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Oxygen isotopes in geology. Bottinga, Jan 1963

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OXYGEN ISOTOPES  IN GEOLOGY  by  JAN  B.Sc.,  A THESIS  BOTTINGA  University  of  Toronto,  1961  SUBMITTED IN P A R T I A L FULFILMENT  OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE  i n the  Department of  PHYSICS  We  a c c e p t t h i s t h e s i s as  required  conforming to  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA February,  1963  the  In presenting  t h i s thesis i n p a r t i a l f u l f i l m e n t of  the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study.  I further agree that permission  for extensive copying of t h i s thesis f o r scholarly purposes may granted by the Head of my Department or by his  be  representatives.  It i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department of Physics The University of B r i t i s h Columbia, Vancouver 8, Canada. Date  February 22,  1963  -ii-  ABSTRACT  A c r i t i c a l survey has been conducted on the research done i n oxygen isotopes.  Only those aspects are considered which are of interest to  the earth s c i e n t i s t s . Oxygen isotopes have been used f o r geothermometric purposes and f o r rock genesis problems.  The p h y s i c a l p r i n c i p l e s underlying these  l i n e s of research are stressed. are e x p l i c i t l y stated.  two  Assumptions which are usually implied  It i s shown that the influence of pressure on  the equilibrium constant of oxygen isotope exchange reactions i s only a minor one i n comparison with the temperature influence. The s i g n i f i c a n c e of determined temperatures i s discussed i n the l i g h t of possible oxygen d i f f u s i o n i n s i l i c a t e s and carbonates.  It i s  concluded that d i f f u s i o n i s usually neglected without j u s t i f i c a t i o n .  As  f a r as data are available i t i s shown that d i f f u s i o n can be responsible f o r many discrepancies between oxygen isotope temperatures and' temperatures derived by other means. Studies on the o r i g i n of rocks by means of oxygen isotopes are discussed.  Attention i s focussed on the Southern Californian b a t h o l i t h .  The r e s u l t s of Taylor and Epstein's preliminary study of t h i s b a t h o l i t h are interpreted here as evidence i n favour of a metamorphic o r i g i n of t h i s huge rock body.  -xi-  ACKNOWLEDGEMENT  The author would l i k e to acknowledge the suggestions he received from Professors W. F. Slawson and G. P. Erickson, who both read the draft of t h i s t h e s i s ; e s p e c i a l l y he i s g r a t e f u l t o Professor W. F. Slawson, who assisted him i n general p r a c t i c a l  matters.  To Professor R. D. R u s s e l l , the writer i s In p a r t i c u l a r indebted f o r the way i n which he made i t possible for the author to switch from geology to the study-of physics, and f o r the suggestion of t h i s research.  Thanks are due to the s t a f f of the Science D i v i s i o n of  the Library, who have aided the author frequently i n obtaining valuable references and foreign p e r i o d i c a l s , and to Miss N. Bernan who typed t h i s t h e s i s .  The author would l i k e to express h i s  appreciation f o r a bursary and a studentship from the National Research Council o f Canada.  -iii-  TABLE OF CONTENTS  ABSTRACT  i i  LIST OF GRAPHS  vii  LIST OF TABLES  ix  ACKNOWLEDGMENT  . xi  INTRODUCTION CHAPTER 1  CHAPTER 2  1 DETERMINATION AND REPORTING OF THE 0  1 8  /0  1 6  RATIO  3  1.1  Introduction  3  1.2  Mass spectrometer gases  3  1.3  Methods of extracting oxygen  4  1.3.1  S i l i c a t e s and iron oxides  5  1.3.2  Carbonates  7  1.3.3  Phosphates  9  1.3.4  Water  9  1.3.5  Inorganic compounds  11  1.3.6  Organic compounds  12  1.4  Contamination  1.5  Reporting of 0  12 1 8  /0  1 6  ratios  13  ISOTOPIC EQUILIBRIUM THEORY  17  2.1  Introduction  17  2.2  Ideal gases  17  2.3  Limitations of the t h e o r e t i c a l treatment  22  2.3.1  22  Ideal gas assumption  -iv-  2.3.2  Anharmonicity  2.3.3  Intramolecular fractionation and the  2.3.4  CHAPTER 3  CHAPTER 4  CHAPTER 5  22  f r a c t i o n a t i o n factor  25  Zero point energy  27  2.4  Liquids  28  2.5  Solids  29  2.6  Numerical example  30  FACTORS INFLUENCING THE EQUILIBRIUM CONSTANT  35  3.1  Introduction  35  3.2  Temperature dependence  35  3.3  Pressure dependence  38  3.4  Thermodynamic a c t i v i t y  41  PALAEOTHERMOMETRY  44  4.1  Introduction  44  4.2  Temperature formulae  46  4.3  O  47  4.4  Phosphate geothermometry  50  4.5  V i t a l effects  50  4.6  I n s e n s i t i v i t y of the fractionation factor  51  4.7  Influence of pressure  51  4.8  Purification  53  4.9  Significance of measured temperatures  54  1 8  /^  6  r a t i o of ocean water  HIGH TEMPERATURE GEOTHERMOMETRY  55  -V-  CHAPTER 6  CHAPTER 7  CHAPTER 8  CHAPTER 9  ISOTOPIC EXCHANGE REACTION KINETICS  74  6.1  Introduction  74  6.2  Homogeneous exchange reactions  74  6.3  Heterogeneous exchange reactions  78  DIFFUSION  84  7.1  Introduction  84  7.2  Oxygen d i f f u s i o n i n carbonates  86  7.3  Oxygen d i f f u s i o n i n quartz  89  7.4  Oxygen d i f f u s i o n i n s i l i c a t e s  92  OTHER PROCESSES BY WHICH OXYGEN ISOTOPES MAY BE SEPARATED  96  8.1  Rayleigh d i s t i l l a t i o n process  96  8.2  Gravitational s e t t l i n g  98  8.3  Other possible separation processes  99  O^/O  16  9.1  Igneous rocks  RATIOS OF ROCKS  9.1.1  9.1.2 9.2  101 101  Southern C a l i f o r n i a n b a t h o l i t h a c i d i c rock  101  Basic rocks  112  Sedimentary rocks  114  9.2.1  General  114  9.2.2  Origin of chert  117  9.2.3  Origin of dolomite  122  9.2.4  Origin of aragonite needles  123  -vi-  9.2.5  The oxygen isotope r a t i o of the ocean  9.3  Metamorphic rocks  BIBLIOGRAPHY  123 125  127  -vii-  LIST OF GRAPHS  Graph 5.1  Relationship between quartz-haematite f r a c t i o n a t i o n and calcite-haematite  f r a c t i o n a t i o n i n quartz*-  c a l c i t e haematite rocks  Graph 5.2  61  Errors i n calculated temperatures, due to errors i n &  measurements, f o r the mineral p a i r s  quartz-  c a l c i t e , quartz-haematite and calcite-haematite  Graph 5.3  65  Errors i n calculated temperatures, due to errors i n measurements, f o r e q u i l i b r i a quartz-water, calcite-water and haematite-water  Graph 5.4  66  Fractionation relationships between the mineral p a i r s q u a r t z - c a l c i t e , calcite-haematite  and  quartz-  haematite  Graph 9.1  Fractionation relationships between mineral p a i r s i n a c i d i c rocks I  Graph 9.2  107  Fractionation relationships between mineral p a i r s i n a c i d i c rocks III  Graph 9.4  106  Fractionation relationships between mineral p a i r s i n a c i d i c rocks II  Graph 9.3  67  Variation diagram showing the relationship between chemical composition and oxygen isotope composition  108  -viii-  f o r various rocks  Graph 9.5  110  Fractionation relationships between mineral p a i r s i n basic rocks  113  Graph 9.6  Oxygen isotope composition of various rock types  115  Graph 9.7  Relationships between  5 o / S i  2  S M O W  and ^ ( y s M O W  f o r quartz and c a l c i t e , p r e c i p i t a t e d under equilibrium conditions from marine and fresh water and the temperature at which equilibrium i s attained  120  -ix-  LIST OF TABLES  Table 2.1  Normal vibrations of carbon dioxide and the water molecule  31  Table 2.2  Anharmonicity c o e f f i c i e n t s f o r C0  Table 2.3  Fractionation factors calculated f o r the systems water vapour-carbon  2  and H 0  32  2  dioxide and water -  carbon dioxide at 25.1° C and 1 atmosphere pressure  33  Table 3.1  Comparison between G(u^) and u^/12  36  Table 3.2  Values of u f o r d i f f e r e n t temperatures  and  frequencies  37  Table 4.1  D i s t r i b u t i o n of 0  Table 5.1  Cogenetic quartz-calcite-haematite h values  Table 5.2  Temperatures of freezing i n of the  Table 5.3 Table 5.4  1 8  i n the hydrosphere  at present  49  59  Q /^ r a t i o 18  6  of three cogenetic mineral p a i r s  60  Modification of table 5.2  63  h values f o r hydrothermal solutions with respect  to PDB  68  Table 6.1  Solutions of eqns. 6.17  and 6.18  Table 7.1  "Diffusion" of oxygen i n c a l c i t e under wet conditions  83  87  -X-  Table 7.2  Oxygen exchange between water and s i l i c a t e s during a period of 24 hours  90  Table 7.3  Oxygen exchange between water and quartz at 500° C  91  Table 7.4  Fractionation factors f o r the system o r t h o s i l i c a t e ions - water  Table 9.1  S  93  values with respect to Hawaiian sea water f o r  various rocks and t h e i r constituent minerals  103  Table 9.2  O^/O  116  Table 9.3  18 16 0/0 r a t i o s of coexisting marine cherts and  16  r a t i o s f o r various quartzose rocks  limestones  118  -1-  INTRODUCTION  This thesis i s a review and c r i t i c a l discussion of research done on oxygen isotopes from 1950  to 1962.  Only those areas are surveyed which  are of i n t e r e s t to earth s c i e n t i s t s . i c e , are not  Meteorological aspects, snow and  considered.  