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The Fe-Mg solution properties of olivine, enstatite, anthophyllite and talc, from ion-exchange experiments… Bartholomew, Paul Richard 1984

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THE Fe-Mg SOLUTION PROPERTIES OF OLIVINE, ENSTATITE, ANTHOPHYLLITE AND TALC, FROM ION-EXCHANGE EXPERIMENTS WITH AQUEOUS CHLORIDE SOLUTIONS By PAUL RICHARD BARTHOLOMEW B.S.,  The U n i v e r s i t y of Minnesota, 1976  M.Sc.'j The U n i v e r s i t y of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE  FACULTY OF GRADUATE STUDIES  THE DEPARTMENT OF GEOLOGICAL SCIENCES  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 November 1984 © P a u l R i c h a r d Bartholomew, 1984  In p r e s e n t i n g t h i s t h e s i s r e q u i r e m e n t s f o r an  in partial  advanced degree at  of  B r i t i s h Columbia, I agree that  it  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  agree t h a t p e r m i s s i o n  by  understood that for  the  be  h i s or her  s h a l l not  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada  DE-6  (3/81)  study.  I  the  be  further this  this  my  It i s thesis  a l l o w e d w i t h o u t my  Columbia  thesis  head o f  representatives.  Department o f  1Y3  University s h a l l make  copying or p u b l i c a t i o n of  f i n a n c i a l gain  the  Library  g r a n t e d by  permission.  V6T  the  for extensive copying of  f o r s c h o l a r l y p u r p o s e s may department or  f u l f i l m e n t of  written  Abstract Ion-exchange e q u i l i b r i a between a 2molal aqueous Mg-Fe c h l o r i d e s o l u t i o n and s y n t h e t i c o l i v i n e s , orthopyroxenes, orthoamphiboles and t a l c s have been e x p e r i m e n t a l l y  bracketed  between 4 5 0 ° and 800°C and between 1 and 4kb. A d d i t i o n a l experiments at lower c h l o r i d e m o l a l i t i e s r e v e a l that the d i s t r i b u t i o n c o e f f i c i e n t measured i s dependent upon c h l o r i d e c o n c e n t r a t i o n . Thermodynamic modelling of the c h l o r i d e s o l u t i o n , assuming i d e a l mixing of Mg and Fe s p e c i e s , q u a l i t a t i v e l y reproduces t h i s behavior i f the Mg and Fe s p e c i e s have c o n t r a s t i n g d i s s o c i a t i o n c o n s t a n t s . consistent the  Internally  thermodynamic p r o p e r t i e s of a l l four m i n e r a l s and  ' d e l t a ' p r o p e r t i e s of a h y p o t h e t i c a l  associated  e l e c t r o l y t e s o l u t i o n are c a l c u l a t e d through a combination of l i n e a r programming and l e a s t - s q u a r e s  optimization  while  simultaneously c o n s i d e r i n g c o n s t r a i n t s provided by c a l o r i m e t r y , n e t - t r a n s f e r e q u i l i b r i a and other  ion-exchange  d a t a . Adequate correspondence between thermodynamic model and  the data cannot be a t t a i n e d ' w i t h o u t a l l o w i n g  the mixing  of Mg and F e . i n the c h l o r i d e s o l u t i o n to be n o n - i d e a l . Q u a l i t a t i v e c o n s t r a i n t s on the c h l o r i d e 'excess' p r o p e r t i e s allow  a preliminary  estimate of the s o l i d s o l u t i o n  p r o p e r t i e s to be made. A l l s o l i d s o l u t i o n s are modelled with a symmetric Margules f o r m u l a t i o n . The r e s u l t i n g o l i v i n e f u n c t i o n has a value near 7 k J at 400°C and drops asymptotically  toward zero at high  orthopyroxene Wr  temperatures. The  i s approximately zero at 400°C and drops  •  toward -3kJ  at h i g h temperatures. A  'microscopic'  orthopyroxene s o l u t i o n model i s formulated to  be  simultaneously c o n s i s t e n t with t h i s bulk excess f r e e energy and  with measured M1-M2  value  (0.58kJ) c a l c u l a t e d  solution Fe  s i t e d i s t r i b u t i o n s . The  single  for the a n t h o p h y l l i t e  solid  i s q u a l i t a t i v e l y c o n s i s t e n t with f r a c t i o n a t i o n  i n t o M4.  The  WQ  of  t a l c s o l i d s o l u t i o n cannot be c o n s t r a i n e d  be d i f f e r e n t from i d e a l by  to  the data presented h e r e . At  p r e s e n t , ion-exchange experiments with Mg-Fe c h l o r i d e solutions  can  only be  to u n c e r t a i n t i e s properties  i n d i s s o c i a t i o n constants and  for the  uncertainties  used to compare m i n e r a l p r o p e r t i e s  aqueous s o l u t i o n . The  in the data a n a l y s i s  solution properties  'excess'  r o l e of  indicates  that  d e r i v e d from p r e v i o u s aqueous  such solid chloride  ion-exchange experiments must be c o n s i d e r e d suspect the  properties  of each p e r t i n e n t aqueous e l e c t r o l y t e  s o l u t i o n have been examined.  due  until  Table of Contents Chapter  Page  Abstract  i i  L i s t of Tables  vi  L i s t of F i g u r e s  ...vii  L i s t of P l a t e s  x  Acknowledgements  ...xi  I. Ion-Exchange E q u i l i b r i u m with Mg-Fe O l i v i n e and M o d e l l i n g of the Aqueous S o l u t i o n  1  Introduction  1  Experimental Techniques  3  Data A n a l y s i s  ....13  Discussion  48  I I . A p p l i c a t i o n to Orthopyroxene, Orthoamphibole and T a l c and Comprehensive A n a l y s i s  53  Introduction  53  Experimental Techniques  56  Data A n a l y s i s  64  Discussion  93  Conclusions  99  References  101  III . APPENDICES  115  APPENDIX A: Oxide Mixes APPENDIX B: Aqueous Analyses  ..115 118  APPENDIX C: E l e c t r o n Microprobe Analyses ...123 APPENDIX D: High Accuracy Powder XRD  -..132  APPENDIX E: Transmitted E l e c t r o n Microscopy 137 APPENDIX F: Orthoamphibole S y n t h e s i s and Characterization 144 iv  APPENDIX G: The Mg-Fe Orthopyroxene Solution  v  1 68  L i s t of Tables Table 1.1. Ion-exchange  run data  14  Table 1.2. F i t parameters f o r equation  (3)  for  s e v e r a l aqueous c h l o r i d e s  23  Table 1.3. I s o t h e r m a l - i s o b a r i c r e g r e s s i o n r e s u l t s for  the ion-exchange r e a c t i o n and the  s t o i c h i o m e t r i c o l i v i n e s o l u t i o n model  38  Table 1.4. Regressed f i t parameters f o r the ion-exchange r e a c t i o n and the s t o i c h i o m e t r i c s o l i d s o l u t i o n model  42  Table 1.5. O l i v i n e c e l l parameters d e r i v e d from powder XRD peaks i n the 4 0 ° to 75°20 range  43  Table II.1 Orthoamphibole d0k0 values measured f o r ion-exchange run products Table II.2 T a l c  rf003  62  values measured f o r  ion-exchange run products Table I I . 3 . Ion-exchange  64  run data  65  * Table I I . 4 . LnK D v a l u e s c a l c u l a t e d f o r a l l o l i v i n e + 2m c h l o r i d e ion-exchange experiments  69  Table II.5 Endmember thermodynamic p r o p e r t i e s f o r Model 1  75  Table II.6 Model 1 Margules parameters  76  Table II.7 Endmember thermodynamic p r o p e r t i e s f o r Model 2  85  Table II.8 Model 2 Margules parameters  86  Table B1 . Quench pH measurements  119  Table C1 . Summary of microprobe analyses  127  Table F 1 . Experimental  parameters f o r orthoamphibole  syntheses  150  Table F2. Orthoamphibole c e l l parameters d e r i v e d from l e a s t squares refinement  of powder XRD  data  151  Table G1 . O r i g i n a l and a d j u s t e d values of l n K D 1 2  173  Table G2. F i t parameters r e s u l t i n g from s u c c e s s i v e p a r t i a l r e g r e s s i o n of the s p e c i a t i o n model to the orthopyroxene data  192 vi  L i s t of F i g u r e s F i g u r e 1.1  Comparison of standard  analyses  and  particle  for cases in which both techniques  were  a p p l i e d to samples of the same product o l i v i n e s F i g u r e 1.2  Compositional  changes measured f o r  ion-exchange experiments at 600°C, 2kb F i g u r e 1.3  12 17  T h e o r e t i c a l trends of lnK^ vs X f Q given  that the aqueous f l u i d behaves as a thermodynamically i d e a l s o l u t i o n of the c h l o r i d e endmembers F i g u r e 1.4  18  Common logarithm of aqueous c h l o r i d e  d i s s o c i a t i o n constants F i g u r e 1.5  The  at 2kb  22  e f f e c t of v a r i a t i o n s i n l o g K F g on  l n K D as p r e d i c t e d by the  first-dissociation  model for the h y p o t h e t i c a l case in which the olivine solid solution  is ideal  29  F i g u r e 1.6 l n K D vs mT f o r i s o t h e r m a l - i s o b a r i c - i s o X ^ subsets F i g u r e 1.7  of the  ion-exchange experiments  33  A c o m p i l a t i o n of the most recent and most  comprehensive measurements of  and  Margules  s o l u t i o n models f o r Mg-Fe o l i v i n e s F i g u r e 1.8 l n K D vs X^Q:  39  2m c h l o r i d e ion-exchange  data and curves c a l c u l a t e d with Model B combined with the f i r s t - d i s s o c i a t i o n model with the same values of T, P and mT F i g u r e 1.9  45  WQ and WH c a l c u l a t e d using the f i t  parameters l i s t e d under Model B in t a b l e 4  51  F i g u r e I I . 1 Values of d0ll0 measured for the s y n t h e t i c orthoamphibole s t a r t i n g m a t e r i a l s F i g u r e II.2 Measured values of t a l c d003  and  61  the  l i n e a r c a l i b r a t i o n curve f i t to the s y n t h e t i c s t a r t i n g m a t e r i a l s produced i n the  present  study  63 *  F i g u r e II.3 Comparison of o l i v i n e l n K Q data  with  curves c a l c u l a t e d with Model 1 thermodynamic parameters  77 vii  *  Figure II.4 Comparison of orthopyroxene  l n K D data  with curves c a l c u l a t e d with Model 1 thermodynamic parameters  79  * Figure II.5 Comparison of orthoamphibole  lnK^ data  with curves c a l c u l a t e d with Model 1 thermodynamic parameters  80  * Figure II.6 Comparison of t a l c l n K D data with curves c a l c u l a t e d with Model 1 thermodynamic parameters  81  Figure II.7 Comparison of the four Model 1  WQ  functions  82  * Figure II.8 Comparison of o l i v i n e l n K D data with curves c a l c u l a t e d with Model 2 thermodynamic parameters  87  * Figure II.9 Comparison of orthopyroxene  l n K D data  with curves c a l c u l a t e d with Model 2 thermodynamic parameters.  89  * Figure 11.10  Comparison of orthoamphibole  lnK^ data  with curves c a l c u l a t e d with Model 2 thermodynamic parameters  90 *  Figure 11.11  Comparison of t a l c l n K D data with  curves c a l c u l a t e d with Model 2 thermodynamic parameters Figure 11.12  91  Comparison of the four Model 2  WQ  functions  92  Figure C1. E m p i r i c a l c a l i b r a t i o n curve f o r p a r t i c l e analysis correction  126  F i g u r e F 1 . Orthoamphibole u n i t c e l l parameters  153  F i g u r e G1. U n c e r t a i n t i e s inherent i n measurement of orthopyroxene  s i t e occupancies  from Mossbauer  s p e c t r a of the products of d i s o r d e r i n g experiments  viii Figure G2. C o r r e c t e d l n K D 1 2 v a l u e s p l o t t e d versus F i g u rX Saxena e G3.TheL and nfKi Ghose(l970) l l e dcurves symbols c a l crepresent u l a t e d from datathefrom  171 175  s p e c i a t i o n model formulation f o r sample v a l u e s of AG L , AGg, and Wg  Pec  189  F i g u r e G4. Comparison of macroscopic d a t a , formulated as Margules parameters, with e q u i v a l e n t s c a l c u l a t e d at X En =0.5 from the orthopyroxene s p e c i a t i o n model  193  F i g u r e G5. Comparison of l n K D 1 2 data from Saxena and Ghose(l970) with l n K D 1 2 curves c a l c u l a t e d  from  the orthopyroxene s p e c i a t i o n model F i g u r e G6. G g ^  lk  194  (equation (G18)) and i t s components  c a l c u l a t e d as a f u n c t i o n of temperature f o r the orthopyroxene s p e c i a t i o n model  195  F i g u r e G7. Species c o n c e n t r a t i o n s c a l c u l a t e d as a f u n c t i o n of temperature at a constant X En =0.5 f o r the c a l i b r a t e d orthopyroxene  speciation  model  196  F i g u r e G8. C a l c u l a t e d t o t a l free energy of mixing f o r the orthopyroxene s p e c i a t i o n model as a f u n c t i o n of X ^ „  1 97  ix  L i s t of P l a t e s Plate  1. Low m a g n i f i c a t i o n  the  bright f i e l d  images of  s y n t h e t i c orthoamphiboles  P l a t e 2. High m a g n i f i c a t i o n diffraction  patterns  159  images and e l e c t r o n  f o r specimens i n ( O k l )  or i e n t a t ion  163  P l a t e 3. E l e c t r o n d i f f r a c t i o n magnification  patterns  and one  high  image f o r specimens i n ( h O l )  orientation  165  x  Acknowledgements I g r a t e f u l l y thank a l l of those who support along the  p r o v i d e d h e l p and  way.  Dr. H.J. Greenwood p r o v i d e d u n f a i l i n g academic f i n a n c i a l support throughout  and  the s t u d y . Dr. Martin Engi  c o n t r i b u t e d many f r u i t f u l d i s c u s s i o n s and h i s p e r s o n a l c o o p e r a t i o n with the database Brown, E.P. Meagher and R.G.  c a l c u l a t i o n s . Dr.'s  T.H.  Berman and Derry McPhail a l s o  c o n t r i b u t e d to f r u i t f u l d i s c u s s i o n s . Dr.'s Greenwood, Engi and Brown have a l l reviewed p r e l i m i n a r y p o r t i o n s of  this  document. Dr.'s Scudder and C a l v e r t each generously provided access to needed a n a l y t i c a l equipment. I n v a l u a b l e t e c h n i c a l support was Cranston  p r o v i d e d by Ed Montgomery (photography), Bryon  (probe mounts), John Knight  Mager (TEM), L a u r i e F r e d e r i c k  (TEM)  (hydrothermal l a b ) .  xi  (microprobe), Mary and L y l e Hammerstrom  I. Ion-Exchange E q u i l i b r i u m with Mg-Fe O l i v i n e and  Modelling  of the Aqueous S o l u t i o n  INTRODUCTION  Experimental and  t h e o r e t i c a l i n v e s t i g a t i o n of the Fe-Mg  o l i v i n e s o l i d s o l u t i o n has in the  recieved considerable  l i t e r a t u r e . Most of the experimental  attention  contributions  are Fe-Mg ion-exchange experiments studying  the  of o l i v i n e with orthopyroxene (Nafziger  Muan,  Kitayama and Matsui and 1977;  K a t s u r a , 1968;  Wood, 1979;  ( E n g i , 1978,  L i n d s l e y , 1979,  Williams,  1971; Matsui,  Kawasaki and M a t s u i , 1983), or  1983), or i l m e n i t e  (Andersen  and  1981), or Fe-Mg c h l o r i d e aqueous s o l u t i o n s  ( S c h u l i e n , F r i e d r i c h s e n and using c a l o r i m e t r y and  Medaris, 1969;  1967;  Nishizawa, 1974), or garnet (Kawasaki and  O ' N e i l l and  spinel  and  equilibrium  Hellner,  i n c l u d e Sahama and  Kleppa(1981), and  1970).  Contributions  Torgeson(1949), Wood  T h i e r r y et a l ( l 9 8 l ) .  e f f o r t s to analyze (or reanalyze) p o r t i o n s  Additional of  the  experimental data i n c l u d e work by Wi11iams(1972), Saxena(1972), Obata, Banno and  Mori(l974),  Engi(l980a)  and  Sack(1980). T h i s chapter i s aimed at making two  contributions.  1) To extend an o l i v i n e s o l u t i o n model with confidence down to temperatures where o l i v i n e metamorphic 2) To c r i t i c a l l y  i s important as a  mineral. evaluate the u t i l i t y  1  of aqueous c h l o r i d e s ,  2 p a r t i c u l a r l y Fe-Mg c h l o r i d e s , f o r c h a r a c t e r i z i n g  solid  s o l u t i o n s through ion-exchange experiments.  Of the above exchange e q u i l i b r i u m experimental only S c h u l i e n  studies,  et a l ( l 9 7 0 ) and Andersen and Lindsley(1979)  p r o v i d e data below 800°C which span the Fe-Mg composition range. The Fe-Mg exchange e q u i l i b r i u m experiments reported here were performed over a range of c o n d i t i o n s  from 450 to  800°C and 1 to 4 kbar using aqueous Fe-Mg c h l o r i d e as the second phase. Although S c h u l i e n  solutions  et a l ( l 9 7 0 ) performed  s i m i l a r experiments under s i m i l a r c o n d i t i o n s , the s i z e of t h e i r c o m p o s i t i o n a l e r r o r brackets r e s t r i c t s t h e i r study to q u a l i t a t i v e c h a r a c t e r i z a t i o n of the o l i v i n e s o l i d s o l u t i o n . Aqueous c h l o r i d e s have been i n use as ion-exchange media  f o r over 20 y e a r s . Some workers have simply used  aqueous c h l o r i d e s as a f l u x to speed up r e a c t i o n and r e c r y s t a l l i z a t i o n r a t e s of s o l i d phases ( e . g . Gunter, 1974; M e d a r i s , 1969). Ion-exchange experiments which c o n s i d e r aqueous c h l o r i d e s as an e q u i l i b r i u m phase have been performed with nepheline (Debron et a l , 1961), alkali-feldspar  ( O r v i l l e , 1963), o l i v i n e  1970), p l a g i o c l a s e 1970; E l l i s ,  (Schulien  ( O r v i l l e , 1972), s c a p o l i t e  et a l ,  (Wellman,  1978), Ca-garnet, epidote (Perchuk and  A r a n o v i c h , 1979) and b i o t i t e  (Schulien,  1980).  The a t t r a c t i o n s of aqueous c h l o r i d e s as an exchange medium i n c l u d e : f a s t e r r e a c t i o n r a t e s , an assumed lack of c o m p o s i t i o n a l inhomogeneity i n the aqueous  s o l u t i o n , ease of  3 phase s e p a r a t i o n f o r independent chemical a n a l y s i s , and  the  common assumption that the mixure of c h l o r i d e s i n aqueous s o l u t i o n c o u l d be t r e a t e d as an  'ideal'  solution.  Engi(1980b) has a l r e a d y p o i n t e d out the f a l l a c y of t h i s assumption f o r Fe-Mg c h l o r i d e  last  solutions.  To h e l p e v a l u a t e the r o l e of the c h l o r i d e s o l u t i o n i n the study presented h e r e , a d d i t i o n a l experiments conducted  were  at constant o l i v i n e s t a r t i n g composition while  v a r y i n g the t o t a l c o n c e n t r a t i o n of c h l o r i d e s . Using  this  data along with p u b l i s h e d s t u d i e s of aqueous e l e c t r o l y t e p r o p e r t i e s , a working model i s e s t a b l i s h e d f o r the behavior of the Fe-Mg c h l o r i d e s o l u t i o n w i t h i n the range of c o n d i t i o n s spanned by the ion exchange  experiments.  EXPERIMENTAL TECHNIQUES  STARTING  MATERIALS:  S y n t h e t i c o l i v i n e s were made from reagent grade oxides at composition  i n t e r v a l s of 0.1  f o r s t e r i t e endmember). The  X^o  (mole f r a c t i o n of the  i r o n bearing o l i v i n e s were  s y n t h e s i z e d using Method 2 of Turnock, L i n d s l e y  and  Grover(1973) . Oxygen-balanced mixes made from F e ° , F e 2 0 3 , MgO  and S i 0 2  ( c r i s t o b a l i t e ) were loaded i n t o  pure-silica  4 g l a s s tubes i s o l a t e d from the g l a s s by A g 7 0 P d 3 0  foil.  The  tubes were evacuated, s e a l e d , and heated at 1050°C f o r 3 to 6 days, depending  on mix c o m p o s i t i o n . The products of the  f i r s t h e a t i n g were ground, reloaded and reheated f o r a s i m i l a r length of time. In g e n e r a l , the more F e - r i c h compositions reacted more q u i c k l y and grew to a l a r g e r s i z e . The Mg end-member mix was  grain  heated i n a i r at 1400°C f o r  24 hours, ground, and heated f o r another 24 h o u r s . A l l s y n t h e s i s products were examined both o p t i c a l l y and by and found to c o n t a i n 99% or more o l i v i n e . G r a i n s i z e s from  <2um  XRD ranged  f o r the magnesian compositions to 1-5/im f o r the  Fe-rich compositions. Endmember c h l o r i d e s o l u t i o n s at 2 molal c o n c e n t r a t i o n were prepared from reagent grade MgCl 2 '6H 2 0 and  FeCl2*4H20.  Intermediate composition s o l u t i o n s were prepared by mixing the end-members. The Fe and Mg c o n c e n t r a t i o n s i n each of these s o l u t i o n s was checked by standard flame atomic a b s o r p t i o n . In some c a s e s , s o l u t i o n s of i n t e r m e d i a t e composition were c r e a t e d i n the run c a p s u l e by p i p e t t i n g small a l i q u o t s of the end-member s o l u t i o n s i n t o the c a p s u l e and c a r e f u l l y weighing each a l i q u o t . Run  s o l u t i o n s at  c o n c e n t r a t i o n s l e s s than 2m were c r e a t e d the same way,  using  d i s t i l l e d water as one a l i q u o t . D e n s i t i e s determined by weighing known volumes of the end-member s o l u t i o n s allowed c o n v e r s i o n of weights to volumes and c o n v e r s i o n of m o l a l i t y to m o l a r i t y when needed.  5 ION  EXCHANGE EXPERIMENTS:  Weighed amounts of o l i v i n e and c h l o r i d e s o l u t i o n were sealed i n t o noble metal c a p s u l e s . A t y p i c a l run capsule c o n t a i n e d 40 to 70mg of o l i v i n e and s o l i d - t o - f l u i d r a t i o s were t y p i c a l l y  weight  1 to 2. I n i t i a l compositions were  chosen t o produce opposing brackets on the e q u i l i b r i u m . Gold p  c a p s u l e s were used above 600°C, both gold and  Ag 6 o cUo  capsules were used at 600°C, and both Ag 60 Pdi,o c a p s u l e s and thin-walled  (.1mm) gold c a p s u l e s were used below 600°C. A l l  runs were made i n 3.2x30.5cm c o l d - s e a l pressure v e s s e l s ; e i t h e r S t e l l i t e 25 or Rene 41. A quick-quench c o n f i g u r a t i o n (5cm f i l l e r  r o d , unextended bomb) was used above 600°C so  t h a t , when quenching, the capsule c o u l d be dropped c l o s e to the  c o o l end of the bomb (see a l s o Wellman, 1970).  Full-length steel f i l l e r In  rods were used at and below 600°C.  a l l c a s e s , the bomb was c o o l e d with a stream of  compressed a i r with water a s p i r a t e d i n t o the stream. The r e s u l t s of a few quick-quench runs at 600°C c o u l d not be d i s t i n g u i s h e d from the r e s t of the 600°C data s e t . Run temperature was measured with a c a l i b r a t e d chromel-alumel thermocouple  i n s e r t e d i n t o an e x t e r n a l w e l l i n each bomb.  The temperature d i f f e r e n c e between t h i s e x t e r n a l w e l l and the  run capsule p o s i t i o n was c a l i b r a t e d once f o r each bomb  using a working standard thermocouple which had been c a l i b r a t e d a g a i n s t a 'lab s t a n d a r d ' thermocouple. T h i s l a b standard thermocouple had been c a l i b r a t e d a g a i n s t NBS m e l t i n g p o i n t s t a n d a r d s . The bomb c a l i b r a t i o n was performed  6 at 1atm and  for f u l l - l e n g t h f i l l e r  rod c o n f i g u r a t i o n s and at 1  2 kbar f o r quick-quench c o n f i g u r a t i o n s . The  combination  of c a l i b r a t i o n and t i m e - v a r i a t i o n temperature e r r o r s i s estimated to be no more than ±5°C. The pressure medium methane f o r the  1 and 2 kbar r u n s . The  was  hydrogen pressure  e s t a b l i s h e d by the graphite-methane e q u i l i b r i u m  prevented  o x i d a t i o n of the capsule contents f o r runs at and above 600°C. Below 600°C , a higher hydrogen pressure was to keep f_  needed  i n the capsule below that of the  f a y a l i t e - m a g n e t i t e - q u a r t z b u f f e r . To accomplish t h i s , H 2  was  introduced i n t o the bomb before p r e s s u r i z i n g with methane, and g r a p h i t e was  not  i n t r o d u c e d . The amount of H 2  designed to r e s u l t i n a H 2  added  was  p a r t i a l pressure between values  c a l c u l a t e d f o r the f a y a l i t e - m a g n e t i t e - q u a r t z - H 2 0 e q u i l i b r i u m and .the magnetite-wiistite-H 2 e q u i l i b r i u m . At T>600°C, the amount of g r a p h i t e which p r e c i p i t a t e d from pure C H „ while reaching the C H „ = C + H 2 to prevent  e q u i l i b r i u m was  'drop' quenching. Hydrogen was  runs to minimize t h i s p r e c i p i t a t i o n . The  usually  sufficient  added to these runs at 4kbar were  p r e s s u r i z e d with water. For these runs a button of g r a p h i t e introduced along with the run capsule was  found to prevent  o x i d a t i o n at 600°C. The goal of these f 0  control  was  to keep the experimental  than b u f f e r i n g f  n  f~  s l i g h t l y below FMQ  techniques rather  to a c a l c u l a b l e v a l u e . Pressure on the  u2 methane l i n e was  measured with an A s h c r o f t gauge c a l i b r a t e d  a g a i n s t a f a c t o r y c a l i b r a t e d 2000bar Heise gauge. At 4kbar, pressure was  measured with a 7000bar Heise gauge. Stated  7 p r e s s u r e s are c o n s i d e r e d accurate to w i t h i n 60 b a r s . F o l l o w i n g each experiment the capsule was c l e a n e d , weighed, punctured an a r g o n - f l u s h e d The  with a needle at both ends and p l a c e d i n  1ml c e n t r i f u g e v i a l  (Pierce  'Reacti-Vial').  v i a l was s e a l e d and c e n t r i f u g e d . T y p i c a l l y 50 to 70% of  the run f l u i d was e x t r a c t e d and any s o l i d s e x t r a c t e d with the f l u i d were simultaneously c e n t r i f u g e d o u t . For a few runs, quench pH was measured d i r e c t l y on the c e n t r i f u g e d run f l u i d with a micro-combination  e l e c t r o d e . That p o r t i o n of  the e x t r a c t e d f l u i d which c o u l d be drawn o f f uncontaminated by s o l i d s was d i l u t e d with s l i g h t l y a c i d i f i e d d i s t i l l e d water i n p r e p a r a t i o n f o r chemical  (0.03m HN03)  analysis.  Whenever s u f f i c i e n t f l u i d c o u l d not be e x t r a c t e d by c e n t r i f u g i n g , the capsule was cut open and the contents washed i n t o the c e n t r i f u g e v i a l with d i s t i l l e d vial  water. The  was s e a l e d , a g i t a t e d and c e n t r i f u g e d and the  supernatant  l i q u i d was drawn o f f and d i l u t e d with  acidified  water . The s o l i d products of each experiment were washed with d i s t i l l e d H 2 0, c e n t r i f u g e d , washed with  alcohol,  c e n t r i f u g e d and d r i e d .  FINAL  COMPOSITIONS:  The c o n c e n t r a t i o n s of Fe and Mg i n the d i l u t e d s o l u t i o n s were measured with standard  product  acetylene-flame  a t o m i c - a b s o r p t i o n t e c h n i q u e s . T o t a l CI i n a r e p r e s e n t a t i v e p o r t i o n of these product  s o l u t i o n s was measured with a  8  B u c h l e r - C o t l o v e c h l o r i d o m e t e r . Since the volume of aqueous s o l u t i o n c o u l d not always be a c c u r a t e l y determined,  only  c o n c e n t r a t i o n r a t i o s and mole f r a c t i o n s were used i n subsequent numerical a n a l y s i s of aqueous e q u i l i b r i a  and  ion-exchange e q u i l i b r i a . A l l s o l i d products were examined o p t i c a l l y and many were checked with XRD.  In a d d i t i o n to o l i v i n e , the  products of a m a j o r i t y of the ion-exchange  solid  experiments  i n c l u d e d an Mg-Fe s i l i c a t e more s i l i c e o u s than o l i v i n e . T h i s a d d i t i o n a l phase was orthoamphibole  and  e i t h e r q u a r t z , t a l c , orthopyroxene  i t s modal amount was  2%, but o c c a s i o n a l l y up to 5%. The phase at each p r e s s u r e , temperature  or  g e n e r a l l y l e s s than  i d e n t i t y of the accessory and bulk composition  p r o v i d e s i n f o r m a t i o n about the s t a b i l i t y of the accessory phases from a synthesis-experiment p o i n t of view. The presence  of these s i l i c e o u s a c c e s s o r y phases was  attributed  to incongruent d i s s o l u t i o n of the o l i v i n e i n t o the aqueous s o l u t i o n at P and T. Since the c o n c e n t r a t i o n of aqueous CI i s c o n s t a n t , n o n - c h l o r i d e s p e c i e s of Mg and/or Fe must have been present at P and T. Traces of a green, amorphous substance  found  be a p r e c i p i t a t e  i n many of the experimental run products  may  formed from these n o n - c h l o r i d e s p e c i e s upon  quenching. F i n a l o l i v i n e compositions were e s t a b l i s h e d by one more of 4 methods. Three of these are e l e c t r o n  or  microprobe  techniques and the f o u r t h i s a mass-balance c a l c u l a t i o n . O l i v i n e f i n a l compositions c a l c u l a t e d by mass-balance were  9 c o n s i d e r e d t o be more than j u s t approximations f o r two reasons: (1) I n d i v i d u a l weights of the i n i t i a l phases were known to ±0.2mg out of 30 to 60mg. (2) Due to l a r g e molar r a t i o s of ( M g , F e ) S i 0 . 5 0 2  to ( M g r F e ) C l 2  (typically  10 to 20),  propagation of f l u i d a n a l y s i s e r r o r s through the mass-balance r e s u l t s i n standard e r r o r s s i m i l a r to those t y p i c a l of the microprobe a n a l y s e s . The p o s s i b l e weaknesses of the mass-balance c a l c u l a t i o n s are zoning of the o l i v i n e g r a i n s and the unaccounted-for e f f e c t of minor product phases. The three microprobe  techniques used were standard  a n a l y s i s , p a r t i c l e a n a l y s i s , and c r y s t a l - f a c e a n a l y s i s . For standard a n a l y s i s , product o l i v i n e g r a i n s were hot-pressed i n t o Buehler  ' T r a n s o p t i c ' p l a s t i c and p o l i s h e d with diamond  a b r a s i v e s . S y n t h e t i c end-member o l i v i n e g r a i n s (50 to 150Mm), i d e n t i c a l l y mounted, were used as standards and the c o r r e c t i o n procedures of Bence and Albee(1968)  and Albee and  Ray(l970) were used. The o p e r a t i n g c o n d i t i o n s were l5kV with 15nA specimen c u r r e n t . Mg, Fe and S i were analyzed simultaneously employing  20 second c o u n t i n g t i m e s . For each  sample, 6 t o 10 analyses were averaged. A p o r t i o n of the a n a l y s e s were done on an automated ARL-EMX at the U n i v e r s i t y of Washington, S e a t t l e , and the remainder U n i v e r s i t y of B r i t i s h Columbia  were done at the  on an ARL-SEMQ. Standard  a n a l y s i s was judged inadequate f o r a m a j o r i t y of the samples for 2 reasons: (1) The o l i v i n e g r a i n s i z e i n some samples was too small to c o n t a i n the beam and i t s e x c i t a t i o n volume.  10 (2) Compositional zoning was i n f e r r e d to be present  i n many  samples. For  15 to  2bixm  g r a i n s (a very common s i z e range) only  core analyses would produce acceptable t o t a l s and s t o i c h i o m e t r y . Fine  s c a l e c o m p o s i t i o n a l zoning was  (5fim)  i n f e r r e d t o be present  i n many of these g r a i n s by comparing  microprobe and mass-balance c o m p o s i t i o n s . I f the two compositions composition mass-balance  were s i g n i f i c a n t l y d i f f e r e n t , the probe ( X ^ ) was, with few e x c e p t i o n s , between the and the i n i t i a l X^ Q , o r , i n extreme c a s e s ,  i d e n t i c a l t o the i n i t i a l  X ^ . For g r a i n s l a r g e r than 25*xm,  analyses were taken as c l o s e as p o s s i b l e to g r a i n edges, but, once a g a i n , edge zoning on a 5#m s c a l e c o u l d not be measured d i r e c t l y . To e l i m i n a t e minimum g r a i n s i z e and f i n e - s c a l e problems, many samples were analyzed with p a r t i c l e  zoning analysis  t e c h n i q u e s . The o l i v i n e g r a i n s were d i s p e r s e d on p o l i s h e d g r a p h i t e stubs and carbon and  c o a t e d . While o p e r a t i n g at  I5kv  35nA on the ARL-SEMQ, the beam was r a s t e r e d over a lOum  square. Secondary e l e c t r o n  imaging  made i t p o s s i b l e to  s e l e c t g r a i n s e n t i r e l y c o n t a i n a b l e w i t h i n the lOjum square for  a n a l y s i s . Mg, Fe and S i were analyzed  simultaneously  employing 40 second c o u n t i n g t i m e s . A f i r s t p a r t i c l e formula composition  was e s t a b l i s h e d using the same  s t a n d a r d i z a t i o n and c o r r e c t i o n procedures for  approximation of  d e s c r i b e d above  standard a n a l y s i s . An e m p i r i c a l c o r r e c t i o n curve was  e s t a b l i s h e d by using the same procedures  to analyze a l l of  11 the s y n t h e t i c o l i v i n e s used as s t a r t i n g m a t e r i a l s . Each p a r t i c l e a n a l y s i s r e p o r t e d i s an average of 10 t o 15 individual analyses. Some of the higher temperature run products d i d not c o n t a i n o l i v i n e g r a i n s smaller than  lO/nm and c o u l d not be  analyzed using the same p a r t i c l e a n a l y s i s p r o c e d u r e s . Edge compositions were measured f o r s e v e r a l of these  large-grain  samples using standard a n a l y s i s techniques on p a r t i c l e a n a l y s i s mounts. Most of the product  o l i v i n e s were q u i t e  e u h e d r a l . As a r e s u l t , many of the g r a i n s d i s p e r s e d f o r p a r t i c l e a n a l y s i s l i e f l a t on t h e i r l a r g e s t c r y s t a l f a c e : (010). The upper (010) face i s then both f l a t and h o r i z o n t a l . Standard a n a l y s i s of (010) faces l a r g e r  than  15um a c r o s s produced a c c e p t a b l e t o t a l s and f o r m u l a . Comparison of standard microprobe analyses with the p a r t i c l e and c r y s t a l face a n a l y s e s tends to c o n f i r m the e x i s t e n c e of the f i n e s c a l e zoning which was o r i g i n a l l y  only  i n f e r r e d t o be p r e s e n t . The p o i n t s p l o t t e d on f i g u r e 1.1 i l l u s t r a t e the d i f f e r e n c e between p a r t i c l e and standard analyses  ( X ^ o ( p a r t i c l e ) - X ^ o ( s t a n d a r d ) ) f o r cases i n which  both techniques had been a p p l i e d . The t r i a n g u l a r p o i n t i n the d i r e c t i o n of zoning displacement  symbols  p r e d i c t e d by  the d i r e c t i o n of approach toward e q u i l i b r i u m i n the ion-exchange experiment.  