220  i  i  240  1  1 260  1  r  280  TEMPERATURE ( d e g . C) F i g u r e 30. P-T d i a g r a m o f 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 the phase m a r g a r i t e f r o m 2 0 0 - 3 0 0 ° C and 1000-2500 b a r s . R e f e r to the caption of Figure 9 for details of t h e c o n s t r u c t i o n of t h e diagram.  47  0  40  80  120  160  TEMPERATURE ( d e g .  200  240  C)  F i g u r e 31. P-T d i a g r a m o f 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 the phase margarite 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 construction of the diagram.  48  260  280  300  320  340  360  380  400  TEMPERATURE ( d e g . C) Figure 32. P-T d i a g r a m o f 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 t h e phase m a r g a r i t e f r o m 2 5 0 - 4 0 0 ° C a n d 0-9000 b a r s . Refer to the caption of Figure 9 for details of t h e c o n s t r u c t i o n o f t h e diagram.  49  TEMPERATURE ( d e g .  C)  F i g u r e 33. P-T d i a g r a m o f t h e s t a b l e r e a c t i o n s pretaining to the alumina hydroxyl 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 t h e c o n s t r u c t i o n of the d i a g r a m .  .50  Q  <  200  220  240  260  280  TEMPERATURE  300  320  340  360  ( d e g . C)  F i g u r e 34. P-T d i a g r a m o f t h e s t a b l e r e a c t i o n s pretaining to the alumina hydroxyl phases from 150-375°C a n d 0-350 b a r s . R e f e r t o t h e c a p t i o n o f F i g u r e 9 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 t h e d i a g r a m .  51  0  100  200  300  TEMPERATURE ( d e g .  400  500  C)  F i g u r e 35. P-T d i a g r a m o f t h e stability boundaries for the phases stellerite, heulandite, laumontite, w a i r k i t e , p r e h n i t e a n d l a w s o n i t e t a k e n from t h e p r e c e d i n g f i g u r e s . Refer to the caption of Figure 9 for details of t h e c o n s t r u c t i o n o f t h e diagram. The a r r o w s a r e p o s s i b l e P-T paths for the mineral assemblages observed with increasing depth o f b u r i a l by t h e above a u t h o r s .  f  .52  Figure  15.  diagram  Therefore,  can  equilibria Figure  do  identifying and  not  at  by  chosen  of  therefore, The  Perkins  of  figure  of  in  7740 b a r s  292.75  a t 320°C.  J/mol-K  experiments  of L i o u  of  9350  at  between three  bars  The  of the  are  self-explanatory,  of i n t e r e s t prehnite entropy  shown  entropies  was  2PR=LW+GR+eQZ,  the  the  data  equilibrium of  entropy  which  pressure  for prehnite  similar  of the d i f f e r e n t  increased  of  t o both of  maximum  of  of  pressure  entropy  corresponding  curve  field  o f 6800 b a r s a t  The maximum t e m p e r a t u r e  effect  (1971b)  stability  a l . (1980)  was v e r y  24 i s  between  of L i o u  a prehnite  (1971b) r e s u l t e d i n a  slope  covered.  discrepancies  et  and,  in Figure  i n a maximum p r e s s u r e  The g r e a t e s t  on  be  r e s u l t e d i n a maximum  4 4 0 ° C a n d 450°C a t 1000 b a r s entropies.  will  The p r e h n i t e  The P e r k i n s  347°C.  and t h e  l a r g e number o f s t a b l e r e a c t i o n s .  3 0 5 ° C , w h e r e a s a 264.77 J/mol-K e n t r o p y the  point  The  was  2) w h i c h  resulted  phase.  invariant  24 was c a l c u l a t e d u s i n g  (see Table  by  the invariant point  graphical  i n t h e DATA s e c t i o n .  Figure  in  determined  that  e t a l . (1980) a n d t h e e x p e r i m e n t a l  discussed  points  presentation  points  field  be  showing  This  each  However, t h e m i s s i n g  can  the  in  wairakite-absent  invariant  phases about  reactions  specific  the  figure.  contain  the  because  279.0 J/mol-K of  will  stability  questionable  shown  the  points  example,  point  the other  stable  only  i n that  reaction.  because  figures  as  of  referencing  wairakite-absent  For  invariant  figure  invariant  f o r a l l of  appear  each one  referenced  the  incomplete.  reactions  15  reaction  be  some o f  the  for  a l l  prehnite reaction  as t h e p r e h n i t e  53  entropy 0°C K the  increased.  intercept entropy true  The e n t r o p y  f o r t h e c u r v e a t 964 b a r s ,  resulted  high  pressure different  particularly  a t lower  the  than  steam  had  a  i n other  that  of  limit  prehnite  depicted  r e a c t i o n shown  zoisite, repeated  130 b a r s a n d a t 420°C, occurred  limit  Therefore may  be  in Figure  24,  temperatures.  prehnite-bearing  phases p r e h n i t e ,  and  stability  a  w h e r e a s a 264.77 J / m o l -  i n a 0°C i n t e r c e p t a t 9032 b a r s .  