A knowledge of oxygen isotope d i s t r i b u t i o n s i n minerals and rocks may provide information about the temperature of formation of the minerals and about the genesis of rocks.  This i s a reason why  s c i e n t i s t s are interested i n oxygen isotopes.  earth  In t h i s thesis attention  i s mainly directed toward these two aspects.  Other n a t u r a l l y occurring  stable isotopes are i n p r i n c i p l e also suitable f o r investigation along t h i s l i n e , but the great natural abundance of oxygen, the r e l a t i v e l y large mass difference between O ^ 1  and 0 , 16  and the well developed  a n a l y t i c a l procedures favour the usage of oxygen. The theory of isotopic equilibrium has been discussed by Urey and by Bigeleisen and Mayer (15).  I t w i l l be assumed that the reader  has a knowledge of these two important papers. reviewed by Dole (55) i n 1952, i n 1954.  From 1951  isotopes i n general.  to 1956  Oxygen isotopes were  by Ingerson (97) i n 1953  and Rankama (129)  annual reviews (2) were published on  In 1959  Epstein (72) wrote a general paper about  O^/O^ r a t i o v a r i a t i o n s i n nature. 6  (158)  The l a s t review published i n the  English language was by Mayne (114) i n I960.  An exhaustive bibliography  -2-  on oxygen isotopes was compiled by Samuel and Steckel (135); i t covers papers published before 1959.  In 1961 a supplement (136) to t h i s  bibliography appeared f o r the period 1958-1960.  -3-  CHAPTER 1  DETERMINATION AND REPORTING OF THE 0  1 8  /0  1 6  RATIO  1.1 Introduction Over the years, gas source mass spectrometry has proven to be the most precise method for the determination of 0 /0"^ r a t i o s . 18  It i s  for, t h i s reason that only data obtained by t h i s method w i l l be considered here.  Almost a l l of the abundance r a t i o s have been deter-  mined using a Nier type spectrometer, although some investigators (55, 119) have made modifications i n the basic instrument.  Two features  normally employed f o r oxygen r a t i o determination are dual c o l l e c t i o n of the desired isotopes and provisions f o r rapid intercomparison with a standard sample.  1.2  Mass spectrometer gases Oxygen i s usually introduced into the mass spectrometer as carbon  dioxide, but carbon monoxide and molecular oxygen have also been used. Sulphur dioxide i s not suitable because of "memory" effects (95). has the same disadvantage.  Water  Carbon monoxide has the problem of a quite  large background i n the mass range 28 and 30 due to the almost universal  -4-  presence of molecular nitrogen and hydrocarbons. adverse features can be obviated (26). has a number of d i s t i n c t -  Fortunately these  On the other hand carbon monoxide  advantages.  In many processes i n which oxygen i s extracted from rock samples, the oxygen i s released as carbon monoxide and not as carbon dioxide.  -  The pump out time of carbon monoxide i s shorter than f o r carbon dioxide (105).  -  "Memory" effects f o r carbon monoxide are almost completely absent (105). Molecular oxygen has been used by Baertschi and Silverman (7).  They  mention the p o s s i b i l i t y of oxidation of the tungsten mass spectrometer filament.  This has been further investigated and confirmed (40).  The  oxidation process w i l l cause a f r a c t i o n a t i o n and shorten the l i f e time of the filament. Carbon dioxide.has been used most frequently as a mass spectrometer gas f o r 0 / 0  determinations.  are r e a d i l y available (122).  Widely accepted standards of t h i s gas  Craig (41) has given absolute abundance  r a t i o s f o r several carbon dioxide standards.  He also has published  correction factors f o r the mass spectrometrical analysis of t h i s gas.  1.3  Methods of extracting oxygen To obtain accurate r e s u l t s , either the O-^/O  16  r a t i o of the mass 1  1 8  spectrometer gas sample must be i d e n t i c a l to the 0  /0  r a t i o of the  rock sample, or the precise calculation of t h i s l a t t e r r a t i o should be possible.  Therefore, when the oxygen from a rock sample i s extracted,  the following requirements should be f u l f i l l e d : -  A l l the oxygen of the rock sample i s converted to gas sample.  Thus,  -5-  100% conversion i s usually needed to be sure that no fractionation of an unknown extent occurs during the conversion i n process. -  A l l possible precautions against oxygen contamination are taken.  -  The gas sample does not i n t e r a c t with the apparatus r e s u l t i n g i n a f r a c t i o n a t i o n of i t s 0  1.3.1  1 8  /0  1 6  ratio.  S i l i c a t e s and iron oxides Carbon reduction method. In 1952 Baertschi and Schwander (6) described a method i n which  the rock sample was reacted with carbon at 2000° C i n a high vacuum resistance furnace.  According to the reaction:  MeSiOg + 6 C = MeC + SiC + 3 CO 2  carbon monoxide was produced. By t h i s method 60-80% of the oxygen i n the s i l i c a t e was l i b e r a t e d . spectrometer gas. Schwander (137).  The carbon monoxide was used as the mass  A detailed account and r e s u l t s are published by Comparison with more recent r e s u l t s have shown that  Schwander s method i s not free of f r a c t i o n a t i o n . f  t h i s are discussed by Clayton and  Epstein (28, 32).  (59) has described a very s i m i l a r technique. y i e l d of 95-100%.  Possible causes f o r In 1959 Dontsova  She claimed an oxygen  Clayton and Epstein (28, 32) applied a modified form  of t h i s method i n which the resistance furnace was replaced by an induction heater, and the carbon monoxide was converted to carbon dioxide over a n i c k e l catalyst. quartz, i r o n oxide and zircon.  They obtained y i e l d s of 90-100% f o r For a l l other minerals the oxygen  -6-  recovery was s i g n i f i c a n t l y l e s s .  However Russian workers (59, 166, 167)  judged the carbon reduction method as successful f o r a l l minerals.  Halogen method. This method was devised by Baertschi and Silverman (7).  They used  either chlorine t r i f l u o r i d e or pure f l u o r i n e .  3 Me Si0 2  4  + 8 C1F  3  = 6 MeF + 3 S i F 2  4  +  4 Cl  2  + 6 0  2  and  Me Si0 2  4  + 4 F  2  =  2 MeF  2  + SiF  4  + 2 0  2  The reaction was carried on at about 430° C, and oxygen y i e l d s were 80-100% f o r most minerals and rocks.  A drawback of the method i s that  everything which comes i n contact with f l u o r i n e or chlorine t r i f l u o r i d e has to be made of nickel,ihconel or other i n e r t materials.  Taylor and  Epstein (144, 147) used f l u o r i n e and found i t s a t i s f a c t o r y f o r a l l but a few minerals, such as magnetite, epidote and garnet.  Taylor con-  verted the molecular oxygen which i s produced to carbon dioxide. He has described extensively h i s experimental technique and how to p u r i f y the f l u o r i n e , which i s often contaminated with oxygen.  Fluorine  and chlorine t r i f l u o r i d e have .in common that they react with the n i c k e l reaction chambers at 500° C, so t h i s becomes a temperature l i m i t .  The  e f f e c t of t h i s l i m i t may have been the reason why Taylor did not have any success with epidote, magnetite and garnet. F i n a l l y i n 1962, Clayton and Mayeda (34) have refined the method  -7-  so that i t i s suitable f o r a l l minerals. which i s l e s s reactive towards n i c k e l , encountered by Taylor. i n f u l l d e t a i l (34). are obtained.  They use bromine pentafluoride,  thus removing the l i m i t a t i o n  They have described t h e i r apparatus and technique Oxygen y i e l d s of 100 ± 2%:,of the t h e o r e t i c a l amount  Their i s o t o p i c r e p r o d u c i b i l i t y i s 0.1-0.2%». This method  seems to be the best one available at present.  Hoekstra and Katz (93)  report on the usage of bromine t r i f l u o r i d e f o r the quantitative determination of oxygen i n various metal oxides. 0.4%.  They claim an accuracy of  A l i s t of metal oxides which may be treated i n t h i s way i s given  i n their publication.  However, Clayton and Mayeda judged bromine  pentafluoride to be more suitable because of i t s higher vapour pressure.  1.3.2. Carbonates The carbon reduction method i s i n general not applicable to carbonates.  However i t has been used to determine the 0 / 0 ^ r a t i o i n 18  1  manganese carbonate (32). Thermal decomposition of carbonates has been attempted unsuccessfully.  McCrea (115) states:  "The k i n e t i c s of the decomposition of  calcium carbonate thermally are such that carbon dioxide can not be obtained with the desired r e p r o d u c i b i l i t y of isotopic composition". Vedder (163) noticed that thermal decomposition r e a d i l y takes place i n an environment of 0.1 mm.Hg water vapour. c a t a l y t i c influence.  The water vapour has a  However carbon dioxide obtained i n t h i s way can  only be used f o r carbon isotope analysis, because of oxygen exchange between the water vapour and the carbon dioxide. The most frequently used way.to decompose carbonates i s by means  -8-  of acid (115).  