12  0.10  o c  0.05-  D  -M  00  0.00 _0)  o  O -0.05 QL  -0.  Xfo Figure  1.1  Comparison  of standard and p a r t i c l e a n a l y s e s f o r  cases i n which both techniques were a p p l i e d to samples of the same product o l i v i n e s . The t r i a n g u l a r symbols p o i n t i n the d i r e c t i o n of edge-zoning displacement which would be predicted considering  the d i r e c t i o n of approach  ion-exchange e q u i l i b r i u m f o r each experiment.  toward  13 DATA ANALYSIS  Run are 1.2)  conditions  listed  and  i n t a b l e 1.1.  compositions for the c r i t i c a l A p l o t of Xj^gd  v s  X  f  runs  (figure  D  i l l u s t r a t e s the magnitude of c o m p o s i t i o n a l changes  c o m p o s i t i o n a l p r e c i s i o n f o r the c h l o r i d e . To monitor the  runs at 2kb,  thermodynamic behavior of  system, a more u s e f u l v i s u a l r e p r e s e n t a t i o n l n K D a g a i n s t X^o  600°C,  at constant T and  d i s t r i b u t i o n c o e f f i c i e n t of the  2m the  is a plot  P, where K D  is  o v e r a l l exchange  and  of  the reaction:  M g ( o l i v i n e ) + Fe(aq) = F e ( o l i v i n e ) + Mg(aq)  KD  X f a  = X  F i g u r e 1.3  FeCl2  X  (2)  fo  i l l u s t r a t e s the  hypothetical  trends on  cases i n which the  p l o t s of the  such a p l o t  shows l n K D vs  apparent i n f l u e n c e  m o l a l i t y , mT,  ion-exchange e q u i l i b r i u m  the  X^  2m data along with t h e o r e t i c a l models which  e x p l a i n e d below. The  The  for  aqueous s o l u t i o n i s  thermodynamically ' i d e a l ' . F i g u r e 1.8  in figure  (1)  on  the  of t o t a l  are  chloride  is illustrated  1.6. general c h a r a c t e r i s t i c s of the data that  nature of the p h y s i c a l  a n a l y z i n g the data are:  and  influenced  thermodynamic models used in  the approximately l i n e a r trend of  Table 1.1. Ion-exchange run d a t a .  - - -INITIAL- - RUN*  T('C) P(kb) HOURS  X, fo  X,. Mg  mT T  MINOR PRODUCT PHASES  TA 2  - - - - - - - - - X,. Mg  Cl/Mg+Fe  FINAL X, ro  - - - - - - - - - - HOW  1 nK n D  1o  0 296  1.94  0 338  P  -0 13  0 10  0 334  1.87  0 455  P  -0 44  0 07  0 251  1.85  0 163  P  0 61  0 07  0 504  1.87  0 728  P  -0 90  0 05  TA  0 759  1.87  0 984  P  -2 91  0 64  142  450  996  0 400  0 000  2 0  143  450  1  996  0 400  0 700  10  145  450  1  1000  0 104  0 500  2 0  146  450  1  100O  0 710  0 700  2 0  TA  147  450  1  1000  1 000  0 700  2 0  163  450  1  840  0 104  0 000  2 0  0+OA  0 094  1 85  0 074  P  0 33  0 17  164  450  1  840  0 400  0 500  0 2  O+TA?  0 374  1 67  0 4 19  P  -0 12  0 06  165  450  2  842  0 400  0 100  2 0  TA  0 450  1 67  0 334  P  0 55  0 06  166  450  2  842  0 400  0 100  O 5  TA  0 506  1 62  0 347  P  0 72  0 07  167  450  2  842  0 400  0 500  0 2  TA  0 588  --  0 388  P  0 88  0 07  1 16  600  1  510  0 496  0 100  2 0  TA  0 152  --  0 492  M  - 1 62  0 05  1 17  600  1 '  528  0 496  0 500  0 2  TA  0 146  --  0 504  M  - 1 72  0 05  121  600  1  435  0 496  0 000  0 2  TA?  0 120  2 1 1  0 478  P  - 1 84  0 06  122  600  1  436  0 496  0 500  2 0  OP  0 205  1 90  0 529  P  - 14 1  0 09  124  600  1  436  0 800  0 500  P  - 1 73  0 07  135  600  1  650  0 496  136  600  1  650  0 496  199  600  1  627  200  600  1  25  600  2  26  600  27  600  2 0  TA  0 41 1  1 81  0 807  0 500  10  OP  0 156  2 02  0 582  P  - 1 95  0 10  0 000  0 5  0 106  2 07  0 472  P  - 1 95  0 08  0 104  0 300  2 0  OA  0 040  1 94  0 123  P  - 1 15  0 08  627  0 300  0 300  2 0  OA  0 095  --  0 327  P  -1 47  0 11  240  0 104  0 100  2 0  •A  0 070  --  0 101  S  -o 34  0 06  2  240  0 300  0 200  2 0  OA  0 157  0. 299  P  -0 76  0 1 1  2  240  0 300  0 000  2 0  OA  0 138  ---  0 270  P  -o 77  0 10  Table 1.1.  (continued) - - -INITIAL- - -  ?UN/C  T('C)  P(kb)  HOURS  fo  Mg  m. T  MINOR PRODUCT PHASES  - - - - - - - - - Mg  37  600  2  338  0 .600  0 . 300  2 .0  TA  0 . 265  38  600  2  338  0 .710  0 . 100  2 .0  TA  0 .275  39  600  2  697  0 . 800  0 . 200  2 .0  TA  0 . 359  40  600  2  697  0 . BOO  0 .500  2 .0  TA  0 . 443  41  600  2  697  0 .900  0 .400  2 .0  TA  0 .524  42  600  2  697  0 900  0 . 700  2 .0  TA  O .617  43  600  2  360  0 . 496  0 .OOO  2 .0  OA  0 . 200  64  600  2  1212  o . 800  0 .900  2 .0  TA  0 .685  66  600  2  1436  0 .496  0..300  2 .0  OA+TA  67  600  2  1436  0. . 496  0. OOO  0.2  OA + TA  68  600  2  1436  o 496  0..500  0.2  OA + TA  1 19  600  2  435  0 496  0. 500  133  600  2.  758  0 496  0. 000  134  600  2  758  0. 496  0. 000  101  600  4  382  o. 496  0. 000  2 .0  OA+TA  0. 269  102  600  4  382  0. 496  0. 000  0.2  TA  0. 352  103  600  4  382  o. 496  O.500  0. 2  TA  0. 387  128  600  4  385  o. 496  0. 500  2 .0  TA  0. 4 10  129  600  4  385  0. 496  0. 100  1.0  TA  0. 369  130  600  4  385  0. 496  0. 100  0 .5  174  600  4  601  0. 900  0. 300  2 .0  TA  0. 577  197  600  4  530  0. 104  0. 000  2 .0 .  0  0. 060  225  600  4  579  0. 104  0. 300  2 .0  OA  0. 126  Cl/Mg+Fe  FINAL X  fo  HOW1  lnK D  1<J  --  0 .607  P  - 1 . 39  0.07  ------  0 .679  P  -1 .65  0.08  0 .770  P  - 1 . 72  0.06  0 .792  P  -1 .50  0.08  0 .882  P  -1 .85  0.08  0 .909  P  -1 .76  0. 10  0 .465  P  -1.18  0.06  1 . 82  0 . 942  M  - 1 . 95  0.19  0 .219  1 .93  0 .500  M  -1.21  0.05  0.. 154  2 .09  0 .501  P  - 1 .64  0.05  0.. 166  2.09  0 . 503  S  -1 .56  0.06  0.5  0. 184  --  0 .533  P  -1 .56  0.06  1.0  0. 189  1 . 94  0 .463  P  - 1 . 24  0.06  0 .5  0. 165  2 .05  0 482  M  - 1 . 48  0.05  0. 474  P  -0.83  0.08  0. 503  P  -0.56  0.06  0. 472  P  - 0 . 28  0.05  1 . 79  0. 519  P  - 0 . 37  0. 10  1 .85  0. 465  P  -0.33  0.07  0. 469  P  - 0 . 32  0.06  1 .67  0. 855  P  - 1 . 40  0.09  1 .93  0. 078  P  -0.22  0. 10  1 . 93  0. 130  P  0.03  0. 13  0. 376  ---  --  Table I.1  (cont i nued) - - -INITIAL- - -  RUN*  T C C)  226  m  P(kb)  HOURS  X. fo  600  4  579  0 . 300  0. OOO  2 .0  227  600  4  579  0 . 800  0.. 900  69  725  2  1 106  0 . 104  0..000  70  725  2  1 106  0 . 104  O. 100  71  725  2  1 106  0.. 400  Mg  T  MINOR PRODUCT PHASES  - - - - - - - - - Mg  Cl/Mg+Fe  --  OA  0 . 189  2 .0  TA  0 . 598  2 .0  0  0 .023  1 .99  2 .0  0  0 .024  O 300  2 .0  OP  0 .089  FINAL 1  fo 0 .270  HOW  lnK D  1<J  0.08  P  -0.40  0 .820  P  -1 .05  0.09  0 . 102  M  -1.51  0.07  2 .03  0 . 107  S  - 1 . 52  0.05  1.91  0 . 423  S  - 1 . 95  0.05 0.05  72  725  2  1 105  o 800  0. 500  2 .0  OP  0 . 308  1 .88  0 .811  s  -2 . 20  21 1  725  2  351  o 800  0. 100  2 .0  OP  0 . 287  1 .99  0..780  p  -2.11  0.07  2 12  725  2  351  0 .600  0. 300  2 .0  OP  0 . 175  p  -1 .99  0.05  2 13  725  2  351  0. 400  0. 000  2 .0  OP  0 .088  ---  0..623 0. 392  p  -1.83  0.05  75  800  2  1 101  0 104  0. 100  2 .0  0 .031  -'-  0.. 105  S  - 1 . 23  0.06  169  800  2  494  o. 800  0. 700  2 .0  0. 877  F  -2.29  0.07  -2 . 20  0.07  OP  0 .404  1 . 73  170  800  2  494  o. 800  0. 100  2 .0  OP  0 329  1 . 38  0. 825  F  202  800  2  256  0 104  0. 000  2 .0  0  0 .015  1 . 59  0. 113  P  -2 .06  0.05  203  800  2  256  0. 400  0. 300  2 .0  OP  0..083  1 .84  0. 420  S  -2.01  0.08  204  800  2  256  o. 7 10  0. 500  2 .0  OP  0. 244  o. 745  P  -2.14  0.08  Method of f i n a l F=crystal  --  X^. d e t e r m i n a t i o n : M=mass b a l a n c e , S=standard microprobe, P = p a r t i c l e a n a l y s i s ,  face a n a l y s i s .  OA=orthoamphibole, OP=orthopyroxene, TA=talc, and Q=quartz.  17 1.0-  0.8-  2kb  600°C  LU  Q  0.6  CC  o _l  2m CHLORIDE  X o  g> 0.4-  0.2-  —  0.2  i  X F i g u r e 1.2 experiments and  —  1  0.4  M g  1  0.6  1  i  0.8  r  1.0  OLIVINE  Compositional changes measured f o r ion-exchange at 600°C, 2kb. The  s o l i d l i n e connects  initial  f i n a l c o m p o s i t i o n s . F i n a l compositions are surrounded  1a e r r o r  boxes.  by  18  IDEAL SOLID SOLUTION  ^  ^  ^  ^  ^  %  s.  v> \  IDEAL AQUEOUS SOLUTION  X fo  F i g3 u r e  3 1.3 T h e o r e t i c a l trends of lnK_ vs X f given t h a t the D to aqueous f l u i d behaves as a thermodynamically i d e a l s o l u t i o n  of the c h l o r i d e endmembers. Non-ideal s o l i d s o l u t i o n examples assume a Margules  formulation.  19 l n K D vs X^o a t each temperature, the decrease i n l n K D with mT  at 600°C, and the p o s s i b l e  increase  i n lnK^ with  d e c r e a s i n g mT at 450°C (the lack of opposing p a i r s of half-brackets  at 450°C leaves t h i s trend  poorly  c o n s t r a i n e d ) . Note a l s o the s c a t t e r of Cl/(Mg+Fe) data around some value l e s s than 2.0. The data a n a l y s i s attempts to answer the f o l l o w i n g quest i o n s :  Can the a p p l i c a t i o n of p r e v i o u s l y  established  knowledge of  aqueous e l e c t r o l y t e s account f o r those f e a t u r e s dependent only on the p r o p e r t i e s  How do u n c e r t a i n t i e s  of the data  of the aqueous s o l u t i o n ?  i n t h i s i n t e r p r e t a t i o n of the aqueous  s o l u t i o n p r o p e r t i e s a f f e c t subsequent a n a l y s i s of the olivine solid  solution?  Is there a thermodynamic s o l i d s o l u t i o n model that i s consistent published  with the present data and with a l l p r e v i o u s l y experimental s t u d i e s of Mg-Fe o l i v i n e  solution  behavior?  THE  AQUEOUS SOLUTION'.  In the p a s t , most t h e o r e t i c a l i n t e r p r e t a t i o n s of c h l o r i d e ion-exchange data have t r e a t e d the aqueous s o l u t i o n as thermodynamically ' i d e a l ' Orvilie(1963,  (or i t s e q u i v a l e n t ) .  1972) concluded, on the b a s i s of a few  20  experiments over a range of c h l o r i d e c o n c e n t r a t i o n s , that ion-exchange e q u i l i b r i u m of aqueous c h l o r i d e s with f e l d s p a r s was independent of t o t a l c h l o r i d e c o n c e n t r a t i o n . Based on t h i s c o n c l u s i o n , he t r e a t e d the aqueous s o l u t i o n as i d e a l when i n t e r p r e t i n g h i s experiments. Perchuk and Aranovich(1979) based t h e i r assumption of i d e a l i t y i n AlCl3-FeCl3  mixtures on experiments with KCl-NaCl s o l u t i o n s  (Perchuk and Andrianova, 1968). Schulien(1980) based h i s assumption of i d e a l i t y  i n M g C l 2 - F e C l 2 mixures on a  q u a l i t a t i v e c o n c l u s i o n that the n e u t r a l MgCl 2 s p e c i e s mixes i d e a l l y with H 2 0  (Frantz and Popp, 1979) and d i d not attempt  to t e s t t h i s assumption e x p e r i m e n t a l l y . In c o n t r a s t , Saxena(l972) analyzed the ion-exchange data of S c h u l i e n et a l ( l 9 7 0 ) by modelling the bulk p r o p e r t i e s of the Mg-Fe c h l o r i d e s o l u t i o n with a Margules-type excess f u n c t i o n . In doing so he chose to ignore the i d e n t i t y of the a c t u a l Fe and Mg s p e c i e s i n the aqueous s o l u t i o n . Thompson and Waldbaum(1968), i n a n a l y z i n g the data of O r v i l l e ( 1 9 6 3 ) , c o n s i d e r e d the p o s s i b i l i t y that KC1 and NaCl are p a r t i a l l y +  +  d i s s o c i a t e d to N a , K  and C I " . However they only c o n s i d e r e d  the case i n which KC1 and NaCl are d i s s o c i a t e d to the same extent and proceeded to show that t h i s case was i n d i s t i n g u i s h a b l e from the ' i d e a l s o l u t i o n ' assumption when a n a l y z i n g the ion-exchange e q u i l i b r i u m . E n g i ( l 9 8 0 ) demonstrated the consequences of c o n t r a s t i n g d i s s o c i a t i o n - e q u i l i b r i u m c o n s t a n t s i n a binary aqueous c h l o r i d e s o l u t i o n by a p p l y i n g q u a l i t a t i v e  equilibrium  21 constant data f o r MgCl 2 = Mg 1979)  and  FeCl2  = Fe  +2  + 2C1"  +2  + 2C1"  (Frantz and  Popp,  (Boctor et a l , 1980)  o l i v i n e exchange e q u i l i b r i u m data of S c h u l i e n  to  the  et a l ( l 9 7 0 ) .  In g e n e r a l , aqueous e l e c t r o l y t e s are e s s e n t i a l l y e n t i r e l y d i s s o c i a t e d i n t o charged s p e c i e s increasingly associated  at STP  with i n c r e a s i n g T and  and  decreasing  Although a l a r g e amount of q u a n t i t a t i v e data has published  become P.  been  f o r many aqueous e l e c t r o l y t e compounds, only a  small p o r t i o n of the measurements were made at p r e s s u r e s temperatures above.the c r i t i c a l p o i n t et a l ( l 9 8 l ) f o r c o m p i l a t i o n ,  of H 2 0  c r i t i q u e and  and  (see Helgeson  a n a l y s i s ) . More  s p e c i f i c a l l y , the data a v a i l a b l e on the behavior of MgCl 2 in s u p e r c r i t i c a l H20 FeCl2  are  s o l u t i o n s are  incomplete and  scant. Figure  1.4  s u p e r c r i t i c a l data f o r illustrates  the  a v a i l a b l e d i s s o c i a t i o n constant data f o r c h l o r i d e compounds at P-T  conditions  pertinent  to t h i s s t u d y . These  d i s s o c i a t i o n c o n s t a n t s have been d e r i v e d  from e l e c t r i c a l  c o n d u c t i v i t y measurements by the authors l i s t e d 1.2.  The  empirical  curves i n f i g u r e 1.4  where KM  empirical  the  Marshall(1982):  + clogpH 2 0  (3)  i s an e q u i l i b r i u m constant on the  concentration pure H 2 0  were generated with  f u n c t i o n used by F r a n t z and  l o g K M d i s s = a + b/T  in table  molarity  s c a l e , T i s in k e l v i n s , pH 2 0 i s the d e n s i t y  at P and  T of  i n t e r e s t , and  a, b and  f i t parameters. Conversion to the  c  are  molality  of  22  400  450  500  550  600  650  700  750  800  Temperature (°C) Figure 1.4  Common logarithm of aqueous c h l o r i d e d i s s o c i a t i o n  constants at 2kb. references.  See  text f o r e x p l a n a t i o n s  and  table 2 for  23 Table 1.2. F i t parameters f o r equation (3) f o r s e v e r a l aqueous c h l o r i d e s . See t e x t f o r d e t a i l s .  a  b  c  DATA ' SOURCE  NaCl  -1 .43  1470  10.2  1  5  KC1  -2.68  590  3.26  2  5  LiCl  -2.61  970  3.65  3  5  B a C l 2 K, K2  -3.97  1 530  6. 1 3  2  5  -6.24  2580  7.39  2  5  C a C l 2 K, K2  -3.21  2407  10.6  4  4  -5.05  3112  16.5  4  4  (2407)  (10.6  4  4  3415  19.2  4  4  MgCl 2 K 1  (-3.21 )  K2  -4.80  1: Q u i s t and Marshall(1968) 2: R i t z e r t and Franck(l968) 3: Mangold and Franck(!969) concentration scale throughout  )  REGRESSION TO EQUATION (3)  4: F r a n t z and Marshall(1982) 5: T h i s study  (which i s used i n f i g u r e 1.4  the remainder of t h i s paper) was  and  done with the  approximation:  l o  K  9 diss  =  l o g K M  diss  "  l o  9P  H 2  °  which i s reasonably a c c u r a t e f o r d i l u t e s o l u t i o n s . P o r t i o n s of some of the curves i n f i g u r e 1.3  extend beyond the data  from which they were d e r i v e d . Table 1.2 parameters f o r equation  lists  the f i t  (3) f o r each compound along with the  a p p r o p r i a t e r e f e r e n c e s . Note t h a t , f o r s e v e r a l p a i r s of c h l o r i d e s , the d i s s o c i a t i o n constants may  be i d e n t i c a l at  24 one  temperature and  an order of magnitude apart at a  temperature 200°C (or l e s s ) away. For  the d i c h l o r i d e s ,  d i s s o c i a t i o n constants are c a l c u l a t e d ; one step-wise d i s s o c i a t i o n r e a c t i o n s : MC12 = M  +2  +  = MC1  + CI"  + C I " . Experimental d i f f i c u l t i e s a t t r i b u t e d  h y d r o l y t i c p r e c i p i t a t i o n of MgO and  f o r each of and  two two MC1  +  to  or Mg(OH) 2 prevented F r a n t z  Marshall(1982) from d i r e c t l y measuring the  first  d i s s o c i a t i o n constant of M g C l 2 . They i n f e r r e d from what data they d i d gather that K,MgCl 2 c o u l d be  t r e a t e d as i d e n t i c a l  to K , C a C l 2 . Only q u a l i t a t i v e information  i s a v a i l a b l e for  the  d i s s o c i a t i o n e q u i l i b r i a of aqueous F e C l 2 . S o l u b i l i t y of magnetite (Chou and et a l , 1980)  E u g s t e r , 1977)  and  in s u p e r c r i t i c a l F e - c h l o r i d e  hematite  2kb  i s the dominant aqueous s p e c i e s  and  from 400  to 600°C at  1kb. information  for  been adopted here in an attempt to  account f o r the dependence of lnK^ on concentration. to as the  be:  to 650°C at  s p e c i a t i o n , a s i m p l i f i e d model of the Mg-Fe c h l o r i d e  aqueous s o l u t i o n has  A)  associated  from 400  In l i g h t of the d e a r t h of q u a n t i t a t i v e FeCl2  (Boctor  s o l u t i o n s were  i n t e r p r e t e d by t h e i r authors to i n d i c a t e that FeCl2  studies  The  Here are  the  features  total  chloride  of that model, r e f e r r e d  f i r s t - d i s s o c i a t i o n model i n f o l l o w i n g  dominant ion-exchange e q u i l i b r i u m was  discussions:  assumed to  25  MgSi0.502  (l K  =  X  ' fo  E  X  +  FeCl2  )m  = FeSi0.502  (  y  MqCl2 ' fa^MgCl2 m  fo  FeCl2  ( 7  7  + MgCl 2  (5)  )  fo FeCl2  (fi) )  A c t i v i t i e s of the aqueous s p e c i e s were assumed to i n f l u e n c e d only by  i n t e r a c t i o n with H 2 0.  aqueous s p e c i e s with each other was  B)  Only the  Figure  s i m p l i f i c a t i o n may  be  1.4  i l l u s t r a t e s that  the ideal.  chlorides  this  j u s t i f i e d s i n c e , over the  range of i n t e r e s t h e r e , K 2 M g C l 2  temperature  i s more than 1 l o g u n i t  fc^MgClz.  MgCl 2 = MgCl  m K  assumed to be  f i r s t d i s s o c i a t i o n r e a c t i o n s f o r the  were c o n s i d e r e d .  below  Mixing of  be  M g  =  +  m  (7  (7)  7  MgCl+ Cl- MgCl+ Clm MgCl2  = FeCl  ) ( 8 )  (<v ) MgCl2  m  FeCl2  + CI"  W  +  + Cl"  ;  (9)  26  K  m  m  (  7  = FeCl+ Cl- 7Feci* Clm  ( 7  FeCl2  FeCl2  (10  )  )  +  C)  }  +  M g C l 2 , F e C l 2 , M g C l , F e C l , and CI" were the only  aqueous s p e c i e s c o n s i d e r e d . In other words, a l l p o s s i b l e r e a c t i o n s of these s p e c i e s with the s o l v e n t , H 2 0, were ignored. Therefore: X  K  _ °" fo X  Although  fo  )  (m  ( m  +  Mqd2  FeCl2  +  m  m  Mgd  FeCl  J (  n  )  + )  Helgeson et a l ( l 9 8 l ) p r o v i d e an extended  Debye-Hiickel a c t i v i t y c o e f f i c i e n t equation a p p l i c a b l e to any aqueous s p e c i e s over a wide range of P, T and c o n c e n t r a t i o n , once again the lack of a p p r o p r i a t e experimental q u a n t i f y the f i t parameters p r e c l u d e s to the s p e c i e s c o n s i d e r e d  D)  i t s direct  data to application  here.  A c t i v i t y c o e f f i c i e n t s of a l l n e u t r a l s p e c i e s were  assumed t o be 1.0, and a l l s i n g l y charged s p e c i e s were assumed to have i d e n t i c a l a c t i v i t y c o e f f i c i e n t s . These a c t i v i t y c o e f f i c i e n t s were c a l c u l a t e d with an unextended Debye-Hiickel  expression 2  -Z A(I)°l o g 7 .1 =  0  5  1+aB(l) '  5  (12)  where Z i s the i o n i c charge, I i s the true i o n i c s t r e n g t h , A and B are the Debye-Hiickel c o e f f i c i e n t s and a i s the  27 i o n - s i z e parameter. A value of 4.0 was for a based upon values t a b u l a t e d  judged  appropriate  for MgCl2, F e C l 2  and NaCl  (Helgeson et a l , 1981). A and B were taken from Helgeson and Kirkham(1974) up to 600°C and were extended to 800°C with equations (2) and (3) of Helgeson and Kirkham(1974) with H 2 0  d i e l e c t r i c constants p r o v i d e d by Quist  along  and  Marshall(1965).  The standard s t a t e s i m p l i c i t  i n the above  formulation  a r e : the pure s o l i d phase at P and T, and a h y p o t h e t i c a l i d e a l 1-molal aqueous s o l u t i o n at P and T. The mass-balance c o n s t r a i n t s on the model a r e :  m  T  =  VjCI,  where mT  +  m  MgCl*  +  m  FeCl2  +  m  FeCl  +  ( 1 3  i s the t o t a l m o l a l i t y of Mg+Fe i n aqueous s o l u t i o n  and:  m  Cl"  =  m  MgCl  +  +  m  FeCl  From (14) i t follows  +  ( 1 4 )  that  I = mcl_  Equations  ( 6 ) , ( 8 ) , ( 1 0 ) , (13) and  manipulated to produce a q u a d r a t i c  (15)  (14) can be combined  i n the m o l a l i t y of one  s p e c i e s which can, i n t u r n , be solved r o o t . Using a s u b s t i t u t i o n d e r i v e d  and  for a r e a l , p o s i t i v e  from ( 6 ) :  28  1  Q = "V * m  and  7  FeCl2  s o l v i n g for  0  =  7 f  =  S^ y  m M  °  X f  ( 1  fa  °  (16)  }  - fo  g d + results in: b)m  (Q  KF  X  +  +  Mg  Mg  M9Cl  +  +  bm  m  ( 1 7 )  MgCl* - T  where K b = 1 +  (18) QK  Mg  The  d i s t r i b u t i o n of aqueous s p e c i e s p r e d i c t e d by t h i s model  was  c a l c u l a t e d i n an  i t e r a t i v e procedure which solved  calculated  (combining ( 8 ) , (10),  c a l c u l a t e d 7C^-  (with  (12) and  (14), and  (15)) and  s a t i s f a c t o r y convergence on 7Q±-' K M g and M a r s h a l l ( 1 9 8 2 ) , and  KFg  was  (17),  (16)),  tested for  was  taken from  Frantz  modelled with equation  (3),  r e q u i r i n g 3 f i t parameters. Figure  1.5  shows the  i n f l u e n c e of e l e c t r o l y t e  d i s s o c i a t i o n on the o l i v i n e exchange K D f i r s t - d i s s o c i a t i o n model. The  as p r e d i c t e d by  illustration  i s for  the  the  h y p o t h e t i c a l case in which the o l i v i n e s o l i d s o l u t i o n i s i d e a l , lnK^, = -1.0,  l o g K M g = -2.0,  =  K  logK  Mg "  l o g K  Fe  a n d  av  =  ( l o g K  Mg  600°C, 2kb  + l o g K  Fe  then lnK^ i s i d e n t i c a l to InK,,. If ALK then l n K D - lnK^ has value i n c r e a s e s as mm d e c r e a s e s . The T  } / 2  i n c r e a s e s , as K  i n f l u e n c e of X, on fo  small except p o s s i b l y near the  I f  A L K  where =  0  3 V  and  ALK  0  * '  i s d i f f e r e n t from  the same s i g n as ALK  |ALK|  '  and  0.0  i t s absolute  i n c r e a s e s , and  l n K „ - lnK„ is quite D E ^  l i m i t s of  as  I  I  ! n K £ = - 1.0  0-  -1-  I l  I  °g Mg=- K  2  0  logKpe  ALK  0.2  -3.0  +1.0  2.0  -3.0  + 1.0 — - 2 . 5 0  2.0  -2.0  0.0  -2.00  2.0  -1.5  -0.5  -1.75  2.0  -1.0  -1.0  -1.50  2kb  Ideal Olivine  m  T  ov -2.50 K  •  _E - 2 -  - 3 600°C -4 0.0  I 0.2  I 0.4  I 0.6  I 0.8  1.0  Xfo F i g u r e 1.5 The e f f e c t  of v a r i a t i o n s i n l o g K p e on l n K ^ as  p r e d i c t e d by the f i r s t - d i s s o c i a t i o n  model f o r the  h y p o t h e t i c a l , case i n which the o l i v i n e ideal,  (a) l n K ^ vs X f o  at 600°C, 2kb.  s o l i d solution i s  30  lnKE=-1.0  0 -  logK  -  Q  Mg  Fe  ALK  3.0  +1.0  -2.50  -2.0  0.0  -2.00  -1.5  -0.5  -1.75  -1.0  -1.0  -1.50  r  -1  logK =-2.0  -3600°C -4 0.0  2kb  T  0.5  Ideal Olivine: X  1.0 1.0  1.5  Total Molality F i g u r e 1.5  (b) l n k D vs mT  at 600°C, 2kb.  =0.5  T  2.0  2.5  31  To apply the f i r s t - d i s s o c i a t i o n model t o the o l i v i n e ion-exchange d a t a , i t was necessary  to e s t a b l i s h  equation  (3) f i t parameters f o r l o g K p e . The f i t parameters r e q u i r e d to reproduce  the e n t i r e data s e t were c a l c u l a t e d by  simultaneous  r e g r e s s i o n of l o g K F e  solid solution final  f i t parameters and o l i v i n e  f i t parameters using experimental P, T and  as independent v a r i a b l e s  and l n K ^ as the dependent  v a r i a b l e . The c a l c u l a t i o n s were performed with a ' d e r i v a t i v e - f r e e ' n o n - l i n e a r r e g r e s s i o n program c a l l e d BMDPAR: a FORTRAN program d i s t r i b u t e d by BMDP S t a t i s t i c a l Software, I n c . Unconstrained  r e g r e s s i o n of the experimental  data produced u n r e a l i s t i c f i t parameters f o r K p e . In p a r t i c u l a r , a negative temperature c o e f f i c i e n t was calculated  implying a temperature v a r i a t i o n of l o g K F e  which  i s i n c o n t r a s t to a l l other e l e c t r o l y t e d i s s o c i a t i o n constants f o r which data e x i s t . A review of the data i n f i g u r e 1.6 shows why t h i s r e s u l t was i n e v i t a b l e . Regression produces a moderate p o s i t i v e ALK at 450°C, 2kb and a moderate negative ALK a t 600°C, 2kb. S a t i s f y i n g both of these would give l o g K F e  a p o s i t i v e slope on f i g u r e 1.4.  More reasonable v a l u e s f o r l o g K F e established solubility  f i t parameters were  by combining general c o n s t r a i n t s  p r o v i d e d by  s t u d i e s , the o l i v i n e ion-exchange d a t a , and the  examples s e t by d i s s o c i a t i o n constants measured f o r other chloride  e l e c t r o l y t e s . F i t parameters for l o g K F e  calculated  a c c o r d i n g t o the f o l l o w i n g  criteria:  were hand  32 FeCl2  i s e s s e n t i a l l y a s s o c i a t e d at 800°C,  (logKpe  <  2kb  -3.0).  ALK  < 0.0  at 600°C,  2kb.  ALK  > 0.0  at 450°C,  2kb.  ALK  * 0.0  at 600°C,  4kb.  The  r e s u l t i n g f i t parameters are a=-2.1, b=l000 and  The  s o l i d curves on f i g u r e 1.6  c=6.0.  i l l u s t r a t e the behavior  the f i r s t - d i s s o c i a t i o n model using these  of  l o g K F e parameters  and Model B f o r the o l i v i n e s o l i d s o l u t i o n  (described  below). The  behavior  of the  d e p i c t e d i n f i g u r e 1.6, only; missing  f i r s t d i s s o c i a t i o n model, as s a t i s f i e s the low m^  s e v e r a l of the  data  in form  1a b r a c k e t s . In an attempt to  improve the a b i l i t y of the aqueous model to f i t the low d a t a , two  of the more obvious extensions  of  f i r s t - d i s s o c i a t i o n model were added. (1) The  mT  the 'extended' mean  i o n i c a c t i v i t y c o e f f i c i e n t expression of Helgeson et a l (1981) was  introduced using t h e i r b  M g C l 2 . (2) The  a r e l a t i o n s h i p to K 2 MgCl 2 f o l l o w i n g  the same ALK  criteria  of these  extensions  used in c a l c u l a t i n g K , F e C l 2 . Neither was  found to s i g n i f i c a n t l y improve  correspondence of the aqueous model to the low mT D i s c r e p a n c i e s between the model and c o u l d be a t t r i b u t e d considered  for  second d i s s o c i a t i o n e q u i l i b r i a were added  using a K 2 F e C l 2 having  two  values c a l c u l a t e d  to a d d i t i o n a l  data.  the data at low  aqueous s p e c i e s  in the model. There i s evidence that  s p e c i e s must, i n f a c t , be p r e s e n t . For  not  other  i n s t a n c e , the  mT  33  450°C  2kb  Xfo =0.4  t 0 -  450°C  1  1kb  X  f o  =0.4  1  \£ - 1  T  h  -2  600°C  1kb  X =0.5 fo  -3 0.0  0.5  1.5  1.0  2.0  2.5  Total Molality Figure  1.6  l n K ^ vs mT  for isothermal-isobaric-isoX^  subsets  of the ion-exchange experiments. The symbols marking each experimental measurement p o i n t  i n the d i r e c t i o n of approach  toward e q u i l i b r i u m . The measurement i t s e l f i s at the center of the symbol and the l e n g t h of the symbol represents  ±1a i n  Minor d e v i a t i o n s i n measured X £ from the s t a t e d D ro constant value have been c o r r e c t e d f o r by a d j u s t i n g l n K D lnhw.  parallel  to Model B (see text  f o r d e s c r i p t i o n of the  m o d e l s ) . The s o l i d l i n e s i l l u s t r a t e l n K Q p r e d i c t e d by the f i r s t - d i s s o c i a t i o n model combined with Model B. (a) Data at 450°C (Ikb and 2kb) and 600°C d k b ) .  34  0 600°C V  4kb  A  4  A ^  Q  -1  I  I  1—  1 600°C  2kb  - 2 -  Xf o =0-5 -3 0.0  r  0.5 1.0  Total F i g u r e 1.6  1.5  Molality  (b) Data at 600°C (2kb and  4kb).  2.0  2.5  35 Cl/(Mg+Fe) r a t i o s in t a b l e 1.1 2.0  average s l i g h t l y  i n d i c a t i n g that n o n - c h l o r i d e  l e s s than  s p e c i e s of aqueous Mg  Fe must be p r e s e n t . A l s o , the formation  and  of minerals more  s i l i c e o u s than o l i v i n e d u r i n g the ion-exchange experiments i n d i c a t e s that MgO solubility The  and FeO  (as components) have a higher  i n the aqueous s o l u t i o n than S i 0 2 .  equation  (3) f i t parameters f o r K , F e C l 2 should  u s e f u l as an e m p i r i c a l f i r s t - a p p r o x i m a t i o n . The  be  observable  shortcomings of the f i r s t - d i s s o c i a t i o n model i n d i c a t e that f u r t h e r research  i s needed i n order  of the c h l o r i d e f l u i d  in these and  to understand the  role  other c h l o r i d e  ion-exchange experiments. Such research c o u l d i n c l u d e independent measurement of K , F e C l 2 and  K2FeCl2,  i d e n t i f i c a t i o n and c o n c e n t r a t i o n measurement of s p e c i e s , and measurements of l n K D f u n c t i o n of mT  THE  SOLID  at other  non-chloride  (ion-exchange) as a  temperatures and  pressures.  SOLUTION:  A s i n g l e - s i t e s t o i c h i o m e t r i c s o l i d s o l u t i o n model deemed a p p r o p r i a t e f o r the Mg-Fe o l i v i n e s o l i d s i n c e long range o r d e r i n g of Mg  was  solution  and Fe i n o l i v i n e has been  shown to be minor or absent (see Brown, 1980,  f o r review of  o l i v i n e s i t e occupancy). A 'Margules' type of  formulation  was  chosen for the sake of comparison. It has been  widely  a p p l i e d to s i l i c a t e s o l u t i o n s f o l l o w i n g i t s i n t r o d u c t i o n to the g e o l o g i c l i t e r a t u r e by Thompson(1967; see a l s o Grover, 1977;  Berman and Brown, 1984). I t i s a l s o the  formulation  36  used i n most Mg-Fe o l i v i n e s o l i d s o l u t i o n s t u d i e s p r e v i o u s l y published. A second o r d e r , 'symmetric* Margules f o r m u l a t i o n was found most a p p r o p r i a t e to model the o l i v i n e - a q u e o u s c h l o r i d e exchange e q u i l i b r i u m data presented h e r e . I f we adopt the f i r s t - d i s s o c i a t i o n model f o r the aqueous s o l u t i o n and c o n s i d e r , f o r the moment, the case  i n which MgCl 2 and F e C l 2  are both f u l l y a s s o c i a t e d , we can w r i t e :  K  D  =  K  7  f o  ( 1 9 )  E7— fa  Taking the n a t u r a l l o g a r i t h m of both s i d e s and s u b s t i t u t i n g in Margules e x p r e s s i o n s f o r l n 7 we have:  l n K D = l n K E + l / R T [ ( l - X f o ) M W M g+ 2X f o (W F e -W M g )) -X|o(WFe+2(l-Xfo)(WMg-WFe))]  (20)  f o r a t h i r d o r d e r , 'asymmetric' Margules f o r m u l a t i o n and: l n K D = l n K E + W G (1-2X f o )/RT  f o r the symmetric model. As i l l u s t r a t e d equation curved  (21) i s l i n e a r  (21)  i n f i g u r e 1.3,  i n X^Q and equation  l i n e i n lnK_. vs X. . A D fo  (20) d e s c r i b e s a  review of the d i s t r i b u t i o n of  data p o i n t s and t h e i r standard e r r o r s on f i g u r e 1.8 shows that a f u n c t i o n l i n e a r polynomial  i n X^Q i s the highest order  i n X^Q that the data seem to r e q u i r e . T h i s  37 judgement i s not a f f e c t e d by i n c l u s i o n of p a r t i a l dissociation 1.5,  i n the aqueous model s i n c e , as shown i n f i g u r e  the i n f l u e n c e of the f i r s t - d i s s o c i a t i o n model on  i s only weakly dependent on X^ Q , e s s e n t i a l l y l i n e a r over  and that dependence i s  intermediate values of  Regression of the Margules parameter exchange r e a c t i o n  X^ Q .  