appreciably  The  o f 292.75 J / m o l - K r e s u l t e d i n  grossular,  in Figure  Repeated  figures particularly  involving  quartz,  anorthite  occurring  a t 392°C,  alpha  invariant point  590 b a r s .  27  invariant points  near  the boiling  also  curve of  water. The  f i g u r e s show o n l y  curves  of r e a c t i o n s  these  figures  understand  example,  shown  temperature  phase.  in  the  also  the metastable to  useful  aid in  portions.  the  f o r the  of the m e t a s t a b l e  design  extension.  behaviour  and  which  reaction  This  curve.  (Figure  normally reactions  approached expected  1  of  the  b a r , which  in reactions  LM=2cQZ+2LW+2H 0 2  is  side of the  2 0 ) , t h e c u r v e a c t u a l l y went t o a  as the pressure  the  present  which  2  extension  is  results.  2pQZ+3GR+H 0=220+5WO,  When t h e m e t a s t a b l e  to  extensions  could  i s on t h e low t e m p e r a t u r e  If of  experimentor  s e l e c t e d examples of m e t a s t a b l e  1 9 , water  of that For  used  of the e q u i l i b r i a  i n the i n t e r p r e t a t i o n of the experimental  calculated  opposite  be  unusual  in Figure  equilibrium was  is  by t h r e e  exhibited  difficulties For  i t  to  the behaviour  illustrated which  a n d do n o t show  are  experiments,  the s t a b l e p o r t i o n s  curve higher  i s the  i n v o l v i n g a gas  (Figure  14)  and  54  ST=LM+3GQZ+3H 0  ( F i g u r e 4)  2  equilibrium examples  curves  illustrate  equilibrium portion  of  curve the  recommended calculated result  to  the  its  t o be  zones  the  not  34  of an  the  of  some c o n f i d e n c e .  delineate  the  and  figure  sequence  of  depth  of  fields sequence al. New  P-T  given  those  (1969) a l s o  reported  by  very  35  of  illustrates  some o f  by  Liou  to  for  be  which in  sequence  of  and be  Figure  above  Coombs e t a l . (1959) a n d  f o r the  Ca-  phases  metamorphism, stratigraphic  the  generalized  The  increasing laumontite,  the  stability  stratigraphic  reported  by  Seki  sequence.  laumontite  shown on  with  temperature  heulandite,  generalized  the  consistent  phases with  35.  in  These  observed  i n Japan  heulandite,  the  interpreted with  i s s u b s t a n t i a t e d by  Tanzawa M o u n t a i n s the  internally  reported  Ca-bearing  stellerite,  phases  followed  He  be  petrogenesis.  sub-greenschist  (1971).  is  if  in conjunction  shown.  the  It  contained  area's  can  are  stable  for a reaction  phase boundaries  lawsonite  the  an  experiments.  used  the  three  misleading.  pressure  the  only  the  of  particularly of  events  These  behaviour  minerals  be  conditions  prehnite  f o r the  Zealand  and  occurrence  and  for  can  the  In F i g u r e  burial  wairakite  be  design  metamorphic  prehnite  as  using  f i g u r e s were c a l c u l a t e d from  conditions  zonations  made  determine  properties,  the  the  various  area  to  about  behaviour,  the  p o r t i o n s of  loops.  e q u i l i b r i u m curve  i n the  thermodynamic  zeolites,  be  i t can  true  used  of  9 through  Because  assumptions  entire  metastable  continuous  because  observations  metamorphic Figures  that  should  show  i s going  Field  formed  curve,  that  s t a b l e and  Figure  et The  and  prehnite  35  appears  55  to  have  greater  been  from F i g u r e  phases  lesser  geothermal g r a d i e n t  35 t h a t a  maximum  manner  in field  ' These  P-T  temperature  to  interpret  the  diagrams  observation  product  p h a s e s c a n be d e t e r m i n e d a s w e l l  regime  in  or  hand  retrograde.  f o r t h e specimen of  the  predicted  information  empirically.  described  properties  for  experimental order  thermodynamic  the  in  the  data  to  The  specific  a  undertaking  new  thermodynamic  the i n c o n s i s t e n t  resulting  properties  from  of  in  that  2  same  thermodynamic are  based  on  removed  properties. consistent  The set  by r e p e a t i n g t h e  inconsistent These  the  d a t a were  the  s t u d y c a n be r e f i n e d  experiments. data  set  a n d a P-T  approximate  for  the  Table  observed  the experimental  searching  in  consistent  resulted  obtain  the  curve,  section,  given  the reaction  reaction  Knowing  With  phases and the  i n the f i g u r e s ,  of  DATA  from which  properties  which  effort  phases  obtain  experiments  to  zones  specimens.  as whether  equilibrium  the  a n a l y s i s performed i n t h i s  selected  c a n be  i n t e r p r e t i n g the  the r e a c t a n t  determined.  