The carbonate powder i s treated with 100% phosphoric  acid.  CaCOg + 2 H  +  =  Ca  + +  + H0 2  + C0  2  I t i s important that the conditions under which the conversion takes place are known, because there w i l l be a temperature dependent oxygen f r a c t i o n ation between the reaction products.  Oxygen exchange between the  orthophosphate ion and carbon dioxide or the carbonate ion i s n e g l i g i b l e . This i s shown by McCrea (115) and Ault (3).  The reproducible f r a c t i o n -  ation ( CX') between the reaction products has been determined recently by Clayton (30).  ( 0  18 16y / 0  i n CO2 from acid decomposition of carbonate .  (018/0 ) carbonate 16  1.1 = 1.00999  This i s f o r 100% phosphoric acid decomposition of calcium carbonate at 25° C.  The O^/O^  r a t i o i n the denominator of eqn. 1.1 was  by means of the f l u o r i d e method (30).  determined  For 100% phosphoric acid  decomposition of rhodocrosite (MnCOg) at 25° C, Clayton and Epstein (32) measured  ot' = 1.010  by means of the carbon reduction method.  work (115) had already indicated that the  McGrea's  CX's f o r calcium-, strontium-,  and barium carbonate are v i r t u a l l y the same.  -9-  1.3.3  Phosphates Phosphates can be treated by bromine t r i f l u o r i d e (155).  A l l the  oxygen i s released without f r a c t i o n a t i o n and the p r e c i s i o n i s claimed to be 0.15&,. There are several other methods, but usually not a l l of the oxygen i s released.  Orthophosphate can be pyrolysed to metaphosphate and water  (36) and the water may then be analysed by one of the methods mentioned below.  One may heat Ag P04 to 1000° C to give molecular oxygen ( l ) . 3  Another method i s to heat KH2PO4 with Hg(CN) to produce carbon dioxide 2  (87).  Cohn and Drysdale (37) heated B a ( P 0 ) 3  4  2  with carbon to 1350° C  to produce carbon monoxide, while Boyer et a l . (20) thermally reacted with KH P04 with guanidine hydrochloride and achieved i n t h i s way that 2  two oxygens per KH2PO4 molecule were l i b e r a t e d as carbon dioxide.  1.3.4  Water  The older method of measuring the density of water (104) i s not considered here. at present.  E q u i l i b r a t i o n with carbon dioxide i s most often used  A measured volume of water i s put i n a f l a s k together 1 8  16  with a certain amount of carbon dioxide whose 0 / 0 The temperature  r a t i o i s known.  of the f l a s k i s kept constant at say 25° C.  When  isotopic equilibrium i s attained between the water and the carbon dioxide a small sample of gas i s withdrawn and analysed mass spectrometrically.  Because the fractionation factor f o r the exchange  reaction H 0 (1) + \ C0 18  2  1 6 2  (g) = H 0 (1) + \ C0 16  2  1 8 2  (g)  -10-  at 25° C i s known, the 0  1 8  /0  1 6  r a t i o of the water can be deduced.  f r a c t i o n a t i o n factor was measured by Compston and Epstein  This  (39)  . ( O ^ / O ) i n C0 Ck = 1 L L ^ = 1.04070 (O /© ) in H 0 16  2  1 8  1.2  1 6  2  at 25° C. The rate of t h i s reaction i s pH dependent (121).  To obtain  equilibrium i n a reasonable time i n t e r v a l i t i s necessary that the water i s a c i d i c (pH = 5-6) because the oxygen, exchange between water and carbon dioxide i s due to r e v e r s i b l e hydration of the carbon dioxide  C0  2  + H0 2  ^  H C0 ^ 2  3  H  + HCOg""^  2 H  +  and no d i r e c t exchange occurs between the bicarbonate  + COg  ~~  ion and the water.  The experimental procedure has been described by Epstein and Mayeda (77).  Craig (41) gives correction formulae f o r t h i s procedure and  Dansgaard (46) also provides p a r t i c u l a r s . To assure that i s o t o p i c equilibrium i s established Hoering (95) added the enzyme carbonic anhydrase to the water.  Disadvantages of the e q u i l i b r a t i o n method  are that i t takes at l e a s t two hours (Epstein and Mayeda waited 3 days) before equilibrium i s reached, that small quantities of water are d i f f i c u l t to handle, and that the water has to. be i n the l i q u i d phase. Dostrovsky and K l e i n (60) reduced the e q u i l i b r a t i o n from hours to minutes by speeding up the reaction. action of a hot platinum wire.  This i s done by the catalysing  Unfortunately  t h i s procedure does not  y i e l d reproducible r e s u l t s with d i f f e r e n t e q u i l i b r a t i o n chambers (81).  -11-  Cameron et a l . (25) used a similar technique but equilibrated the water with molecular oxygen.  The exchange, catalysed by a red hot platinum  filament, was completed i n about one h a l f hour.  The f i n a l composition  18 of the oxygen equilibrated with water of known 0  content agreed  exactly with the value calculated from the mole r a t i o  water/oxygen.  Falcone (80) catalysed the reaction through a high voltage discharge. Boyer et a l . (20) heated the water with HCl guanidine and thus converted the oxygen i n the water to carbon dioxide.  A way to treat small amounts  of water or water vapour i s described by Compston and Epstein (39). The procedure i s based on. the reactions 3 Fe + 4 H 0  = Fe 0  Fe 0  = 4 CO + 3 Fe  2  3  4  +4C  3  + 4 H  4  2  The water vapour i s reduced at 500° C by a.mixture of iron and carbon; at t h i s temperature no carbon monoxide i s formed and hydrogen i s released.  Then the temperature i s increased to 1000° C, the iron oxide  i s reduced by carbon and carbon monoxide i s produced which may be converted to carbon dioxide over a n i c k e l catalyst.  1.3.5  Inorganic compounds  According to Finikov (81), many oxygen containing solids can be treated with K Fe(CN) 4  at temperatures lower than 600° C.  6  released without f r a c t i o n a t i o n as carbon dioxide.  Finikov analysed  successfully A 1 0 , L i S 0 , BaS0 , B a ( P 0 ) , and NaW0 . 2  3  2  4  4  3  4  2  Oxygen i s  4  -12-  1.3.6  Organic compounds Organic compounds can be analysed i n d i f f e r e n t ways, depending on  the type of compound.  The Untersaucher (157), method i s often used.  In t h i s method the compound is pyrolysed on a carbon surface, carbon monoxide i s formed, and subsequently converted to carbon dioxide. f u l l p a r t i c u l a r s see (24,54).  For  A variety of organic compounds can be  treated with O-phenylendiamine monohydrochloride;  the oxygen i s con-  verted quantitatively to water i n t h i s reaction.  The process takes  place at 300° C and the duration i s about three hours (46).  1.4  Contamination Contamination of the gas sample produced by exchange with oxide  layers or with oxygen containing parts of the apparatus used i s d i s cussed b r i e f l y .  This e f f e c t i s i n practice evaluated by the usage of  blanks. Experimentally i t i s determined that there i s no measurable exchange between a clean and baked out s i l i c a vessel and dry carbon dioxide or dry molecular oxygen at 900° C (8).  Maass (113) did a  series of experiments to measure the exchange between water and glass. A measurable exchange was found only above 100° C. t i o n i s published by M i l l s and Hindin (121). enriched i n 0  1 8  A similar observa-  They sealed water  i n pyrex vessels and maintained the temperature at  105° C f o r periods up to four days.  The same i s done with 0.1 N .  alkaline solutions at 100° C f o r periods of eight hours.  In neither  case has exchange been observed. Dole (55) summarised data about the oxygen exchange between metal oxides and water, carbon dioxide or molecular oxygen.  In the majority  -13-  of cases no exchange takes place at temperatures lower than 100° C. Winter's (177) experiments are i n agreement with t h i s .  Hence the major  source of contamination w i l l be leaks and exchange between gases absorbed to the walls, of the apparatus and the gas sample to be analysed.  1.5  Reporting of 0  1 8  /0  1 6  ratios 18  When carbon dioxide or molecular oxygen i s used and 0 are mentioned, one means more often than not the 0  1 8  The l a t t e r i s the r a t i o which i s actually measured. i s o t o p i c r a t i o i s usually given as a ( (0  1 6  /0  1 6  0  1 6  1 6  /0  /0  1 6  0  ratios ratio.  1  The oxygen  value  ) sample (OlSnlS/ol^O ) standard 1 8  0  ^  0  16  1 1 t 1000  1.3  16  During the l a s t decade a great variety of standards has been used. Presently the most used standards are SM0W (Standard Mean Ocean Water) and PDB  (see Sect. 4.2).  Relationships between the standards and the  absolute oxygen isotope r a t i o s of various standards are given by Craig (41). When carbon monoxide or water are employed as a mass spectrometer 1 ft i  gas, true 0  ft  /0  r a t i o s are reported.  I t i s only i n rare cases when  authors state whether they record t h e i r results as the 0  1 8  0  1 6  /0  1 6  0  1 6  r a t i o or as the 0 /0 r a t i o . I t i s also rare when mention i s made ' of the nature of the corrections which were applied to the raw mass spectrometer data.  Generally, American investigators seem to apply  Craig's corrections (41).  Russian data appear not to be corrected f o r  17 0  while Baertschi and Dansgaard apply t h i s correction.  -14-  The Russian analogue f o r the o O value i s  .  _ [ ( O / 0 ) sample l 8  | (O  _  1 6  1 8  ±  1 J  / ^ ) standard 6  100  Among the Russian standards are - River water (58)  °  3.2  atmospheric oxygen/river water  Atmospheric oxygen i s f a i r l y uniform i n i t s isotopic Nier  1.4  composition.  (125) gives  0 U  0  0 -5 " = 408.8 x l O 16 16 1 8  1 6  S  1.5  0  f o r atmospheric oxygen. Hence Russian r i v e r water has the r a t i o  0  1 8  0  1 6  -5 = 396 x 10 b  1.6  016Q16 and thus  £ ° r i v e r water/PDB  <  - -47  °river water/SMOW =  1.7  -9  1.1  - Quartz from the Neroika deposit from the A r t i e Urals (165). 7?  1  Nier made a small numerical error i n the percentage calculation of 0 f o r atmospheric oxygen j t h i s should be 0.20.35% instead of 0.2039%.  X O  -15-  Absolute r a t i o of the quartz standard  $1 = 0l6  —2  487  Chupakhin (26) has described how t h i s r a t i o was determined. Thus  (W  6  =  412 x IO"  1.9  5  quartz standard and  ^ N e r o i k a quartz/SMOW  3  0  2  ,  0  In the c a l c u l a t i o n of eqns. 1.8 and 2.0 the [o 0^'^/0 0''"^]„ ^ , r a t i o SMOW 18  16  w  r  u  as given by Craig (42) was used. The quartz  & value f o r the Neroika quartz i s f a r beyond the range of S values measured by investigators i n the U.S.A. (see also  graph 9.6).  Moreover no published exchange" of samples between Russian  and Western laboratories has taken place, to establish a d i r e c t correlation.  Therefore, i t i s not possible to compare quantitatively  the Russian r e s u l t s (165, 167) measured r e l a t i v e to Neroika quartz, with r e s u l t s obtained elsewhere.  The Russian r i v e r water standard  agrees better with similar measurements done outside the USSR. Not a l l investigators use the  £ notation.  are Rankama (129) and Dansgaard (46).  Some notable exceptions  Rankama records the data as the  absolute or r e l a t i v e value of the O-^/O  16  ratio.  Dansgaard follows  -16-  the usage of tracer technique workers who report concentrations of the 18 rare isotope i n parts.per m i l l i o n .  Dar.sgaard records the 0  content as  parts per m i l l i o n of the t o t a l oxygen content of the sample with respect to the Danish standard.  He has correlated h i s Danish standard with  American standards. In t h i s survey the American p r a c t i c e i s followed;  wherever  r a t i o s are mentioned, the molecular 0  l  8 o  16 /O^O^  r a t i o i s meant.  CT^/O^  -17-  CHAPTER 2  ISOTOPIC EQUILIBRIUM THEORY  2.1  Introduction This chapter deals with the c a l c u l a t i o n of the equilibrium constant  f o r i s o t o p i c exchange reactions, from spectroscopic  data.  I t i s assumed  that the reader i s f a m i l i a r with the publications by Urey (158) and by Bigeleisen and Mayer (15).  2.2  Ideal gases Consider the exchange reaction  w  AXy + v BXJJ#  w AX + v BX v w  2.1  tt  The superscript # denotes the presence of the heavy (usually the rarer) isotope.  The compounds AX  K  y  and BX,^ are i d e a l gases.  By d e f i n i t i o n  (AXj)  2.2  eq  ( wl BX  Theoretically successful calculations of K ^ have been, performed only e  -18-  f o r i d e a l gases.  These calculations have been the subject of many papers,  among which references (15, 56, 133, 156, 158, 168 and 174) are only a few.  Thermodynamically the equilibrium constant i s related to the free  energy by  - RT In K  =  A  F°  2.3  eq  where F° = standard free R  energy,  .= gas constant,  T • = absolute temperature. The free energy i s related to the p a r t i t i o n function Q according to  Qe F = - RT In - 7 N  2.4  where  e = base of natural logarithme, N = Avogadro's number. To a.very good approximation the p o t e n t i a l energy functions are the same for i s o t o p i c a l l y d i f f e r e n t molecules.  Therefore i t i s j u s t i f i e d to  take as the reference datum f o r the energies appearing i n the p a r t i t i o n function, the hypothetical v i b r a t i o n l e s s state of the molecule.  For  normal chemical reactions t h i s procedure i s not followed, the ground state of the molecule i s taken as reference l e v e l , and the zero point energy i s neglected.  However, since i t i s mainly the difference i n zero  -19-  point energies which make i s o t o p i c a l l y substituted molecules behave d i f f e r e n t l y , i t i s e s s e n t i a l not to neglect the zero point energy. Thus zero point energy i s included i n the energy appearing i n the p a r t i t i o n function. For reaction  2.1  B X  w  /  [«AxJ  V  - M V  v  / ) v  w  Q x#)  r  - RT In  BX  AX.  W  B  - 'C„H w  BX  V  )]  P  2.5  w  where ^AX  =  v P =  v  °l  u m e  °f molecule AXy  i n the ground state,  pressure.  Usually the change i n volume due to i s o t o p i c substitution i s neglected, because i t s influence on K q e  K  i s only a minor one.  Therefore  eq  Under nonextreme conditions the p a r t i t i o n function may by  2.6  be approximated  -20-  Q  =  Q  2.7  %ot  t rvib Q  where Q^tr  .= t r a n s l a t i o n a l p a r t i t i o n  Q £k = v i b r a t i o n a l p a r t i t i o n  function,  v  Q  = rotational partition  r o t  function,  function.  Using t h i s approximation the p a r t i t i o n function r a t i o becomes  #  i•Sc y i  J  #  #  l  I  x x  1  irf z  r #-i hF_J  3/2  y  "  1 - e  e  1  -Ui/2  2.8  e  where s = symmetry number, I I I • x'- y z L  L  the three p r i n c i p a l moments of i n e r t i a ,  x  u. = h S) /kT, ±  I  i  vibration frequency of the i  ^ mode,  h = Planck's constant, k = Boltzmann's constant, T = absolute temperature, M = molecular weight. Degenerate modes of vibration are counted as many times as they are degenerate.  After making use of the Teller-Redlich product rule (131)  which states  jtt"  I#  j#  *X  *y *z  x  y  -, 1. 2  3/2  3n/2 fml  z  M .  u  i  u? l  2.9  -21-  one obtains  I  p  —  ni  3n/2  Q  e  s  s#  =  u  i  *  1-e  l-e ?  2.10  e" i  u  u  / 2  where n = number of i s o t o p i c atoms being exchanged, m,m  = atomic weights of the two isotopes.  Following Bigeleisen and Mayer (15) one defines  Q# f  rm^ /2 3n  Q  =  2.11  :\m#  as the reduced p a r t i t i o n function r a t i o . Thus  K  2.12  eq  and  " # i  -uf/2 e  u  . i  Substituting u.. = uY  u  1  i  2.13  -u,/2 / 1 - e " i e i ' u  + & u.. into eqn. 2.13 and expanding the r e s u l t ,  one obtains # 1 e  In .2u#  r  i  „-2u}l i _ e-uf ~ i- -" i u  " Wf " 2  e  A u.  " 2! (I - eu|) J 2  u  e  31  (1 - " ? )  2  1  3  2.14  -22-  Vojta (169) gives a detailed account of t h i s expansion.  When A-uj i s  small, the higher powers of eqn. 2.14 may be neglected. Put  G(u,)  = i  - -4  + —Tri  2.15  Eqn. 2.13 becomes now  In f .= In ^ s  Q(u ) A u..  +  2.16  ±  i  Except f o r the case of very l i g h t atoms (Hydrogen), enough t o make t h i s approximation a good one.  A u.. w i l l be small  Values f o r the function  G(u^) are calculated' and tabulated conveniently by Bigeleisen and Mayer (15).  These tables are reproduced i n (56).  The equilibrium constant  i s given by  In K =w eq  In  J# + E  G(u.) A  -v  Ujj  In ^ L  1  AX  S  + X G(u.) A u. •  —  1 V  B  2.17 Higher accuracy may be obtained by including the second term of eqn. 2.14 i n the calculations f o r K  .  eq  When one defines u  S  K)  =  1  u  i  e  i 2.18  n u  i  (e i-l) u  an alternative equation f o r In f i s obtained  2  -23-  ln f  •+  i  2~S(u.)(A  2.19  ) /2ui 2  U i  i  This development i s due to Bigeleisen (13, 14) who has also published tabulated values f o r the function S(u^) (13).  2.3  2.3.1  Limitations of the t h e o r e t i c a l treatment  Idea gas assumption Eqns. 2.17 and 2.19 are only v a l i d f o r i d e a l gases.  In applying  them to condensed phases one neglects the influence of the presence of other molecules on the i n t e r n a l vibrations of the molecule under consideration.  2.3.2  Anharmonicity In the derivation of eqn. 2.17 the v i b r a t i o n a l p a r t i t i o n function  f o r the harmonic o s c i l l a t o r was used.  At moderate temperatures t h i s w i l l  be adequate, but anharmonicity becomes more pronounced when the temperature increases.  The usual procedure i s to correct only the zero point  v i b r a t i o n a l energy f o r anharmonicity.  Thus  2.20  where  -24-  Then the correction f o r  f w i l l be  " I 4?  k hcAT (xf-: - * i j )  2.21  because the anharmonicity contribution to the p a r t i t i o n function i s  -\ he AT Qanh =  X ,\  e  Xi,1 3  2  '  2 2  Therefore  in  f . i n 'if I +  G f u ^  -  £ IT  Normally the anharmonicity constants molecule are not known.  (x  -  x ) t j  f o r the i s o t o p i c a l l y substituted  But these constants can be calculated, provided  they are known f o r the nonsubstituted molecule  With respect to eqn. 2.24, Herzberg (91) remarks that i t has not been rigorously proven, but that r e s u l t s j u s t i f y i t , i . e . i t agrees with the experimentally determined values. anharmonicity i s unimportant.  At low temperature the influence of  One may also consider the influence of  anharmonicity on the t o t a l v i b r a t i o n a l energy.  