and AG  The  0  of the  (equation (5)) f o r i s o t h e r m a l - i s o b a r i c  p o r t i o n s of the data produced the values l i s t e d 1.3.  lnKQ  in table  thermodynamic parameters presented are a l l molar  q u a n t i t i e s f o r the formula u n i t s used i n equation data set as a whole can be adequately  ( 5 ) . The  f i t u s i n g the  standard  l i n e a r e x p r e s s i o n f o r AG?  AG§ = AH5-  and  TAS§+ PAV§  (22)  i t s e q u i v a l e n t f o r V?G WG  = WH  - TWS  + PWy  (23)  but only i f p r e - e x i s t i n g data o u t s i d e the P-T the present  c o n d i t i o n s of  study are i g n o r e d . However, only equation  need be m o d i f i e d to s a t i s f y p r e - e x i s t i n g data s i n c e no data e x i s t which would c o n s t r a i n equation s u p e r c r i t i c a l p r e s s u r e s and F i g u r e 1.7  values of The  other  (22) at  temperatures.  compares values from t a b l e 1.3  isotherms p l u s the  (23)  (2kb  1kb, 450°C isotherm) with p u b l i s h e d  and p u b l i s h e d s t o i c h i o m e t r i c s o l u t i o n models.  data from Obata et a l ( l 9 7 4 ) are the product of  Table 1.3. I s o t h e r m a l - i s o b a r i c r e g r e s s i o n r e s u l t s f o r the ion-exchange r e a c t i o n and the s t o i c h i o m e t r i c o l i v i n e s o l u t i o n model. See a l s o equations ( 5 ) , ( 6 ) , and ( 2 1 ) .  P(bars)  T(°C)  AG|(J)  (1a)  W G (J) (1a)  1000  450  1 580 (520)  7770 (1300)  1 000  600  1 0970 (490)  3200 (1200)  2000  600  7730 (280)  5920  4000  600  2050 (610)  6280 (1400)  2000  725  1 4280 (300)  3720  (500)  2000  800  1 721 0 (340)  1750  (500)  (560)  c o m p i l a t i o n and r e - i n t e r p r e t a t i o n of o l i v i n e - o r t h o p y r o x e n e ion-exchange e q u i l i b r i u m data assuming an i d e a l l y d o u b l e - s i t e d s o l u t i o n model f o r the orthopyroxene. The experimental data compiled by Obata et a l ( l 9 7 4 ) were a l l c o l l e c t e d at 1atm excepting the data at 1073K and 1173K which were c o l l e c t e d at 500bars from Kawasaki  (Medaris, 1969). W_  values  and Matsui(1977) and O'Neil and Wood(l979) are  based upon o l i v i n e - g a r n e t exchange  equilibria  50kbar and 30kbar r e s p e c t i v e l y . Kawasaki  s t u d i e d at  and Matsui(1983)  experimentally studied garnet-orthopyroxene-olivine  exchange  e q u i l i b r i a at 50kbar. The second order Margules model from Andersen and L i n d s l e y ( 1 9 8 1 ) i s based on o l i v i n e - i l m e n i t e exchange  equilibria  (Andersen and L i n d s l e y , 1979) and  ilmenite-magnetite exchange  equilibria  (Lindsley,  Andersen and L i n d s l e y ( 1 9 7 9 ) conducted exchange  1978).  equilibrium  39  14000 12000 -  K&M(1977)  10000 CD  8000 K&M(1983)  0&W(1979)  40002000-  E( 1980a) W  Mg  0 -2000 400  F i g u r e 1.7  I 600  —, 800  1  r  1  1000  1200  1400  Temperature (K)  1800  A c o m p i l a t i o n of the most recent and most  comprehensive measurements of models f o r Mg-Fe o l i v i n e s . The from o l i v i n e - o r t h o p y r o x e n e compiled  1 1600  and  and Margules s o l u t i o n diamonds represent  values  ion-exchange experiments as  r e - i n t e r p r e t e d by Obata et a l . ( l 9 7 4 ) .  v e r t i c a l bars below 1200K represent values produced in the present  The  1a e r r o r bars about  study by r e g r e s s i o n of  i s o t h e r m a l - i s o b a r i c subsets of the data  (see t a b l e ' 3 ) . The  remaining  authors have been a b b r e v i a t e d as f o l l o w s : E =  E n g i , A&L  = Andersen and L i n d s l e y , K&M  M a t s u i , O&W  W^  = O ' N e i l l and Wood.  = Kawasaki  and  40 experiments at both  latin (700 to 980°C) and 13kb (800 to  9 0 0 ° C ) . The t h i r d - o r d e r Margules model of Engi(1980a) i s based upon the o l i v i n e - o r t h o p y r o x e n e data as i n t e r p r e t e d by Obata et a l ( l 9 7 4 ) and oxide-melt  s o l u t i o n c a l o r i m e t r y by  Wood and Kleppa(1981). The  s o l u t i o n models of Engi(1980a) and Anderson and  Lindsley(1981) are the most s e n s i b l e g u i d e l i n e s f o r the high temperature behavior of the o l i v i n e s o l i d s o l u t i o n at relatively  low p r e s s u r e s . They agree"quite c l o s e l y with each  other above 1000K, where most of the data were c o l l e c t e d . A s o l u t i o n model c o n s i s t e n t with the present study and these two p u b l i s h e d models would be c h a r a c t e r i z e d by 3Wg/3T < 0 and  2  9 WG/9T  2  > 0 such that WQ  and 3WQ/9T both approach zero  at about 1600K where the s o l i d s o l u t i o n  i s essentially  i d e a l . T h i s agrees with the concept that the s o l i d  solution  should a s y m p t o t i c a l l y approach i d e a l behavior at a sufficiently  high temperature.  The p u b l i s h e d data on f i g u r e  1.7 which are o b v i o u s l y i n c o n s i s t e n t with g e n e r a l i z a t i o n are a l l the product  this  of high p r e s s u r e exchange  experiments with Fe-Mg g a r n e t s . T h e i r i n c o n s i s t e n c y c o u l d stem from i n a p p r o p r i a t e assumptions about the garnet  solid  s o l u t i o n or from a s u b s t a n t i a l pressure dependence of the olivine solid solution properties, a p o s s i b i l i t y  discussed  below. V a r i a t i o n of WH  and Wg  with temperature must be  i n t r o d u c e d i f the s o l i d s o l u t i o n model i s to f o l l o w the above g u i d e l i n e s . One way t o accomplish  t h i s i s to p o s t u l a t e  41 a constant excess heat c a p a c i t y as d i d Engi(1980a)  W  H  Ws  =  W  5  W  +  C  ( T  "  T 0 )  ( 2 4 )  = W°+ W c l n ( T / T ° )  Regression of W ° ,  (25)  W ° , Wc  and Wv  using  choosing T°= 298K and c o n s t r a i n i n g WG produced the parameters l i s t e d The  the data i n t a b l e 1.1, to be 0.0 at 1600K  as Model A i n t a b l e  value of V?v produced by r e g r e s s i o n  poorly constrained  1.4.  (Model A) i s  by the data and i s seen to be  unacceptably l a r g e when compared to the 0.13J/bar AV between f o r s t e r i t e and f a y a l i t e , and when compared to Wv derived  from u n i t c e l l  r e f i n e m e n t s . Published  s t u d i e s of s y n t h e t i c o l i v i n e s c o n s t r a i n Wv  values  cell  dimension  at STP to be  0.007±.005J/bar  (Akimoto and F u j i s a w a , 1968),  0.0l5±.004J/bar  ( F i s h e r and M e d a r i s , 1969) and  0.011±.001J/bar  (Schwab and K u s t n e r , 1977). C a l c u l a t i n g the  Wv  necessary to b r i n g the high pressure g a r n e t - o l i v i n e  studies into consistency  with low pressure s t u d i e s at  s i m i l a r temperatures (assuming that the mixing p r o p e r t i e s of Fe-Mg garnet are independent of pressure; M a t s u i , 1977) y i e l d s a value of 0 . l 2 J / b a r . to have l i t t l e be  Kawasaki and I f Wv  or no dependance on p r e s s u r e ,  i s assumed  t h i s too must  r e j e c t e d as too l a r g e , i n d i c a t i n g that o l i v i n e mixing  p r o p e r t i e s c a l c u l a t e d by O ' N e i l l and Wood(1979) and Kawasaki  42 Table 1.4. Regressed f i t parameters f o r the ion-exchange and the s t o i c h i o m e t r i c s o l i d s o l u t i o n model. See equations (5) , ( 6 ) , and (21) -(25) .  A  Model:  (la)  AHg(J)  33500  -33400  (2000)  AS|(J/K)  -53.3  -53.3  (2.3)  AV?(j/bar)  -2.74  -2.75  (0.2)  wH(j)  35700  37700  (5400)  48.7  (7.0)  -29.0  (4.1 )  0.011*  (0.6)  46. 1  W S (J/K)  -27.4  W C (J/K) W y (J/bar)  *  B  0.16  Fixed v a l u e ;  reaction  not regressed  and M a t s u i ( l 9 7 7 , 1983) are t r u e l y i n c o n s i s t e n t with the low pressure  studies.  The study by Schwab and Kustner employed by f a r the l a r g e s t number of o l i v i n e compositions and a t t a i n e d the highest measurement a c c u r a c y . However, the o l i v i n e s they s t u d i e d were a l l s y n t h e s i z e d at temperatures g r e a t e r than 1000°C. T h e i r measurements may not apply e q u a l l y w e l l to o l i v i n e s annealed at the lower temperatures i n c l u d e d i n the present s t u d y . In order to check t h i s p o s s i b i l i t y , u n i t refinements were performed on the product o l i v i n e s ion-exchange  cell  from  experiments conducted at 450°C and 1kb. Also  i n c l u d e d were an endmember f o r s t e r i t e annealed at 800°C, 2kb and an endmember f a y a l i t e s y n t h e s i z e d at 450°C, 4kb. Powder XRD techniques were employed using a P h i l i p s PW1710 d i g i t a l  43 diffTactometer  equipped  monochromator.  Least-squares  parameters  accomplished  was  with  a C U K q source and a refinement with  of  unit  graphite c e l l  a USGS FORTRAN IV program  (Evans et a l , 1963). T a b l e 1.5. O l i v i n e c e l l parameters d e r i v e d from powder XRD peaks i n the 40' t o 75' 20 range. (CuK a , s y n t h e t i c s p i n e l i n t e r n a l s t a n d a r d )  RUN*  INITIAL fo  FINAL fo  OS- 16 147 146 143 142 145 132  1 OOO 1 OOO 0.710 0. 400 0. 400 0.104 0.000  1 OOO 0 984 0. 728 0. 455 0. 338 0. 163 O.OOO  a(A) 4 . 7547(4)* 4 .7552(2) 4 7763(3) 4 .7977(2) 4 .7990(3) 4 .8153(2) 4 8205(4)  b(A)  c(A)  10.1985(8) 10.1981(5) 10.2806(9) 10.3642(5) 10.3670(6) 10.4479(7) 10.4758110)  5 .9816(5) 5 .9812(2) 6 .0154(4) 6 .0476(3) 6 0481(3) 6 .0780(3) 6 .0881(6)  V( A' )  * OF PEAKS  290.06(3) 290.05(2) 295.38(3) 300.72(2) 300.90(2) 305 78(2) 307.44(4 )  22/8 12/5 17/8 22/ 10 25/ 1 1 21/16 18/7  * *  In p a r e n t h e s e s i s one s t a n d a r d e r r o r of r e g r e s s i o n as a p p l i e d t o the l a s t s i g n i f i c a n t d i g i t l i s t e d . K peaks / K ot i peaks CL I  Comparing the c e l l parameters of o l i v i n e s taken from a b r a c k e t i n g  p a i r of exchange runs (each  having the same i n i t i a l o l i v i n e composition) i n d i c a t e d t h e i r XRD s i g n a t u r e  that  was dominated by an o l i v i n e core  composition i d e n t i c a l t o the i n i t i a l c o m p o s i t i o n . Since the c o n t r i b u t i o n of the rim composition t o XRD peak p o s i t i o n s could be a n t i c i p a t e d to be g r e a t e s t  a t low a n g l e s , the c e l l  refinements were repeated using only peaks above 4O°20. The r e s u l t s are l i s t e d  i n t a b l e 1.5. Note that the c e l l  parameters of o l i v i n e s from runs 142 and 143 a r e almost i n d i s c e r n a b l e from each other d e s p i t e than 0.1 X,  rim compositions more  a p a r t . Regression of u n i t c e l l volume  (using  44  i n i t i a l  o l i v i n e compositions) to a q u a d r a t i c  i n X^ a , f o r the  sake of d i r e c t comparison with Schwab and Kiistner's 3  regression, resulted in V ( A ) = 2 9 0 . 0 4 ( ± . 0 4 ) + l8.8(±.2)Xf 1.4(±.2)X| . T h i s equation and the V E X indiscernable  -  i m p l i e d by i t i s  from that of Schwab and Kiistner (1977) . The  r e s u l t s of r e g r e s s i o n while h o l d i n g Wv  of the remaining model parameters  constant at O.OlU/bar are a l s o presented  i n t a b l e 1.4. The s o l i d l i n e s on f i g u r e 1.8 are c a l c u l a t e d from Model B.  45  J  L  2m Chloride  600°C  2kb  800°C  2kb  •1-  ^  - 2 -  -3-  -4 0.0  0.2  0.4  0.6  0.8  1.0  Xfo Figure 1.8  l n K ^ vs  curves c a l c u l a t e d  : 2m c h l o r i d e  ion-exchange data and  with Model B combined with the  f i r s t - d i s s o c i a t i o n model with the same values of T, P and mT«  See f i g u r e 1.6  f o r e x p l a n a t i o n of symbols, (a) Data at  600°C (2kb) and 800°C  (2kb).  46  F i g u r e 1.8  (b) Data at 450°C (1kb)  and  725°C  (2kb).  -1  0.0  F i g u r e 1.8  1  r  1  1  |-  0.2  0.4  0.6  0.8  1.0  (c) Data at 600°C (Ikb) and  600°C  (4kb).  48 DISCUSSION  THE  CHLORIDE:  The  remaining u n c e r t a i n t i e s i n the behavior of the  aqueous c h l o r i d e s o l u t i o n render mineral-aqueous c h l o r i d e ion-exchange experiments  such as these of l i m i t e d use i n  determining the a b s o l u t e value of endmember and  solid  solution properties for a single mineral. U n t i l  these  u n c e r t a i n t i e s are removed (by independent research) t h i s experimental medium i s best used f o r comparison of mineral p r o p e r t i e s using the aqueous c h l o r i d e as a 'common denominator'. If the f i r s t - d i s s o c i a t i o n model i s c o r r e c t i n form, then u n c e r t a i n t i e s i n the d e t a i l s of t h i s model should have little  e f f e c t on the s o l i d s o l u t i o n model d e r i v e d from the  ion-exchange experiments. The  'excess' p r o p e r t i e s of the  s o l i d s o l u t i o n are d e r i v e d only from the v a r i a t i o n of with  KQ  (mineral) composition and not from the a b s o l u t e value  of K D » F i g u r e I.5a  shows t h a t , f o r aqueous e l e c t r o l y t e  s o l u t i o n s resembling the f i r s t - d i s s o c i a t i o n model, K D  i s at  most weakly dependent on the composition of the aqueous solution  (at constant t o t a l m o l a l i t y ) . The  strongest e f f e c t  of u n c e r t a i n t i e s i n the f i r s t - d i s s o c i a t i o n model i s i n the value of Kg, the e q u i l i b r i u m constant f o r the model ion-exchange r e a c t i o n . F i g u r e I.5b  shows that t h i s e f f e c t i s  49 minimized  at high t o t a l m o l a l i t i e s . As a r e s u l t of t h i s  uncertainty in  , endmember thermodynamic p r o p e r t i e s f o r  the s o l i d s o l u t i o n c o u l d not be unambiguously c a l c u l a t e d from the ion-exchange e q u i l i b r i u m d a t a . T h i s would be true even i f the thermodynamic p r o p e r t i e s of the endmember n e u t r a l c h l o r i d e s p e c i e s had been determined The  independently.  f i r s t - d i s s o c i a t i o n model assumes that Mg and Fe  endmembers of otherwise  i d e n t i c a l aqueous s p e c i e s i n t e r a c t  i d e n t i c a l l y with the s o l v e n t . I t a l s o assumes that these Mg and Fe endmember s p e c i e s i n t e r a c t i d e a l l y with each o t h e r . If e i t h e r of these assumptions i s i n e r r o r , then Mg-Fe s o l i d solution properties calculated d i r e c t l y ion-exchange experiments  from the  w i l l be i n e r r o r .  In s p i t e of a l l of these u n c e r t a i n t i e s , aqueous chlorides s t i l l  have u t i l i t y as an experimental medium f o r  e s t a b l i s h i n g mineral p r o p e r t i e s . The use of a c h l o r i d e aqueous s o l u t i o n as an ion-exchange phase reduces the difficulties  inherent i n performing the experiments:  s y n t h e s i s of s t a r t i n g m a t e r i a l s ; attainment  of e q u i l i b r i u m ;  measurement of c o m p o s i t i o n s . I f m i n e r a l - c h l o r i d e exchange e q u i l i b r i a a r e determined P and T (and mT)  s e p a r a t e l y over the same range of  using the same binary s o l u t i o n of aqueous  c h l o r i d e s , then the r e l a t i v e thermodynamic p r o p e r t i e s of these minerals can be determined the aqueous s o l u t i o n  without dependence on how  i s t r e a t e d . If the a b s o l u t e p r o p e r t i e s  of one of these m i n e r a l s i s known from independent e v i d e n c e , then the absolute p r o p e r t i e s of the remaining phases can be  50 estimated.  THE  OLIVINE-.  F i g u r e 1.9 i l l u s t r a t e s the temperature dependence of W^ and WH  f o r Model B a t 1bar. Comparison with the t h e o r e t i c a l  unmixing l i m i t f o r a symmetrical Margules f o r m u l a t i o n (W^ = 2RT) shows that Model B p r e d i c t s a s o l v u s c r i t i c a l p o i n t at about 400°C. Although comparison of t h i s model with the 2molal ion-exchange data model may s t i l l  Functional  be judged  inadequate:  a s y m p t o t i c a l l y approaches zero at high  temperatures. For a s o l i d s o l u t i o n approaching behavior as a high temperature l i m i t , Wu similar  Calorimetry.  solution  The model f o r W^, smoothly and  Form'.  more-or-less  ( f i g u r e 1.8) i s f a v o r a b l e , t h i s  'ideal'  should have a  f u n c t i o n a l form.  The v a l u e s of Wu  p r e d i c t e d by Model B are  i n c o n s i s t e n t with a l l of the c a l o r i m e t r i c c o n s t r a i n t s on  Wu.  To review; HF c a l o r i m e t r y at 345K found no evidence of excess enthalpy of mixing  (±1400J i n W^;  Sahama and  Torgeson, 1949), Pb-borate melt s o l u t i o n - c a l o r i m e t r y at 970K was i n t e r p r e t e d t o be c o n s i s t e n t with an asymmetric  solution  model with Wu(Mg) * 4200J and W „ ( F e ) * 8400J (±2500J i n Wu; Wood and Kleppa,  1981), and (Na,Li)-borate m e l t - c a l o r i m e t r y  at 1180K d i d not d e t e c t an enthalpy of mixing  significant  51  18000 -  14000 -  10000 0)  6000  2000-  -2000 -  i  400  F i g u r e 1.9  600  and WH  800  1 1000  r  1200  1400  Temperature(K)  1600  1800  c a l c u l a t e d u s i n g the f i t parameters  l i s t e d under Model B i n t a b l e 4. See a l s o equations (23) through ( 2 5 ) .  52 compared to the e r r o r b r a c k e t s of t h e i r methods (±4000J f o r WH;  T h i e r r y , et a l , 1981). Even compared to the l a r g e r of  the two WH  values c a l c u l a t e d by Wood and Kleppa(1981), Model  B d i f f e r s by a f a c t o r of 2. At 1180K, Model B i s s t i l l a f a c t o r of 2 away from c o n s i s t e n c y with c a l o r i m e t r y . The HF c a l o r i m e t r y i s g r o s s l y i n c o n s i s t e n t with Model B, but i t was performed at a temperature  f a r from the range covered by the  present s t u d y . On the other hand, the c a l o r i m e t r y of Wood and  Kleppa(l98l)  and T h i e r r y  et a l ( l 9 8 l )  was performed at  temperatures o v e r l a p p i n g the present study and should i d e a l l y be i n c l u d e d as c o n s t r a i n t s on the o l i v i n e  solution  model. These remaining problems are addressed i n the next chapter.  I I . A p p l i c a t i o n to Orthopyroxene, Orthoamphibole  and T a l c  and Comprehensive A n a l y s i s  INTRODUCTION  The experimental methods and t h e o r e t i c a l models e s t a b l i s h e d i n the study of s y n t h e t i c Fe-Mg o l i v i n e s have been a p p l i e d to the study of 3 other s y n t h e t i c Fe-Mg s i l i c a t e s : orthopyroxene, orthoamphibole, and t a l c . These m i n e r a l s can be seen t o be l o g i c a l c h o i c e s f o r pragmatic a p p l i c a t i o n of the Fe-Mg c h l o r i d e exchange e q u i l i b r i u m technique based upon c o n s i d e r a t i o n of experimental and t h e o r e t i c a l p r a c t i c a l i t i e s and the need f o r p r a c t i c a l a p p l i c a t i o n of the r e s u l t s to n a t u r a l assemblages. Although the t h e o r e t i c a l t o o l s being used can be a p p l i e d to multicomponent s o l i d  (and aqueous) s o l u t i o n s , the study of  multi-component systems  i s best preceeded by thorough  understanding of the b i n a r y subsystems. T h e r e f o r e , components o u t s i d e the Mg0-Fe0-Si0 2 -H 2 0-HCl system are u n d e s i r a b l e u n t i l the p r o p e r t i e s of m i n e r a l s w i t h i n  this  system are understood. In the p r e v i o u s c h a p t e r , t h e o r e t i c a l i n t e r p r e t a t i o n of the r o l e of the aqueous s o l u t i o n i n o l i v i n e - a q u e o u s c h l o r i d e ion-exchange  experiments has shown  that the p r o p e r t i e s of the Fe-Mg c h l o r i d e aqueous s o l u t i o n are s t i l l  incompletely understood. Therefore a p p l i c a t i o n of  the technique i s best r e s t r i c t e d to the P-T regime of the olivine  ion-exchange  experiments. Fe-Mg orthopyroxenes,  53  54 orthoamphiboles and t a l c s have a l r e a d y been shown to a l l be: (1) p o s s i b l e to s y n t h e s i z e w i t h i n the MgO-FeO-Si0 2 -H 2 0 system (Greenwood, 1963; H e l l n e r et a l , Popp et a l , P-T  1965; F o r b e s , 1969;  1976); (2) s t a b l e over at l e a s t a p o r t i o n of the  range covered i n the o l i v i n e  ion-exchange experiments  (Greenwood, 1963; F o r b e s , 1971a; Ravior and H i n r i c h s e n , 1975; Chernosky, 1976; Popp et a l ,  1977; Chernosky and  A u t i o , 1979; Chernosky et a l , submitted f o r p u b l i c a t i o n ) ; (3) s u f f i c i e n t l y common i n n a t u r a l assemblages to be r e f e r r e d to as 'rock forming m i n e r a l s ' (Deer et a l ,  1966).  T h i s system of 4 m i n e r a l s ( i n c l u d i n g o l i v i n e ) has the unusual d i s t i n c t i o n of being represented i n nature as major m i n e r a l s i n rocks c o n t a i n i n g only very minor amounts of components o u t s i d e the s y n t h e t i c subsystem: i . e . metamorphosed p e r i d o t i t e s  (see Trommsdorff and Evans, 1974).  The orthopyroxene Fe-Mg s o l i d s o l u t i o n has r e c e i v e d considerable attention still  some u t i l i t y  i n the l i t e r a t u r e . However, there i s  i n f u r t h e r experimental and  theoretical  s c r u t i n y of Fe-Mg orthopyroxenes. The bulk of the p u b l i s h e d s t u d i e s are d i r e c t e d toward documentation, experimental c a l i b r a t i o n and t h e o r e t i c a l m o d e l l i n g of Fe-Mg i n t e r c r y s t a l l i n e exchange between orthopyroxene and C a - r i c h c l i n o p y r o x e n e , o l i v i n e , or garnet (see Deer et a l ,  1978;  Sack, 1980). The i n t r a c r y s t a l l i n e exchange of Fe and Mg between the M1 and M2 o c t a h e d r a l s i t e s i s a l s o w e l l documented (see Appendix G ) . The experimental s t u d i e s of intercrystalline  ion-exchange have few c o n t r i b u t i o n s to  55 o f f e r f o r temperatures below 800°C. Sack(1980), i n f o r m u l a t i n g a s o l u t i o n model c o n s i s t e n t with both the i n t r a c r y s t a l l i n e and i n t e r c r y s t a l l i n e d a t a , was f o r c e d to i n c l u d e s e v e r a l approximations and assumptions. The c h o i c e of orthorhombic over m o n o c l i n i c Fe-Mg amphiboles  i s not n e c e s s a r i l y the most pragmatic  i f based  upon n a t u r a l occurrences a l o n e . Occurrences of n a t u r a l anthophyllites  (low i n A l and a l k a l i s ) only span about 35%  of the composition range between Mg and Fe endmembers (Rabbit, 1948; Deer et a l , 1963). N a t u r a l cummingtonites cover 85% of the Fe-Mg s o l u t i o n  (Deer et a l , 1963; K l e i n and  Waldbaum, 1967; Rice et a l , 1974). The d e c i s i o n t o study Fe-Mg orthoamphiboles i s based upon experimental f e a s i b i l i t y and maximum u t i l i t y . I t has been proven p o s s i b l e t o s y n t h e s i z e orthorhombic amphiboles solid solution  over 86% of the Fe-Mg  (Popp et a l , 1976). S y n t h e s i s of pure  F e - g r u n e r i t e has only been accomplished with d i f f i c u l t y and low y i e l d s  (Forbes, 1971b). S y n t h e s i s of i n t e r m e d i a t e Fe-Mg  cummingtonites  has only been accomplished by adding small  amounts of CaO (Schiirmann, 1966; Cameron, 1975); an undesired a d d i t i o n a l component. Phase e q u i l i b r i u m experiments d e l i n e a t i n g m i n e r a l s t a b i l i t i e s  i n the Mg  end-member system have a l l been conducted using amphiboles  orthorhombic  ( F y f e , 1962; Greenwood, 1963; Chernosky and  A u t i o , 1979; Chernosky  et a l , s u b m i t t e d ) . Thermodynamic  c h a r a c t e r i z a t i o n of the orthoamphibole Fe-Mg s o l i d i s thus a d i r e c t e x t e n s i o n of the Mg endmember  solution  studies.  56 The  range of Fe-Mg compositions covered here i n  studying orthoamphibole  and t a l c  i s c o n s i d e r a b l y wider  than  the p o p u l a t i o n of n a t u r a l c o m p o s i t i o n s . The u t i l i t y of t h i s approach  i s to maximize the ' l e v e r a g e ' the data has on the  s o l i d s o l u t i o n p r o p e r t i e s . T h i s approach a l s o w i l l h e l p d e f i n e the true s t a b i l i t y of each mineral as opposed to the p r o b a b i l i t y of i t s occurrence based upon the d i s t r i b u t i o n of n a t u r a l bulk c o m p o s i t i o n s .  EXPERIMENTAL  TECHNIQUES  The hydrothermal ion-exchange  apparatus, s t a r t i n g  materials,  experimental t e c h n i q u e s , and methods employed  for c o m p o s i t i o n a l measurements are v i r t u a l l y  i d e n t i c a l to  those employed i n the o l i v i n e - a q u e o u s c h l o r i d e s t u d y . Any d i f f e r e n c e s are n o t e d . The Chapter  I and the appendices  ion-exchange  reader i s r e f e r r e d to  for d e t a i l s .  SYNTHESES:  In c o n t r a s t to the Fe-Mg o l i v i n e s y n t h e s e s , a l l syntheses employed hydrothermal  t e c h n i q u e s . In most cases an  aqueous s o l u t i o n of Mg-Fe c h l o r i d e s was the i n t e n t of i n c r e a s i n g r e a c t i o n and  used as a f l u x with  recrystallization  rates.  Orthopyroxene:  Oxide mixes on orthopyroxene  compositions at X ° ^  x  = 1.0,  0.8,  0.6  and 0.4  bulk were s e a l e d  57 i n t o g o l d capsules along with a 2molal aqueous c h l o r i d e f l u x . The capsules were kept at 800°C (±10°) and 2kb for 16 days. The s y n t h e s i s products were a l l ' c o a r s e l y ' c r y s t a l l i n e with i n d i v i d u a l p r i s m a t i c g r a i n s up t o 4mm l o n g . XRD p a t t e r n s f o r these products contained only peaks a t t r i b u t a b l e to orthopyroxene.  O p t i c a l examination  revealed  t r a c e s of o l i v i n e or q u a r t z . A p o r t i o n of each s y n t h e s i s was set a s i d e f o r microprobe a n a l y s i s and the remainder was ground t o a g r a i n s i z e <1(DMm. Using standard  analysis  t e c h n i q u e s , microprobe analyses of the i n t e r m e d i a t e composition  s y n t h e s i s products  r e v e a l e d that most g r a i n s  were s l i g h t l y zoned. Averages of 15 evenly analyses gave f i n a l compositions and  distributed  at 0 . 3 7 0 ± 0 . 0 2 5 , 0.570±0.024  x  0.770±0.025 (X°P ±1a). The d i s c r e p a n c y between mix  compositions  and f i n a l compositions  with the aqueous c h l o r i d e  i s due t o ion-exchange  flux.  Six orthoamphibole compositions  Orthoamphibole:  1  from X^*"*  = 0.1 t o 1.0 were s y n t h e s i z e d using a v a r i e t y of s y n t h e s i s s t r a t e g i e s . Appendix F c o n t a i n s the d e t a i l s of the s y n t h e s i s runs and c h a r a c t e r i z a t i o n of the p r o d u c t s . The techniques employed f o r phase c h a r a c t e r i z a t i o n  i n c l u d e powder XRD,  e l e c t r o n d i f f r a c t i o n and high m a g n i f i c a t i o n TEM imaging. The  s y n t h e s i s products a r e a l l f i n e l y  f i b r o u s . The  i n d i v i d u a l a c c i c u l a r g r a i n s a r e up to 80Mm long and seldom g r e a t e r than  1 jum i n diameter. Chemical a n a l y s i s of the  aqueous run f l u i d enabled product amphibole compositions t o  58 be a c c u r a t e l y c a l c u l a t e d by mass-balance. U n i t refinements  of the s y n t h e s i s products  cell  revealed discrepancies  i n c e l l dimensions ( p r i m a r i l y the a-repeat) when compared to n a t u r a l a n t h o p h y l l i t e s . C h a i n - s t a c k i n g d i s o r d e r i s proposed as the primary cause of the c e l l dimension d i s c r e p a n c i e s . The  TEM  study q u a l i t a t i v e l y supports  Four t a l c compositions  Talc:  this  theory.  were s y n t h e s i z e d at 2kb  using  talc a -Imolal aqueous c h l o r i d e f l u x . Mix 0.5,  0.7,  0.9,  and  1.0  compositions  were heated at 450,  525,  at  XMg  610  and  700°C r e s p e c t i v e l y . S y n t h e s i s d u r a t i o n s ranged from 7 days for  the Mg  endmember to 16 days for the most F e - r i c h  c o m p o s i t i o n . The grained  s y n t h e s i s products  (<5um). Powder XRD  were a l l very  patterns contained  fine  only  talc  peaks. O p t i c a l examination r e v e a l e d t r a c e s of quartz as  the  only impurity in a l l s y n t h e s i s p r o d u c t s . A sample of each intermediate composition analyzed  t a l c was  f o r Fe and Mg with standard  t e c h n i q u e s . The measured f i n a l 0.531, 0.740, and ION-EXCHANGE  The  d i g e s t e d i n HF + H C 1 0 „  flame atomic a b s o r p t i o n talc  compositions  are  0.926 ( ± 0 . 0 0 5 ) . EXPERIMENTS:  techniques  employed i n conducting  the  ion-exchange  experiments are i d e n t i c a l to those employed i n the study  and  excepting  the s e p a r a t i o n of run f l u i d  orthoamphibole run p r o d u c t s . The p o r o s i t y of these experimental  olivine  from t a l c  and  high s u r f a c e area and  charges prevented  direct  high  59 e x t r a c t i o n of the aqueous f l u i d by c e n t r i f u g i n g . F o l l o w i n g each t a l c and orthoamphibole ion-exchange experiment the capsule was c l e a n e d , cut open with a l e n g t h - p a r a l l e l c u t , and p l a c e d i n a c e n t r i f u g e v i a l c o n t a i n i n g 700yl of water. An u l t r a s o n i c bath was used to ensure thorough washing of the c h a r g e . A f t e r removing the empty c a p s u l e , the v i a l contents were c e n t r i f u g e d and the supernatant s o l u t i o n  was  drawn o f f f o r a n a l y s i s . For each m i n e r a l , the ion-exchange experimental temperatures were r e s t r i c t e d to a range in which the m i n e r a l is stable  (or p e r s i s t e n t l y metastable) over at l e a s t 50% of  i t s Fe-Mg s o l i d  FINAL  Orthopyroxene:  solution.  COMPOSITIONS'.  The products of orthopyroxene ion-exchange  experiments g e n e r a l l y included g r a i n s l a r g e enough f o r standard microprobe a n a l y s i s . However, l i k e the s y n t h e s i s p r o d u c t s , these g r a i n s were found to be c h a r a c t e r i z e d by minor, but s i g n i f i c a n t , Fe-Mg z o n i n g . F i n a l compositions s u i t a b l e f o r b r a c k e t i n g the ion-exchange e q u i l i b r i u m had to be obtained using an a n a l y s i s technique which  preferentially  samples g r a i n .edges. Both p a r t i c l e a n a l y s i s and  crystal-face  a n a l y s i s techniques were used.  Orthoamphibole:  F i n a l orthoamphibole compositions were  60 e s t a b l i s h e d with a powder XRD c a l i b r a t i o n curve f o r  dn. 0  0  T h i s peak was chosen s i n c e i t depends only on the b c e l l repeat which, of the three strongest XRD c e l l  orthogonal axes, e x h i b i t s the  dependence on Mg-Fe s u b s t i t u t i o n . Although powder refinements and e l e c t r o n microscopy i n d i c a t e the  presence of chain-arrangement f a u l t s  i n the s y n t h e t i c  s t a r t i n g m a t e r i a l s , comparison with n a t u r a l and  anthophyllites  other s y n t h e t i c s i n d i c a t e s that the fe-repeat i s not  s t r o n g l y a f f e c t e d by the presence of these f a u l t s (see Appendix F ) . F i g u r e full cell The in  II.1  shows the d ^ 0  values d e r i v e d  Q  refinements of the s y n t h e t i c s t a r t i n g  c a l i b r a t i o n curve i s a l e a s t - s q u a r e s th  x5" Mg  from  materials.  f i t of a q u a d r a t i c  nth  t o a l l but the datum at x5 =0.9. I t s formula i s Mg  rfo«o = 4.616 - 0 . l 8 5 X M g + 0.049X^ g . I n d i v i d u a l peak measurements using d i g i t a l  peak-seeking procedures and  quartz as an i n t e r n a l standard a r e accurate t o ±0.01°26 (CuKa, see a l s o Appendix D). The f i n a l estimated t o be accurate t o ±0.03 i n  compositions a r e nt  xf. ^. The measured Mg  values of d  0llQ  are l i s t e d  i n t a b l e I I . 