can a v o i d  As  f o r the  metamorphic  thin-section  of the specimen,  petrologist  in  and  t h e p h a s e s c a n t h e n be l o c a t e d  position  be  with the  limit  a r e a l s o u s e f u l when  careful  between  can  relationships.  observed  prograde  It  and a  A l l of the f i g u r e s  phases  was  sequence.  the prescence of l a w s o n i t e  a t t h e s e low p r e s s u r e s .  i n t h e above  observed  a  than the Japanese  provides  metamorphism used  at  depth of b u r i a l  deduced other  formed  data  and  new e x p e r i m e n t s s h o u l d  will  of the phases. .  further  refine  by be the  56  The those  following  necessary  experiments  to refine  a  the  thermodynamic  stability  estimate  the  boundary  of  can  set  data  in this  consistent  data  i n Table  When new  phases  number  Because  on o n l y  The by and  the  high  t h e thermodynamic  one r e v e r s a l o f t h e  data  better  from t h i s  estimates  reaction of  f o r any  also  new  with  then  f o r which  be g e n e r a t e d  experimental  the  reaction  data  involving data  c a n be  set analysis  consistency.  properties  new  p r o p e r t i e s of  By t h i s  consistent  The  phases not  f o r these  t h e thermodynamic  internally  absolute  by t h e method  can contain  be d e t e r m i n e d .  properties  and  consistent  for internal  2, a n d t h e r m o d y n a m i c  can  of phases  s e t of thermodynamic  programming  retested  phases which a r e c o n s i s t e n t all  delineate  2 become a v a i l a b l e , t h e s e  linear  and a l l of the data  listed  improved 2  can or w i l l  i n Table  t o the e x i s t i n g  equilibria  be  n o t be v i e w e d a s t h e f i n a l  that  study.  of t h e phases  added  would  CONCLUDING REMARKS  2 should  properties  outlined any  internally  i n Table of  prehnite  heulandite.  V. The  (Figure 24),  of p r e h n i t e .  can  15), which  provide  The two  WR=AN+2aQZ+2H 0  experimental  2  properties  wairakite  were b a s e d  HE=LM+3aQZ+2H 0,  3HE=LM+2ST+3cQZ  given  of  f o rwairakite.  of heulandite  of  f o r the entropy  (Figure  2  and  boundaries  experiments  5WR=MA+2ZO+12cQZ+8H 0  reaction  t h e thermodynamic p r o p e r t i e s .  properties  completing  properties  a r e some e x a m p l e s o f  2  better  temperature  experiments  5PR=4H 0+2ZO+2GR+3cQZ a n d 2PR=LW+GR+oQZ  which d e l i n e a t e provide  proposed  process the  thermodynamic  57  properties  a r e known c a n be  Every further  new  delimit  properties change  item  one  or s e v e r a l  the p r e d i c t e d that  of e x p e r i m e n t a l  the thermodynamic  of  essential  new  i s not s i m p l y  and  This  calculating  relatively  short  efficiency  of  computer  process new  period the  program.  on"  of  of  data,  old  and  c a l c u l a t i o n and  because  l i n e a r programming  to the to  i t is  new,  be  that  the  thermodynamic  the thermodynamic  relationships time  For t h i s reason  to the e x i s t i n g  of u p d a t i n g  phase  ranges  of the phases and, u l t i m a t e l y ,  set analysis  "tacked  has the p o t e n t i a l  maxima-minima  a l l of the e x p e r i m e n t a l  i n the c o n s i s t e n t  properties.  data  phase r e l a t i o n s h i p s .  included data  increased.  data set  c a n be c o m p l e t e d i n a of  the  power  and  method and t h e PT-SYSTEM  58  REFERENCES  A n d e r s o n , G.M. 1977. 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Thermodynamic P r o p e r t i e s of M i n e r a l s a n d R e l a t e d S u b s t a n c e s a t 298.15 K and 1 b a r ( 1 0 pascals) P r e s s u r e and a t H i g h e r T e m p e r a t u r e s . U.S. Geological S u r v e y B u l l e t i n 1452, pp. 456 s  Seki,  Y., O k i , Y., M a t s u d a , T., M i k a m i , K., a n d Okumura, K. 1969. Metamorphism i n t h e Tanzawa M o u n t a i n s , C e n t r a l Japan. J o u r n a l of t h e J a p a n e s e A s s o c i a t i o n o f M i n e r a l o g i s t s , V o l . 61, p. 1-75.  S t o r r e , B. and N i t s c h , K.H. 1974. Zur s t a b i l i t a e t von m a r g a r i t im s y s t e m C a 0 - A l 0 - S i 0 - H 0 . Contributions t o M i n e r a l o g y and P e t r o l o g y , V o l . 43, p . 1-24. 2  3  2  2  S t u l l , D.R. and P r o p h e t , H. 1971. JANAF t h e r m o c h e m i c a l tables. N a t i o n a l Standard Reference Data S e r i e s , U.S. N a t i o n a l B u r e a u o f S t a n d a r d s , V o l . 37, pp. 1141.  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