According to Vojta (170)  t h i s correction would amount to 0.1% to 1% of the anharmonicity correct i o n f o r the zero point energy at about 273° K.  I t would increase to  -25-  0.5%  to 5% at about 500 K. The  correction f o r the anharmonicity can be evaluated t h e o r e t i c a l l y  when one uses a semi-empirical p o t e n t i a l energy function l i k e the Morse p o t e n t i a l , instead of the Hooke's law p o t e n t i a l , i n the wave functions f o r the o s c i l l a t o r . The  Teller-Redlich product rule which i s used to derive eqn. 2.10 can  not be applied when the vibrations are anharmonic.  2.3.3  Intramolecular f r a c t i o n a t i o n and the f r a c t i o n a t i o n factor Generally i t i s assumed that the d i s t r i b u t i o n of the isotope X i n  the molecular species AXy i s governed only by the symmetry numbers of the various i s o t o p i c configurations  of the species AX . V  In other words  the heavy isotope w i l l be d i s t r i b u t e d at random through the assemblage of molecules of a certain species.  18  K  + C0  For example  2  = 2 CO  0"  eq  2.25  2.26  Because when eqn. 2.17 i s applied one finds that  2.27  -26-  However eqn. 2.27  represents an i d e a l i z a t i o n and observations (116) have  shown that f o r reaction 2.25  K, = 3.983 eq  The discrepancy of 0.017  i s due to intramolecular f r a c t i o n a t i o n caused  by the presence of the heavy isotope.  The presence of the heavy isotope  has changed the v i b r a t i o n a l frequencies of the molecule.  In t h i s case  the concentration of 018 s very respect to asthelong 0 asconcent r a t i o n and the e f f e c t i si not of psmall r a c t i with c a l importance all oxygen atoms occupy s t r u c t u r a l l y equivalent p o s i t i o n s i n the molecule. Intramolecular f r a c t i o n a t i o n can be evaluated only i f one knows a l l zero order v i b r a t i o n a l frequencies of the d i f f e r e n t l y substituted molecules. In the course of numerical evaluation of the equilibrium constant (see sect. 2.6) i t i s i m p l i c i t l y assumed that there w i l l be no i n t r a molecular f r a c t i o n a t i o n .  One takes f o r granted that a l l atoms which  can be exchanged have equal p r o b a b i l i t i e s of doing so, provided they are i n s t r u c t u r a l l y equivalent p o s i t i o n s . The f r a c t i o n a t i o n factor  i s defined as  f o r the reaction  CO2  + 2  .18 H 0' 2  (*) With regard to the usage of 0  C07 2 /0  X O  + 2  .16 H 0' 2  9  r a t i o s see sect. 1.5.  -27-  while  now  ^  2  "  [co^  ^O ^ 1  1 8  [co o ] 16  +  ]  +  /fe)  18  2 [CO^ ] 6  /  1 8  ]  [H 0 ] 1 6  2  eq  provided eqn. 2.26  i s valid.  Hence the r e l a t i o n  K  eq  , vw = CN  2.28  f o r the reaction 2.1 i s also an i d e a l i z a t i o n .  2.3.4 Zero point energy For the calculations of K ^ one must use zero order frequencies. e  From empirical formulae f o r the molecular energy l e v e l s one can estimate the zero point energy and thus one may convert the observed frequencies to zero order frequencies.  -28-  2.4  Liquids The equilibrium constant f o r an isotopic exchange reaction between  a gas and l i q u i d phase i s e a s i l y evaluated provided information i s available about the vapour pressure of the normal and of the i s o t o p i c liquid.  Let 0^^ be the fractionation factor f o r the  reaction  \ CO^Cg) + H 0 ( 1 ) = \ C 0 " ( g ) + H 0 ( 1 ) 18  16  2  and  2  i s the f r a c t i o n a t i o n factor f o r the corresponding reaction  h C 0 ( g ) + H 0 ( g ) = \ C o f (g) + H 0 ( g ) 6  18  2  18  2  2  then  2.29 P  H 0l6 2  where  P^ ^  g  H 0,18  = vapour pressure of  2  Theoretical calculations of vapour pressures of isotopic l i q u i d s are not t r i v i a l and have been successfully undertaken only f o r argon, neon, etc.  But there are experimental equations available to calculate  the vapour pressure r a t i o .  Riesenfeld  and Chang (132)  found  experimentally P  16 H0' log — t = J  2  P  H  018  2.74 T  _ 0.0056  2.30  -29-  Zhavoronkov et a l . (179) derived from an independent  set of experimental  data P l o  g  h^" 3.449 T -P ~ 18 = - 0.00781 H 0  2.31  1 8  2  Eqns. 2.30 and 2.31  give the same r e s u l t at room temperatures, but  s l i g h t l y f o r high and low temperatures.  differ  Devyatekh et a l . (53) derived  the equation  ln  __92-l = i - i i P  CO  18  - 0.0610  2.32  T  But usually such equations are not available. Waldmann (174) gives the following r u l e of thumb:  the phase i n  which the molecule or atom group has the most v i b r a t i o n a l degrees of freedom, w i l l be enriched i n the heavy isotope.  2.5  Solids As w i l l be shown i n the numerical example of isotopic exchange  between gaseous carbon dioxide and water (sect. 2.6), the calculated values are s l i g h t l y d i f f e r e n t from the experimental ones.  The  differ-  ence i n the example i s only 2.2% but i t i s s t i l l f a r greater than the present day experimental accuracy.  This discrepancy between t h e o r e t i c a l  and experimental values w i l l increase when one applies the calculations of sect. 2.2 to s o l i d s .  The reason being that the assumptions become  worse and the spectroscopic data l e s s dependable.  Only two cases of  i s o t o p i c exchange calculations involving s o l i d s are reported i n the  -30-  recent l i t e r a t u r e . Grant (85) assumed that the isotopic exchange of s i l i c o n isotopes in s i l i c a t e s i s exclusively governed by the i n t e r n a l vibrations of the o r t h o s i l i c a t e ion.  By means of t h i s approximation the problem  reduced to an i d e a l gas McCrea (115)  was  case.  t r i e d to determine the temperature dependence of the  f r a c t i o n a t i o n factor for  H 0 ( 1 ) + | CaC0g (calcite) .= H 0 ( l ) + | CaCO*^calcite) 18  6  1 6  2  2  He assumed that the i n t e r n a l vibrations remained unchanged and he to evaluate the contribution  of the l a t t i c e motions to the  The acoustical mode of the c a l c i t e l a t t i c e was  fractionation.  approximated by a Debye  function, while the o p t i c a l modes and the rotation of the COg expressed as Einstein functions. necessitated  Because of several ad hoc  ion were  assumptions,  by lack of data and the complexities of the problem,  McCrea's treatment could not be expected to give quantitatively results.  tried  correct  However q u a l i t a t i v e l y the agreement between McCrea's c a l c u l a -  tions and the experiment i s f a i r l y good.  The  greatest drawback seems  to be the lack of good spectroscopic data, which r e s u l t s from the inherent d i f f i c u l t i e s i n the interpretation of Raman and  Infrared  spectra.  2.6  Numerical example The t h e o r e t i c a l c a l c u l a t i o n of the equilibrium  exchange reaction  constant f o r the  -31-  +H 0  \-C0  2  2  1 8  = \ C0  2  8  + H0 2  i s performed t o various degrees of accuracy (table 2.3).  Table 2.1  gives the v i b r a t i o n a l wave numbers which were used.  TABLE  2.1  Normal vibrations of the carbond dioxide and the water molecule  Normal vibrations  w  i ^2 ^3  ^  < cm  H 0 cm 2  cm  -1  1351.20  -1  1273.9  672.2o( ) x  2396.4  661.94^ ) x  2359.81  V ' 1  1 6 x  cm"  1  3825.32  3815.5  1633.91  1647.8  3935.59  3919.4  The OJ^ v i b r a t i o n i s twice degenerate f o r carbon dioxide. A l l data are from Urey (158).  For H 0 the symmetry numbers s and 2  are always unity.  For C0 the 2  r a t i o s/s^ equals one because a l l oxygen atoms are considered to be exchanged  (see eqn. 2.17).  To calculate the anharmonicity correction  (eqn. 2.23) the c o e f f i c i e n t s of table 2.2 were used.  -32-  TABLE 2.2  Anharmonicity c o e f f i c i e n t s f o r C0 and H 0. 2  Anharmonicity coefficient  2  < < cm-'-  H /  cm"*"  cm"'"  -  Ref. (158)  -  8  -1 cm  x  ll  - 0.3  - 0.27  - 43.89  - 43.66  x  22  - 1.3  - 1.26  - 19.5  -'19.36  x  33  -12.5  -12.12  - 46.37  - 45.99  x  12  + 5.7  + 5.29  - 20.02  - 19.89  x  13  -21.9  -20.33  -155.06  -154.03  x  23  -11.0  -10.67  - 19.81  - 19.66  From data given i n tables 2.1 and 2.2 the following f r a c t i o n a t i o n factors are calculated (table 2.3).  -33-  TABLE 2.3  Fractionation factors calculated f o r the systems water vapour - carbon dioxide and water - carbon dioxide at 25.1° C and 1 atmosphere pressure  o4  System water vapour - carbon dioxide  (a)  from eqn. 2.17  1.0450  (b)  from eqn. 2.19  1.0458  (c)  from eqns. 2.19, 2.21  1.0468  System water - carbon dioxide  (d)  from eqns. 2.19, 2.21, 2.29  1.0385  (e)  experimentally determined (39)  1.0407  The data of table 2.3.show how by r e f i n i n g the calculations the accuracy may be increased, provided the basic information ( v i b r a t i o n a l frequencies and anharmonicity c o e f f i c i e n t s ) allows t h i s .  I f eqn. 2.17  i s used t o calculate ot> , a l l but the f i r s t term of eqn. 2.14 are neglected; i f eqn. 2.19 i s used, only the f i r s t two terms of eqn. 2.14 are  employed.  