1. The d t  o u o  f o r the  1  s y n t h e t i c orthoamphibole at X^g ^ =0.9 does not conform t o the c a l i b r a t i o n c u r v e . Examination of t h i s s y n t h e t i c with TEM has revealed  an anomalously high amount of  chain-width d i s o r d e r . T h i s type of s t r u c t u r a l d e f e c t not  'anneal out'  product  will  since t h i s would r e q u i r e a n e t - t r a n s f e r  r e a c t i o n . F i n a l orthoamphibole compositions f o r experiments using  this s t a r t i n g material  were measured v i a  a c i d - d i g e s t i o n p l u s atomic a b s o r p t i o n ,  or c a l c u l a t e d v i a  61  I  1  0.0  1  0.2  X F i g u r e II.1 Values of  0.4  1  0.6  1  0.8  M g  (orthoamphibole)  d0k0  measured f o r the s y n t h e t i c  1  1.0  orthoamphibole s t a r t i n g m a t e r i a l s . The c a l i b r a t i o n curve i s a quadratic  in XMg  f i t to a l l measured values excepting  for the s y n t h e t i c at X M o - 0 . 9 .  that  62 Table I I . 1  Orthoamphibole d  0ll0  v a l u e s measured f o r  ion-exchange run p r o d u c t s . d no(A)  RUN#  d no(A)  RUN#  0  0  255  4.540  307  4.505  257  4.531  308  4.502  309  4.551  249  4.500  310  4.597  250  4.535  31 1  4.598  251  4.518  252  4.558  280  4.530  253  4.544  281  4.499  254  4.501  282  4.508  283  4.559  305  4.501  284  4.537  306  4.500  285  4.504  mass-balance.  F i n a l t a l c compositions  Talc:  were a l s o measured using a  powder XRD c a l i b r a t i o n . The d 03 peak (one l a y e r , 0  cell  indexing) was chosen f o r c a l i b r a t i o n  reflections and  triclinic  s i n c e the b a s a l  were the only peaks which proved t o be strong  sharp f o r a l l of the s y n t h e t i c t a l c s . Since the d o 3 0  peaks were s t r o n g , sharp and i n t e n s i f i e d by p r e f e r r e d o r i e n t a t i o n , a 28 accuracy  of ±0.003° was t y p i c a l l y  o b t a i n e d . F i g u r e II.2 shows d 3 00  values measured f o r the  s y n t h e t i c s t a r t i n g m a t e r i a l s and a l i n e a r c a l i b r a t i o n with the formula are d  Q03  d  0 0 3  curve  = 3.1442-0.0278X Mg . A l s o i l l u s t r a t e d  v a l u e s f o r s e v e r a l n a t u r a l t a l c s and other  synthetic talcs  (see f i g u r e c a p t i o n f o r r e f e r e n c e s ) . The  63  XM 9  Figure  (talc)  II.2 Measured v a l u e s of t a l c cf0 0 3 and the l i n e a r  c a l i b r a t i o n curve f i t to the s y n t h e t i c  starting  produced i n the present study. The f i l l e d  materials  symbols represent  these s y n t h e t i c s . The open symbols represent s y n t h e t i c from Chernosky et a l ( s u b m i t t e d ) and Forbes(1969). hatched  The  symbols represent n a t u r a l t a l c s from Rayner and  Brown(l973) and K i o s h i and G i l l e s ( 1 9 7 9 ) .  talcs  64 fi?003  values measured f o r the experimental run products a r e  listed  i n t a b l e I I . 2 . F i n a l t a l c compositions are estimated  to be a c c u r a t e t o ±0.03 i n 3LV*  Table II.2 T a l c  d003  .  values measured f o r  ion-exchange run p r o d u c t s . RUN#  d0o3(A)  RUN#  d003(A)  222  3.1291  238  3.1218  292  3.1267  239  3.1212  293  3.1230  286  3.1189  294  3. 1174  287  3. 1177  313  3.1233  289  3. 1279  314  3.1195  290  3.1256  237  3. 1255  DATA ANALYSIS  Table I I . 3 l i s t s a l l of the data gathered f o r those ion-exchange experiments  judged c r i t i c a l  f o r b r a c k e t i n g the  ion-exchange e q u i l i b r i a . The l a s t column i n t a b l e I I . 3 represents the r e s u l t s of the f i r s t  step of the data  a n a l y s i s p r o c e d u r e . To f a c i l i t a t e comparison of the three crystalline  s o l u t i o n s with each o t h e r , and with the Mg-Fe  o l i v i n e d a t a , each exchange e q u i l i b r i u m was modelled  as a  r e a c t i o n of Mg and Fe endmember m i n e r a l s with the n e u t r a l c h l o r i d e s p e c i e s . Each of these r e a c t i o n s was balanced with  Table 11.3. Ion-exchange run d a t a . A l l experiments were performed a t 2kb.  1  RUN*  T('C)  HOURS  - - -INITIAL- - SOLID FLUID X„ X,. Mg Mg  mT T  MINOR PRODUCT PHASES  - - - - - FINAL SOLID . X„ Cl/Mg+Fe 3 Mg  - - - - - - - - - - - - - - - - FLUID X,. HOW 1 nK_. 1o Mg D  t  InK. D  ORTHOPYROXENE EXPERIMENTS 264  680  719  0 .370  0 OOO  2 .0 2  0 . 06 1  0 .00  0 . 345  P  -2 .09  0 . 12  - 1. 92  265  680  719  0 . 370  O .500  2 .0  OA  0 . 108  0 .00  0 .567  P  -2 . 38  O .08  -2 .21  266  680  7 19  0 . 570  0 . 500  2 .0  OA  0 . 197  0 .00  0 .689  P  -2 .20  0 .09  -2 .03  267  680  883  0 . 770  0 .000  2 .0  TA  0 . 183  0 .00  0 . 738  P  -2 .53  0 . 12  -2 . 36  268  680  883  0 . 770  0 . 700  2 .0  0 . 440  0 .00  0 . 886  P  -2 . 29  0 . 25  -2 . 1 1  269  680  883  1.000  0.. 100  2 .0  0 . 4 16  0 .00  0 .937  P  -3 .04  0 . 16  -2 .86  277  680  833  0 . 370  O..212  2 .0  0  0 .063  1.98  0.. 400  P  -2 . 29  0 .08  -2 . 12  278  680  833  0. 770  0 412  2 .0  0  0 .258  1 98  0. 818  P  -2 .56  0 .09  -2 . 38  279  680  833  1 .000 .  0. 105  2 .0  0 . 345  1 97  0. 896  P  -2 . 79  0 . 18  -2 . 62  228  800  300  0.. 370  0. 000  2 .0  0  0 .066  1 .98 .  0. 466  F  -2 ..51  0.06  -2 . 35  229  800  300  0. 370  O. 300  2 .0  0  0 .092  0.00  0. 527  F  -2 40  0 06  -2 . 24  230  800  300  0..570  O. 500  2 .0  0  0 195  1 .96  0.750  P  -2 ..52  0.09  -2 . 36  231  800  302  0. 770  0.000  2 .0  0  0. 232  1 . 86  0. 788  P  -2 .51  0.06  -2 . 35  232  800  302  0. 770  0. 700  2 .0  0  0. 296  0.OO  0.874  P  -2 .80  0. 14  -2 .64  233  800  302  1 . 000  0. 100  2 O  0.542  0.00  0.966  P  -3 . 18  0 16  -3 02  0. 105  2 .01  0. 465  X  -2 00  0. 13  - 1 86 .  UH0AMPH1BOLE EXPERIMENTS 255  600  1475  0. 509  0.000  2 .0  257  600  1475  0. 339  O.700  2 .0  0  0. 156  2 .07  0. 517  M  - 1 76 .  0.06  - 1 61 .  309  600  904  0. 339  0. 210  2 .0  0  0.084  0.00  0.391  X  - 1 95 .  0. 13  - 1 81 .  310  600  904  0. 102  0. 1 14  2 .0  0  0.020  0.00  0. 105  X  - 1 75 .  0. 32  - 1 6. 1  Table 11. 3.  RUN*  (continued)  T('C)  HOURS  - - -INITIAL- - SOLID FLUID X,. X,. Mg Mg  mT T  MINOR PRODUCT PHASES  - - - - - FINAL SOLID Xu Cl/Mg+Fe Mg  - - - - - - - - - - - - - - - - FLUID Xu HOW 1 nK n \a Mg u  „ lnKn 0  31 1  600  904  0 . 102  0 OOO  2 .0  0  0 .018  0 .00  0 .093  X  -1 . 72  0 . 36  - 1. 58  252  650  1473  0 . 339  0 .000  2 .0  0  0 .049  2 .00  0 . 347  X  -2 . 33  0 . 14  -2 . 16  253  650  1473  O . 339  0 .500  2 .0  OP  0 .077  1.94  0 . 442  X  -2 . 25  0 . 13  -2 .07  254  650  1473  0 . 509  0 . 700  2 .0  OP  0 .196  1.98  0 . 787  X  -2 . 72  0 . 18  -2 . 54  283  650  1550  0 . 339  0 . 208  2 .0  0  0 .059  1.92  0 341  X  -2 . 1 1  0 . 14  - 1.93  284  650  1550  0 .509  0 .000  2 .0  0  0 .090  1.87  0 . 485  X  -2 .25  0 . 13  -2 .08  285  650  1550  0 . 753  0 . 101.  2 .0  0  0.. 177  1.91  0 . 754  X  -2 .66  0 . 17  -2 . 48  307  650  7 10  0 .907  0 .608  2 .0  TA  0..566  0 .00  0 .939  W  -2 .47  0 . 10  -2 . 27  308  650  7 10  O . 907  0 314  2 .0  TA  0. 347  0 .00  0 923  M  -3 . 12  0. 15  -2 . 93  249  700  497  0. 509  0 . 500  2 .0  OL  0. 280  0 .00  0 . 798  X  -2 . 32  0 . 19  -2 . 14  250  700  497  0. 509  0..000  2 .0  0+OL  0. 096  0 00  0. 505  X  -2 26  0 13  -2 .08  251  700  497  0. 753  0. .000  2 .0  0  0. 185 .  1..95  0. 743  X  -2 . 54  0.. 16  -2 . 36  280  700  833  0. 509  O. 311  2 0  OP  0. 103  1. 99  0. 543  X  -2 . 34  0. 13  -2 . 16  281  2 .0 .  OP  0. 259  2 . 17  0. 808  X  -2 . 49  0. 20  -2 ..31 -2 . 26  700  833  0. 753  0. 4 13  282  700  833  0. 753  0. 109  2 0  0. 182  1 99 .  0. 7 19  X  -2 . 44  0. 16  305  700  7 10  0. 907  O. 6 17  2 .0  o. 591  0. 00  0. 934  M  -2 . 28  O. 17  -2 . 09  306  700  710  0. 907  0. 259  2 .0  0. 426  0. 00  0. 916  W  -2 . 69  0. 08  -2 .,50  ILC EXPERIMENTS 222  400  1361  0. 531  O. 000  2 .0  OL  0. 115  1 92 .  0. 545  X  -2 . 22  0. 13  -2 82  292  400  1627  0. 531  0. 308  2 .0  0+OA  0. 21 1  0. 00  0. 630  X  - 1 85 .  0. 14  -2 . 44  293  400  1627  0. 740  0. 206  2 .0  0  0. 28 1  2 . 27  0. 761  X  -2 . 10  0. 17  -2 . 68  294  400  1627  O. 926  0. 51 1  2 .0  0  0. 515  2 . 34  0. 963  X  -3 . 20  0. 84  -3 . 76  Table I I . 3 .  (continued)  RUN*  T('C)  HOURS  313  - - -INITIAL- - SOLID FLUID X X  m  MINOR PRODUCT PHASES  - - - - - FINAL SOLID X Cl/Mg+Fe  - - - - - - - - - - - - - - - - FLUID X HOW 1 nK 1o  „ 1 nK  400  1907  0 . 740  0 .413  2 .0  0. 352  0 .00  0 . 753  X  - 1.72  0.. 17  -2 . 30  314  400  1907  0..926  0 .677  2 .0  0. 655  0 .00  0 .887  X  - 1.42  0. 30  - 1.97  237  500  7 18  0.. 531  0.. 500  2 .0  0  0. 207  1.89  0 .671  X  -2 .06  0. 14  -2 .04  238  500  7 18  0. 740  0 .000  2 .0  Q+OA  0. 124  0 .00  0 .804  X  -3 .37  0. 20 '  -3 . 35  239  500  7 18  0..740  0 .700  2 .0  0  0. 427  0 00  0 .828  X  - 1.87  0. 22  - 1.85 -2 . 39  286  500  161 1  0..926  0 .615  2 .0  0. 479  1.65  0. 911  X  -2 . 4 1  0. 37  287  500  1611  1 . OOO  0. 514  2 .O  0  0. 527  2 .06  0. 952  X  -2 . 88  0. 66  -2 .86  289  500  161 1  0. 531  O.OOO  2 .0 .  OA+0  0. 1 19  2 .00  0. 588  X  -2 . 36  0 13  -2 . 34  290  500  1611  0. 531  0. 355  2 .0 .  OA+0  0. 108  2 .02  0. 669  X  -2 .82  0. 14  -2 . 79  Method of f i n a l F=crystal  X,, d e t e r m i n a t i o n : M=mass b a l a n c e , S=standard microprobe, Mg f a c e a n a l y s i s , X=XRD c a l i b r a t i o n , W=wet chemistry.  OA = orthoamphibo 1e, OP = orthopyroxene,  TA = t a l c , and 0 = q u a r t z .  P=particle analysis,  68 one  mole of Fe and  equation  Mg  on each side of the  reaction  (5) in the p r e v i o u s c h a p t e r ) . For  the c o n c e n t r a t i o n s c a l c u l a t e d using  (see  each experiment,  of the n e u t r a l c h l o r i d e species were the  f i r s t - d i s s o c i a t i o n model (see Chapter  I ) . Given these c o n c e n t r a t i o n s , a new d i s t r i b u t i o n * coefficient, , was c a l c u l a t e d . The r e s u l t s of a p p l y i n g same procedure to the listed  in t a b l e I I . 4 . The *  of these K D properties any  2molal o l i v i n e - c h l o r i d e data following  are  thermodynamic a n a l y s i s  values r e s u l t s in c a l c u l a t i o n of thermodynamic for a h y p o t h e t i c a l  f a l l a c i e s of the  (Mg,Fe)Cl 2 phase (subject  f i r s t - d i s s o c i a t i o n model). Since  a b s o l u t e p r o p e r t i e s of e i t h e r end-member of hypothetical the  the  phase cannot be  the  this  independently e s t a b l i s h e d , only  ' d e l t a ' p r o p e r t i e s , d i f f e r e n c e s between the  endmembers, are  to  two  calculated.  Thermodynamic a n a l y s i s of the  ion-exchange data  was  made comprehensive by adding these data d i r e c t l y to a mineral data base ( f o r the Si0 2 -MgC—Fe-C-O-H system) e s t a b l i s h e d by Engi et a l ( l 9 8 4 ) . The  generous c o o p e r a t i o n of  Dr. Martin Engi i s acknowledged. T h i s computer data base system simultaneously c o n s i d e r s  net-transfer  e q u i l i b r i u m d a t a , c a l o r i m e t r i c d a t a , and  phase  both n a t u r a l  and  experimental ion-exchange e q u i l i b r i u m data compiled from l i t e r a t u r e . The e s t a b l i s h e d by  g e n e r a l features of t h i s data base, as i t s a u t h o r s , are as  follows:  the  69  * Table I I . 4 . LnK D values c a l c u l a t e d f o r a l l o l i v i n e + 2m c h l o r i d e ion-exchange experiments. RUN#  *  RUN#  lnKD  InK*  RUN#  *  lnKD  1 42  -0..40  1 45  0..34  1 46  -1 .17  1 47  -3..17  1 63  0,.05  1 65  0 .29  11 6  -1 ,.55  1 22  -1 ..33  1 24  -1 .64  99  -1 ,.08  200  -1 ..39  25  -0 .26  26  -0,.69  27  -o,.70  37  -1 .31  38  -1 ,.57  39  -1,.64  40  -1 .41  41  -1 ,.76  42  -1,.67  43  -1 .10  64  -1 ,.85  66  -1.. 1 3  101  -0 .75  1 28  -0,.29  174  -1,.31  197  -0 .14  226  -o,.32  227  -0 .96  1  225  0,. 1 1  69  -1..40  70  -1,.41  71  -1 .84  72  -2..08  21 1  -1,.99  212  -1 .87  213  .72 -1 ,  75  -1,. 14  169  -2 .19  1 70  -2,.10  202  -1,.96  203  -1 .92  204  -2,.04  Computational  Method'.  The computational method i s  based upon a p p l i c a t i o n of MINOS (Modular In-core Nonlinear O p t i m i z a t i o n  System, Murtagh and Saunders,  1980). To g e n e r a l i z e : a l i n e a r programming a l g o r i t h m i s used t o f i n d a s o l u t i o n - s e t of thermodynamic parameters which i s i n t e r i o r t o i n e q u a l i t y c o n s t r a i n t s d e r i v e d net-transfer  e q u i l i b r i u m b r a c k e t s and i n e q u a l i t y  c o n s t r a i n t s bounding the a n a l y t i c a l e r r o r of c a l o r i m e t r i c data (see Halbach and C h a t t e r j e e , 1982; Berman et a l , 1984). Then an i t e r a t i v e  nonlinear  from  70 o p t i m i z a t i o n procedure squares  i s used to minimize the sum  of  of the r e s i d u a l s , f o r example, between  calculated  ion-exchange Kp's  and the ion-exchange  equilibrium data.  Fe-Mg  Solution  Included are  Minerals'.  olivine,  orthopyroxene, a n t h o p h y l l i t e , t a l c , m i n n e s o t a i t e , cummingtonite and s e r p e n t i n e .  Net-Transfer  Equilibrium  Constraints:  experimental brackets r e p r e s e n t i n g 20  195  individual  different  r e a c t i o n s are i n c l u d e d .  Bounds:  76 i n d i v i d u a l bounds on thermodynamic  parameters are i n c l u d e d . These bounds are d e r i v e d from c a l o r i m e t r y , u n i t c e l l volume measurements and theoretical considerations.  P r e s s u r e , temperature,  and  I on-Exchange  Data:  compositions  f o r 314 n a t u r a l and experimental  mineral  p a i r s are i n c l u d e d . However, to reduce the s i z e of the computational  task and to remove any  redundancy, the  data f o r each type of m i n e r a l p a i r has been grouped a c c o r d i n g to s i m i l a r i t i e s  i n P, T and c o m p o s i t i o n . Each  group i s represented i n the data base by a mean c a l c u l a t e d from the i n d i v i d u a l s i n the group. Each datum entered i n t o the data base i s assigned a weight which i s  71 used by the o p t i m i z a t i o n a l g o r i t h m . These weights are c a l c u l a t e d i n p r o p o r t i o n to the standard e r r o r inherent in each (average) v a l u e .  Heat  A heat c a p a c i t y equation m o d i f i e d by  Capacities'.  Berman et a l ( l 9 8 4 ) i s used.  c  P  = k0 + —  Solid  + —  cpO'5  Solution  rp 2  + —  (k,, k 2 < 0)  rp3  Symmetric  Models:  (26)  Margules-type  s o l u t i o n models are used throughout. For f u n c t i o n a l f l e x i b i l i t y , an excess h e a t - c a p a c i t y with 3 f i t parameters i s i n c l u d e d i n the f o r m u l a t i o n :  W  *-p  C = A + — ip2  Q + —  (27)  !J1«  Ion-exchange data from the present study were added to the data base with procedures  s i m i l a r to those of the  p r e - e x i s t i n g system. For each i s o t h e r m a l - i s o b a r i c data set (for  each m i n e r a l ) , groups of brackets spanning a l i m i t e d  *  range of composition and.lnK D were averaged  *  t o g e t h e r . In  t h i s way the t o t a l set of l n K D data was reduced t o 33 p o i n t s . The e s t a b l i s h e d weighting scheme c o n s i d e r s only  72 c o m p o s i t i o n a l s c a t t e r and error  a n a l y t i c a l e r r o r s . However, the  l i m i t s in pressure and  temperature t y p i c a l of  the  present study are much narrower than those t y p i c a l of natural  ion-exchange data which dominate the  the  pre-existing  * data base. A c c o r d i n g l y , the averages were a r t i f i c i a l l y f a c t o r of The  advanced by approximately a  p l a c e d on  to t h i s study are as The  Olivine:  to l i e w i t h i n calorimetry  the  follows: constrained  e r r o r bars of the high temperature  by Wood and  Kle.ppa (1 98 1 ; approximated by  Thierry  1180K). In a d d i t i o n , W ° ^ " and aproach that of an  ^=  1  to  \j  i d e a l s o l u t i o n at  c o n s t r a i n e d to be  w  et a l ( l 9 8 l ; W° =0±4kJ at W ° ^ " were both c o n s t r a i n e d  rl  0±500J at  the Mg-Fe s o l u t i o n phases  o l i v i n e s o l i d s o l u t i o n model was  8kJ±2kJ at 970K) and  W°"*" was  lnKD  10. constraints  pertinent  weights entered for the  1600K. S p e c i f i c a l l y ,  0±100J and  was  constrained  to  1600K.  The  Orthopyroxene:  constrained within Chatillon-Colinet  Mg-Fe orthopyroxene s o l i d s o l u t i o n  the c a l o r i m e t r i c measurements of et a l ( l 9 8 3 ) . In l i g h t of orthopyroxene  s i t e o r d e r i n g rate s t u d i e s  (Besancon, 1981  Vaughan, submitted; see. a l s o Appendix G) px  measurements i n d i c a t i n g W ° = 4kJ±4kJ at interpreted  was  here as the bulk W °  order-disorder equilibrium  p x  at the  and their  Besancon  and  calorimetric  1023K are  of orthopyroxene in temperature of  the  73 c a l o r i m e t r i c experiments. In a d d i t i o n , a high l i m i t was  temperature  p l a c e d on the excess p r o p e r t i e s of the  orthopyroxene s o l i d s o l u t i o n to ensure an approximate  trend  toward i d e a l i t y with i n c r e a s i n g temperature. At 2000K both W°P  X  and W°P  X  were c o n s t r a i n e d between -3kJ and +3kJ.  C o n s t r a i n t s c l o s e r to OJ c o u l d not be j u s t i f i e d  i n l i g h t of  the range of p r e v i o u s e s t i m a t e s f o r the orthopyroxene  solid  s o l u t i o n p r o p e r t i e s (Kitayama, 1971; Navrotsky, 1971;  Sack,  1980).  AnthophylI  ite:  A correspondence between a n t h o p h y l l i t e and  the s y n t h e t i c orthoamphiboles was assumed. In l i g h t of the l i m i t e d temperature range of the n a t u r a l and  synthetic  1  a n t h o p h y l l i t e ion-exchange d a t a , W^"*"* was c o n s t r a i n e d to be temperature  Talc:  independent.  The wide brackets c h a r a c t e r i s t i c of the  t a l c - c h l o r i d e data cannot c o n s t r a i n the c o m p o s i t i o n a l * talc dependence of K D (see f i g u r e I I . 6 ) . T h e r e f o r e WQ c o n s t r a i n e d to be zero f o r the t a l c s o l i d M i n n e s o t a i t e was  was  solution.  not t r e a t e d as Fe-endmember t a l c . T h i s  approach i s supported by known s t r u c t u r a l  distinctions  between t a l c and minnesotaite (Guggenheim and B a i l e y , 1982). In a d d i t i o n , chemical a n a l y s e s of n a t u r a l m i n n e s o t a i t e i n d i c a t e a c o n t r a s t i n the amount of s t r u c t u r a l H 2 0 1965).  (Blake,  74  The  The  Chloride'.  behave i d e a l l y  MODEL  constrained  to  (Wg = 0 ) .  1:  The using II.6  (Mg,Fe)Cl 2 s o l u t i o n was hl  numerical r e s u l t s of the data base c a l c u l a t i o n s  the above c o n s t r a i n t s are for the phases p e r t i n e n t  l i s t e d in t a b l e s II.5  and  to t h i s study. T h i s set of  * parameters w i l l be r e f e r r e d to as Model 1. Model lnK^ curves c a l c u l a t e d from the parameters in these t a b l e s are compared with the experimental b r a c k e t s in f i g u r e s II.3 Figure  II.7 compares the  through  s o l u t i o n models f o r the  four  s i l i c a t e s c o n s i d e r e d h e r e . A number of i n c o n s i s t e n c i e s be  i d e n t i f i e d between the  1 and  the  II.6.  can  s o l u t i o n set represented by Model  ion-exchange d a t a . These i n c o n s i s t e n c i e s are most  e a s i l y described  separately  f o r each phase.  * Olivine'.  Figures  II.3a and  II.3b show that the model  lnK^  i s too weakly composition dependent at temperatures below 800°C to s a t i s f y the d a t a . T h i s behavior can sets of c o n s t r a i n t s . The  be  calorimetric constaints  t r a c e d to 2 on n  l i m i t s the  rate at which W ° ^ "  temperature. In a d d i t i o n , the  increases  with d e c r e a s i n g  lack of c o m p o s i t i o n a l  dependence assumed f o r the c h l o r i d e s o l u t i o n prevents * ol c h l o r i d e phase from c o n t r i b u t i n g to 91nK D /3X M g . Orthopyroxene'.  I t can  be seen from f i g u r e II.4 that  the  the  Table I I . 5 Endmember thermodynamic p r o p e r t i e s f o r Model 1  NAME  FORMULA  H° 298 (Jx10" " ) H  s'0 298 (d/*C)  k0  ki  V  k2 3  5  :  ( J / '•c)  (x10- ) - 1 1700  -4683  17916  148 . 74 136 .04  (x10" )  (cm  " )  Fe-Ta1c  Fe 3 S i « 0 . o ( O H ) J  -4798 . 1  365 .00  678 .86  Talc  MgoSi.0,D(0H),  -5897 .6  261 .86  664 . 1 1  -2147  -5187  -3274  Fayalite  FeISi0»  - 1476 .8  150 .60  248 .93  0  -1924  -1391  46 . 12  F o r s t e r i te  Mg;Si0«  -2174..0  94 .21  238 .64  0  -2001  -1 162  43 .60 .  F e r r o s i 1 i te  FeSiOi  - 1 193.6  95 .08  -946  -1367  1116  Enstat i te  MgSiOj  - 1545.. 7  Fe-Anthophyl1i te  F e . S i . O n (OH) 2  -9425. 8  Anthophy11i te  Mg ? S i i O i J(OH):  FeCl 2  FeCl 2  MgCl2  MgCl 2  33 . 1 1  166 .58  -2271  -1201  2792  877 .49  1316 .31  -24235  -8445  35523  279. 05  - 12069.7  536 . 15  1219 .31  -34766  -5767  44009  265 .77  0.0  84 . 14  0 .0  0  0  0  28 .25  0 .0  0 .0  0  0  0  0.0  -381 .1  66 . 17  • 173 . 74  31 .. 34  76 Table II.6 Model 1 Margules parameters. A l l parameters p e r t a i n to 1 mole of Fe+Mg. Talc  01ivine  Chloride  Ortho-  Antho-  pyroxene  phyllite 2. 028  0.0  WH(kJ)  0.0  44.63  1 4.27  WS(J/°C)  0.0  50.00  18.87  0.0  0.0  Wy(J/bar)  0.0  0.012  -0.016  0.0  0.0  A  0.0  26.41  -9.73  0.0  0.0  (J/°C) 5  C  (x1U- )  0.0  -710.8  0.0  0.0  0.0  Q  (X10-  0.0  923.2  0.0  0.0  0.0  1  0  )  correspendence between the thermodynamic model and orthopyroxene- c h l o r ide data i s adequate i f  the  the e r r o r bars  on  the data are expanded to 2a. However, there remains a problem with the orthopyroxene s o l i d  s o l u t i o n model which i s  more e a s i l y e x p l a i n e d using f i g u r e II.7 as an S a t i s f a c t i o n of the c h l o r i d e minimal c o n t r a s t i n  ion-exchange data  between o l i v i n e and  S a t i s f a c t i o n of the n a t u r a l and  illustration. requires a  orthopyroxene.  experimental  olivine-orthopyroxene  ion-exchange data g e n e r a l l y r e q u i r e s a  larger contrast in  (M. E n g i , p e r s . comm.). The  weight assigned  to the c h l o r i d e  about the minimum i n W^1-  W°?  x  temperatures, where most of the o l i v i n e - o r t h o p y r o x e n e data  high  ion-exchange data  brings  at about 1000K. At  higher  experimental  l i e s , the two  f u n c t i o n s are  f o r c e d to d e v i a t e . The  magnitude of t h i s d e v i a t i o n i s  77  0.0  0.2  0.4  X  Mg  0.6  0.8  1.0  (Olivine) *  F i g u r e II.3 Comparison of o l i v i n e l n K ^ data with  curves  c a l c u l a t e d with Model 1 thermodynamic parameters, (a) A l l 2kb data p l u s 450°C (1kb) d a t a .  78  F i g u r e II.3  (b) Data at 600°C (1kb and 4kb).  79  0-  A 680°C  2kb  A  2kb  800°C  -1 *  Q  _E - 2 -  680°  A v  800°  A  TV  u  n  \  -3-  -4 0.0  0.2  *Mg  0.4  0.6  0.8  1.0  (Orthopyroxene)  F i g u r e II.4 Comparison of orthopyroxene  l n K Q data with  curves c a l c u l a t e d with Model 1 thermodynamic  parameters.  80  I  4 0-  600°C  2kb  A 650°C  2kb  A  2kb  700°C  -1-  *a  S-2-3-  -4 0.0  0.2  X  0.4 M g  0.6  0.8  1.0  (Orthoamphibole)  F i g u r e II.5 Comparison of orthoamphibole  l n K D data with  curves c a l c u l a t e d with Model 1 thermodynamic  parameters.  81  A 400°C 2kb A  500°C 2kb  -n «a J£  -2  T  400fl  t  500 s -3^  -4 0.0  0.2  0.4  X  M g  F i g u r e II.6 Comparison of t a l c  0.6  0.8  (Talc) l n K ^ data with curves  c a l c u l a t e d with Model 1 thermodynamic  parameters.  1.0  82  400  600  800  1000  1200  1400  1600  1800  Temperature (K) F i g u r e II.7 Comparison of the four Model 1 W_ f u n c t i o n s . ol Also included i s W c a l c u l a t e d from Model 1 parameters.  83  l i m i t e d by the c o n s t r a i n t s l i m i t i n g t h e i r excess  functions  at T>1600K.  i t e:  AnthophylI  net-transfer  The lack of c a l o r i m e t r i c data and  e q u i l i b r i u m c o n s t r a i n t s on  permits the data r e d u c t i o n  Fe-anthophyllite  complete freedom to s a t i s f y the  o r t h o a m p h i b o l e - c h l o r i d e d a t a . However, l n K D models c a l c u l a t e d f o r o l i v i n e - a n t h o p h y l l i t e and t a l c - a n t h o p h y l l i t e ion-exchange e q u i l i b r i a these e q u i l i b r i a  to s a t i s f y n a t u r a l examples of  (M. E n g i , p e r s . comm.). The mis-match i n  both cases i s c o n s i s t e n t and  fail  with a standard free-energy  T) f o r F e - a n t h o p h y l l i t e  which i s higher than  (at P  that  r e q u i r e d by the data on the n a t u r a l s o l i d s o l u t i o n . I t i s proposed here that t h i s r e f l e c t s "a r e a l - d i f f e r e n c e between s t r u c t u r a l l y ordered n a t u r a l a n t h o p h y l l i t e s and the p a r t i a l l y disordered  s y n t h e t i c orthoamphiboles employed i n  t h i s study (see Appendix F ) .  MODEL  2:  In an e f f o r t to remove some of the remaining i n c o n s i s t e n c i e s between the data and the thermodynamic model, the data-base c a l c u l a t i o n s were repeated with one major c o n s t r a i n t  removed. The assumption of i d e a l mixing i n  the c h l o r i d e s o l u t i o n was removed s i n c e there i s no p h y s i c a l data which d i r e c t l y supports t h i s c o n s t r a i n t . However, the c h l o r i d e s o l u t i o n model was not l e f t  completely  u n c o n s t r a i n e d . To e s t a b l i s h q u a l i t a t i v e c o n s t r a i n t s on the  84 c h l o r i d e s o l u t i o n model, i t was assumed that n o n - i d e a l i n t e r a c t i o n s i n the aqueous s o l u t i o n are l a r g e l y due to the presence of charged s p e c i e s . A c c o r d i n g l y , the c h l o r i d e s o l u t i o n model was c o n s t r a i n e d to trend toward i d e a l i t y i n the temperature region where the n e u t r a l c h l o r i d e  species  chl dominate. WQ was  f o r c e d to be l i n e a r l y temperature chl chl dependent by a l l o w i n g only WH and Wg to be non-zero. In chl a d d i t i o n , WH  chl and Wg  were c o n s t r a i n e d to have the same  chl s i g n , and WG was a r b i t r a r i l y c o n s t r a i n e d to be 0±1kJ at 1000°C. To allow l n K D f o r the t a l c - c h l o r i d e e q u i l i b r i u m to talc remain approximately composition independent,  was  allowed to be non-zero, but temperature independent. The r e s u l t s of a second MINOS run with these changes i n the c o n s t r a i n t s are l i s t e d i n t a b l e s II.7 and I I . 8 . T h i s set of parameters w i l l be r e f e r r e d to as Model 2. C a l c u l a t e d * l n K Q curves are compared to the data i n f i g u r e s II.8 through 11.11  and the  f u n c t i o n s are p l o t t e d on f i g u r e 11.12. Many  of the i n c o n s i s t e n c i e s noted above f o r Model 1 are absent from Model 2. U n f o r t u n a t e l y , the p r i c e of t h i s  improved  model-data correspondence i s r e j e c t i o n of one of the most convenient b a s i c assumptions about the p r o p e r t i e s of the aqueous c h l o r i d e s o l u t i o n . The d e t a i l s are l i s t e d  by  mineral. Olivine:  Model 2 l n K D curves are i n c l u d e d w i t h i n 2a e r r o r  b r a c k e t s f o r the e n t i r e o l i v i n e - c h l o r i d e data s e t . Only a few of the 1a brackets are m i s s e d . A review of Model 1 and  Table  II.7 Endmember thermodynamic p r o p e r t i e s f o r Model 2  NAME  FORMULA  H° 298 :1 (dx10" ) H  0  k0  k,  (J/'C)  (x10" ) - 11701 -2147  :  k,  kz  s! 298 ( J / "c)  3  Fe-Ta1c  FeiSiiOio(OH);  -4790 . 7  365 .00  678 .86  Talc  MgiSi «0io(OH)7  -5898..6  261 .04  664 . 1 1  V 5  :  (x10- )  (cm ' )  -4683  17916  148 . 74  -5187  -3274  136 .04  F a y a l i te  Fe*S10.  - 1476 . 8  150 .60  248 .93  0  - 1924  -1391  46 . 12  F o r s t e r i te  Mg2 S i 0 «  -2174..0  94 .21  238 .64  0  -2001  -1 162  43 .60  F e r r o s i 1 i te  FeSiOs  -1193. 2  95 . 25  173 . 74  -946  - 1367  1116  32 .96 31 . 34  -2271  -1201  2792  Fe-Anthophy11i te  Fe/Si .0*.(OH) z  -9365. 8  934 .12  1316 .31  -24235  -8445  35523  277 .04  Anthophy11i te  Mg,S i•0; ;(OH ) ,  -1207 1.O  535 .20  1219 .31  -347G6  -5767  44009  265 .63 .  e n s t a t i te  . MgSi0 3  FeCl*  FeCl ?  MgCl !  MgCl ,  - 1545.. 7  0.0 -382 . 1  66 . 17  166 . 58  88 . 19  0 .0  0  0  0  34 ., 59  O .0  0 .0  0  0  0  0.,0  00 cn  86 Table II.8 Model 2 Margules parameters. A l l parameters p e r t a i n to 1 mole of Fe+Mg. Talc  WH(kJ)  Ortho-  Antho-  pyroxene  phyllite 0.575  Olivine  -2.830  44.63  7.48  WS(J/°C)  0.0  50.00  1 1 .45  W v (J/bar)  0.0  0.012  A  0.0  26.41  0.0 0.0  (J/°C) 5  C (xlO' ) Q (xlO"  10  )  Chloride  -10.63  0.0  -7.57  -0.016  0.0  0.0  -5.905  0.0  0.0  -710.8  0.0  0.0  0.0  923.2  0.0  0.0  0.0  Model 2 parameters, and comparison of f i g u r e s II.7 and 11.12,  shows that t h i s improvement i n model-data  correspondence i s e n t i r e l y due to the added n o n - i d e a l i t y i n the c h l o r i d e s o l u t i o n . O p t i m i z a t i o n of the o l i v i n e  solid  s o l u t i o n model c o n t i n u e s to s t r a i n a g a i n s t the upper of the c a l o r i m e t r i c  Orthopyroxene'.  limit  constraints.  F i g u r e II.9 shows very l i t t l e  change i n  model-data correspondence compared to Model 1 . However, comparison of f i g u r e s II.7 and 1 1 . 1 2 shows that the W ° ^ X model i s now  separated f a r t h e r from the W°^" model. T h i s  r e s u l t s i n improvement of the correspondence between thermodynamic model and the o l i v i n e - o r t h o p y r o x e n e ion-exchange data i n c l u d e d i n the data base c omm.).  (M. E n g i , p e r s .  87  J  -*i 0.0  I  I  I  1  1  1  1  r  0.2  0.4  0.6  0.8  1.0  X  M g  (Olivine) *  F i g u r e II.8 Comparison of o l i v i n e l n K ^ data with  curves  c a l c u l a t e d with Model 2 thermodynamic parameters, (a) A l l 2kb data p l u s 450°C (1kb) d a t a .  88  F i g u r e II.8  (b) Data at 600°C (1kb and 4kb).  89  A 680°C  2kb  A  2kb  800°C  -1 -  _E - 2 -  680 c 800  4  v  e  TV  -3  -4 0.0  0.2  X  0.4 M g  0.6  0.8  (Orthopyroxene)  F i g u r e II.9 Comparison of orthopyroxene  1.0  l n K Q data with  curves c a l c u l a t e d with Model 2 thermodynamic  parameters,  90  1 0 -  600°C  2kb  A 650°C  2kb  A  2kb  700°C  -1 -  *a _E - 2 -  -3-  -4 0.0  0.2  X F i g u r e 11.10  0.4 M g  0.6  0.8  1.0  (Orthoamphibole)  Comparison of orthoamphibole  l n K D data with  curves c a l c u l a t e d with Model 2 thermodynamic  parameters.  91  A 400°C 2kb OH  A  500°C 2kb  - H  *a <= - 2 - I  -4 0.0  0.2  0.4  X  M g  F i g u r e 11.11 Comparison of t a l c  0.6  0.8  (Talc) l n K ^ data with curves  c a l c u l a t e d with Model 2 thermodynamic  parameters.  1.0  92  F i g u r e 11.12 Comparison of the four Model 2 W~  functions.  93 L i k e the W ° ^  Anthophyllite:  s o l i d s o l u t i o n model has of ^0.5kJ i s now  x  model, the  orthoamphibole  s h i f t e d to a lower WQ  s u f f i c i e n t to f i t the  discrepancy between thermodynamic model and o l i v i n e - a n t h o p h y l l i t e and  value. A lnK^ d a t a .  The  natural  talc-anthophyllite pairs p e r s i s t s .  DISCUSSION ENDMEMBER  PROPERTIES:  C o l l a b o r a t i v e e f f o r t s are a l r e a d y evaluation  underway to conclude  of the MgO-Si02-Fe-0-H-C database. The  c h l o r i d e ion-exchange data w i l l be  i n c l u d e d , but  Mg-Fe the  'weight' t h i s data i s given must be a d j u s t e d given  the  u n c e r t a i n t i e s exposed h e r e . A complete d e s c r i p t i o n of contents of the database, along with the r e s u l t s and  their petrologic  the  computational  i m p l i c a t i o n s , w i l l appear  elsewhere. Both the Mg  and  Fe endmembers of the o l i v i n e  orthopyroxene s o l u t i o n s are c o n s t r a i n e d n e t - t r a n s f e r phase e q u i l i b r i a . The  and  by c a l o r i m e t r y  thermodynamic  and  properties  presented here f o r these endmembers w i l l change very  little  when the r o l e of the data presented here i s r e e v a l u a t e d . same i s true of the Mg-endmembers of the anthophyllite  s o l u t i o n s . No  talc  The  and  experimental c o n s t r a i n t s e x i s t  f o r the Fe-endmembers of t a l c and  anthophyllite.  thermodynamic p r o p e r t i e s c a l c u l a t e d f o r these two  The endmembers  must be expected to change as more data becomes a v a i l a b l e f o r the t a l c , a n t h o p h y l l i t e and  aqueous Mg-Fe c h l o r i d e  94 solutions. SOLID  SOLUTION  The solution  MODELS:  ideal-mixing  constraint  p l a c e d upon the  in Model 1 appears to be  inappropriate.  