Since eqn. 2.14 converges f a i r l y r a p i d l y , these f i r s t  two terms should give a good approximation.  Usually one neglects even  -34-  th e second term of eqn. 2.14. correction can be evaluated.  By means of eqn. 2.21 the anharmonicity Line (c) i n table 2.3 gives thus the best  value of Oi. f o r the system water vapour - carbon dioxide.  Applying  eqn. 2.29 one obtains the fractionation factor f o r the system water carbon dioxide.  I t i s generally f e l t that the experimental value i s  more accurate than the t h e o r e t i c a l l y derived one.  However i t should be  noted that the actual difference between the two oi. s (lines (d) and T  (e)) i s f a i r l y small, when one considers a l l the approximations used to arrive at the t h e o r e t i c a l l y derived o^. In conclusion one may say that t h e o r e t i c a l l y derived ^ only of value f o r semi-quantitative purposes. c a l c u l a t i o n of '  's are  However a t h e o r e t i c a l  w i l l provide insight about the phenomena  one may  anticipate, because i t i l l u s t r a t e s the basic features of isotope behaviour.  -35-  CHAPTER 3  FACTORS INFLUENCING THE EQUILIBRIUM CONSTANT  3.1  Introduction This chapter i s a continuation of chapter 2.  The equilibrium  constant i s dependent on the temperature, pressure and thermodynamical activity.  These three factors are considered i n some d e t a i l .  Formulae f o r the temperature and pressure dependence are derived.  3.2  Temperature dependence When s =. s^, eqn. 2.17 becomes  In K  Z  eq  G(u.) A u ] 4  BX  w  Bigeleisen and Mayer (15) have pointed out that the function G(u^) may be approximated by u-/12 when u^ ^! 2.  As u^ becomes large the  approximation becomes bad (see table 3.1).  -36-  •  TABLE 3.1  Comparison between G(u.) and u./12  U./12  G( )  ui/12 - G ( )  1  0.083  0.082  0.001  1  2  0.167  0.157  0.010  6  3  0.250  0.219  0.031  14  4  0.333  0.267  0.066  25  5  0.416  0.307  0.109  35  6  0.500  0.336  0.164  49  U i  U i  % difference  At high temperatures u.. becomes small enough to j u s t i f y the approximation  l  n  K  eq  =  x  /  T  +  y  '  3  1  From tables 3.1 and 3.2 and eqns. 2.15 and 2.17 one may conclude that i f U j i s large, at low temperatures, K ^ i s better approximated by Q(  ln K  e q  where x, y, r and s are constants.  = | + s  T i s the absolute temperature.  3.2  -37-  Most polyatomic oxygen containing compounds have v i b r a t i o n a l frequencies of the order of 1000 cm . -1  of about 4000  But 0-H bonds have v i b r a t i o n a l frequencies  cm . -1  TABLE 3.2  Values of u f o r d i f f e r e n t temperatures and frequencies  Temperature  U> = 1000 cm  1  U)= 4000  °K  u  u  273  5.28  21.1  400  3.60  14.4  500  2.88  11.5  600  2.40  9.60  700  2.06  8.25  800  1.80  7.20  1200  1.20  4.80  cm  -1  Therefore when no 0-H bonds are involved one may anticipate a temperature dependence l i k e eqn. 3.1 ( c f . tables 3.1 and 3.2). When the temperature increases various assumptions employed become l e s s good.  i n eqn. 3.1  The anharmonicity becomes more pronounced.  The  r i g i d rotator assumption does not hold any longer, because of stretching of the molecule by i t s own c e n t r i f u g a l force, and therefore one finds  -38-  an increase i n the difference between the average moment of i n e r t i a of the molecule i n an excited v i b r a t i o n a l state and that of the molecule i n the ground state.  The usage of the Teller-Redlich product rule becomes  less justifiable.  At very high temperatures  a l l p a r t i t i o n functions have  t h e i r c l a s s i c a l value and no i s o t o p i c f r a c t i o n a t i o n w i l l take place.  Cross over temperature I t i s f a i r l y common that a phase which concentrates the l i g h t isotope at low temperatures, w i l l concentrate the heavy isotope at high temperatures.  This phenomenon i s c a l l e d "cross-over".  I t may happen  phase A i s enriched i n the heavy isotope at low temperature and has lower v i b r a t i o n a l frequencies than phase B, which i s enriched i n the l i g h t isotope at that low temperature.  Phase A w i l l have more v i b r a t i o n a l  degrees of freedom than phase B i n t h i s case.  The occurrence of "cross  over" under these circumstances follows d i r e c t l y from eqn. 2.17  and from  the f a c t that G(u;[) i s a monotonically increasing function of u^ (see table 3.1) f o r which  3.3  dG(uj) dui  tends to zero when u^ increases.  Pressure dependence Returning to eqn. 2.5 one obtains f o r the equilibrium constant  -P(wAV  K.  eq  A  - v AV )/RT B  3.3  e  where  V  v  -39-  and  3 In K_  -TOP  -  n  q  = -(w*V  A  -VAV )/RT B  3.4  since  d In  K  eq  d P  3  K 1  9  - (wAV  - VAV )/RT  A  B  3.5  p  Following the method of Joy and Libby (100) the term (w^V^.-• vAVg) w i l l now be estimated.  They assume that the f r a c t i o n a l volume change  on i s o t o p i c substitution i s about equal to the cube of the f r a c t i o n a l change i n the distance from the centre of the molecule t o the furthest p o s i t i o n of any constituent atom i n the course of normal vibrations of the molecule i n the ground state. . Also i t i s assumed that the bonds are harmonic o s c i l l a t o r s .  The bond length i t s e l f w i l l not be affected by  i s o t o p i c s u b s t i t u t i o n , however, the root mean square distance between the atom's p o s i t i o n and i t s equilibrium s i t e w i l l change as a r e s u l t of the substitution.  The wave function f o r the groundstate of the harmonic  oscillator i s  4Tn> l4  -2^ -Vmx /h 2  m  "  2  3.6  -40-  The root mean square expectation value o f x I 2  4? =  8TT V nj 2  3.7  and  f m  M  21  3.8  where y - vibration frequency of the harmonic o s c i l l a t o r , f = force constant, m = reduced mass. Only the stretching mode (  i  s considered i n the calculation of the  change i n distance on i s o t o p i c substitution.  &r  =  -  4'7  .4  \ l x *  2  he \ 2 f stretching  s  (*)  3.9  and  3 A V  "  R  r  The distance r may be calculated from the molecular volume or may be (*) The corresponding formula as given i n (100) i s i n error, see also (106).  3.10  -41-  put equal to h a l f of the distance between the centres of neighbouring molecules i n the s o l i d state.  The v i b r a t i o n frequency of the stretching  mode of the i s o t o p i c a l l y substituted molecule can be calculated by. means of the product r u l e . Hoering (94) has asserted that the maximum e f f e c t of pressure on the equilibrium constant can be derived from the anharmonicity correction to the r a t i o of the v i b r a t i o n a l p a r t i t i t i o n functions. following l i n e of reasoning:  This i s based on the  I f chemical bonds are harmonic o s c i l l a t o r s ,  then the e f f e c t of isotopic substitution w i l l be only a change i n f r e quency, the amplitude and hence the volume of the molecule w i l l be constant. But a c t u a l l y , chemical bonds are anharmonic o s c i l l a t o r s , thus the amplitude w i l l change as a r e s u l t of isotopic substitution.  Therefore, the anhar-  monicity correction i s a measure of the maximum influence of pressure on the equilibrium constant.  I t i s true that c l a s s i c a l l y the amplitude  pf any harmonic o s c i l l a t o r depends only on the i n i t i a l conditions, and i s thus mass independent. oscillator.  However the same i s true f o r the anharmonic  Quantum mechanically the concept of amplitude i s empty, but  the root mean square expectation value f o r x (eqn. 3.7) i s mass dependent for a harmonic o s c i l l a t o r .  In section 4.7 i t w i l l ' be shown that the  pressure dependence i n carbonate palaeothermometry i s r e l a t i v e l y insignificant.  3.4  Thermodynamic a c t i v i t y Besides the temperature  and the pressure, the thermodynamic a c t i v i t y  of the components of the system w i l l influence the equilibrium constant. Thus f o r the reaction  -42-  CoJ (g) + H 0 (1) = C0 0 (g) + H 0 ( i ) 8  18  1 6  1 8  1 6  2  / r #i  co2/  a  .a J H 0 2  C0  jr. co2  _  16 18 Q  C 0  2  1 6  / _r. /  ko 1 8 l H0 2  H O"J 2  3.11  where a = thermodynamic  activity,  ^ = activity coefficient, o*- = f r a c t i o n a t i o n factor f o r the system with a c t i v i t y c o e f f i c i e n t r a t i o s equal to unity, f ( ^) = function of the a c t i v i t y c o e f f i c i e n t s , cJv ' = actual measured f r a c t i o n a t i o n factor. Hoering (94) has measured the change i n r^,' when one replaces the pure water by a 10 molar aqueous l i t h i u m chloride solution.  I t i s believed  that the l i t h i u m chloride interacts s o l e l y with the water, therefore only the r a t i o ( ^ # / ^ ) H 0 2  i s  affected.  Taking f ( ^) = 1.000 f o r the  system with pure water Hoering has observed f ( ^ ) = 1.0008 f o r the l i t h i u m chloride solution.  He attributes t h i s to selective solvation  16 of the l i t h i u m ions by water, so that the solvent becomes enriched i n 0  -43-  Unfortunately l i t t l e i s known about a c t i v i t y c o e f f i c i e n t s of hydrothermal solutions.  I t should be noted that Hoering's solution i s quite con-  centrated.  Thus f o r natural occurring aqueous solutions one may  anticipate that the a c t i v i t y dependence of K q i s only of secondary g  importance.  -44-  CHAPTER 4  PALAEOTHERMOME TRY  4.1  Introduction Palaeothermometry u t i l i z e s the temperature dependence of the equi-  l i b r i u m constant f o r the oxygen isotope exchange reaction between c a l c i t e and water.  Urey (158) suggested that palaeotemperatures could be deter-  mined i n t h i s way. Experimentally  In 1948 he published some preliminary r e s u l t s (159). one does not determine the constant K ^ but the e  f r a c t i o n a t i o n f a c t o r dL . McCrea has grown calcium-carbonate very slowly from an aqueous solution at d i f f e r e n t temperatures. he determined the temperature dependence of e>(. .  In t h i s way  The f r a c t i o n a t i o n factor  could not be evaluated because of the constant f r a c t i o n a t i o n occurring when c a l c i t e i s treated with acid to produce CO2 (see sect. 1.3.2). 18 CO2 i s used t o measure the 0  The  1 r. /0  1  r a t i o of the c a l c i t e mass  spectrometrically. By comparing McCrea's inorganic r e s u l t s with organically p r e c i p i t a t e d c a l c i t e one can conclude whether the biogenic c a l c i t e was p r e c i p i t a t e d i n thermodynamical equilibrium with the water or not. by Epstein et a l . (73).  This has been done  Marine calcareous shelled invertebrates were  -45-  grown at known temperatures and t h e i r s h e l l s were analysed.  Because  of d i f f i c u l t i e s i n the p u r i f i c a t i o n of biogenic c a l c i t e , Epstein et a l . (74) had t o publish a r e v i s i o n of t h e i r 1951 paper (73). "I  o  relationship was established between the 0 of the c a l c i t e .  "I  A temperature  £  /0  r a t i o s of the water and  This r e l a t i o n s h i p i s i n v i r t u a l agreement with McCrea's  work. Urey et a l . (161) have calculated Upper Cretaceous temperatures. They used belemnite guards, and assumed that the guards were i n i s o t o p i c equilibrium with the Upper Cretaceous ocean.  This assumption has with-  stood the t e s t of i n t e r n a l consistency of r e s u l t s .  They also assumed the  habitat of belemnites was characterised by a s a l i n i t y of 34.8% , that of 0  the present ocean, and a ^ s e a water/PDB = -0.47.  The absolute tempera-  ture measured i n t h i s way may not be too s i g n i f i c a n t because of the uncertainty i n the 0  /0  r a t i o of the sea water.  But t h e i r tentative  conclusions about temperature trends during the Upper Cretaceous have been l a t e r confirmed by Lowenstam and Epstein ( i l l ) .  Emiliani and  Epstein (68) have shown that c e r t a i n recent foraminifera form t h e i r tests in i s o t o p i c equilibrium with t h e i r surroundings.  This has been the s t a r t  of the Pleistocene temperature work. Once the pioneering papers (73, 74, 161) were published a great many publications appeared dealing with Pleistocene, T e r t i a r y , Cretaceous, Jurassic and Permian temperatures. Samuel and Steckel (135, 136).  The majority of them are l i s t e d by  Among the papers published i n 1961 and  1962 are: - (134, 162) on Pleistocene temperatues; - (166,67, 69) on Tertiary temperatures; - (19) on Jurassic temperatures.  -46-  This subject i s reviewed by Durham (61) and Thorley (15.3). In the following sections various aspects of carbonate thermometry w i l l be considered.  4.2  Temperature formulae Epstein et a l . (74) have derived experimentally the equation  t = 16.5 - 4.3 &  + 0.14 &  4.1  2  where  t = temperature i n °C at which the carbonate i s formed, £> = the per mil difference between the O ^ / O ^  r a t i o of COv,  obtained from the sample and a standard C0 . 2  The standard carbon dioxide i s produced by reacting the c a l c i f i c  guard  of Belemnitella americana with 100% phosphoric acid at 25.2° C.  This i s  the PDB standard.  The belemnite was collected from the Upper Cretaceous  * Peedee formation i n South Carolina.  Equation 4.1 i s only applicable when  ^ sea water /PDB ~ " " ^ . l (see Craig (41)). value - 0.1 i s the &  value of the carbon dioxide, equilibrated with  mean ocean water at 25° C. O-^/O  1 6  To avoid confusion, t h i s  I t was r e a l i z e d that l o c a l l y the ocean water  r a t i o may vary appreciably from the r a t i o f o r mean ocean water  (76) and thus eqn. 4.1 was changed t o t = 16.5 - 4.3 ( £ - A) + 0.14 ( £ - A)  :  4.2  * Parenthetically, there are also authors who claim that the belemnite was collected i n North Carolina.  -47-  Again &  r e f e r s to the 0  /0  r a t i o of the carbonate and A equals the  value f o r the water i n which the sample•carbonate p r e c i p i t a t e d .  Equations 4.1 and 4.2 are based on data i n the temperature range 0 - 30° C. Employing high pressure techniques Clayton (29) has been able to obtain experimentally the following equation which f i t s the data over the range 0 - 750° C.  In K =2730 T  - 0.00256  - 2  4.3  K = f r a c t i o n a t i o n f a c t o r f o r the water - c a l c i t e system.  Clayton's  nomenclature i s followed here. T = absolute temperature i n degrees Kelvin.  Since Clayton used Epstein's low temperature r e s u l t s eqns. 4.2 and 4.3 give p r a c t i c a l l y the same r e s u l t i n the i n t e r v a l 0 - 30° C.  4.3  18 16 0 /0 r a t i o of ocean water Epstein and Mayeda (76) have analysed 93 marine water samples and  found that  the 0 18 16 /0  r a t i o of normal marine water- ( i . e . not s u r f i c i a l or shoal water, or water contaminated with fresh water) varies only 0.3%. Due to evaporation s u r f i c i a l marine water i s more-salty and enriched i n 0 , 1 8  while fresh water i s enriched i n O ^. 1  The reason f o r t h i s i s the  higher vapour pressure of P^O ^, as compared to H^O , under meteoro1  l o g i c a l conditions. the  18  In palaeotemperature work i t i s often assumed that  ocean i n the past had the same CP-S/O r a t i o as the ocean has  presently, i . e . A = 0 i n eqn. 4.2.  16  Emiliani (64) approximates the  -48-  Ql8yol6 r a t i o of the ocean i n the past by taking the weighted average of t h i s r a t i o f o r the present day hydrosphere. nonglacial times.  This i s , of course, f o r  For g l a c i a l times he assumes that the glacier i c e i n  the past had the same average 0^/0^  r a t i o as at present. 18  the extent of past glaciations one can deduce the 0 ocean during these glaciations.  By estimating  16 /Cr  r a t i o of the  In t h i s way he arrives at the following  values f o r A: - at maximum g l a c i a t i o n : A = + 0.4, •• corresponding to a correction of + 1.7°  C.  - at nonglacial times: A = - 0.3, corresponding to a correction of - 1.3°  temperature  temperature  C. 6  Emiliani (64) has taken f o r the present day volume of i c e 18.8 x 10 with an average  & = - 25.  3 km  Both values seem to be underestimated i n  the l i g h t of recent measurements.  Information given by Epstein and Benson  (77). f o r i c e from Antarctica and Greenland indicates that the average S> value f o r glacier i c e at present i s approximately - 35.  Donn et a l . (57)  report two estimates on the present world i c e volume which are given i n table 4.1.  These estimates have been used to calculate weighted  & ' s f o r the hydrosphere ponding temperature  average  (these are p o s s i b l e values of A) and corres-  corrections f o r nonglacial times (see table 4.1).  The suggestion that the i s o t o p i c composition of the ocean has been constant f o r a s i g n i f i c a n t part of the geological history i s a t t r a c t i v e and p o s i t i v e evidence f o r t h i s hypothesis i s available (see also sect. 9.2.5).  -49-  TABLE 4.1  18 D i s t r i b u t i o n of 0  i n the hydrosphere at present  II volume 10" km 6  ' 3  volume 10 km _6  ^/SMOW 3  1360.0  1360.0  30.6  25.0  0.5  0.5  1391.1  1385.5  , /SMOW hydrosphere ("A" f o r nonglacial times)  -0.87  -0.73  temperature correction for nonglacial times  -3.6°C  -3.1°C  ocean ice fresh water t o t a l hydrosphere  £  - 0.1 -35 - 7  (*) columns I and II are d i f f e r e n t because of the d i f f e r e n t present day g l a c i e r i c e volume estimations by respectively Novikov (126) and Crary (43). J a l l volumes are given as water at STP, taking the average density of i c e as 0.88 gram/cm . 3  -50-  4.4  Phosphate geothermometry The d i f f i c u l t i e s caused by the uncertainty about the values of  the 0  1 8  /0  1 6  Urey (159)  r a t i o of the ocean-in the past can perhaps be circumvented. suggested i n 1948  that probably use could be made of the  temperature dependence of the f r a c t i o n a t i o n factor f o r the hypothetical exchange reaction between cogenetic phosphate and carbonate i n s h e l l s . Although t h i s a t t r a c t i v e p o s s i b i l i t y existed, i t was not u n t i l 1960  that  Tudge (155) published a method, accurate enough, f o r extracting oxygen from orthophosphates. Oxygen isotope exchange does not take place d i r e c t l y between the s o l i d phosphate and the s o l i d carbonate.  