chloride The  c o n s t r a i n t s p l a c e d upon the c h l o r i d e s o l u t i o n model in Model 2 are  somewhat a r b i t r a r y and  m o d i f i e d by  need to be confirmed or  independent d a t a . U n t i l such data are  the only q u a n t i t i e s unambiguously e s t a b l i s h e d chloride  by  available, the  ion-exchange experiments are endmember a c t i v i t y  ratios: mineral:chloride  a c t i v i t y r a t i o s and,  where  d i f f e r e n t m i n e r a l s have been s t u d i e d  over the  same P-T-mT  conditions, mineral:mineral a c t i v i t y  ratios.  Accordingly,  any  modifications  made to the a b s o l u t e value of the  solution properties  must a l s o modify the value of  solution properties  constrained  by the  i m p l i c a t i o n s of s o l i d s o l u t i o n p r o p e r t i e s  The  Olivine:  be  solid  ion-exchange  experiments. In the mean time, some of the  above examples can  chloride  features  and  c a l c u l a t e d in  discussed.  o l i v i n e s o l i d s o l u t i o n model represented  the Model 2 parameters i s f i r m l y sandwiched between  will  ion-exchange d a t a . The  in the aqueous s o l u t i o n can  disproved) and  q u a n t i f i e d . The  model i s i t s p r e d i c t i o n of a W^"*"  the  Model 2 o l i v i n e s o l u t i o n  remain the most comprehensive model u n t i l the  non-ideality  by  two  opposing c o n s t r a i n t s : the c a l o r i m e t r i c measurements and chloride  the  be confirmed  most notable feature at low  implied (or  of t h i s  temperature (<800°C)  95 which  i s s i g n i f i c a n t l y higher than p r e d i c t e d by p r e v i o u s  models (e.g. Engi,1980a; Orthopyroxene:  Andersen  and L i n d s l e y ,  The Mg-Fe orthopyroxene s o l i d  1981). solution  models represented by Model 1 and Model 2 parameters s i m i l a r i n form, but d i f f e r  are  i n d e t a i l . The primary  d i s t i n c t i o n between Model 1 and Model 2 i s i n the treatment of the c h l o r i d e phase. A c c o r d i n g l y , the d e t a i l s of the orthopyroxene model, p a r t i c u l a r l y at T<800°C, must remain somewhat t e n t a t i v e u n t i l the p r o p e r t i e s of the aqueous s o l u t i o n are more thoroughly understood. In the mean t i m e , the Model 2 parameters must be chosen as most a p p r o p r i a t e for the orthopyroxene s o l i d s o l u t i o n based upon the more f a v o r a b l e model-data  correspondence of Model 2.  The a v a i l a b l e data c o n s t r a i n i n g the p r o p e r t i e s of Mg-Fe orthopyroxenes i n c l u d e s measurements of the  intracrystalline  exchange of Mg and Fe between the M1  octahedral  and M2  s i t e s . A p r e v i o u s a n a l y s i s of orthopyroxene bulk p r o p e r t i e s based upon the i n t r a c r y s t a l l i n e exchange alone (Navrotsky, 1971)  i s c o n s i s t e n t with the Model 2 orthopyroxene only at  high temperatures. (Navrotsky's c a l c u l a t e d v a l u e s of  GEX  px  correspond to W ° = - 4 3 0 0 J at 500°C and -2440J at 1250°C) In Appendix G i t i s shown that a d e t a i l e d ' m i c r o s c o p i c ' s o l u t i o n model can be s i m u l t a n e o u s l y c o n s i s t e n t with the intracrystalline  ion-exchange  data and with the bulk  solid  s o l u t i o n p r o p e r t i e s p r e d i c t e d by the Model 2 parameters the temperature  over  range i n which Model 2 i s c o n s t r a i n e d by  d a t a . The d e t a i l s of t h i s m i c r o s c o p i c model imply that the  96 observed bulk p r o p e r t i e s of the orthopyroxene s o l i d  solution  are the summation of two opposing e n e r g i e s : a negative f r e e energy produced by o r d e r i n g of Mg and Fe and a p o s i t i v e ' l a t t i c e s t r a i n ' energy  r e s u l t a n t from mixing ions of  unequal s i z e i n a continuous s t r u c t u r e . (The Model 2 o l i v i n e i s an apt example of a s o l i d s o l u t i o n dominated  by t h i s  second e f f e c t . ) In a d d i t i o n , the m i c r o s c o p i c model p r e d i c t s that the orthopyroxene bulk G E X w i l l  r i s e with  temperature only u n t i l about 550°C. At lower  falling  temperatures  the negative free energy c o n t r i b u t i o n of s i t e  ordering  becomes the dominant e f f e c t . Both the macroscopic model used i n the database c a l c u l a t i o n s and the m i c r o s c o p i c model used i n Appendix G are f o r m u l a t i o n s symmetric  x  about X ° ^ = 0 . 5 . The  c h l o r i d e - o r t h o p y r o x e n e data-do not r e q u i r e an asymmetric s o l u t i o n model, but these data only cover 2/3 of the X  p o s s i b l e range i n X ° P . Saxena and G h o s e ( l 9 7 l ) noted that t h e i r Mossbauer s p e c t r o s c o p i c measurements of Mg-Fe s i t e o r d e r i n g were asymmetric it  x  with r e s p e c t to X ° ^ .  In Appendix G  i s shown that the u n c e r t a i n t i e s inherent i n the Mossbauer  data tend to drown out t h i s asymmetry. However, i t i s q u i t e p o s s i b l e that f u t u r e r e s e a r c h w i l l c o n f i r m that the Mg-Fe orthopyroxene s o l u t i o n must be modelled as asymmetric  with  respect to X M g . t e:  Models 1 and 2 both a s s i g n a small p o s i t i v e  Ant  hophylIi  WG  to the a n t h o p h y l l i t e s o l i d s o l u t i o n . Due to the narrow  temperature  range of the c h l o r i d e  ion-exchange  data and the  97 remaining u n c e r t a i n t i e s i n the r o l e of the aqueous s o l u t i o n , it  i s i n a p p r o p r i a t e at t h i s time to c a l c u l a t e a temperature nt  dependence f o r Wg ^. Once a g a i n , the success of Model 2 nth  r e l a t i v e to Model 1 i n d i c a t e s that the Model 2 W^  i s the  better.estimate. As with the orthopyroxene, Mg-Fe o r d e r i n g has been detected in anthophyllites  (e.g. F i n g e r , 1970). The  i n t r a c r y s t a l l i n e Mg-Fe ion-exchange has been measured as a f u n c t i o n of temperature and time ( S e i f e r t and V i r g o , 1975; S e i f e r t , 1977,  1978). There appears to be l i t t l e  o r d e r i n g amongst the M1, M2, and M3 preference of F e  2+  preference f o r M2 Ghose, 1971  1974,  f o r M4  s i t e s , but the  i s even stronger than the  i n orthopyroxene  and S e i f e r t ,  or no  (compare Saxena and  1978).  Formulation of a 'microscopic' a n t h o p h y l l i t e  solution  model i s not attempted here because the number of s i t e - c o n f i g u r a t i o n s to be considered i s l a r g e and the available intracrystalline  ion-exchange data covers only a  narrow composition range. However, the i n s i g h t gained from a p p l y i n g such a model to the orthopyroxene s o l u t i o n a l l o w s us to q u a l i t a t i v e l y p r e d i c t the c h a r a c t e r i s t i c s of the a n t h o p h y l l i t e s o l i d s o l u t i o n . Although F e  2+  f r a c t i o n a t i o n in  a n t h o p h y l l i t e i s somewhat stronger than that i n orthopyroxene, F e  2+  i s fractionated  i n t o only 2 of 7 s i t e s  (per formula u n i t ) . T h e r e f o r e the c o n t r i b u t i o n of s i t e o r d e r i n g to the bulk s o l i d s o l u t i o n p r o p e r t i e s i s expected to be subdued compared to i t s e f f e c t i n the the  98 orthopyroxene  s o l u t i o n . If the c o n t r i b u t i o n of  s t r a i n energy i s s i m i l a r nt  bulk W^ ^  may  lattice  for these two c h a i n s i l i c a t e s , the  be p r e d i c t e d to be somewhat higher than 1  1  The Model 2 W^""* i s q u a l i t a t i v e l y c o n s i s t e n t with  W°^  x  these  considerations. Talc:  The  t a l c - c h l o r i d e ion-exchange data i s of l i t t l e  use  in d e f i n i n g t a l c s o l i d s o l u t i o n p r o p e r t i e s while the p r o p e r t i e s of the aqueous s o l u t i o n  remain u n c e r t a i n . The  t a l c data are not even of much use  for estimating p r o p e r t i e s  by comparison with the other m i n e r a l s s t u d i e d h e r e . T h i s i s because the t a l c data were c o l l e c t e d under P-T c o n d i t i o n s at and beyond the P-T  l i m i t s of the other data s e t s . (The  o v e r l a p i s with three o l i v i n e h a l f - b r a c k e t s at 450°C,  only 2kb)  In a d d i t i o n , the t a l c data-set i s c h a r a c t e r i z e d by r e l a t i v e l y wide c o m p o s i t i o n a l b r a c k e t s and uncertainty in talc  relatively  high  f i n a l c o m p o s i t i o n s . More research i s  r e q u i r e d before the t a l c  s o l i d s o l u t i o n p r o p e r t i e s can  be  c o n s t r a i n e d by ion-exchange experiments with aqueous chlor ides. In the meantime, i t may  be f r u i t f u l to compare t a l c  parameters from Model 1 and Model 2 with estimates from the example set by the m i c r o s c o p i c  orthopyroxene  s o l u t i o n model. Mossbauer spectroscopy has Fe-Mg o r d e r i n g i n n a t u r a l t a l c s  f a i l e d to d e t e c t  (Blaauw et a l , 1980).  Q u a l i t a t i v e comparison with the orthopyroxene t h e r e f o r e p r e d i c t that the t a l c s o l i d s o l u t i o n by the p o s i t i v e  inferred  model would i s dominated  99  gx  contributed  by ' l a t t i c e s t r a i n ' . Model 1 and Model 2  talc values f o r WQ consistent  (0 and -2.8kJ r e s p e c t i v e l y ) are not  with t h i s argument. U n t i l more dependable  c o n s t r a i n t s are a v a i l a b l e , the Fe-Mg t a l c s o l u t i o n may be best modelled as i d e a l . CONCLUSIONS  The use of aqueous c h l o r i d e s as a s o l u t i o n phase o f f e r s d i s t i n c t p r a c t i c a l advantages when performing ion-exchange experiments with s o l i d s o l u t i o n phases. However, i t appears that thermodynamic i n t e r p r e t a t i o n of such experiments i s not at a l l s t r a i g h t f o r w a r d .  The Mg-Fe ion-exchange data  presented here show that the c o n t r i b u t i o n of the aqueous c h l o r i d e s to K D  i s dependent on the t o t a l  chloride  c o n c e n t r a t i o n . Thermodynamic a n a l y s i s of the data i n d i c a t e s that the c o n t r i b u t i o n of the aqueous c h l o r i d e s may a l s o be composition dependent. U n t i l the r o l e of the aqueous solution  i s more q u a n t i t a t i v e l y e s t a b l i s h e d , such  ion-exchange experiments are of l i t t l e  use i n c h a r a c t e r i z i n g  a s i n g l e s o l i d s o l u t i o n phase. For the moment, the primary u t i l i t y of aqueous c h l o r i d e s i s as a medium through which mineral p r o p e r t i e s can be compared. The  i m p l i c a t i o n s of u n c e r t a i n t i e s i n the c h l o r i d e  solution properties  on the c a l c u l a t e d s o l u t i o n p r o p e r t i e s of  m i n e r a l s s t u d i e d here are d i s c u s s e d above. The i m p l i c a t i o n s these u n c e r t a i n t i e s have on p r e v i o u s l y  published chloride  100 ion-exchange s t u d i e s must a l s o be addressed. P r e v i o u s chloride-ion-exchange s t u d i e s have put l i t t l e  or no e f f o r t  i n t o c h a r a c t e r i z i n g the aqueous s o l u t i o n and i t s r o l e i n the experimental r e s u l t s . In l i g h t of the data a n a l y s i s presented h e r e , s o l i d s o l u t i o n p r o p e r t i e s c a l c u l a t e d from these p r e v i o u s s t u d i e s must be.considered suspect u n t i l the p r o p e r t i e s of each p e r t i n e n t aqueous mixture of c h l o r i d e s have been examined. The q u e s t i o n s that need to be addressed by future research  with aqueous Mg-Fe c h l o r i d e s i n c l u d e : What i s the  dependence of K Q on mT at 450°C (1kb and 2kb) where only h a l f b r a c k e t s are e s t a b l i s h e d here? What i s the dependence of K D on mT at T > 600°C? What i s the magnitude of the chl i m p l i e d dependence of K D on compositional  ? What i s the cause of t h i s  dependence? What are the i d e n t i t i e s of a l l  aqueous s p e c i e s which s i g n i f i c a n t l y c o n t r i b u t e measured d i s t r i b u t i o n  to the  coefficient?  The above a n a l y s i s of the o l i v i n e , orthopyroxene, t a l c and a n t h o p h y l l i t e s o l i d s o l u t i o n s suggests  mineralogical  q u e s t i o n s to be answered by f u t u r e research:  Are the  orthopyroxene s o l u t i o n p r o p e r t i e s asymmetric with respect t o X  X5!|L ? What a r e the e n e r g e t i c  and c r y s t a l l o g r a p h i c  d i f f e r e n c e s between s y n t h e t i c and n a t u r a l  anthophyllite?  What are the p r o p e r t i e s of the t a l c s o l u t i o n ? What i s the r e l a t i o n s h i p between t a l c and minnesotaite?  References Akimoto, S - I . , and F u j i s a w a , H. 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S e i f e r t , F., and  V i r g o , D.  (1974) Temperature dependence of  2+  i n t r a c r y s t a l l i n e Fe -Mg d i s t r i b u t i o n in a  natural  a n t h o p h y l l i t e . Carnegie I n s t i t u t e of Washington Yearbook, 73, S e i f e r t , F., and  405-411. V i r g o , D.  order-disorder cooling S e i f e r t , F.  reaction  in a n t h o p h y l l i t e s :  r a t e s . S c i e n c e , 188,  2+  Fe -Mg  Quantitative  1107-1109.  (1977) Compositional dependence of the  i n t e r a c t i o n of  57  F e in a n t h o p h y l l i t e . Physics  Chemistry of M i n e r a l s , S e i f e r t , F.  (1975) K i n e t i c s of the  1,  hyperfine and  43-52.  (1978) E q u i l i b r i u m Mg-Fe  2+  cation d i s t r i b u t i o n  in a n t h o p h y l l i t e . American J o u r n a l of S c i e n c e ,  278,  1323-1333. S e k i , Y.,  and  Yamasaki, M.  ferroanthophyllite  (1957) Aluminian  from the Kitakami Mountainland,  Northeastern Japan. American M i n e r a l o g i s t ,  42,  506-520.  Spence, J.C.H. (1981) Experimental High-Resolution  Electron  M i c r o s c o p y . Clarendon P r e s s , O x f o r d , 370p. T h i e r r y , P., J.R., the  and  Chatillon-Colinet, C ,  Mathieu, J.C.,  Regnard,  Amosse, J . (1981) Thermodynamic p r o p e r t i e s  forsterite fayalite  (Mg2SiO„-Fe2SiOu)  solid  s o l u t i o n . Determination of heat of f o r m a t i o n . P h y s i c s and  Chemistry of M i n e r a l s ,  Thompson, J.B.,  7, 43-46.  J r . (1967) Thermodynamic p r o p e r t i e s  of  simple s o l u t i o n s . In: Researches in Geochemistry II (P.H.Abelson, e d . ) , John Wiley and  Sons, 340-361.  Thompson, J . B . J r . (1969) Chemical r e a c t i o n s  in c r y s t a l s .  of  11 3 American M i n e r a l o g i s t , 54, Thompson, J . B . , J r . and  petrology  (1981) An  i n t r o d u c t i o n to the mineralogy  of the b i o p y r i b o l e s . Reviews in  M i n e r a l o g y , 9A, Thompson, J.B.,  341-375.  and  141-188. Waldbaum, D.R.  (1969) Mixing  properties  of s a n i d i n e c r y s t a l l i n e s o l u t i o n s . I . C a l c u l a t i o n s based on  ion exchange d a t a . American M i n e r a l o g i s t ,  278,  1965-1969. Trommsdorff, V.,  and  Evans, B.W.  (1972)  Progressive  metamorphism of a n t i g o r i t e s c h i s t i n the t o n a l i t e aureole 272,  Bergell  ( I t a l y ) . American J o u r n a l  of  Science,  423-437.  Turnock, A.C.,  L i n d s l e y , D.H.,  Synthesis  and  and  Grover, J.E.  u n i t c e l l parameters of Ca-Mg-Fe  pyroxenes. American M i n e r a l o g i s t , 58, V e b l e n , D.R.,  and  (1973)  Burnham, C.W.  50-59.  (1978) New  b i o p y r i b o l e s from  C h e s t e r , Vermont: I . D e s c r i p t i v e m i n e r a l o g y . American M i n e r a l o g i s t , 63, V e b l e n , D.R.,  and  disorder  1000-1009.  Buseck, P.R.  (1979) Chain-width order  i n b i o p y r i b o l e s . American M i n e r a l o g i s t ,  and  64,  687-700. V i r g o , D.,  and  Hafner, S.S.  cation distribution e f f e c t . E a r t h and V i r g o , D.,  and  (1968) R e - e v a l u a t i o n of  i n orthopyroxenes by  Planetary  Hafner, S.S.  (1970) The  synthetic Journal Wenk, H.-R.  the Mossbauer  Science L e t t e r s , 4, 265-269.  (1969) F e  in heated orthopyroxenes. MSA Wellman, T.R.  2 +  , Mg  order-disorder  S p e c i a l Paper, 2, 67-81.  s t a b i l i t y of s o d a l i t e in a  s y e n i t e p l u s aqueous c h l o r i d e f l u i d  of P e t r o l o g y ,  the  11,  system.  49-71.  ( c o o r d i n a t i n g e d i t o r ) ( 1 9 7 6 ) E l e c t r o n Microscopy  in M i n e r a l o g y . Springer W i l l i a m s , R.J.  V e r l a g , New  York, 564p.  (1971) Reaction c o n s t a n t s in the  system  11 4 Fe-MgO-Si0 2 -0 2 at 1 atm between 900 and 1300 C: Experimental r e s u l t s . American J o u r n a l of S c i e n c e , 270, 334-360. W i l l i a m s , R.J. (1972) A c t i v i t y - c o m p o s i t i o n r e l a t i o n s i n the fayalite-forsterite  s o l i d s o l u t i o n between 900°C and  1300°C at low p r e s s u r e s . E a r t h and P l a n e t a r y  Science  L e t t e r s , 48, 296-300. Wood, B . J . , and Kleppa, O.J. (1981) Thermochemistry of f o r s t e r i t e - f a y a l i t e o l i v i n e s o l u t i o n s . Geochimica Cosmochimica A c t a , 45, 529-534.  I I I . APPENDICES  APPENDIX A: OXIDE MIXES  A l l Mg-Fe s i l i c a t e s were s y n t h e s i z e d oxygen-balanced mixes of S i 0 2 , MgO,  Fe203  from and F e . The term  'oxygen-balanced' r e f e r s to the f a c t that the Fe and were added i n p r o p o r t i o n s  Fe203  c o r r e s p o n d i n g to s t o i c h i o m e t r i c  FeO. A l l oxide components were heated to remove adsorbed  H20  j u s t p r i o r to weighing. Rather than attempting to remove adsorbed H 2 0  and oxygen (as F e 2 0 3 ) from the Fe source, the  t o t a l excess 0 2  (from both H 2 0  and F e 2 0 3 ) was measured f o r a  sample of the Fe metal and r e c a l c u l a t e d as a weight%  MIX  FeO.  COMPONENTS:  Si02: S i l i c i c acid  (H2Si03'nH20;  F i s h e r reagent grade, l o t  730944) was heated to =400°C f o r a few minutes to d r i v e o f f the bulk of the H 2 0  ad then heated at 1200°C f o r 12  h o u r s . The r e s u l t i n g s o l i d , but f r i a b l e mass of f i n e l y c r y s t a l l i n e a - c r i s t o b a l i t e was broken up, ground  under  a l c o h o l f o r 2 hours to reduce g r a i n s i z e , and then d r i e d at MgO:  1000°C f o r 2 hours.  F i s h e r A.C.S. grade MgO  ( l o t 741694) was heated at  1300°C f o r 24 hours to dry and a l s o to increase size  ( t h i s reduces m a t e r i a l  d u r i n g the weighing  grain  l o s s due to a i r c u r r e n t s  process).  1 15  1 16 F e 2 0 3 : F i s h e r reagent grade f e r r i c - o x i d e ( l o t 725030) was heated at 900°C f o r 10 hours to dry and to grain  increase  size.  Fe: Johnson, Matthey and Co. i r o n sponge ( l o t S7294) was stored  in a d e s s i c a t o r  f o r more than 2 months p r i o r to  use. The oxygen content of a r e p r e s e n t a t i v e  sample of  t h i s i r o n sponge was determined with the method of Turnock et a l ( l 9 7 3 ) . From the measured v a l u e of wt.% 11.0  MIX  0 2 , the e q u i v a l e n t  2.45  FeO content was c a l c u l a t e d to be  wt.%.  CALCULATIONS'.  For each mix the r e q u i r e d weights of S i 0 2 , MgO were c a l c u l a t e d such that the t o t a l mix weight was weights of F e 2 0 3  and i r o n sponge r e q u i r e d  and  FeO  3.0g.  to produce  The  1.0g of  s t o i c h i o m e t r i c FeO were c a l c u l a t e d and then m u l t i p l i e d by the FeO weight r e q u i r e d weighed s e p a r a t e l y with a l c o h o l  f o r each mix. Each mix component  was  i n t o a p l a s t i c weighing boat and washed  i n t o an agate mortar.  HOMOGENIZATION:  The homogenization process began with hand g r i n d i n g ; both under a l c o h o l dry  f o r about  (reagent grade; 95% e t h a n o l ,  10 minutes each. Hand g r i n d i n g  5% H 2 0)  and  i s t e d i o u s , but  much more e f f e c t i v e than an automatic mortar i n breaking up the  l a r g e r lumps of m a t e r i a l . The hand g r i n d i n g was  followed  1 17 by g r i n d i n g under a l c o h o l i n an automatic mortar f o r =0 hour. T h i s was g r i n d i n g to mix  followed by a few more minutes of dry hand in p o r t i o n s of the mix which had d r i e d onto  the p e s t l e and high on the s i d e s of the mortar  during  automatic g r i n d i n g . G r i n d i n g Fe-bearing mixes i n the automatic mortar q u i c k l y r e v e a l e d that small amounts of the Fe metal tended to adhere to the s u r f a c e of the m o r t a r . T h i s t h r e a t to maintaining  the mixes on composition was  negated, or at  l e a s t minimized, by ' p r e - t r e a t i n g ' the s u r f a c e of the mortar. T h i s pre-treatment c o n s i s t e d of g r i n d i n g a p o r t i o n of an i r o n bearing mix of s i m i l a r composition i n the automatic mortar and then washing out the mortar. The amount of Fe thus l e f t adhered to the mortar s u r f a c e should be c l o s e to a 'steady s t a t e ' amount f o r that mix. The mixes used f o r pre-treatment were e a r l y (unuseable) mixes which had s u f f e r e d i r o n l o s s d u r i n g g r i n d i n g .  118 APPENDIX B: AQUEOUS ANALYSES  QUENCH  PH:  Quench pH of the run f l u i d c o u l d be measured f o r cases in which the run f l u i d c o u l d be separated from the c a p s u l e and  i t s c r y s t a l l i n e contents by c e n t r i f u g i n g . The pH  measurement was made u s i n g a micro-combination pH e l e c t r o d e ( M i c r o e l e c t r o d e s , I n c . , Londonderry, N.H., U.S.A.) which r e q u i r e s as l i t t l e as 5M1 c o l l e c t e d the c e n t r i f u g e v i a l  (Pearce  React  i  i n the c o n i c a l bottom of vial).  E a r l y quench pH measurements e x h i b i t e d a continuous drift  which was i n t e r p r e t e d to be the r e s u l t of chemical  r e a c t i o n of atmospheric a i r with the run f l u i d . To prevent such r e a c t i o n s from o c c u r i n g p r i o r to and d u r i n g the pH measurement, capsule c e n t r i f u g i n g was conducted with the centrifuge v i a l  f l u s h e d with argon, and the pH measurement  was made with the open volume immediately surrounding the e l e c t r o d e f l u s h e d with argon. Quench pH measurements made with these p r e c a u t i o n s were f r e e of d r i f t . Table B1 l i s t s the quench pH measurements, a l l of which are  from o l i v i n e ion-exchange  experiments.  1 19  Table B1. Quench pH measurements.  Run#  ATOMIC  pH  Run#  pH  64  5.64  129  5.85  66  5.44  1 30  4.80  67  5.39  1 33  5.73  68  4.97  134  5.78  69  5.10  1 35  5.67  70  5.12  1 36  4.74  71  5.18  142  4.74  101  5.53  145  4.67  1 02  4.88  1 46  5.45  1 03  4.89  147  4.59  1 16  5.49  1 63  5.32  1 17  4.97  1 64  5.93  121  5.53  1 65  5.18  1 22  5.35  166  5.78  1 28  5.42  169  3.86  ABSORPTION  SPECTROPHOTOMETRY:  A n a l y s i s of aqueous Fe and Mg was performed on a V a r i a n Techtron model AA4 spectrophotometer using an a i r - a c e t e l e n e flame. S p e c t r a l l i n e s at 2852A and 2483A were used f o r Mg and Fe r e s p e c t i v e l y . The standard c o n c e n t r a t i o n s and sample d i l u t i o n s used were designed to r e s t r i c t absorbance  levels  to the 0.1 t o 0.4 range. A s e r i e s of 3 s t a n d a r d s , which span the c o n c e n t r a t i o n range of the 'unknown' samples, was  1 20 measured once before and once a f t e r each group (5 t o 10) of samples was measured. Each sample group was measured 3 to 5 times  (depending  on a v a i l a b l e s o l u t i o n volumes) with each  group measurement separated by a s i n g l e measurement of the standard s e r i e s . The absorbance meter was zeroed while a s p i r a t i n g a 'blank' (a sample of the a c i d i f i e d water used i n a l l d i l u t i o n s ) before every absorbance r e a d i n g . Sample c o n c e n t r a t i o n s were c a l c u l a t e d s e p a r a t e l y f o r each sample group by means of a c a l i b r a t i o n by l e a s t squares  fitting  f u n c t i o n which was produced  to the s i x standard absorbances (3  leading and 3 t r a i l i n g ) a s s o c i a t e d with that group. The calibration  f u n c t i o n used i s a q u a d r a t i c i n absorbance which  i s c o n s t r a i n e d to pass through zero c o n c e n t r a t i o n at zero absorbance. Adding together the standard e r r o r of r e p l i c a t e measurements, estimated accuracy of standards and estimated accuracy of d i l u t i o n s  i n d i c a t e s t h a t , i n g e n e r a l , Mg  c o n c e n t r a t i o n s are accurate to ±3% and Fe c o n c e n t r a t i o n s a r e accurate t o ±3.5%.  Standards  :  Atomic a b s o r p t i o n standards were made by c a r e f u l l y weighing  d r i e d , reagent grade MgO and F e 2 0 3  into volumetric  f l a s k s c o n t a i n i n g d i s t i l l e d water and s u f f i c i e n t grade HC1 to d i s s o l v e the o x i d e . Primary  reagent  standards were made  i n t h i s manner at c o n c e n t r a t i o n s of lOO^g MgO per ml and 500Mg P e 2 0 3 per m l . Secondary standards were made by d i l u t i n g the primary standards with the same a c i d i f i e d  121 d i s t i l l e d water used to d i l u t e the experimental run f l u i d s . The secondary standard  selection  judged optimal was 1, 2, 4  and 6ngMgO/ml and 20, 40, 60 and 80MgFe 2 0 3 /ml.  Dilution  of  Run  Fluids:  A l l d i l u t i o n s were made using a c i d i f i e d d i s t i l l e d  H20  to s t a b i l i z e the s o l u b i l i t y of i o n i c Fe and Mg. The a c i d i f i e d water c o n s i s t e d of 2ml of reagent grade HN03 i n each l i t e r  of d i s t i l l e d water  (0.03m i n HN0 3 ). N i t r i c a c i d  was chosen over HCl t o allow measurement of the c h l o r i n e concentration  i n the ( d i l u t e d ) run f l u i d .  I n i t i a l d i l u t i o n volumes were chosen to produce s o l u t i o n s c o n t a i n i n g approximately 0.005 moles t o t a l Fe+Mg. T h i s r e s u l t s i n convenient volumes of s o l u t i o n c o n t a i n i n g s u f f i c i e n t concentrations  of Fe and Mg f o r atomic  a b s o r p t i o n ; even at the extremes of Fe-Mg compositon This concentration  level  i s a l s o i n the range  range.  appropriate  for c h l o r i n e a n a l y s i s . For 2m run f l u i d s , 25/ul was t y p i c a l l y e x t r a c t e d and added t o 10ml of a c i d i f i e d water r e s u l t i n g i n an i n i t i a l d i l u t i o n  f a c t o r of 400.  The secondary d i l u t i o n f a c i l i t a t e atomic a b s o r p t i o n  f a c t o r s a p p r o p r i a t e to a n a l y s i s were g e n e r a l l y  c a l c u l a b l e s i n c e the approximate p r o p o r t i o n s of Fe and Mg i n the run f l u i d c o u l d be p r e d i c t e d based on the work of S c h u l i e n et a l ( l 9 7 0 ) . Secondary d i l u t i o n  f a c t o r s were  g e n e r a l l y between 1 and 10 f o r Fe and between 5 and 50 f o r Mg.  1 22  CHLORINE  ANALYSIS:  Aqueous c h l o r i n e c o n c e n t r a t i o n s were measured with a Buchler Cotlove Chloridometer  (Buchler Instruments, I n c . ,  F o r t L e e , N.J., U.S.A.). The instrument  measures the time  r e q u i r e d f o r complete c o u l o m e t r i c t i t r a t i o n a l i q u o t of s o l u t i o n  of CI" i n an  (see Cotlove et a l , 1958).  C o n c e n t r a t i o n s are determined by comparison with and  standards  n o r m a l i z i n g from the a c t u a l a l i q u o t volume to l l i t e r .  Any n o n - l i n e a r i t y of the dependence of t i t r a t i o n total  time on  CI" was avoided by a d j u s t i n g a l i q u o t volumes so that  every t i t r a t i o n  took approximately  seconds). T i t r a t i o n  of standards  (^60  i n d i c a t e d that there was no  s i g n i f i c a n t dependence of t i t r a t i o n (keeping t o t a l  the same time  time on a l i q u o t volume  CI" i n the a l i q u o t constant) f o r a l i q u o t  volumes i n the 50 to 200jul range. For r o u t i n e o p e r a t i o n , sample d i l u t i o n s were designed c o n t a i n i n g approximately Statistical  to produce  solutions  Ijtxmole CI" i n a 100M1 a l i q u o t .  a n a l y s i s of r e p l i c a t e measurements  indicates  that the c h l o r i n e analyses are accurate to ±6% of the amount present.  1 23 APPENDIX C: ELECTRON MICROPROBE ANALYSES  The main f e a t u r e s of the standard a n a l y s i s and a n a l y s i s techniques and d e t a i l s of t h e i r  particle  r e s p e c t i v e sample  mounting techniques are l i s t e d below f o l l o w e d by a summary of a l l microprobe analyses a n a l y s i s technique technique  ( t a b l e C 1 ) . The  i s not d i s c u s s e d s e p a r a t e l y : I t s mounting  i s that of the p a r t i c l e a n a l y s e s and  procedure i s that of the standard  STANDARD  Sample  crystal-face  i t s analysis  analyses.  ANALYSIS:  M i n e r a l g r a i n s were mounted in 1 inch  Mounting:  d i s k s of fused Buehler  Transoptic:  a c l e a r p l a s t i c powder  with a 20 to lOOMm g r a i n s i z e . Blank d i s k s of pure Transoptic  pressure  are f i r s t  fused at =150°C under a 4200psi  in a 1 inch c y l i n d r i c a l mold. Six shallow  holes are d r i l l e d  i n t o one  (2mm)  s u r f a c e of each b l a n k . Each hole  i s packed with a homogenized mixture  of  powder  Transoptic  (=*70%) and mineral g r a i n s . The mount i s then r e t u r n e d to the c y l i n d r i c a l mold and  re-pressed at the same P and  T.  To o b t a i n a f l a t p o l i s h a c r o s s each mineral g r a i n ( i n s p i t e of the hardness c o n t r a s t between the g r a i n Transoptic),  coarse g r i n d i n g and a l l but  and  the f i n a l  polishing  stage i s performed with diamond a b r a s i v e s on metal l a p s . f i n a l p o l i s h i n g stage c o n s i s t s of wet  The  p o l i s h i n g on a c l o t h  124 covered  l a p with  Microprobe  Li nde  B  alumina  for  a few  seconds,.  Analysis'.  (ARL-SEMQ and ARL-EMX) Accelerating Emission Objective  potential  current  1 5kV 1 50MA  aperture  1 OOMm  Specimen c u r r e n t  1 5nA  Beam diameter  -3 Mm  Counting time  20 seconds  Standards  30 to lOOum s y n t h e t i c f o r s t e r i t e , synthetic fayalite and  synthetic enstatite grains;  mounted as above. Data r e d u c t i o n  PARTICLE  Sample  Bence-Albee  ANALYSIS'.  Mounting:  M i n e r a l g r a i n s were d e p o s i t e d on a  p o l i s h e d g r a p h i t e s u b s t r a t e from an a l c o h o l s u s p e n s i o n . A l l p a r t i c l e mounts were carbon coated p r i o r to a n a l y s i s . The  g r a p h i t e stubs used as a s u b s t r a t e f o r p a r t i c l e  a n a l y s i s were cut from l / 4 i n c h diameter high  purity  s p e c t r o s c o p i c e l e c t r o d e r o d s . The stubs of g r a p h i t e rod were mounted v i a set-screws  i n t o 1inch diameter s t e e l h o l d e r s (5  125  stubs per holder) which f i t d i r e c t l y  i n t o the microprobe  specimen s t a g e . While mounted i n the s t e e l h o l d e r , the stubs were p o l i s h e d f l a t by dry g r i n d i n g on a s e r i e s of a b r a s i v e g l a s s p l a t e s . The a b r a s i v e s u r f a c e of each g l a s s p l a t e had been l i g h t l y ground with a d i f f e r e n t grade of s i l i c o n c a r b i d e or aluminum oxide a b r a s i v e powder.  Microprobe  Analysis:  (ARL-SEMQ) Accelerating potential  1  Emission  1 50uA  Objective  current aperture  5kV  40  Mm  Specimen c u r r e n t  35nA  Beam diameter  10MHI  Counting time  100 seconds  Standards  same as those used f o r standard  square r a s t e r  analysis Data r e d u c t i o n  Bence-Albee plus an e m p i r i c a l graphical correction  The of The  e m p i r i c a l c o r r e c t i o n curve was formulated  i n terms  s i n c e t h i s was the d e s i r e d product of the a n a l y s e s . c o r r e c t i o n curve was c a l i b r a t e d by a n a l y z i n g a s e r i e s of  f i n e - g r a i n e d s y n t h e t i c o l i v i n e s . The c o r r e c t i o n curve used is illustrated  in figure C 1 .  126  X  0.04  0.0  0.2  0.4  0.6  Apparent  0.8  XMg  F i g u r e C I . E m p i r i c a l c a l i b r a t i o n curve f o r p a r t i c l e c o r r e c t i o n . The  1a e r r o r boxes surround  1.0  the standard  analyses which were used to d e f i n e the c u r v e .  analysis olivine  Table C I .  Summary of microprobe  analyses.  The  more c r y p t i c column headings a r e : PH=phase, M=method.  The  a b r e v i a t i o n s are O L = o l i v i n e , OP=orthopyroxene, OA=  orthoamphibole, S=standard a n a l y s i s , P = p a r t i c l e a n a l y s i s , F=crystal  face a n a l y s i s . The formula c a t i o n s are based upon  4 oxygens f o r o l i v i n e , 6 f o r orthopyroxene, and 23 f o r orthoamphibole. For the p a r t i c l e a n a l y s e s , only has  XMg  been c o r r e c t e d v i a the e m p i r i c a l c a l i b r a t i o n  ( f i g u r e C1). The l a s t column i n d i c a t e s the number of analyses  averaged i n c a l c u l a t i n g the l i s t e d WT%  RUN  PH  M  TOTAL  1 42  OL  S  91.60  1 42  OL  P  1 43  OL  1 43  Formula Mg  values.  Cations Fe  Si  X  (1a)  #  0.744  1.235  1.010  0.376( 13)  6  20.45  0.646  1.363  0 .995  0.338( 19)  13  S  96.74  0.804  1.174  1.011  0.407( 18)  6  OL  P  20.96  0.864  1. 1 47  0 .995  0.455( 14)  1 1  145  OL  S  99.81  0.207  1.781  1.006  0. 1 04( 3)  7  1 45  OL  p  20.86  0.308  1.697  0 .998  0. 1 63( 7)  6  1 46  OL  s  96.73  1.390  0 .599  1.010  0.702(  8)  7  146  OL  p  12.58  1.298  0 .549  1.076  0.728(  4)  5  1 47  OL  P  21.83  1.945  0 .036  1.010  0.984( 10)  13  163  OL  s  98.75  0.211  1.786  1.002  0. 1 06( 4)  3  1 63  OL  p  24.41  0.140  1.895  0 .983  0.074( 11)  12  164  OL  p  19.77  0.722  1.228  1.000  0.4 1 9 (8)  15  1 65  OL  s  97.99  0.764  1.227  1.005  0.384( 11)  7  165  OL  p  23.53  0.662  1.416  0 .961  0.334< 8)  16  166  OL  s  97.90  0.766  1.223  1.006  0.385( 12)  4  166  OL  p  16.75  0.642  1.367  0 .996  0.347) 1 1 ) 18  167  OL  s  00.11  0.647  1.345  1.004  0.325< 5)  5  167  OL  p  18.55  "0.793  1.240  0 .984  0.388< 14)  14  0.984  0 .999  1.008  0.496 ( 5)  7  11 6  OL  s  99.45  11 6  OL  p  11.93  0.927  1.045  1.014  0.493< 4)  10  11 7  OL  s  99.82  0.984  1.004  1.006  0.495< 5)  7  121  OL  s  00.07  0.996  1.006  0 .999  0.498(  8  3)  128  WT%  Formula C a t i o n s  RUN  PH  M  TOTAL  121  OL  P  17.54  0.906  1 .083  122  OL  S  100.26  0.997  122  OL  P  21.31  124  OL  P  1 35  OL  1 35  Mg  Fe  Si  (1a)  #  1 .006  0.478 (10)  9  1 .009  0.997  0.497 ( 3)  8  1 .005  0.985  1 .005  0.529 (20)  10  10.40  1 .548  0.427  1.012  0.807 ( 9)  16  S  97.81  1 .043  0.953  1 .002  0.522 (24)  5  OL  P  20.81  1.111  0.888  1 .000  0.582 (21 )  10  1 36  OL  s  97.39  0.983  1 .005  1 .005  0.494 ( 4)  8  1 36  OL  P  20. 12  0.894  1 .092  1 .007  0.472 ( 15) 1 0  1 99  OL  s  100.40  0. 196  1 .791  1 .007  0.098 ( 5)  8  199  OL  P  30.43  0.239  1 .824  0.968  0. 1 23 (20)  7  200  OL  s  99.87  0.556  1 . 436  1 .004  0.279 (20)  7  200  OL  P  1 4. 96  0.627  1 .391  0.990  0.327 (23)  10  25  OL  s  99.66  0.203  1 .778  1 .009  0. 1 02 ( 4)  8  26  OL  s  99.18 •  0.558  1 .422  1.010  0.282 (14)  8  26  OL  p  21.17  0.575  1 .427  0.999  0.299 (19)  22  27  OL  s  99. 18  0.527  1 .462  1 .005  0.265 (18)  8  27  OL  p  20.86  0. 521  1 .505  0.987  0.270 (18)  13  37  OL  s  99.55  1 . 180  0.800  1 .010  0.596 ( 4)  8  37  OL  p  15.17  1 . 142  0.823  1.018  0.607 (12)  13  38  OL  s  98.98  1 .374  0.596  1.015  0.698 ( 5)  8  38  OL  p  1 6.42  1 .290  0.690  1 .010  0.679 (13)  12  39  OL  s  99.42  1 .486  0.486  1.014  0.754 ( 6)  5  39  OL  p  10.50  1 .458  0.500  1 .021  0.770 ( 8)  12  40  OL  p  5.30  1 .528  0.462  1 .005  0.792 (11)  17  41  OL  s  98.70  1 .800  0. 192  1 .004  0.904 ( 3)  6  41  OL  p  3.80  1 .660  0.269  1 .035  0.882 ( 9)  8  41  OL  F  86.20  1 .755  0.233  1 .006  0.883 ( 9.)  7  42  OL  s  99.46  1.916  0.081  1 .002  0.960 (14)  6  42  OL  p  7.93  1 .745  0.223  1.016  0.909 (10)  16  43  OL  s  99.56  0.985  1.011  1 .002  0.494 ( 2)  8  43  OL  p  17.27  0.880  1 . 1 07 1 .007  0.465 ( 9)  13  64  OL  s  100.17  1 .980  0.016  0.992 ( 1 ) 8  1 .002  Mg  129  WT%  Formula Cations  RUN  PH  M  TOTAL  66  OL  S  98.08  0.976  1 .000  1.012  0.494 ( 2)  8  67  OL  P  15.56  0.954  1 .050  0.998  0.500 ( 5)  13  68  OL  S  99.46  0.999  0.988  1 .006  0.503 ( 8)  7  1 19  OL  s  100.04  0.995  1 .005  1 .000  0.497 ( 3)  8  1 19  OL  p  1 9.44  0.999  0.963  1 .019  0.533 (10)  12  133  OL  s  99.51  0.991  1 .007  1 .001  0.496 ( 1 )  1 33  OL  p  20.31  0.885  1 . 1 24 0.996  0.463 (11)  134  OL  s  100.09  0.985  0.999  1 .008  0.497 ( 2)  7  101  OL  s  99.48  0.986  1 .002  1 .006  0.496 ( 3)  8  101  OL  p  18.26  0.891  1 .081  1.014  0.474 (15)  13  102  OL  s  99.10  0.986  1 .003  1 .005  0.495 ( 4)  7  1 02  OL  p  20.22  0.946  1 .027  1.013  0.503 ( 8)  12  1 03  OL  s  98.74  0.982  1 .000  1 .009  0.496 ( 4)  7  103  OL  p  1 6. 44  0.883  1 .081  1.018  0.472 ( 6)  12  128  OL  p  16.30  0.990  1.010  1 .000  0.519 (23)  10  129  OL  s  100.41  0.990  1 .009  1 .001  0.495 ( 3)  129  OL  p  17.85  0.883  1.110  1 .004  0.465 (12)  130  OL  s  100.54  0.989  1 .004  1 .004  0.496 ( 5)  6  130  OL  p  17.61  0.883  1 .091  1.013  0.469 ( 8)  10  174  OL  p  6.88  1 .645  0.324  1.016  0.855 ( 9)  1 1  197  OL  s  100.12  0. 1 96  1 .790  1 .007  0.099 ( 7)  6  197  OL  p  24.71  0. 1 47  1 .865  0.994  0.078 ( 6)  1 1  225  OL  p  25.30  0.257  1 .794  0.974  0. 1 30 (14)  16  226  OL  p  24.21  0.537  1 .504  0.979  0.270 (12)  26  227  OL  p  1 6.84  1 .595  0.399  1 .003  0.820 (12)  19  69  OL  s  99.90  0.208  1 .780  1 .006  0. 1 05 ( 2)  8  70  OL  s  99.25  0.214  1 .780  1 .003  0. 1 07 ( 1 ) 8  71  OL  s  99.23  0.844  1 . 150  1 .064  0.423 ( 4)  6  72  OL  s  99.38  1 .621  0.378  1 .001  0.811 ( 2)  8  21 1  OL  s  99.05  1 .598  0.403  1 .000  0.799 ( 5)  8  21 1  OL  p  9.98  1 .486  0.482  1.016  0.780 ( 3)  6  212  OL  s  98.38  1 . 1 94  0.786  1.010  0.603 (14)  6  Mg  Fe  Si  Mg  (1a)  #  2 10  7 10  1 30  WT%  Formula Cations  RUN  PH  M  TOTAL  212  OL  P  1 4.40  1 . 188  0.800  1 .006  0.623 ( 7)  12  213  OL  s  98.36  0.787  1 .204  1 .005  0.395 ( 4)  6  21 3  OL  P  1 7.70  0.753  1 .264  0.991  0.392 ( 6)  9  75  OL  s  99.44  0.209  1 .782  1 .004  0. 1 05 ( 2)  7  169  OL  s  99.94  1.721  0.270  1 .005  0.865 ( 1 ) 8  169  OL  P  24.58  1 .6.50  0.293  1 .028  0.868 ( 2)  2  169  OL  F  96.29  1 .790  0.251  0.979  0.877 ( 4)  3  1 70  OL  s  100.09  1 .623  0.386  0.995  0.808 ( 6)  7  170  OL  F  97.62  1 .641  0.349  1 .005  0.825 ( 7)  7  202  OL.  S  99.25  0.228  1.759  1 .007  0.115 ( 5)  8  202  OL  P  22.47  0.214  1 .798  0.994  0.113 (12)  7  203  OL  100. 10  0.843  1 . 148  1 .004  0.420 (12)  7  204  OL  s s  100.97  1.517  0.461  1 .005  0.768 (20)  5  204  OL  p  16.53  1 .427  0.557  1 .008  0.745 (12)  9  264  OP  s  98.65  0.730  1 .251  2.009  0.369 (41 )  8  264  OP  p  21 .95  0.644  1.316  2.019  0.345 (26)  9  265  OP  s  98.87  0.790  1 . 194  2.008  0.398 (16)  6  265  OP  p  14.76  1 .086  0.920  1 .996  0.567 (16)  8  266  OP  s  97.98  1 . 140  0.839  2.011  0.576 (20)  6  266  OP  p  1 5.88  1 .232  0.628  2.069  0.689 (17)  10  267  OP  s  98.31  1 .525  0.460  2.007  0.768 (41 )  6  267  OP  p  22.20  1 .406  0.568  2.013  0.738 (22)  9  268  OP  s  99.26  1 .642  0.362  1 .998  0.819 (43)  7  268  OP  p  21 .74  1 .671  0.253  2.038  0.886 (25)  7  269  OP  p  18.05  1 .821  0. 1 43  2.018  0.937 ( 9)  8  277  OP  s  99.08  0.721  1 .268  2.005  0.363 (20)  5  277  OP  p  16.90  0.774  1 .261  1 .982  0.400 (17)  9  278  OP  s  98.72  1 .582  0.397  2.011  0.799 (19)  9  278  OP  p  16.13  1 .562  0.402  2.018  0.818 (11)  8  279  OP  s  98.08  1 .891  0. 100  2.005  0.950 (55)  5  279  OP  p  18.32  1 .739  0.236  2.013  0.896 (16)  10  228  OP  s  98.89  0.851  1 . 134  2.008  0.429 (45)  10  Mg  Fe  Si  Mg  (1a)  #  131  WT%  Formula C a t i o n s Mg  RUN  PH  M  TOTAL  228  OP  P  27.77  0.831  1 .068  2.050  0.458I 15)  6  228  OP  F  100.41  0.899  1 .001  2.050  0.466I 9)  6  229  OP  S  98. 16  1 .035  0.953  2.006  0.520< 42)  229  OP  P  16.45  0.982  0.975  2.022  0.526 17)  7  229  OP  F  99.65  1 .027  0.923  2.025  0.527 (11)  8  230  OP  S  99.09  1 .398  0.590  2.007  0.703 (62)  9  230  OP  P  15.73  1 .365  0.520  2.058  0.750 (14)  8  230  OP  F  99.35  1 .485  0.498  2.008  0.749 (16)  4  231  OP  S  97.81  1.611  0.407  1  .991  0.798 (17)  7  231  OP  P  1  1 .454  0.451  2.047  0.788 ( 7)  6  2 32  OP  s  97.79  1 .736  0.289  1  0.857 (39)  8  232  OP  p  17.90  1 .568  0.265  2.083  0.874 (15)  10  233  OP  s  98. 16  1  .930  0.051  2.010  0.974 (16)  9  233  OP  p  16.21  1 .727  0.083  2.095  0.966 ( 5)  7  304  OA  p  6.31  0.843  6.961  7.598  0.114 (12)  8  215  OA  p  15.12  2.362  4.958  7.840  0.340 ( 7)  7  188  OA  p  11  3.585  3.998  7.709  0.496 (21 )  10  218  OA  p  13.90  4.823  2.351  7.713  0.699 (54)  9  300  OA  p  12.84  5.940  0.890  8.085  0.887 (34)  10  252  OA  p  5.56  2.532  5.294  7.587  0.341 (14)  10  253  OA  p  4.28  3.675  4.088  7.618  0.497 (27)  9  283  OA  p  5.84  2.654  5.239  7.553  0.354 (13)  10  284  OA  p  8.08  3.432  4. 179  7.694  0.473 (18)  10  285  OA  p  8.11  4.860  2.560  7.790  0.682 (28)  9  307  OA  p  8.66  5.965  0.977  8.029  0.879 (58)  10  308  OA  p  5.50  6. 1 25  0.637  8.119  0.919 (38)  9  309  OA  p  5.13  2.888  4.824  7.644  0.394 (16)  10  310  OA  p  4.39  0.940  7.151  7.455  0. 122(17)  10  6.70  .09  Fe  Si  .988  X  Mg  { ] o )  #  1  0  1 32 APPENDIX D: HIGH ACCURACY POWDER XRD  The high accuracy XRD  peak p o s i t i o n measurements  r e q u i r e d f o r u n i t c e l l r e f i n e m e n t s , c a l i b r a t i o n of peak p o s i t i o n as a f u n c t i o n of c o m p o s i t i o n , and measurement of mineral composition (based on such a c a l i b r a t i o n ) were performed on a P h i l i p s PW1710 Automatic Powder DiffTactometer. T h i s u n i t employs a stepping-motor d r i v e n goniometer and, i s microcomputer  controlled. Accordingly,  automatic, d i g i t a l peak-seeking procedures were used  instead  of a n a l o g , c h a r t - r e c o r d i n g methods. A l l measurements were made using Ni f i l t e r e d Cu r a d i a t i o n . A g r a p h i t e monochromator reduced Fe f l u o r e s c e n c e problems  PEAK  POSITION  to a minimum.  MEASUREMENT:  The s t r a t e g y chosen  f o r peak measurement with the  PW1710 i s one of e s t a b l i s h i n g the 26 p o s i t i o n having the absolute maximum i n t e n s i t y f o r each peak, at low angles rf-spacings  are  c a l c u l a t e d using the Ka, wavelength. For  sharp peaks the d i g i t a l peak-seeking procedures can and measure Ka, and Ka 2  resolve  peaks at angles as low as 4O°20. The  e f f e c t s of counting s t a t i s t i c s are minimized by using longish  (10 second) counting t i m e s . The p r e c i s i o n of each  peak p o s i t i o n measurement i s e s t a b l i s h e d through r e p e t i t i o n s . Although the peak measurement procedure i s subsequently time consuming (6 to 12 minutes or more depending on d e t a i l s of the p r o c e d u r e ) , the e n t i r e process  133 for a number of peaks measured f o r a c e l l still  refinement can  be f a s t e r than t y p i c a l analog instrument p r o c e d u r e s .  If the approximate  p o s i t i o n of the t a r g e t peaks i s a l r e a d y  known, a c o n t r o l program, s p e c i f i c to the m i n e r a l , can be w r i t t e n s p e c i f y i n g these p o s i t i o n s . T h i s avoids of time i n measuring  the continuum between  investment  peaks.  In programming the above s t r a t e g y I made use of two peak-seeking  f u n c t i o n s p r o v i d e d by P h i l i p s and one  programmed by m y s e l f . The two d e l i v e r e d with the machine are: MAX:  §steps,  stepsize,  count  and goniometer  lime  p o s i t i o n are u s e r - s p e c i f i e d . MAX counts x-ray pulses f o r count  time  seconds at each of  p o s i t i o n s , each  %steps-2+]  s t a r t i n g at a p o s i t i o n  apart,  stepsize  #5t eps•stepsi  p o s i t i o n of the goniometer  ze  below the  when MAX i s invoked.  The p o s i t i o n with the maximum x-ray i n t e n s i t y i s p r i n t e d out and the goniometer that p o s i t i o n . Some smoothing statistics  i s returned to of c o u n t i n g  i s accomplished by summing the  i n t e n s i t y f o r each p o s i t i o n with the i n t e n s i t i e s of on adjacent p o s i t i o n on e i t h e r s i d e , and comparing CSP:  i n t e n s i t i e s based on these sums.  T h i s i s a continuous scanning r o u t i n e with peak i d e n t i f i c a t i o n and measurement procedures i n . The user s p e c i f i e s a and the  29  scanrate,  a  d i s t a n c e to scan o v e r . The  which separates d i g i t a l scanrate•countt  CSP, the f i v e  ime.  built counttime  26  stepsize  i n t e n s i t y measurements i s  For each peak i d e n t i f i e d by  i n t e n s i t i e s at p o s i t i o n s c l o s e s t to  the peak maximum are f i t t e d to a p a r a b o l a , from which the a b s o l u t e maximum p o s i t i o n i s  134 calculated. The  need f o r a t h i r d r o u t i n e i s a r e s u l t of the  i n a b i l i t y of the above r o u t i n e s t o handle low i n t e n s i t y and broad peaks. CSP i s very p r e c i s e f o r s t r o n g , sharp peaks. However, the p e a k - i d e n t i f i c a t i o n p a r t of the r o u t i n e , over which the user has no c o n t r o l , o f t e n misses broad,weak peaks when using a small  slepsize.  Although MAX always r e t u r n s a  measurement, i t i s only as p r e c i s e as the  being  stepsize  used. In p r i n c i p l e then, MAX can be p r e c i s e to ±0.005°,. the minimum step s i z e of the goniometer. In p r a c t i c e , counting s t a t i s t i c s confuse the p o s i t i o n of the peak maximum over a  26 (at  d i s t a n c e of about 0 . 0 2 ° and MAX only samples 0 . 0 1 ° swaths the 0 . 0 0 5 ° The  stepsize).  optimum user-programmed r o u t i n e t o circumvent the  problems inherent fitting  i n MAX and CSP would probably be a curve  r o u t i n e s i m i l a r to CSP. However, the programming  c a p a c i t y of the PW1710 ( o p e r a t i n g i n an Assembler  hybrid)  makes programming of such a r o u t i n e complicated and memory-expensive. I chose i n s t e a d to w r i t e a r o u t i n e which i s very has  s i m i l a r to MAX, which I w i l l  r e f e r to as MAX9. MAX9  no v a r i a b l e s since v a r i a b l e s a r e not a f e a t u r e of the  PW1710 c o n t r o l language. MAX9 uses a 10 second counting and  the minimum  stepsize.  time  I t assumes that the s t a r t i n g  goniometer p o s i t i o n i s c l o s e to the peak maximum and measures i n t e n s i t i e s at each of 8 steps on e i t h e r s i d e of the s t a r t i n g p o s i t i o n (and a l s o a t the s t a r t i n g p o s i t i o n i t s e l f ) . L i k e MAX, comparison of i n t e n s i t i e s i s made based  135 on sums of i n t e n s i t i e s symmetric  about the p o s i t i o n i n  q u e s t i o n . MAX9, however, uses sums of 9 i n t e n s i t i e s . T h i s means that MAX9 sums over 0 . 0 4 ° swaths, but i t has a p r e c i s i o n of 0 . 0 0 5 ° . For s i n g l e peak measurements, n e i t h e r CSP nor MAX9 were used a l o n e . I f e r r o r due to specimen  height and the e f f e c t  of s o l i d s o l u t i o n on m i n e r a l c e l l parameters are c o n s i d e r e d , it  i s c l e a r t h a t , i n g e n e r a l , the goniometer  p o s i t i o n of a  p a r t i c u l a r XRD peak cannot be p r e d i c t e d to c l o s e r than ±O.25°20! An optimum, h i g h p r e c i s i o n set up f o r CSP was found to be: 0.002°/s  scanrate;  10s  0.02° total  counttime;  scan range. MAX9, as w r i t t e n , has an e f f e c t i v e range of only O.O4°20. To ensure that the goniometer  i s w i t h i n the range  of these two r o u t i n e s s u c c e s s i v e i n v o c a t i o n s of MAX with coarser  stepsizes  and 4 t o 5 second  count  times  were used.  Although CSP proved to be ( p o t e n t i a l l y ) more p r e c i s e than MAX9, the two procedures were not measuring  a pattern  mixed when  i n c l u d i n g both sharp and broad peaks  s i n c e the e f f e c t of peak shape on the answer each gives i s unknown. In cases where the XRD p a t t e r n to be measured has a very l a r g e number of c l o s e l y spaced peaks, a s i n g l e i n v o c a t i o n of CSP c o v e r i n g the e n t i r e t a r g e t range of 26 was used. A 0.005°/s  scanrate  and a 5s  t h i s 26 range was g r e a t e r than  counttime  was used i f  20°.  The accuracy of these peak-seeking p r o c e d u r e s , i n c l u d i n g the p r e c i s i o n of standard peak measurement, i s  136 about ±0.01 °28 0.002°/s scanrat  f o r MAX9, ±0.005°26  1  f o r CSP using the  and ±O.O2°20 f o r CSP using the 0.005°/s  scanrate  e.  STANDARDS:  Although  the P h i l i p s goniometer i s p r e c i s e t o  O . O O 2 5 ° 2 0 , accurate measurements cannot be obtained by goniometer c a l i b r a t i o n a l o n e . Geometric a n a l y s i s of the goniometer dimensions shows t h a t small v a r i a t i o n s i n specimen height r e s u l t  i n unacceptable  systematic  errors.  For example, a change i n specimen height of 0.1mm r e s u l t s i n a systematic 28 e r r o r of 0 . 0 6 ° . The m i n e r a l s used as i n t e r n a l standards were i n t i m a t e l y mixed with the mineral being measured. The standards employed i n c l u d e S i m e t a l , s y n t h e t i c s p i n e l , s y n t h e t i c p e r i c l a s e , and n a t u r a l quartz (which had been ground, leached and a n n e a l e d ) .  SAMPLE  MOUNTING:  All  samples were d e p o s i t e d from t h i c k  suspensions  onto g l a s s d i s c s designed  alcohol  t o f i t the P h i l i p s  sample h o l d e r s . In cases where p r e f e r r e d o r i e n t a t i o n was an u n d e s i r e a b l e tendency, the mineral powder was mixed with Buehler  Transoptic  powder which had been s i e v e d t o <50  nm.  When d e p o s i t e d from a s u s p e n s i o n , the m i n e r a l g r a i n s would adhere to the s u r f a c e of the s p h e r i c a l , p l a s t i c grains.  Transoptic  1 37 APPENDIX E: TRANSMITTED ELECTRON MICROSCOPY  TEM  lattice  images are b a s i c a l l y i n t e r f e r e n c e  r e s u l t i n g from d i f f r a c t i o n of a p a r a l l e l beam of as  electrons  i t passes between r e g u l a r l y spaced planes of atoms. To  obtain a s t r u c t u r a l l y i n t e r p r e t a b l e TEM  image the  c r y s t a l l o g r a p h i c planes of i n t e r e s t must be o r i e n t e d p a r a l l e l to the e l e c t r o n beam and magnification  a high  ELECTRON  the  p r a c t i c a l requirements and  to be c o n s i d e r e d i n o b t a i n i n g  The  accurately  must be employed i n order to r e s o l v e  i n t e r f e r e n c e p a t t e r n . The  THE  patterns  lattice  images are as  factors follows.  MICROSCOPE'.  instrument must be p h y s i c a l l y and  electronically  s t a b l e to prevent l o s s of r e s o l u t i o n d u r i n g photographic exposures of a few  seconds. The  instrument must be  of r o u t i n e a p p l i c a t i o n of m a g n i f i c a t i o n s  greater  200,000X. Smoothly o p e r a t i n g , high t o l e r a n c e both l i n e a r and  THE  t i l t i n g , are  than  stage motions,  desireable.  SPECIMEN:  Specimen g r a i n s must be t h i n enough to allow a of the beam to be t r a n s m i t t e d be  capable  through them. The  separated from each other so that  i n d i v i d u a l l y . The strong  be  g r a i n s must studied  p h y s i c a l support of the g r a i n s must be  enough to be  generally  they can  majority  s t a b l e under the e l e c t r o n beam, and  transparent to the e l e c t r o n beam. In a d d i t i o n ,  the  1 38 support f i l m should have holes  i n i t so that  grains  p r o j e c t i n g over these holes can be s t u d i e d without any f o r e i g n c o n t r i b u t i o n s to the image.  THE  BEAM:  The  e l e c t r o n beam should be small  i n diameter, f r e e  from astigmatism and a c c u r a t e l y a l i g n e d along the a x i s of the  instrument. Choosing an a c c e l e r a t i n g v o l t a g e  requires  c o n s i d e r a t i o n of the t r a d e - o f f between b r i g h t n e s s and contrast  i n the l a t t i c e  in stronger  contrast  image. A l e s s e n e r g e t i c  beam r e s u l t s  i n the i n t e r f e r e n c e p a t t e r n . A more  e n e r g e t i c beam has more p e n e t r a t i n g b r i g h t e r and has a higher  power and so i t i s  l i m i t of maximum specimen  thickness. For d e t a i l s of the theory and p r a c t i c a l requirements of lattice  imaging and review of i t s a p p l i c a t i o n s , u s e f u l  references  i n c l u d e Wenk et al(eds.,1976) and Spence(1981).  ORTHOAMPHIBOLE The  lattice  LATTICE IMAGING  imaging employed i n c h a r a c t e r i z i n g the  s t r u c t u r e of s y n t h e t i c orthoamphiboles was performed on a H i t a c h i H-800 STEM i n the U.B.C. M e t a l l u r g y  Department. The  H-800 i s a d i g i t i z e d , microcomputer c o n t r o l l e d instrument with a s i d e - e n t r y goniometer s t a g e . I t has a maximum a c c e l e r a t i n g p o t e n t i a l of 200kV and a maximum m a g n i f i c a t i o n of 600,000 d i a m e t e r s . The c r y s t a l l o g r a p h i c o r i e n t a t i o n of specimen g r a i n s i s f a c i l i t a t e d with a motor d r i v e n  1 39 d o u b l e - t i l t specimen holder having a maximum t i l t  of ±45° on  each a x i s . The lattice  instrument o p e r a t i n g c o n d i t i o n s g e n e r a l l y used f o r imaging are as  follows:  Accelerating potential  200kV  Beam diameter  1 Mm  Condenser aperture  300MITI  O b j e c t i v e aperture  50 or 70MHI  magnification  400,000X  SPECIMEN  MOUNTING:  S y n t h e t i c amphibole g r a i n s were d e p o s i t e d from an a l c o h o l suspension onto a holey carbon f i l m which supported by a 600mesh copper TEM  support g r i d .  Production of the holey carbon f i l m measuring  was  i s begun by  i n t o a v i a l , by volume, 5% c o l l o d i o n , 10%  water, and 85% amyl a c e t a t e . The v i a l  soapy  i s s e a l e d and a g i t a t e d  in a b a l l - m i l l shaker u n t i l the f l u i d appears u n i f o r m l y milky white due to f i n e l y d i s s e m i n a t e d water and a i r b u b b l e s . S e v e r a l drops of t h i s f l u i d are dropped i n t o a c o n t a i n e r of water. Below the water surface i n t h i s c o n t a i n e r are s e v e r a l TEM  support g r i d s which s i t on a  coarse wire s c r e e n . The f i l m that forms on the water  surface  i s allowed to 'dry' f o r a few minutes. The f i l m i s d e p o s i t e d onto the support g r i d s by slowly d r a i n i n g the water out through the bottom of the c o n t a i n e r . A f t e r a l l remaining  1 40 water has and  d r i e d from the  s c r e e n , the TEM  g r i d s are  removed  carbon c o a t e d . F i n a l l y the g r i d s are c a r e f u l l y dipped  i n t o acetone f o r about 20 collodion  seconds each to remove  f i l m ; l e a v i n g behind only the carbon  IMAGING  the  coating.  PROCEDURES'.  Each TEM  session  alignment and  i s begun with beam and  f i n e tuning of beam astigmatism  An amphibole b e a r i n g TEM  i n s e r t e d i n t o the  z e r o e d . Using low  magnification  appropriate grain  i s sought. go  stage with a l l t i l t  bright  field  i n t o s e l e c t i o n of an  g r a i n ; I t must be t h i n enougn f o r l a t t i c e about 0.1 Mm  corrections.  g r i d i s loaded onto the d o u b l e - t i l t  sample holder and  Several c r i t e r i a  aperature  imaging, an  'appropriate'  imaging ( l e s s than  (1000A) f o r Mg-Fe s i l i c a t e s ) . It must be  s u f f i c i e n t l y s p a t i a l l y separated from other g r a i n s  to allow  independent o b s e r v a t i o n of i t s e l e c t r o n d i f f r a c t i o n A portion  axes  pattern.  of the g r a i n must l i e i n a p o s i t i o n which i s  r e l a t i v e l y c l o s e to the d e s i r e d  crystallographic  o r i e n t a t i o n . G r a i n s near the center of the mount are preferable by the  since t h e i r s p a t i a l p o s i t i o n s are  stage t i l t  The  least affected  motions.  proportion  of g r a i n s which can  be o r i e n t e d  to a  s p e c i f i c c r y s t a l l o g r a p h i c d i r e c t i o n i s , in p r i n c i p l e , q u i t e large  s i n c e the  tilt  motions of the  stage have a t o t a l swing  of 9 0 ° on each a x i s . In p r a c t i c e , i t was  found that the  motions were only p r a c t i c a l to ±20° above which stage  tilt drift  141 became unacceptable f o r photography at high O r i e n t a t i o n of orthoamphibole g r a i n s  magnification.  (mounted as  d e s c r i b e d above) i s somewhat s i m p l i f i e d by t h e i r and  morphology. At zero stage t i l t  l i e s perpendicular  stucture  the c-axis of most g r a i n s  to the e l e c t r o n beam. Due to the  orthorhombic symmetry, the a and b axes of most g r a i n s then lie  i n a plane p a r a l l e l to the beam. As a r e s u l t , the task  of o r i e n t i n g g r a i n s with  a or b axes p a r a l l e l t o the beam i s  s i m p l i f i e d , and beam p a r a l l e l o r i e n t a t i o n of c-axes i s impossible. Two d i f f e r e n t s t a t e g i e s were used i n searching f o r e a s i l y orientable grains  (a or b a x e s ) . One i s a 'random  walk' method. In t h i s case the sample i s slowly searched f o r g r a i n s a l r e a d y l y i n g very c l o s e t o the d e s i r e d o r i e n t a t i o n by slowly scanning the g r i d with the instrument set i n s e l e c t e d - a r e a - d i f f r a c t i o n mode. The second, and more systematic  s t r a t e g y i s to search  g r a i n which l i e s with of the stage t i l t  ( b r i g h t f i e l d mode) f o r a  i t s long a x i s n e a r l y p a r a l l e l to one  axes. O r i e n t a t i o n of such a g r a i n only  r e q u i r e s motion on that one t i l t  a x i s . U n f o r t u n a t l y , the  number of such g r a i n s which a l s o s a t i s f i e d a l l of the other criteria The  was found to be p a i n f u l l y few. s u c c e s s f u l search  f o r an ' a p p r o p r i a t e ' g r a i n was  o f t e n the most time-consuming step i n o b t a i n i n g each l a t t i c e image. Accurate c r y s t a l l o g r a p h i c o r i e n t a t i o n i s accomplished by t i l t i n g the stage while observing  the e l e c t r o n  142 d i f f r a c t i o n p a t t e r n of the t a r g e t g r a i n . Frequent i n t e r r u p t i o n of t h i s process f o r r e - c e n t e r i n g and r e - f o c u s s i n g the g r a i n are i n e v i t a b l e . The  electron d i f f r a c t i o n pattern  zero-level reciprocal lattice diffraction  i s basically a  image. The s p a t i a l p a t t e r n of  s p o t s , f o r a major a x i s o r i e n t a t i o n , can e a s i l y  be p r e d i c t e d i f the space group and approximate u n i t repeats  are a l r e a d y  i s recognized  cell  known. Proper c r y s t a l l o g r a p h i c alignment  when the d i f f r a c t i o n  spots have the  appropriate  s p a t i a l p a t t e r n and the d i s t r i b u t i o n of  diffraction  intensities  i s symmetric about the d i r e c t beam  spot. Once c r y s t a l l o g r a p h i c o r i e n t a t i o n i s accomplished an o b j e c t i v e a p e r a t u r e which passes about 20 d i f f r a c t e d beams i s i n s e r t e d . The instrument i s returned and  the m a g n i f i c a t i o n  i s advanced to the highest  l e v e l . The image i s then a c c u r a t e l y binocular  t o b r i g h t f i e l d mode practical  focused using the  ( o p t i c a l ) microscope to magnify the f l u o r e s c e n t  s c r e e n . I f the l a t t i c e  interference pattern  i s not v i s i b l e  at t h i s p o i n t , f i n e tuning of the beam astigmatism c o r r e c t i o n may be n e c e s s a r y . To prevent specimen contamination and s t r u c t u r a l damage (from the beam) p r i o r to photography, the time spent f o c u s s i n g and a d j u s t i n g stigmators  should be minimized and/or these adjustments  should be made with the beam on an area other to be photographed. For each l a t t i c e photographs a t s l i g h t l y d i f f e r e n t  than the area  image o b t a i n e d ,  focus  l e v e l s and a  several  143 photographic record of the corresponding  diffraction  pattern  are d e s i r a b l e . The h i g h e s t p r a c t i c a l l e v e l of m a g n i f i c a t i o n  is a  f u n c t i o n of image b r i g h t n e s s and machine s t a b i l i t y . P h y s i c a l and  electronic drift  i n the H i t a c h i H-800 was found to b l u r  photographs taken with exposures longer  than 5 seconds. The  highest m a g n i f i c a t i o n at which the r e q u i r e d photographic exposure was c o n s i s t e n t l y l e s s than 5 seconds was found to be 400,000X.  144 APPENDIX F: ORTHOAMPHIBOLE SYNTHESIS AND  A s e r i e s of orthoamphiboles  CHARACTERIZATION  i n the system  _  MgO-FeO-Si0 2 H 2 0 have been s y n t h e s i z e d f o r use as s t a r t i n g m a t e r i a l s i n ion-exchange ion-exchange  e q u l i b r i u m experiments. These  experiments are designed to p r o v i d e data f o r  thermodynamic c h a r a c t e r i z a t i o n of the Fe-Mg s o l i d in orthoamphiboles. The s y n t h e t i c amphiboles  solution  were produced  with hydrothermal techniques employing aqueous Fe-Mg c h l o r i d e s as a f l u x . Both XRD and t r a n s m i t t e d microscopy  electron  (TEM) techniques have been employed t o  c h a r a c t e r i z e these s y n t h e t i c p r o d u c t s . The s t r u c t u r a l i n f o r m a t i o n gained with these techniques i s needed to f a c i l i t a t e comparison natural  between the s y n t h e t i c g r a i n s and  anthophyllites.  P r e v i o u s s t u d i e s have p o i n t e d out problems  both with  a c c o m p l i s h i n g high y i e l d syntheses and with comparison of s y n t h e t i c orthoamphiboles with n a t u r a l  anthophyllites  (Greenwood, 1963; Popp et a l , 1976). In g e n e r a l , hydrothermal treatment of oxide mixes w i t h i n the orthoamphibole  stability  field  invariably results in  p r o d u c t i o n of s i g n i f i c a n t amounts of metastable  talc,  o l i v i n e , q u a r t z , ± c r i s t o b a l i t e , t o r t h o p y r o x e n e . These metastable phases only slowly r e a c t to b r i n g the amphibole y i e l d up to a c c e p t a b l e l e v e l s to the Mg end-member  (2:99%). At compositions c l o s e  c r e a t i o n of orthoamphibole n u c l e i has  only been accomplished v i a breakdown of t a l c at (high)  1 45 temperatures o u t s i d e the orthoamphibole s t a b i l i t y Popp et a l ( l 9 7 6 ) concluded that t h e i r s y n t h e t i c  field.  orthorhombic  amphiboles possessed a s t r u c t u r e u n l i k e that of any known n a t u r a l amphibole  based upon d i s c r e p a n c i e s in u n i t  cell  volumes and upon a unique d i s t r i b u t i o n of i n t e n s i t i e s on e l e c t r o n d i f f r a c t i o n p a t t e r n s . Subsequent HRTEM s t u d i e s of these same s y n t h e t i c s by Veblen 1982)  (as quoted by G i l b e r t et a l ,  r e v e a l e d v a r y i n g amounts of both chain-width and  chain-stacking disorder  (see a l s o Veblen and Buseck, 1979).  S y n t h e t i c Mn-Mg orthoamphiboles have a l s o been found to c o n t a i n chain-width and c h a i n - s t a c k i n g f a u l t s  (Maresch  and  Czank, 1983). The use of an aqueous c h l o r i d e f l u x study was  i n the present  intended t o : (1) promote r e a c t i o n r a t e s and  minimize the time r e q u i r e d f o r f u l l - y i e l d syntheses; (2) reduce the amount of chain-arrangement  faults.  Experimental Techniques  STARTING  MATERIALS'.  A l l mixes were prepared from reagent grade  Si02  ( H 2 S i O „ • n H z O converted to c r i s t o b a l i t e at 1 2 0 0 ° C ) , Fe203 was  MgO,  and Fe (sponge). The e q u i v a l e n t of s t o i c h i o m e t r i c  FeO  introduced as oxygen balanced p r o p o r t i o n s of Fe and  F e 2 0 3 . A l l oxides were thoroughly d r i e d p r i o r to weighing. Homogenization  of the mixes was  accomplished v i a a  1 46 combination of hand and automatic g r i n d i n g i n an agate mortar  (under e t h y l a l c o h o l ) . See Appendix A f o r a d d i t i o n a l  details. The aqueous c h l o r i d e f l u x c o n s i s t e d of reagent MgCl 2 -6H 2 0 and F e C l 2 - 4 H 2 0 d i s s o l v e d i n d i s t i l l e d  grade  water t o a  t o t a l Mg+Fe c o n c e n t r a t i o n of I m o l a l . S o l u t i o n s were prepared at X M g v a l u e s of 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0.  HYDROTHERMAL  All  TECHNIQUES'.  runs were made i n c o l d - s e a l type p r e s s u r e v e s s e l s  c o n s t r u c t e d of e i t h e r s t e l l i t e  25 or Rene 41. Temperatures  were measured with chromel-alumel thermocouples. T i g h t temperature c o n t r o l was not c o n s i d e r e d c r i t i c a l f o r syntheses, and the temperatures r e p o r t e d are only a c c u r a t e to ±10°C. At 2kb, methane was used as the p r e s s u r e medium i n order to prevent o x i d a t i o n of the charges v i a the graphite-methane  b u f f e r . At 4kb, the n a t u r a l f ~  of the  bomb, using water as the p r e s s u r e medium, was found to be sufficiently  low t o prevent o x i d a t i o n . P r e s s u r e s were  measured with bourdon-tube are  gauges. The r e p o r t e d p r e s s u r e s  a c c u r a t e to ±120 b a r s .  SYNTHESIS  EXPERIMENTS'.  Oxide mixes were prepared f o r amphibole X  Mg  =  compositions at  0.3, 0.5, 0.7, 0.9 and 1.0. For each  experiment,  c a r e f u l l y weighed amounts of oxide mix and aqueous  fluid  were s e a l e d i n t o a gold c a p s u l e . Composition changes i n the  147 c r y s t a l l i n e charge bulk-composition had to be expected due to ion-exchange r e a c t i o n with the aqueous c h l o r i d e  flux.  Steps were taken to both c o n t r o l and measure these compositonal  changes.  Two methods were employed to c o n t r o l the e f f e c t of ion-exchange on the s i l i c a t e bulk-compositon. For each amphibole composition a c h l o r i d e composition  ( X M g ) c o u l d be  chosen which was c l o s e to the e q u i l i b r i u m composition by using ion-exchange experiments  with Fe-Mg o l i v i n e s as an  example (see chapter I ) . The p o t e n t i a l f o r c o m p o s i t i o n a l changes was f u r t h e r reduced by employing  solid:fluid ratios  high enough to r e s u l t i n molar Mg+Fe r a t i o s ( s o l i d : f l u i d ) between 20 and 50. Measurement of amphibole c o m p o s i t i o n a l changes was accomplished  v i a measurement of Mg and Fe c o n c e n t r a t i o n s i n  the product aqueous f l u i d s . Subsequent c a l c u l a t i o n of the s i l i c a t e composition v i a mass balance i s q u i t e accurate due to the combination  of low weighing  errors  (generally  less  than 0.1%) and high Mg+Fe molar r a t i o s . A f t e r each run the capsule was cleaned with a l c o h o l , cut open and i t s contents washed out i n a known volume of a c i d i f i e d d i s t i l l e d water (0.03m i n HN0 3 ). The s o l i d products were suspended and thoroughly washed with the h e l p of an u l t r a s o n i c bath. The s o l i d s were then separated from the aqueous s o l u t i o n by c e n t r i f u g i n g . The supernatant aqueous s o l u t i o n was removed and analyzed f o r t o t a l Mg and Fe with standard flame a b s o r p t i o n techniques  (see appendix B ) . The s o l i d  atomic  products  1 48 are rewashed to remove any  remaining  d r i e d at 120°C. By i n i t i a l l y  t r a c e s of c h l o r i d e s and  washing the run products  with  a c i d i f i e d water, small amounts of n o n - s i l i c a t e quench p r e c i p i t a t e s c o u l d be taken  i n t o s o l u t i o n . The  resulting  s o l u t i o n s were found to c o n t a i n t o t a l Mg+Fe c o n c e n t r a t i o n s significantly  i n excess of that a t t r i b u t a b l e to c h l o r i d e s  only f o r syntheses  at 0.1  and  0.3  XMg  (silicate  bulk-composition). The  s y n t h e s i s s t r a t e g y found most s u c c e s s f u l v a r i e d as  a f u n c t i o n of bulk c o m p o s i t i o n . The composition r u n . The  was  0.7  the only one  0.5  (XMg)  mix  which produced 99% y i e l d i n one  bulk composition  reached a s a t i s f a c t o r y  a f t e r one c y c l e of g r i n d i n g and  yield  r e - h e a t i n g . Near the  c o m p o s i t i o n a l extremes, the s u c c e s s f u l s t r a t e g i e s were more elaborate. At the 0.9  and  1.0  employing t a l c formation  bulk compositions  f o l l o w e d by high temperature  breakdown (Greenwood, 1963) n u c l e i . The water was  was  r e q u i r e d to c r e a t e amphibole  d e s i r e d r e s u l t s were only obtained when pure  the only f l u x employed. The  nuclei-making s o l u t i o n and  the s t r a t e g y  products  of the  c y c l e were reloaded with an aqueous c h l o r i d e re-run at a temperature low  orthopyroxene+water s t a b i l i t y  in the  f i e l d . At higher  (Mg-rich) temperatures,  the rate of the metastable r e a c t i o n : t a l c + f o r s t e r i t e = e n s t a t i t e + H20  ( i n the presence of the c h l o r i d e f l u x )  found to be so high that l a r g e , and  therefore less  g r a i n s of orthopyroxene q u i c k l y formed.  was  reactive,  149 At 0.1 and 0.3 bulk compositions amphibole n u c l e i would form, but f u r t h e r progress of the s y n t h e s i s was q u i t e s l u g g i s h . The amphibole y i e l d was improved c o n s i d e r a b l y by u s i n g seeded oxide mixes. The products of e a r l y , low y i e l d syntheses were ground and combined with oxide mix (same bulk composition)  i n a r a t i o between 2 and 5 ( o x i d e : s e e d ) . .  The d e t a i l s of the s y n t h e s i s experiments  are t a b u l a t e d  in t a b l e F 1 .  UNIT  CELL  REFINEMENTS:  Powder XRD techniques were employed t o o b t a i n u n i t parameters f o r every f i n a l  s y t h e s i s p r o d u c t . The 26 data  were obtained with a P h i l i p s PW1710 Automatic DiffTactometer equipped D i g i t a l peak-seeking filtered  cell  Powder  with a g r a p h i t e monochromator.  procedures were employed using Ni  Cu r a d i a t i o n . Both s y n t h e t i c p e r i c l a s e and n a t u r a l  q u a r t z were used as i n t e r n a l s t a n d a r d s . For t e c h n i c a l d e t a i l s , see Appendix D. Least-squares refinement of the u n i t c e l l  parameters  was performed with the USGS FORTRAN IV program (Evans et a l , 1963). The r e s u l t s are l i s t e d  i n Table F 2 . Indexing of  r e f l e c t i o n s was done using the c a l c u l a t e d  anthophyllite  powder p a t t e r n of Borg and Smith(l969) as a g u i d e . One peak, common to a l l of the powder p a t t e r n s and indexed as (400), i s not given any i n t e n s i t y at a l l by Borg and Smith. Popp et a l ( l 9 7 6 ) and Maresch and Czank(l983)  each found the same  discrepancy when indexing powder p a t t e r n s from t h e i r  Table F1. Experimental parameters for orthoamphibole syntheses. The starting materials are an oxide mix (OX), the prodicts of a previous run (by run #) or a mixture of the two. The product phases are quartz (0), cristobalite (C), olivine (OL), orthopyroxene (OP), orthoamphibole (OA), and talc (TA). Product phases are l i s t e d in decreasing order of abundance with '+' meaning >1% and '-' meaning <1%. 1  RUN*  STARTING MATERIAL  INITIAL SOLID FLUID Xu Xu  mT  0 . 100 O .097 0 . 101 0 . 100 0 . 104  600 600 610 600 500  2 4 4  0 .000 0 .000  1.0 1.0 1.0 1.0 1.0  0 . 300 . O. 297  0 .000 0 .300  2 .0 1.0  PRODUCT PHASES  2 2  233 172 254 767 432  0 .050 0 .075 0 .048 0 .029 0 .037  0 . 102  OL+C-OA OA+OL+0 OA+OL+0 OL+O+OA OA+0  600 600  2 2  180 . 233  0 .079 0 .082  0 . 297 0.. 339  OA+OL+Q OA-OL-C  T('C) P(kb) HOURS  214 244 248  OX 2 14+OX 244  260 304  248+OX 260  207 215  OX 2O7+0X  188  OX  0. 500  0.. 300  1.0  630  2  434  0. 127  0. 509  OA-OP  189 2 18  OX 189  0 700 0.. 705  0 300 0..500  1.0 1.0  680  2 2  434  690  233  0. 243 0.. 207  0. 705 0. 753  OA-OP OA-OP  258 OX 27 1 258 30O 27 1  0. 900 0. 900 0. 903  •--  0 .0 1.0 1.0  720 665 675  2 2 2  612 279 528  0. OOO 0. 440 0. 443  0. 900 o.903 0. 907  TA+OA+OL OA+OL+TA OA-0  315 316 317  1 1 1  0 .0 2 .0 2 0  700 675  2 2 2  183 481 243  0. 000 1.OOO 1.000  1.000 1.000 1.000  TA+OA+OL+C OA+TA+OL OA-TA  OX 315 316  . 000 . 000 . 000  0 .000 0 . 100 0 .000  FINAL FLUID SOLID X„ X„  0. 500 0: 500 ...  1.ooo 1.000  680  0 .097 0 . 101 0 . 100 0 . 104  o  151  Table F2. Orthoamphibole c e l l parameters derived from least squares refinement of powder XRO data.  RUN*  Mg  317 300 218 188 2 15 304  1 .OOO 0.907 0. 753 0.509 0 . 339 0. 102  a(A)  b(A)  18 .659(05) 18 . 579( 19) 18 .685(05) 18 .692(08) 18 .682(07) 18 .705(05)  c(A)  17.920(05) 17.975(39 ) 18.018(05) 18.136(18) 18.226(15) 18.392(09)  * OF PEAKS  V(A' )  5 .304(05 . ) 5 .306(20) . 5 .310(05) 5..325(25) 5..327(35) 5..337(05)  1773.4(1.0) 1772.2(7.5) 1787.6(1 O) 1805.3(8.0) 1813.9110.) 1836 0(1.O)  11 9 12 10 9 11  In parentheses is one standard error of regression as applied to the last significant d i g i t l i s t e d .  s y n t h e t i c orthoamphiboles. I t i s i n t e r e s t i n g to note published  powder p a t t e r n s  1950), n a t u r a l g e d r i t e Ito,  that  for natural a n t h o p h i l l i t e (Beatty,  (Seki and Yamasaki, 1957; M i l t o n and  1961) and s y n t h e t i c g e d r i t e  (James et a l , 1976) a l l  c o n t a i n a peak which indexes as (400). Difficulties  were encountered i n o b t a i n i n g  cell  refinements f o r the products of runs 215 and 300. The powder pattern  f o r each of these was unusually  weak and i n each  case only a s i n g l e weak peak could be indexed with a c component. T h i s s i n g l e peak had a g r o s s l y i n f l u e n c e on a and/or b i n the c e l l the only  c-component  disproportionate  refinement s i n c e i t was  peak and i t was not an (00/) peak. The  c e l l parameters f o r these two s y n t h e t i c compositions were obtained by removing the weak c-component  peak and  introducing a f i c t i t i o u s  i n t o the c e l l  (002) r e f l e c t i o n  1 52 refinement.' The ^-spacing  assigned to t h i s r e f l e c t i o n was  c a l c u l a t e d by i n t e r p o l a t i n g between c-repeats obtained f o r the remaining c o m p o s i t i o n s . The a and b repeats c a l c u l a t e d f o r these two s y n t h e t i c s are then i n f l u e n c e d only by (hkO) r e f l e c t i o n s . The p o s s i b l e e r r o r introduced  into c a l c u l a t i o n  of the u n i t c e l l volume i s probably very small  s i n c e , as  i l l u s t r a t e d below, the orthoamphibole c-repeat i s not strongly  i n f l u e n c e d by e i t h e r Mg-Fe s u b s t i t u t i o n or  c r y s t a l l i z a t i o n c o n d i t i o n s . The standard e r r o r (of regression)  listed  f o r runs 215 and 300 i n t a b l e F2 i s that  c a l c u l a t e d i n the o r i g i n a l c a l c u l a t i o n which i n c l u d e d  only  the weak c-component r e f l e c t i o n present i n each powder pattern. The  u n i t c e l l parameters l i s t e d  i n t a b l e F2 are  presented g r a p h i c a l l y i n f i g u r e F 1 . For comparison, c e l l parameters from the l i t e r a t u r e are p l o t t e d f o r s y n t h e t i c Mg-orthoamphiboles (Greenwood, 1963, as indexed by Cameron, 1975;  Chernosky et a l , 1984), s y n t h e t i c Mg-Fe  orthoamphiboles (Cameron, 1975; Ravior and H i n r i c h s e n , 1975; Popp et a l , 1976) and n a t u r a l a n t h o p h y l l i t e s low i n components outside 1930;  Finger,  the FeO-MgO-Si0 2 -H 2 0 system  1970; S i e f e r t ,  (Johannson,  1977; Veblen and Burnham,  1978). The dashed s t r a i g h t l i n e s a r e the r e s u l t of r e g r e s s i o n by Popp et a l ( l 9 7 6 ) f o r t h e i r  synthetic  orthoamphiboles. The  c-repeats of Mg-Fe orthoamphiboles from a l l sources  are q u i t e c o n s i s t e n t . Neither  Mg-Fe s u b s t i t u t i o n nor  1 53  18.8 B- — — Ch  18.6-  a  a-Repeat  s  J  E 18.4o co CD  i  C 18.2 O  " a Ch •  b—Repeat  \  18.0-  a  p  17.8 0.0  0.2  0.4  0.6  0.8  1.0  XMg F i g u r e F 1 . Orthoamphibole u n i t c e l l parameters. The symbols are data from the present s t u d y . Open represent p u b l i s h e d values f o r other  filled  symbols  synthetic  orthoamphiboles (Popp et a l , 1976; Ravior and H i n r i c h s e n , 1975; Cameron, 1975; Chernosky et a l , s u b m i t t e d ) . Hatched symbols represent n a t u r a l a n t h o p h y l l i t e s  (Johannson, 1930;  F i n g e r , 1970; S e i f e r t , 1977; Veblen and Burnham, 1978). (a) The a and b repeats f o r orthoamphiboles p l u s C h = c h e s t e r i t e  (a  and 2/56, Veblen and Burnham, 1978), J=jimthompsonite (a  and 2/36, Veblen and Burnham, 1978), P=protoamphibole (2a and b, G i b b s , 1969), and C=cummingtonite (2asin/3 and b, Rice et a l ,  1974).  1 54  5.6 CO  E o i_  -*->5.4 V)  H  c—Repeat  C7> C D 5.2 H  •1820 CO  E o  Volume  •1780  L_ -M  CO  cn c 0.0  0.2  r~ 0.4  0.6  0.8  -1740 1.0  F i g u r e F 1 . (b) -The c-repeat and u n i t c e l l volume.  D  1 55 crystallization cell  h i s t o r y appear to have much a f f e c t on  this  parameter. A small systematic discrepancy can be seen i n the  fc-repeats. 6-repeats  Orthoamphiboles from the present study have generally s l i g h t l y  lower than that of the n a t u r a l  a n t h o p h y l l i t e s and many other s y n t h e t i c s . The  discrepancy  amongst the s y n t h e t i c s seems to disappear near the extreme in Fe  substitution. A l l of the s y n t h e t i c Fe-Mg orthoamphiboles  have l a r g e r  a-repeats than n a t u r a l a n t h o p h y l l i t e s . The discrepancy i s even g r e a t e r f o r orthoamphiboles  produced i n the present  study. Once a g a i n , the discrepancy amongst the s y n t h e t i c s disappears at low  X^ g .  Minor element chemistry does not seem to be capable of accounting f o r the c e l l dimension al(!976) concluded  d i s c r e p a n c i e s . Popp et  that n e i t h e r minor A l ( i n the n a t u r a l  examples) nor Fe-Mg s i t e o r d e r i n g c o u l d account f o r c e l l volume d i s c r e p a n c i e s . Although  Popp et a l d i r e c t e d  their  d i s c u s s i o n toward c o n t r a s t s i n c e l l volume, f i g u r e F1 i l l u s t r a t e s that the c e l l volume d i s c r e p a n c y i s p r i m a r i l y due  to the d i s c r e p a n c y i n the a-repeat. Maresch  Czank(l983) have shown that Mn  and  s u b s t i t u t i o n expands the  a-repeat more than Fe s u b s t i t u t i o n does. Most of the n a t u r a l examples i n f i g u r e F1 c o n t a i n l e s s than  1mole% of  M n 7 S i 8 0 2 2 ( O H ) 2 . Minor Cl-OH s o l i d s o l u t i o n must be c o n s i d e r e d as a p o s s i b i l i t y  f o r amphiboles produced in the  present s t u d y . However, the anomalously low  a-repeat  f o r the  1 56 product of run The  300  seems to argue a g a i n s t  most a t t r a c t i v e e x p l a n a t i o n  d i s c r e p a n c i e s may  techniques.  As  cell  order-disorder.  in n a t u r a l amphiboles has  i d e n t i f i e d by Veblen and  possibility.  f o r these u n i t  be chain-arrangement  Chain-width d i s o r d e r  this  been  Burnham(1979) with HRTEM imaging  s t a t e d above, HRTEM s t u d i e s have found both  chain-width f a u l t s and  chain-stacking  Mg-Fe orthoamphiboles and orthoamphiboles. For  f a u l t s in s y n t h e t i c  i n s y n t h e t i c Mn-Mg  the Mg-Fe s y n t h e t i c s , chain-width  f a u l t s were found (by Veblen) to be more common i n the more magnesian examples and be more common in the The  chain-stacking  f a u l t s were found to  i r o n r i c h examples.  e f f e c t of chain-arrangement d i s o r d e r on a powder  XRD  p a t t e r n would i n c l u d e a general  broadening of the peaks  and  a l s o a b i a s i n peak p o s i t i o n . The  s i z e and  d i r e c t i o n of  t h i s p o s i t i o n b i a s w i l l depend on the s t r u c t u r a l dimensions of each type of f a u l t and  the p o p u l a t i o n  A d d i t i o n a l peaks should not enter  of each  the p a t t e r n unless  'disorder' includes v o l u m e t r i c a l l y s i g n i f i c a n t domains of these The  type. the  ordered  'faults'.  e f f e c t of chain-width d i s o r d e r may  be  investigated  by l o o k i n g at the s t r u c t u r a l dimensions of ordered orthorhombic b i o p y r i b o l e s . The ^-repeats  f o r jimthompsonite  (double and  included  s t r u c t u r e s are  a s i l i c a t e chain-width and  scaled  ( t r i p l e chains) and c h e s t e r i t e  t r i p l e chains) are  6-repeats of these two  a-repeats and  in f i g u r e F1.  The  i n t e g r a l m u l t i p l e s of  so each s t r u c t u r e w i l l produce  157 powder XRD  peaks at 26 angles comparable to those of  orthoamphibole. The  XRD  bias produced by these  two  s t r u c t u r e s , as models of the chain-width f a u l t s , i s i n d i c a t e d by comparing the orthoamphibole 2/3fc for j imthompsonite and  2/5/3  fc-repeats  with  f o r c h e s t e r i t e . I t appears  that p o p u l a t i o n s of t r i p l e - c h a i n f a u l t s in an amphibole tend to i n c r e a s e  the apparent Z>-repeat and,  extent, increase  the apparent  s t a c k i n g , see  be used a models  f a u l t s i n c l u d e cummingtonite (++++  Thompson, 1981)  s t a c k i n g ) . The  to a l e s s e r  a-repeat.  C h a i n - s t a c k i n g polymorphs which could for c h a i n - s t a c k i n g  and  protoamphibole  ++++ type of s t a c k i n g  (+-+-  f a u l t does not  appear  capable of c o n t r i b u t i n g to the observed d i s c r e p a n c i e s . values of b and  see  f i g u r e F1)  are e n t i r e l y c o n s i s t e n t  with b and  a f o r n a t u r a l a n t h o p h y l l i t e . The  2a for the  only known protoamphibole s t r u c t u r e  G i b b s , 1969)  of the +-+using 2a may  are a l s o p l o t t e d on  type of s t a c k i n g  fault  t h i s example because the be  l a r g e l y due  is difficult  Mg  examples, a and  r e s p e c t i v e l y and  in b  b for o r t h o e n s t a t i t e are  for protoenstatite  and  A  XRD  f a u l t . For  pure  18.22A and  2a = 18.50A and  8.74A (Deer et a l , 1978). As with the  and  protoenstatite  s i g n of an  type of s t a c k i n g  effect  to evaluate  to the presence of L i i n the M4  +-+-  and  (Gibbs et a l ,  observable c o n t r a s t  h e l p i n d i c a t e at l e a s t the  b i a s produced by the  v a l u e s of b  f i g u r e F1. The  s i t e s . Comparison of the o r t h o e n s t a t i t e and s t r u c t u r e s may  The  2asin/3 for n a t u r a l magnesian cummingtonite  (Rice et a l , 1974;  1960;  will  8.81A  b =  i l l u s t r a t e d proto  and  1 58 ortho amphibole to +-+-  examples, t h i s t r a n s i t i o n  from ++--  stacking  s t a c k i n g i s accompanied by a r e d u c t i o n i n the  chain-width dimension  (b) and an expansion of the  c h a i n - s t a c k i n g dimension ( a ) . If chain-arrangement  f a u l t s are c a l l e d upon to account  for the observed c e l l dimension d i s c r e p a n c i e s and the models presented above are accepted as a q u a l i t a t i v e  g u i d e , then  c h a i n - s t a c k i n g f a u l t s must be common i n the s y n t h e t i c orthoamphiboles produced  i n the present s t u d y . The exception  i s the products of run 300 which have a higher b and a lower  a than the trends e s t a b l i s h e d by the remaining product amphiboles. The e x i s t e n c e of these p o s t u l a t e d  stacking  f a u l t s w i l l be i n v e s t i g a t e d i n the e l e c t r o n microscopy which  study  follows.  ELECTRON  MICROSCOPY:  Transmitted e l e c t r o n microscopy was  performed with an  unmodified H i t a c h i H-800 200kV STEM equipped with a goniometer Lattice  s i d e - e n t r y stage and d o u b l e - t i l t  sample h o l d e r .  images were obtained at a primary m a g n i f i c a t i o n of  400,000X with a  70MIII  o b j e c t i v e aperature and a 200kV beam.  Defocus v a l u e s were g e n e r a l l y 0 to -500A. Each sample was  amphibole  d i s p e r s e d from an a l c o h o l suspension onto a holey,  carbon f i l m which was  supported by a 600-mesh Cu  grid.  A d d i t i o n a l t e c h n i c a l d e t a i l s can be found i n Appendix E . The low m a g n i f i c a t i o n b r i g h t - f i e l d images i n p l a t e 1 illustrate  the morphology of the s y n t h e t i c amphibole  grains.  159  Plate  1. Low  magnification  bright f i e l d  images of  the  s y n t h e t i c orthoamphiboles. Each photograph i s marked with i t s corresponding run#. The photographs.  s c a l e bar  a p p l i e s to a l l of  the  IbO  Plate 1  1  2  Lim  161  The  more m a g n e s i a n e x a m p l e s  t e m p e r a t u r e s ) have t h e synthetics  not  length:width  317  been g r o u n d  had  largest  o n l y have a  smaller  (produced at grain  smaller  r a t i o . The in a  the  s i z e . The  grain  Fe-rich  s i z e , but  photographed  small b a l l  highest  mill  to  also  sample reduce  a  from  run  grain  size. The  sample m o u n t i n g m e t h o d , a l t h o u g h  technologically the  s u c c e s s of  orientation in  (hOl)  obtaining  p r o d u c e d by  c-axis  structural information. grain  of  of  of  orientation  contrast,  the  iron-rich  synthetic  toward the For  grains  a  of  (Okl)  the  been  a-axis near  6-axis  normal near  a-normal  C z a n k , 1 9 8 3 ) . In  orientation  of  o r t h o a m p h i b o l e s was  the  two  most  f o u n d t o be  biased  orientation.  limiting  and  s i z e by . g r i n d i n g  size  proved  f a c t o r . Only a s m a l l p o r t i o n  mounted from r u n s 300 diffraction  normal  Mg-Mn  most m a g n e s i a n c o m p o s i t i o n s , g r a i n  serious  resulted  orientations  f o u n d t o have an  ( M a r e s c h and  preferred  fc-normal  the  electron grain  of  n o r m a l . S i m i l a r l y mounted s y n t h e t i c  preferred  be  orientations  course, a zero population  o r t h o a m p h i b o l e s have a l s o  to  near  on  Preferred  morphology g e n e r a l l y  orientations  lower p o p u l a t i o n  and,  and  simple, proved to place d e f i n i t e l i m i t s  a high population  (O/c/), a  fast  and  lattice  317  were t h i n enough  imaging. Attempts to  succeeded only  in reducing  the  of  the  for reduce length  grains.  Orientation:  Plate  2 presents  (Okl)  lattice  images  162  and corresponding e l e c t r o n d i f f r a c t i o n p a t t e r n s f o r orthoamphibole  g r a i n s from runs  188, 218 and 317. The  v a r i o u s l i m i t s d i s c u s s e d above impeded s u c c e s s f u l imaging  of the remaining  lattice  synthetics. Oriented electron  d i f f r a c t i o n p a t t e r n s were obtained f o r g r a i n s from runs 300 and  215. V i s i b l e chain-width  faults  i n the l a t t i c e  images  * and  s t r e a k i n g of d i f f r a c t i o n  presence  spots along b  i n d i c a t e the  of chain-width d i s o r d e r . The p o p u l a t i o n of  chain-width  f a u l t s appears to be very low f o r the run 215  g r a i n and r e l a t i v e l y high f o r the run 300 g r a i n . For the other g r a i n s represented i n p l a t e 2, chain-width  f a u l t s are  g e n e r a l l y p r e s e n t , but a p p a r e n t l y a f f e c t i n g l e s s than  10% of  each g r a i n volume. (hOl)  P l a t e 3 presents  Orientation-.  {hOl)  diffraction  patterns for a l l six synthetic compositions, plus a lattice  (hOl)  image f o r a g r a i n from run 304. The s t r e a k i n g of *  spots i n the a  direction  i n d i c a t e s that c h a i n - s t a c k i n g  f a u l t s are common i n a l l but the most i r o n - r i c h g r a i n s . In c o n t r a s t to the powder XRD measurements of the a-repeat, the e l e c t r o n d i f f r a c t i o n p a t t e r n f o r the run 300 g r a i n does not appear to be anomalous. DISCUSSION:  If the few g r a i n s s t u d i e d v i a TEM are compared with the powder XRD measurements, the e x p l a n a t i o n put f o r t h f o r the d i s c r e p a n c i e s i n c e l l dimensions i s supported.  1 63  P l a t e 2. High m a g n i f i c a t i o n images and e l e c t r o n  diffraction  p a t t e r n s f o r specimens i n {Okl) o r i e n t a t i o n . Each photograph i s marked with i t s corresponding the double-chain  run#. The =*9A spacing of  repeat serves as i t s own  c h a i n widths other than 2 are  indicated.  scale bar. A l l  1 65  P l a t e 3. E l e c t r o n d i f f r a c t i o n p a t t e r n s and one high magnification  image f o r specimens i n (AO/) o r i e n t a t i o n . The  s c a l e on the high m a g n i f i c a t i o n of P l a t e  2.  image i s i d e n t i c a l to that  300  218  167  Chain-stacking  disorder  i s present i n a l l but  the most  F e - r i c h orthoamphiboles. Chain-width d i s o r d e r  i s detectable  f o r most of the g r a i n s s t u d i e d . The  i s the  from run  300  which, in c o n t r a s t  exception  to the theory based upon  a l o n e , appears to be anomalously high disorder  rather  than anomalously low  the  information  i s i n c o n c l u s i v e s i n c e the TEM For  in  chain-stacking  by  study sampled so few  i t s s e l e c t i o n of the smallest  study i s s t i l l discrepancies structures.  XRD  obtained i n the TEM  the magnesian orthoamphiboles, the TEM  biased  grains.  synthetic  study grains.  sampling i s a l s o  needed to c o n c l u s i v e l y i d e n t i f y between n a t u r a l and  XRD  i n chain-width  d i s o r d e r . T h i s d i r e c t comparison of the powder measurements and  sample  Further the  orthoamphibole  168 APPENDIX G: THE MG-FE ORTHOPYROXENE SOLUTION  The data a v a i l a b l e from the l i t e r a t u r e which c o n s t r a i n the p r o p e r t i e s of the Fe-Mg orthopyroxene intracrystalline  ion-exchange d a t a ,  solution includes  intercrystalline  ion-exchange d a t a , d i s p l a c e d o x i d a t i o n e q u i l i b r i u m data and c a l o r i m e t r i c d a t a . The f i r s t of these data-types can be c l a s s e d as microscopic while the l a t t e r three would be c l a s s e d as macroscopic. Although  orthopyroxene  solution  models have been proposed based upon the m i c r o s c o p i c data alone  (e.g. Saxena and Ghose, 1970, 1971; Navrotsky, 1971;  Saxena, 1973), the i n t e r n a l o r d e r i n g of Fe and Mg need not be the only c o n t r i b u t i o n to the macroscopic b e h a v i o r . A macroscopic the macroscopic  thermodynamic  solution-model need only c o n s i d e r  data i n order to i n t e r p o l a t e between the  data p o i n t s . However, a m i c r o s c o p i c model that i s c o n s i s t e n t with both the macroscopic  and m i c r o s c o p i c data  should  p r o v i d e more i n s i g h t i n t o the nature of the i n t e r n a l c o n t r i b u t i o n s to the macroscopic  p r o p e r t i e s . For t h i s  r e a s o n , a microscopic model should be more s u c c e s s f u l i n e x t r a p o l a t i o n to both c o n d i t i o n s and c h e m i s t r i e s o u t s i d e the o r i g i n a l data-set. In t h i s appendix, a m i c r o s c o p i c model i s a p p l i e d to the Fe-Mg orthopyroxene  solution after  review and c r i t i q u e of  the a v a i l a b l e m i c r o s c o p i c and macroscopic  INTRACRYSTALLINE  I  ON-EXCHANGE'.  data.  169 The  q u a n t i t a t i v e data  f o r the temperature and  x  compositional  (x°P ) dependence  of Mg-Fe o r d e r i n g i n  orthopyroxene have a l l been d e r i v e d  from Mossbauer spectra  of heated n a t u r a l orthopyroxenes (Virgo and Hafner, 1969; Saxena and Ghose, 1971; Besancon, 1981 and submitted f o r p u b l i c a t i o n ; Besancon and Vaughan, s u b m i t t e d ) . Nearly a l l of these data c o n s i s t of h a l f - b r a c k e t s from the low-temperature (more ordered) s i d e . The exceptions  are one o r d e r i n g  experiment by V i r g o and Hafner and an o r d e r i n g - r a t e study at 600°C by Besancon(submitted). D i s o r d e r i n g r a t e s t u d i e s by V i r g o and Hafner(1969) and Besancon(1981) i n d i c a t e that most of the h a l f - b r a c k e t s should adequately e q u i l i b r i u m . The exceptions  represent  are data at 500°C and 1000°C.  E x t r a p o l a t i o n by Besancon of h i s second-order rate down to 500°C i n d i c a t e d that the p u b l i s h e d  equation  500°C heating  experiments were not long enough to a t t a i n e q u i l i b r i u m . E x t r a p o l a t i o n to 1000°C i n d i c a t e d that experiments at t h i s temperature c o u l d not be quenched f a s t enough to preserve the e q u i l i b r i u m s t a t e of d i s o r d e r . P r i o r to a p p l i c a t i o n of the s i t e - o r d e r i n g data t o c a l i b r a t i o n of a s o l u t i o n model, the accuracy of these data must be e v a l u a t e d . The sources of e r r o r inherent  i n the  s i t e - o r d e r i n g s t u d i e s i n c l u d e : p r e c i s i o n i n measuring the Mossbauer s p e c t r a , r e p r o d u c i b i l i t y of the heating experiments, site-assignment octahedral  f o r minor elements occupying  s i t e s and u n c e r t a i n t y  i n the r a t i o between the M1  r e c o i l l e s s f r a c t i o n and the M2 r e c o i l l e s s  f r a c t i o n . (The  170 recoilless  fraction  that c o n t r i b u t e  i s the p r o p o r t i o n  of  to the measured gamma-ray  57  Fe atoms present  absorption  spectrum.) A l l of these w i l l be expressed here i n terms of the n a t u r a l logarithm  of the d i s t r i b u t i o n c o e f f i c i e n t  Fe-Mg exchange between M1  D,2 _  Mg  and  for  M2.  Mg  ,  "Cc-<') Mg  Mg  P r e c i s i o n estimates s t a t e d by the authors i n d i c a t e that e r r o r inherent  ,  the  in Mossbauer spectroscopy i s t y p i c a l l y ±0.02  in l n K D 1 2 « A n a l y s i s of r e p l i c a t e heating V i r g o and H a f n e r ( l 9 6 9 ) and  experiments from  Besancon(1981) i n d i c a t e s that  the  heating  experiment r e p r o d u c i b i l i t y i s approximately ±0.1 in  lnKD12»  Since the Mg  d i s t r i b u t i o n determined i n Mossbauer  s t u d i e s i s c a l c u l a t e d by d i f f e r e n c e , small u n c e r t a i n t i e s in minor-element s i t e assignment and  recoilless fraction  translate into substantial errors in l n K D 1 2 compositions low  in t o t a l  f o r bulk  Mg.  A l l of the orthopyroxene s i t e d i s t r i b u t i o n mentioned above have assumed that the r e c o i l l e s s ratio  , Rrf/  i s u n i t y . V i r g o and  studies fraction  H a f n e r ( l 9 6 8 ) s t a t e that  = 1.0±0.1 based on the Mossbauer spectrum of  H a f n e r ( l 9 6 9 ) s t a t e that  recoilless  and  p e r c e n t " . F i g u r e G1 on  M2  the  are equal " w i t h i n a  few  shows the e f f e c t of a ±5% e r r o r in R ^  s i t e d i s t r i b u t i o n s at l n K D 1 2 = -2.0  1.0).  R^^  synthetic  o r t h o f e r r o s i l i t e . V i r g o and f r a c t i o n s for M1  ratio  (when assuming R ^ =  171  J  Figure G1. U n c e r t a i n t i e s orthopyroxene  I  I  •  Spectroscopy  I  Heating Experiment  inherent  i n measurement of  s i t e occupancies from Mossbauer s p e c t r a of the  products of d i s o r d e r i n g  experiments.  172 Minor occupants  of the o c t a h e d r a l s i t e s have been  assumed to be i n s i g n i f i c a n t and simply ignored i n the c a l c u l a t i o n of Mg  s i t e d i s t r i b u t i o n s . This  treatment  e f f e c t i v e l y assumes that a l l of the minor elements are e q u a l l y d i s t r i b u t e d between M1  and M2.  i l l u s t r a t e s the e f f e c t on l n K D 1 2 formula)  F i g u r e G1  also  of a ±0.0latom e r r o r  i n s i t e assignment (taking 0.01  (Si206  atoms from one  site  and r e - a s s i g n i n g i t to the other s i t e ) . T h i s i s e q u i v a l e n t to a 0.02atom e r r o r i n chemical a n a l y s i s f o r an element which would be ordered e n t i r e l y In l i g h t of the apparent  into a single  importance  site.  of minor element  s i t e assignment, a l l of the measured l n K D 1 2 values have been r e c a l c u l a t e d based on modern estimates of o c t a h e d r a l s i t e p r e f e r e n c e . Using the c o m p i l a t i o n of Cameron and P a p i k e ( l 9 8 l ) as a g u i d e , l n K D l 2 v a l u e s were r e c a l c u l a t e d entirely  o c t a h e d r a l A l i n M2.  r e s u l t s are l i s t e d i n t a b l e G1  illustrated  The  in figure  Notably absent  i n M2  and T i , F e  +3  p l a c i n g Ca, Na, K and Mn  by  and and  G2.  from t h i s t a b l e and  f i g u r e are the data  for specimen #9 from Saxena and G h o s e ( l 9 7 l ) . Heating experiments  px  on samples of t h i s specimen ( X ° = 0 . 8 6 ) were  performed o u t s i d e i t s s t a b i l i t y  f i e l d with respect to  o l i v i n e + q u a r t z . Values of l n K D 1 2 measured f o r t h i s specimen are anomalously temperature p a r t i c u l a r a t t e n t i o n was  independent and  no  p a i d toward c h a r a c t e r i z a t i o n of the  products of these experiments. For these reasons, the data from specimen #9 are not i n c l u d e d i n the present  study.  173 Table G1. O r i g i n a l and a d j u s t e d values of l n K D 1 2 . The r e f e r e n c e s a r e : 1 = V i r g o and Hafner(1969); Ghose(l971);  3 = Besancon(1981); 4 =  5 = Besancon and  Besancon(submitted);  Vaughan(submitted). Reported  T(°C)  2 = Saxena and  Adjusted  XEn  lnKD12  lnKD12  500  0.819  -3.183  -3.294  500  0.619  -3.396  -3.392  500  0.545  -3.461  -3.660  500  0.500  -3.469  -3.682  500  0.420  -3.200  -3.644  500  0.380  -2.896  -3.360  500  0.280  -2.145  -2.646  600  0.819  -2.260  -2.350  600  0.619  -2.451  -2.453  600  0.545  -2.451  -2.595  600  0.500  -2.543  -2.692  600  0.420  -2.527  -2.828  600  0.380  -2.272  -2.589  600  0.280  -1.962  -2.412  600  0.240  -1.794  -2.494  700  0.819  -1.936  -2.024  700  0.619  -2.115  -2.111  700  0.545  -2.014  -2.151  700  0.420  -1.962  -2.187  700  0.380  -1.943  -2.204  800  0.819  -1.721  -1.806  800  0.619  -1.772  -1.769  800  0.545  -1.738  -1.868  800  0.500  -1.709  -1.829  800  0.380  -1.742  -1.979  800  0.280  -1.497  -1.842  Ref.  174 Table G1. (continued) Reported T(°C)  X  En  lnK  D12  Adjusted lnK  D12  Ref .  1000  0.822  -1.405  -1.450  2  1 000  0.728  -1.422  -1.470  2  1 000  0.610  -1.403  -1.340  2  1 000  0.594  -1.648  -1.675  2  1 000  0.469  -1.525  -1.541  2  1000  0.426  -1.368  -1.402  2  1 000  0.369  -1.453  -1.649  2  1 000  0.302  -1.410  -1.406  2  1 000  0.239  -1.050  -1.048  2  1 000  0. 123  -0.645  -0.782  2  500  0.426  -2.864  -2.916  2  600  0.426  -1.936  -1.970  2  700  0.426  -1.772  -1.804  2  800  0.426  -1.518  -1.543  2  600  0.493  -2.121  -2.370  3  600  0.869  -1.706  -1.726  5  600  0.869  -1.801  -1.817  5  700  0.493  -1.780  -1.993  3  700  0.493  -2.116  -2.108  4  700  0.869  -1.319  -1.332  3  800  0.493  -1.444  -1.684  3  800  0.869  -1.003  -1.166  3  Review of f i g u r e G2 r e v e a l s d i s t i n c t  discrepancies  between the data sets from each of the three s o u r c e s . The cause of these d i s c r e p a n c i e s i s not immediately evident from p u b l i s h e d accounts of the experiments. There are no b a s i c d i f f e r e n c e s i n the procedures d e s c r i b e d i n each study f o r  175  + -1-  v  + +  + +  v  m  -2-  • +  + V  T  •  • •  o o  O  •  -3-  + 1000°C v 800°C • 700°C o600°C A 500°C  A  A  •  -4 0.0  0.2  0.4  0.6  1.0  0.8  X En F i g u r e G2. C o r r e c t e d l n K D 1 2 v a l u e s p l o t t e d v e r s u s X E n » filled  The  symbols represent data from Saxena and G h o s e ( l 9 7 0 ) .  The c r o s s e s and symbols c o n t a i n i n g a v e r t i c a l l i n e are from V i r g o and Hafner(1969). The open symbols represent data from Besancon(1981), Besancon(submitted) and Besancon Vaughan(submitted).  and  176 measurement and  i n t e r p r e t a t i o n of the Mossbauer s p e c t r a .  However, there are c o n t r a s t s i n the parameters of the heating experiments. C o n t r a s t s i n experimental appear to be r u l e d out as the source of  pressure  lnKD12  d i s c r e p a n c i e s . D u p l i c a t e h e a t i n g experiments performed on samples of the same specimen at I8kb and  7  I0~ bar  by V i r g o  and Hafner r e s u l t e d i n i n d i s t i n g u i s h a b l e v a l u e s of  lnKDl2.  Three d i f f e r e n t approaches have been used to prevent o x i d a t i o n . These approaches are atmosphere c o n t r o l  (H 2 -C0 2  gas mixing; Besancon, 1981), i n e r t atmosphere (argon at to 1.5kb; Saxena and Ghose, 1971)  and  lack of atmosphere  (evacuated s i l i c a g l a s s c a p s u l e s ; V i r g o and Hafner, In a l l c a s e s , experimental  0.5  1969).  run products which showed  evidence of o x i d a t i o n were d i s c a r d e d . In c o n c l u s i o n , there seems to be no sound reason to d i s c a r d any one d a t a - s e t . The data set of Saxena and Ghose alone  i s used i n the present  study because t h i s data set i s the l a r g e s t  internally  c o n s i s t e n t set of d a t a . It i s proposed here that thermodynamic m o d e l l i n g of lnKDl2  px  need not be asymmetric (with respect to X ° ) i n  order to s a t i s f y the Mossbauer d a t a . Saxena and modelled  the asymmetry i n t h e i r data set with  Margules excess  f u n c t i o n s f o r mixing on M1  Ghose(l971)  separate  and M2.  It i s  noted here that r e j e c t i o n of Saxena and Ghose's specimen and  #9  r e d i s t r i b u t i o n of minor o c t a h e d r a l elements removes much  of t h i s asymmetry. The  remaining amount of asymmetry i s  thrown i n t o doubt by the u n c e r t a i n t y i n R  f  and  the  177 i m p l i c a t i o n s of Besancon's rate study on the i s worth n o t i n g  500°C d a t a . It  here that Besancon(1981) found an  order-of-magnitude d i f f e r e n c e between the d i s o r d e r i n g of h i s two  specimens at  x  ^g  X =  0.49  and  rates  0.87.  CALORIMETRY:  Two  c a l o r i m e t r i c s t u d i e s have compared e n t h a l p i e s  s o l u t i o n of  intermediate Mg-Fe orthopyroxenes. HF  calorimetry  at 73.5°C by Sahama and  Torgeson(1949)  i n t e r p r e t e d by the authors to be c o n s i s t e n t enthalpy of m i x i n g . In f a c t , i t may such c o n c l u s i o n s  not  with zero excess  study includes  3 n a t u r a l orthopyroxenes. Pure endmembers are and  no compositions between X°J^ = 0.27  r e p r e s e n t e d . A recent  Mg-Fe orthopyroxenes that The  and  not  0.96  (Li,Na)B20„-melt solution  study by C h a t i l l o n - C o l i n e t et a l ( l 9 8 3 )  was  be p o s s i b l e to draw  from t h e i r d a t a . T h e i r  X  included  only  included,  are calorimetry 5 synthetic  span the e n t i r e s o l i d s o l u t i o n .  authors i n t e r p r e t e d t h e i r measurements at 750°C to  consistent  of  x  with a symmetric Margules model with W°^ =  be 4kJ.  ri  The  standard e r r o r in t h e i r i n d i v i d u a l c a l o r i m e t r i c  measurements i n d i c a t e s that t h i s c a l c u l a t e d WH  is precise  to  ±4kJ. C h a t i l l o n - C o l i n e t et a l ( l 9 8 3 )  i n t e r p r e t t h i s Wu  to be that of pyroxenes having K D 1 2  values c h a r a c t e r i s t i c of  e q u i l i b r i u m at  1120°C (the temperature of t h e i r s y n t h e s i s ) .  A recent o r d e r i n g - r a t e  study by Besancon  Vaughan(submitted for p u b l i c a t i o n ) are  value  s i m i l a r to d i s o r d e r i n g  and  shows that o r d e r i n g  r a t e s . This strongly  rates  suggests  178 that the s y n t h e t i c orthopyroxenes had s u f f i c i e n t time to reach o r d e r - d i s o r d e r  equilibrium  at  the  temperature  of  the  (750°C) p r i o r to being dropped i n to the borate  calorimeter  m e l t . The r e s u l t i n g value of 4+4kJ f o r  i s interpreted  here as being c h a r a c t e r i s t i c of orthopyroxenes i n order-disorder  e q u i l i b r i u m at 750°C.  OXIDATION  EQUILIBRIA:  Nafziger  and Muan(l967), Kitayama and Katsura(1968) and  Kitayama(1970) have s t u d i e d the  the e f f e c t of Mg  s u b s t i t u t i o n on  reaction:  FeSi03  = Fe + S i 0 2  + 1/20Z  (G2)  T h e i r approach was  to vary P_ (oxygen p a r t i a l pressure was u2 assumed = f^. ) , at constant T, u n t i l m e t a l l i c i r o n f i r s t u2 appeared i n a sample which was  initially  synthetic  pyroxene  or pyroxene + S i 0 2 . The v a r i a t i o n of e q u i l i b r i u m p^ X  Mg  w a s  u s e o  to the WG  -  t o  c a l c u l a t e an a - f a c t o r which i s p r o p o r t i o n a l  of a symmetric Margules f o r m u l a t i o n  The quoted a f a c t o r s t r a n s l a t e i n t o Wg's 2kJ  (WG=2.303RTa).  ranging from 8kJ to  over the temperature range from 1 1 5 0 ° to 1250°C (1atm). U n f o r t u n a t e l y these experiments are of l i t t l e  constraining All  with  the p r o p e r t i e s  of the orthopyroxene s o l u t i o n .  of the data i n the s t u d i e s  half-brackets  use i n  from the low p  l i s t e d above amount to side of r e a c t i o n  u2  (G2). No  1 79  attempts were made to e s t a b l i s h r e v e r s a l s . The X  Mg  X  w a s  a s s u m e  d  t o  D e  that of the s t a r t i n g m a t e r i a l even  though the method employed to d e t e c t r e a c t i o n change the composition of the pyroxene. An ambiguity  equilibrium  (G2)  must  additional  i n the a p p l i c a b i l i t y of these experiments stems  from u n c e r t a i n t y i n the s t r u c t u r a l s t a t e of the pyroxenes. Of the three experimental and Katsura(1968) r e p o r t s t r u c t u r a l pyroxenes. They concluded proto-pyroxene  INTERCRYSTALLINE  synthetic  s t u d i e s , only Kitayama identification  of t h e i r  that t h e i r pyroxenes possessed  the  structure.  ION-EXCHANGE:  Measurements of Fe-Mg d i s t r i b u t i o n between orthopyroxene literature  and other phases are represented i n the  by a l a r g e volume of n a t u r a l m i n e r a l - p a i r  examples p l u s experimental  s t u d i e s with o l i v i n e , C a - r i c h  pyroxene, garnet and cummingtonite (see Deer et a l , 1978, for review p l u s Sack, 1980;  Fonarev. and K o r o l k o v ,  1980;  Kawasaki and M a t s u i , 1983). A n a l y s i s of data from a s i n g l e mineral p a i r can only compare the p r o p e r t i e s of the  two  phases. Absolute v a l u e s of s o l i d s o l u t i o n p r o p e r t i e s can estimated by simultaneously c o n s i d e r i n g s e v e r a l (interdependent) ion-exchange e q u i l i b r i a p l u s  any  n e t - t r a n s f e r e q u i l i b r i u m and c a l o r i m e t r i c c o n s t r a i n t s  on  each of the s o l i d - s o l u t i o n s i n v o l v e d and on each of the endmembers. Chapter II presents a p p l i c a t i o n of a comprehensive database f o r m i n e r a l data i n the system  be  180 MgO-Si0 2 -Fe-0-C-H (Engi et a l , 1984)  to the a n a l y s i s of  ion-exchange e q u i l i b r i a with aqueous Mg-Fe c h l o r i d e s . Remaining i n c o n s i s t e n c i e s between the c a l c u l a t e d thermodynamic model and orthopyroxene  ion-exchange data  (see  Chapter I I ) p o i n t out the need f o r a d d i t i o n a l r e s e a r c h . For the p r e s e n t , the orthopyroxene  solution-model  parameters  l i s t e d under Model 2 i n Chapter II (symmetric Margules f o r m u l a t i o n ) are accepted as d e s c r i b i n g the p r o p e r t i e s of t h i s  THE  SOLUTION  macroscopic  solution.  MODEL'.  A s p e c i a t i o n model (Greenwood and Brown, i n p r e p a r a t i o n ; E n g i , 1983) macroscopic  i s chosen here f o r modelling  and m i c r o s c o p i c behavior of Mg-Fe  orthopyroxenes.  T h i s model c o n s i d e r s a mineral to be made up  of a d d i t i v e s t r u c t u r a l u n i t s et a l 1959;  the  (as with Thompson, 1969;  Kroger  P o w e l l , 1983). These u n i t s are t r e a t e d as  d i s t i n c t molecular  s p e c i e s whose c o n c e n t r a t i o n s depend on  i n t e r n a l e q u i l i b r i a among the s p e c i e s , as c o n s t r a i n e d by mass-balance. The  term ' s p e c i a t i o n model' r e f l e c t s i t s  s i m i l a r i t y to the d i s t r i b u t i o n - o f - s p e c i e s problems t y p i c a l of modelling gaseous and aqueous s o l u t i o n s . The  s t r u c t u r a l u n i t s chosen f o r m o d e l l i n g  orthopyroxene one  the  are s y m m e t r i c a l l y e q u i v a l e n t u n i t s c o n t a i n i n g  each of the s y m m e t r i c a l l y d i s t i n c t o c t a h e d r a l s i t e s ,  and M2.  The  M1  four p o s s i b l e s p e c i e s , Mg(M1)Mg(M2)Si 2 0 6 ,  Mg(M1)Fe(M2)Si 2 0 6 , F e ( M l ) M g ( M 2 ) S i 2 0 6 , and  Fe(Ml)Fe(M2)Si206,  181 are a l l assumed to have d i s t i n c t f r e e e n e r g i e s . The molar f r e e energy of the o l i v i n e w i l l then depend on the concentration  of these four s p e c i e s . Given an o v e r a l l  mass-balance c o n s t r a i n t , three of these c o n c e n t r a t i o n s are independent q u a n t i t i e s . Therefore  the two c o m p o s i t i o n a l  c o n s t r a i n t s , bulk composition and s i t e - o c c u p a n c y , are i n s u f f i c i e n t to determine a l l four  concentrations.  C a l c u l a t i o n of a l l four c o n c e n t r a t i o n s  requires  c o n s i d e r a t i o n of 'mass a c t i o n ' c o n s t r a i n t s : the i n t e r n a l e q u i l i b r i a among the s p e c i e s . The  f o l l o w i n g formulation  non-ideal mixing of the s p e c i e s  i s developed i n c l u d i n g with  each  other  as a  possibility. The  mass balance c o n s t r a i n t s , i n terms of mole  fractions, are: X  MM  +  X  MF  where X ^ M g XEn  +  FM  ( M 1) M  Xps  +  X  +  X  FF  =  1  )S i 2 0 6 g( M 2  ( G 3 )  a n d S O o n ?  = 1  (G4)  where X_ and X „ r e f e r t o the e n s t a t i t e and f e r r o s i l i t e En Fs endmembers;  X  En  =  X  MM  +  ^ M F  +  1  /  2X  4  FM  ( G 5 )  X.—, — X,-.,-, Fs FF  1/2 X.,,-, ' MF  +  1  /  2X  FM  e q u i l i b r i a are:  The i n t e r n a l  Mg(M1)Fe(M2)Si 2 0 6 =  l/2Mg(M1)Mg(M2)Si 2 0 6 + l/2Fe(M1)Fe(M2)Si 2 0 6  ( X  K.  MMXFP)°'  5 (  WFF)  0  • 5  MF MF  'MF  Fe(M1)Mg(M2)Si 2 0 6  = 1/2Mg(M1)Mg(M2)Si 2 0 6 +  (X FM  =  1/2Fe(M1)Fe(M2)Si 2 0 6  0  X ) ° ' 5 ( '7Y 7 i ) " MM FF MM FF  —  7  FM  5  FM  The molar f r e e energy of the s o l i d G  X  G  SS " MM En  +  S p e C  + G EX  where  X  G  FF FS  +  X  G  MF MF  +  X  solution i s : G  FM FM "  TS  conf  183  S  conf  and G g  =  Pec  "  R(X  MM  lnX  MM  + X  FF  l n X  FF  +  X  MF  lnX  MF  +  X  FM  lnX  FM  )( G 1 2 )  i s the excess free energy due to n o n - i d e a l mixing  of the s p e c i e s . The s t o i c h i o m e t r i c  'bulk' excess f r e e energy  of t h i s model i s :  G  EX  lk  G  G  (  " SS " ID  where the f r e e energy of the s t o i c h i o m e t r i c  G  1  3  )  ideal solution  is:  G  and  ID  X  G  " En En  +  X  G  Fs Fs  "  TS  (  Iconf  G  1  4  )  the i d e a l c o n f i g u r a t i o n a l entropy i s : S  Iconf  =  -  Substituting  2 R ( X  En  l n X  En  +  X  Fs  l n X  Fs  )  (  G  1  5  )  (G11) and (G14) p l u s (G5) and (G6) i n t o (G13)  we have:  ^ x "  -  X  +  where  MF X  ( G  FM  2  SF-'/ ^n- / 1  (G  ,  FM- /  2G  2 G  ,  FS>  E,T ''  2G  s F  )  "  T  S  E x "  +  G  i f  C  <  G  ,  6  »  184  l k  S^ EX  = S , - ST f conf Iconf  (G17)  The e x p r e s s i o n s i n parentheses i n (G16) can be equated with the standard f r e e e n e r g i e s of the i n t e r n a l  G  EX  lk  +  =  The numeric  X  (  FM -  A G  ^ "  TS  EX  lk  +  equilibria:  G  EX  8C  (  G  1  8  )  s u b s c r i p t s r e f e r to equations (G7) and (G9).  A second-order (symmetric) Margules f o r m u l a t i o n i s adopted here t o d e s c r i b e the excess f r e e energy of mixing the s p e c i e s . An e x p r e s s i o n f o r G |  pec  was obtained by  a p p l y i n g equation(8) of Berman and Brown(l984)  and modifying  the n o t a t i o n :  G  EX  6C  X  X  = 1 MM MF  + W  W  W  X  X  * MF FM  +  X  X  * MM FM  W  X  +  X  W  X  3 MF FF  X  +  W  X  X  « FM FF  +  (  « MM FF  In an e f f o r t t o reduce the number of f i t parameters,  G  1  9  )  the  excess energy of mixing the s p e c i e s i s modelled as being proportional to e l a s t i c  lattice  s t r a i n energy caused by  volume mis-match between the s p e c i e s difference  (Greenwood, 1979). The  i n volume between the MM and MF s p e c i e s i s  assumed t o be equal t o the d i f f e r e n c e between the MF and FF s p e c i e s . The d i f f e r e n c e between the MM and FF s p e c i e s volumes i s assumed t o be the sum of the MM-MF d i f f e r e n c e and the MF-FF d i f f e r e n c e . The volumes of the MF and FM a r e  185 assumed t o be i d e n t i c a l . T h i s l a s t assumption f o r c e s the G  EX  6C  f  u n c t  i°  n  t  o D e  symmetric with respect t o X E n .  Combining a l l of these assumptions r e s u l t s = W „ plus W5  i n : W, = W2  = W3  = 0 and, because the r e l a t i o n between  displacement and e l a s t i c s t r a i n energy i s a 'square' law,  W6  = 4W,. T h i s reduces the number of Margules parameters t o one, which w i l l be r e f e r r e d (G19)  Q  i n terms of W^  spec  Applying  =  W  ^  e c  ( (  ec  X M M  t o as w^P  (= W,). Rewriting  and r e a r r a n g i n g  +  X  F  P  ) ( X  M  F  X  +  F  M  )  term:  +  the general a c t i v i t y c o e f f i c i e n t  Berman and Brown(l984, equation  RTln  ec  ?MM  =  +  ^ " ^ F S  RTln7Mp  = RTln7pM  RTln7Fp  = 2W^(X  where G E ^  ec  Before  X  FF  }  + X m m  X m m  X  F F  (G20)  )  expression of  (22)) r e s u l t s i n :  G  " EX  = W ^ U ^  E n  4  +  GC  Xpp) -G|P  ) -  i s given by equation  (  8C  G  2  1  )  (G22)  (G23)  (G20).  a p p l y i n g the above f o r m u l a t i o n , a method must be  established for calculation  of the s p e c i e s m o l e - f r a c t i o n s .  If the mass-balance ((G3), (G4) and (G5)) and mass-action  186 ((G8)  and (G10)) equations are combined and solved f o r a  s i n g l e m o l e - f r a c t i o n , the r e s u l t i s a q u a d r a t i c  i n that mole  f r a c t i o n . Solving for X M F results i n :  0  X  =  2 F  ( ^ M F 7  -  2 )+ x  b  7  M p b  +  XEn(XEn-D  (G24)  MM FF  where  b  - 1(,+ b * M ) 2  K  (G25)  7  FM FM  Finding a s o l u t i o n for t h i s quadratic  i s an i t e r a t i v e  process s i n c e the 7 ' s depend on the v a l u e s of the mole-fractions. I l l u s t r a t i o n of the r e l a t i o n s h i p between the above f o r m u l a t i o n and measureable q u a n t i t i e s i s f a c i l i t a t e d by rearrangement of the expressions  for internal equilibrium,  equations (G7) and (G9). The d i f f e r e n c e between these two equations i s the ion-exchange r e a c t i o n that produces the long-range order standard  measured i n the Mossbauer s t u d i e s . The  free-energy  of t h i s exchange r e a c t i o n w i l l be  r e f e r r e d t o as AG L (= AG °-AG 9 ) . The sum of (G7) and (G9) d e s c r i b e s the tendency toward short-range o r d e r i n g : p a i r i n g or a n t i - p a i r i n g of l i k e o c t a h e d r a l free-energy  i o n s . The standard  of t h i s short-range o r d e r i n g r e a c t i o n w i l l be  r e f e r r e d t o as AG g (=  AG7+AG9).  T h i s e n e r g e t i c d r i v e toward short range o r d e r i n g , AGg, i s i d e n t i c a l t o the AG^ or Bragg-Williams energy term used by Sack(l980) i n h i s orthopyroxene model. Although  187 Sack(l980)  s t r e s s e s the importance of i n c l u d i n g t h i s  term,  he does not allow the r e a c t i o n i t r e p r e s e n t s to proceed. In h i s b a s i c f o r m u l a t i o n (see h i s equation  (13)) the  c o n c e n t r a t i o n s of the four 'endmembers'  ( i d e n t i c a l t o the  four s p e c i e s c o n s i d e r e d here) are expressed only i n terms of the site-occupancy numbers. T h i s f o r m u l a t i o n can be shown to directly  imply that A G ° (AG g ) = 0. Assignment of any other  value to A G ° i s then  i n c o n s i s t e n t with h i s b a s i c  formulation. Comparison of the s p e c i a t i o n model with the site-occupancy data i s accomplished  by c a l c u l a t i n g  lnKD12  v a l u e s with the h e l p of the r e l a t i o n s :  *Sg ' MM X  X  Mg  =  X  MM  +  +  X  X  MF  FM  ( G 2 6 )  ( G 2 7 )  Comparison of the s p e c i a t i o n model with the accepted macroscopic  s o l u t i o n model i s accomplished  through the  relation:  (G28)  188 The  general p r o p e r t i e s of the s p e c i a t i o n model can be  estimated by reviewing equation  (G18) with the understanding  that v a r i a t i o n s i n AG^ and AG g (and t h e r e f o r e v a r i a t i o n s i n AG? and AGf) d i r e c t l y  i n f l u e n c e s p e c i e s abundances. I f AG^  i s e i t h e r p o s i t i v e or n e g a t i v e , i t s c o n t r i b u t i o n t o G ^ ^ i s n e g a t i v e . I f AG g i s p o s i t i v e i t s c o n t r i b u t i o n t o G ^ " ^ i s negative and v i c e v e r s a . Any amount of o r d e r i n g w i l l in a small p o s i t i v e c o n t r i b u t i o n p o s i t i v e WgP  ec  result  from the "TSgx^^ term. A  translates directly  into a positive  c o n t r i b u t i o n t o G^"'"'*. Figure G3 i l l u s t r a t e s the e f f e c t of s p e c i a t i o n model parameters on l n K D 1 2 . A l l four curves were c a l c u l a t e d with AG L = 15kJ. A p o s i t i v e AG g ( a n t i - p a i r o r d e r i n g ) encourages long range o r d e r i n g at i n t e r m e d i a t e bulk c o m p o s i t i o n s . The opposite i s true f o r a negative AG g ( i o n - p a i r o r d e r i n g ) . A p o s i t i v e WgP  ec  p r e f e r e n t i a l l y reduces the c o n c e n t r a t i o n s of  the MM and FF s p e c i e s and encourages long-range  ordering.  Comparison with f i g u r e G2 shows that the site-occupancy  data ec  are c o n s i s t e n t with a p o s i t i v e AG g and/or a p o s i t i v e Wg^ . F i g u r e G4 i n c l u d e s a curve r e p r e s e n t i n g the macroscopic  .b'i''' f u n c t i o n ) developed i n Chapter I I . s o l u t i o n model (W^ G 1 1  1  T h i s model i s c h a r a c t e r i z e d by a G p ^ ^ which i s negative at EX high temperatures and i n c r e a s e s with d e c r e a s i n g temperature, Comparison of f i g u r e s G2, G3 and G4 and review  of the  general p r o p e r t i e s of the above f o r m u l a t i o n r e v e a l s that manipulation  of AG L and AG g values  ( h o l d i n g Wg  Pec  =0) cannot  simultaneously s a t i s f y both the macroscopic s o l u t i o n model  189  -1 AG (kJ) s  -5  W*  p e c  (kJ)  0 0  "  \  CN O  0  5  - 3 AG =15kJ L  T =600°C -4 0.0  r  0.2 0.4  0.8  1.0  0.6  F i g u r e G3. L n K D 1 2 curves c a l c u l a t e d from the s p e c i a t i o n model f o r m u l a t i o n All  pec  f o r sample values of AG r , A G „ , and W^ Li  b  (j  four curves were c a l c u l a t e d at AG =15kJ and T=600°C. Li  ,  190 and  the l n K D 1 2  d a t a . In p a r t i c u l a r , the i n c r e a s i n g  c o m p o s i t i o n a l dependence of l n K D 1 2  a t low temperatures would  r e q u i r e AG C t o increase while the i n c r e a s e of G ^ i f ^ with d e c r e a s i n g T r e q u i r e s AGg t o d e c r e a s e . On the other hand, both of these trends i n the data are c o n s i s t e n t with both AG^  and WgP  ec  i n c r e a s i n g with d e c r e a s i n g  temperature.  T h e r e f o r e , f o r t h i s a p p l i c a t i o n of a s p e c i a t i o n model t o the a v a i l a b l e orthopyroxene d a t a , AG g i s assumed t o be z e r o . The method employed i n c a l i b r a t i n g the s p e c i a t i o n model (as m o d i f i e d by assumptions d e s c r i b e d above) a g a i n s t the orthopyroxene data can be d e s c r i b e d as s u c c e s s i v e p a r t i a l r e g r e s s i o n . AG L was d e s c r i b e d by a two parameter f u n c t i o n linear  i n temperature. WG  pec  was given a three parameter  f u n c t i o n c h a r a c t e r i z e d by a constant WrL  . Pressure P  dependence was not i n c l u d e d . The AG_ parameters were regressed to the l n K D 1 2  data while h o l d i n g the Wg  parameters c o n s t a n t . Then the WgP  ec  Pec  parameters were  regressed t o the macroscopic s o l u t i o n model while h o l d i n g the  (regressed) AG L parameters c o n s t a n t . The data p o i n t s  used i n t h i s second r e g r e s s i o n step were values of G p " ^ c a l c u l a t e d from the macroscopic s o l u t i o n model a t 5 0 ° i n t e r v a l s over the temperature range i n which the macroscopic model i s c o n s t r a i n e d by data The  (550° to 1300°C).  computer program employed i s a ' d e r i v a t i v e  free'  n o n l i n e a r r e g r e s s i o n program c a l l e d BMDPAR which i s d i s t r i b u t e d by BMDP S t a t i s t i c a l Software, I n c . . The two r e g r e s s i o n steps were repeated  u n t i l each step r e v i s e d the  191 regressed parameters by l e s s than 0.2%.  Some ' i n t e r v a l  h a l v i n g ' was performed by hand t o speed up the p r o c e s s . The r e s u l t i n g parameters are l i s t e d  i n t a b l e G2.  DISCUSSION:  The  behavior  of the s p e c i a t i o n model d e s c r i b e d by the  parameters i n t a b l e G2 i s i l l u s t r a t e d  i n f i g u r e s G4, G5, G6,  G7, and G8. F i g u r e G5 shows that the model f i t s the  lnKD12  data q u i t e w e l l c o n s i d e r i n g the u n c e r t a i n t i e s which remain U  in the data s e t . F i g u r e G4 shows that the W g ^ e q u i v a l e n t ( c a l c u l a t e d from (G28)  a t X_ =0.5) tin  conforms t o the  macroscopic s o l u t i o n model over the temperature i n t e r v a l of 11  the r e g r e s s i o n d a t a . W^ ^  conforms t o the c a l o r i m e t r i c  data  even though the model c a l i b r a t i o n was not c o n s t r a i n e d t o do s o . The steep plunge of W „ e f f e c t of the constant Wp allow Wu  Pec  u  ^ at high temperature i s a side  Pec  f o r m u l a t i o n which does not  t o curve towards a constant  value a t high T. The  rl 0  steep plunge of W^"^ a transition  1 1  and W^ "^ a t low temperatures  reflects  i n t o a r e g i o n i n which the Mg(M1)Fe(M2)Si 2 0 6  s p e c i e s t o t a l l y dominates the s o l i d s o l u t i o n G7). Although Wg  Pec  continues  t o r i s e with  (see  falling  temperature (see f i g u r e G6), the s p e c i e s which Wg strongly a f f e c t s  figure  Pec  (MM and FF) become so rare that G g  most Pec  plunges towards z e r o . Over t h i s same t r a n s i t i o n  region AG L  and  to r i s e .  i t s negative c o n t r i b u t i o n t o G ^ " ^ continue  To summarize, the r e s u l t s of a p p l y i n g a s p e c i a t i o n model to the orthopyroxene s o l i d s o l u t i o n  imply that the  192 Table G2. F i t parameters r e s u l t i n g from s u c c e s s i v e p a r t i a l r e g r e s s i o n of the s p e c i a t i o n model to the orthopyroxene data. 18820 (J/mole) 4.075 (j/mole/°C) spec H  43690 (J/mole)  r w  ,spec s  58. 1 3 (J/mole/°C)  w  spec C  -34.8  (j/mole/°C)  macroscopic p r o p e r t i e s of t h i s phase are the product of two opposing e n e r g i e s . The  f i r s t of these i s the s t a b i l i z a t i o n  energy gained from o r d e r i n g two d i s t i n c t  ions onto the two  symmetrically and e n e r g e t i c a l l y d i s t i n c t o c t a h e d r a l The  second i s a d e s t a b i l i z a t i o n energy which  here as an e l a s t i c  sites.  i s modelled  s t r a i n energy produced by c o n s t r u c t i n g a  continuous l a t t i c e out of s t r u c t u r a l u n i t s with s l i g h t l y d i f f e r i n g dimensions. As t h i s s t r a i n energy  i n c r e a s e s with  thermal c o n t r a c t i o n of the s t r u c t u r e , the c o n c e n t r a t i o n of the u n i t s with the g r e a t e s t volume c o n t r a s t are reduced until  finally  such u n i t s are v i r t u a l l y  absent.  If no s t a b i l i z a t i o n energy c o u l d be gained by o r d e r i n g of Mg and Fe on the two  s i t e s , then the macroscopic  p r o p e r t i e s of the s o l i d s o l u t i o n would be dominated lattice  s t r a i n energy; a p o s i t i v e  by the  'excess' f r e e energy. The  o l i v i n e s o l i d s o l u t i o n seems to represent an example of t h i s c a s e . T h i s Mg-Fe s o l i d s o l u t i o n  i s c h a r a c t e r i z e d by  little  193  10000  6000-  400  600  800  1000  1200  1400  1600 1800  Temperature (K) F i g u r e G4. Comparison of macroscopic d a t a , formulated as Margules parameters, with e q u i v a l e n t s c a l c u l a t e d at X,, =0.5 from the orthopyroxene s p e c i a t i o n  model. W  p x  (Model 2)  r e f e r s to the macroscopic model developed i n chapter I I . The' v e r t i c a l bar represents the c a l o r i m e t r i c measurement of Chatillon-Colinet  et a l ( l 9 8 3 ) .  1 94  -1 -  CN  -2-  5  -3-  XEn F i g u r e G5. Comparison  of l n K D 1 2 data from Saxena and  Ghose(l970) with l n K D 1 2 curves c a l c u l a t e d orthopyroxene s p e c i a t i o n model.  from the  195  400  600  800  1000  1200  1400  1600  Temperature (K) F i g u r e G6. G E X  (equation  c a l c u l a t e d as a f u n c t i o n  (G18)) and  i t s components  of temperature  orthopyroxene s p e c i a t i o n model.  f o r the  1800  196  X  400  600  800  1000  1200  MM  1400  X  FF  1600  1800  Temperature (K) F i g u r e G7.  Species c o n c e n t r a t i o n s  c a l c u l a t e d as a  function  of temperature at a constant X_=0.5 f o r the c a l i b r a t e d tin orthopyroxene s p e c i a t i o n model.  1 97  1.0  X En F i g u r e G8. C a l c u l a t e d  total  f r e e energy of mixing f o r the  orthopyroxene s p e c i a t i o n model as a f u n c t i o n of X E n . value c a l c u l a t e d terms of G I D  i s Gg S  (equation  (equation (G14)).  The  (G11)) minus the f i r s t  two  198 or no long range Mg-Fe o r d e r i n g  (see Brown, 1980 f o r  r e v i e w ) . The macroscopic excess f r e e energy of the Mg-Fe o l i v i n e s o l u t i o n i s p o s i t i v e (see chapters I and I I ) . A p p l i c a t i o n of the i m p l i c a t i o n s of the orthopyroxene s p e c i a t i o n model leads t o the c o n c l u s i o n of w ° l  l v i n e  with decreasing  temperature must produce some  amount of ion a n t i - p a i r l o c a l  SUGGESTIONS  The  FOR  FURTHER  that the i n c r e a s e  ordering.  RESEARCH:  asymmetry i n l n K D 1 2  with respect  t o bulk  composition noted by Saxena and G h o s e ( l 9 7 l ) may, i n f a c t , be r e a l . I f s o , some of the assumptions used here to s i m p l i f y pec  the G!|  research  f u n c t i o n are i n a p p r o p r i a t e . A d d i t i o n a l Mossbauer aimed at c o n f i r m i n g  t h i s asymmetry should attempt  to remove the u n c e r t a i n t i e s which were noted above. The uncertainty  i n minor element s i t e assignment c o u l d be  removed by studying uncertainty repeating  s y n t h e t i c orthopyroxenes. The  i n the 500°C data set c o u l d be removed by  these experiments with d u r a t i o n s  e x i s t i n g order-disorder  c o n s i s t e n t with  rate s t u d i e s . Consistent  use of an  f_ - b u f f e r e d experimental environment may remove the inter-laboratory discrepancies  found i n the e x i s t i n g  studies. The  ambiguity that remains i n a p p l y i n g  the c a l o r i m e t r y  of C h a t i l l o n - C o l i n e t et a l ( l 9 8 3 ) would not e x i s t i f t h e i r study had included Mossbauer s p e c t r o s c o p y . C a r e f u l c a l o r i m e t r y at a lower temperature would have a greater  199 ability  to measure e n e r g e t i c c o n t r a s t s between ordered and  disordered  pyroxenes.  

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