But i t may  be possible that  equilibrium i s established between these two substances, v i a the water i n which the animal l i v e s .  Unfortunately  there is.apparently no oxygen  exchange between water and orthophosphate under inorganic conditions. The extent to which t h i s i s also true f o r organic conditions i s not yet known.  Hence i t i s not certain whether t h i s l i n e of approach w i l l be  successful.  4.5  V i t a l effects The subject of b i o l o g i c a l f r a c t i o n a t i o n has been reviewed by  Bowen (18). I t w i l l be obvious that the biogenic carbonate used f o r palaeotemperature measurements must have been formed under equilibrium conditions.  Urey et a l . (161) have concluded that nonair  breathing  invertebrates have a body temperature equal (within 0.5° C) to the surrounding water and that t h e i r body f l u i d s are i n i s o t o p i c equilibrium  -51-  with the water.  Lowenstam and Epstein (111) have reported i n t h e i r study  of recent marine invertebrate s k e l e t a l material, that only exoskeletons seem to be formed i n i s o t o p i c equilibrium.  Recent echinoderms secrete  t h e i r skeleton not i n equilibrium with the water.  Nonequilibrium  pre-  c i p i t a t i o n i s also indicated f o r shoal water corals and some algae (112). According  to Emiliani (64), i s o t o p i c exchange between the oxygen l i b e r a t e d  by Zooxanthella phenomenon.  and the a l g a l - and c o r a l carbonate i s the cause of t h i s  Zooxanthella  i s a symbiotic  organism l i v i n g i n the tissue of  the corals and algae under consideration.  4.6  I n s e n s i t i v i t y of the f r a c t i o n a t i o n factor The f r a c t i o n a t i o n factor f o r the system carbonate - water i s not  influenced by the kind of water used, oceanic or fresh (72) ( c . f . sect. 3.4).  Small changes i n pH and/or i o n i c strength appear to be of no  importance.  Epstein (72) reports that also small amounts of magnesium  and/or strontium ions i n the carbonate l a t t i c e do not a f f e c t i n a measurable way the f r a c t i o n a t i o n f a c t o r .  Moreover, the c r y s t a l symmetry  (rhombohedral c a l c i t e or orthohombic aragonite) f i c a n t influence.  does not have a s i g n i -  The p h y s i c a l reason f o r the l a s t two points i s that  the f r a c t i o n a t i o n i s mainly dependent on the i n t e r n a l vibrations of the carbonate i o n ; these vibrations appear to be influenced only i n a minor way by c r y s t a l symmetry and small amounts of impurities.  4.7  Influence of pressure The pressure  dependence of the f r a c t i o n a t i o n factor seems to be  unimportant i n carbonate thermometry.  This w i l l be i l l u s t r a t e d by an  example  | CaCO^ (calcite).+ H 0 6  2  1 8  ( l ) = | CaCO^ ( c a l c i t e ) + H 0 8  2  To estimate the influence of pressure  the  1 6  (1)  following simplifying  assumptions are made: - A l l molecules involved i n the exchange are i n the groundstate. - The molar volume of the water molecule does not change upon oxygen isotopic substitution.  Because of the central p o s i t i o n of the  oxygen atom i n the water molecule, t h i s assumption should be reasonably good. - The e f f e c t i v e volume of the carbonate i o n i s s p h e r i c a l l y shaped. Applying eqn. 3.10, one obtains  AV •=  \J 36Tf V  A r  2  4  Insert t h i s into eqn. 3.6 and put VB = 0  3 K _ _• 1 ^ 36 TI V ?P 3 \  -1 Molecular volume of c a l c i t e = 6.179 x 10  AT  2  RT  (Ref. 91). -23  ,3 cm'  4  -53-  Thus  A V = - 0.043 cm  mole  -1  and  =  6 x 10  -7  atm  -1  Therefore, at depth of 1 km i n the ocean K w i l l be increased by 6 x 10  -5  .  This would cause an error of l e s s than 1° C, which i s not s i g n i f i c a n t when compared with other uncertainties.  4.8  Purification Biogenic carbonate i s always contaminated with organic oxygen con-  taining compounds.  A successful way to get r i d of these compounds i s  described by Epstein et a l . (74). boat f o r 30 minutes.  They roast the sample i n a platinum  During t h i s process a continuous flow of p u r i f i e d  helium gas sweeps away the v o l a t i l e decomposition products of the heated organic compounds and provides an i n e r t atmosphere over the sample. Before the helium sweeps the sample i t passes a copper f i l l e d furnace at o 500  C and a l i q u i d nitrogen trap f i l l e d with activated charcoal, to  p u r i f y the helium.  Craig (41) has checked t h i s procedure by treating i n 18  the same manner a sample of Ticino marble and measuring i t s 0 before and a f t e r the treatment.  16 /0  ratio  He did not detect a difference between  the two measurements. Russian workers (123, 151) use a s i m p l i f i e d version of t h i s process.  -54-  4.9  Significance of measured temperatures The i n t e r p r e t a t i o n of the measured data requires that the s t r a t i -  graphic range, the habitat and the growth c h a r a c t e r i s t i c s of the f o s s i l material used are known.  The s t r a t i g r a p h i c range of many f o s s i l s i s well  established, but the habitat of most f o s s i l s i s only crudely known. For instance, i t i s known that a certain animal i s p e l a g i c , but i t i s usually not known i n what depth range the animal l i v e d .  This i s important because  marine water temperatures change considerably with depth.  The surface  temperature i n the Eastern equatorial P a c i f i c i s about 26° C but the water temperature at 200 meters i s about 11° C.  This aspect i s considered by  Emiliani and Epstein (62, 68) f o r pelagic foraminefera. 18 habitat may be characterized by a certain 0  Further the  1 ft /Cr r a t i o d i f f e r e n t from  SMOW. Only l i m i t e d information i s available about the growth i s t i c s of most f o s s i l s .  character-  I t appears that the growth of many invertebrates  i s c h i e f l y confined to a p a r t i c u l a r season (see f o r example (84)).  Thus,  generally one determines the temperature of the growth season of the animal.  Epstein and Lowenstam (75, 111) have investigated t h i s .  One may conclude that the carbonate thermometer i s a powerful t o o l i n palaeothermometry.  I t s weakest spots are the uncertainties about the  0l8 16 /0  r a t i o of the ocean i n the past, and the required detailed palaeontological knowledge of the f o s s i l material used.  -55-  CHAPTER 5  HIGH TEMPERATURE GEOTHERMOMETRY  Soon a f t e r the low temperature  carbonate geothermometer (chapt. 4)  was established, work started on the isotope determination of higher temperatures.  This work was mainly done by Clayton and Epstein.  They  considered oxygen isotope exchange reactions among oogenetic mineral p a i r s , because the melt or hydrothermal solutions from which minerals were p r e c i p i t a t e d are not available anymore.  Obviously, the oogenetic  p a i r s should be i n thermodynamic equilibrium. Whether t h i s i s the case or not can be shown to various degrees of conclusiveness.  are not i n equilibrium, because i f equilibrium were established quartz would be enriched i n QIS  with regard t o the c a l c i t e , according to - the The experimentally o Q and ^ c ofobtained equilibrium a i r s p r e c i p i t a t e d from eqn. p5.2  hydrothermal  solutions with approximately the same simple l i n e a r fashion (28, 33).  0l8 16 /0  r a t i o are related i n a  -56-  - I f there are three cogenetic minerals, the three possible p a i r s should give consistent r e s u l t s . - I f the quartz and the c a l c i t e are i n equilibrium with the same solution, then the ^ Q and  &^  S  values calculated f o r t h i s solution from  should be i d e n t i c a l .  Clayton (29, 30) has measured the f r a c t i o n a t i o n factor f o r the system o c a l c i t e - water over the temperature range 190 of 1000  o - 750  C under pressure  atmospheres. In K  pw  = 2730 T"  2  - 0.00256  5.1  where  Co /0 3  CaC0  [pl8/0 ]  H0  18  K  °  W  =  16  16  3  2  The low temperature data of Epstein et a l . (74) are incorporated i n eqn. 5.1.  The water was replaced by a dilute aqueous ammonium chloride  solution i n Clayton's experiments.  In 1961 O'Neil and Clayton  (127)  have reported a similar relationship f o r the system quartz - water.  In K  Equation 5.2 was  QW  = 3629 T"  - 0.00256  5.2  derived from experiments done i n the range 380° - 700° C  under 1000 bars pressure.  This time the water was replaced by a dilute  aqueous sodium f l u o r i d e solution. the relationship  2  From eqns. 5.1 and 5.2 one can deduce  -57-  In K,  •QC  = 899 T',-2  5.3  for the oxygen isotope exchange between quartz and c a l c i t e . Equations 5.2 and 5.3 had been deduced by Clayton and Epstein when only the  temperature relationship was known (33).  This was  done by  assuming that the equations would have the general form  -2  - y  5.4  as was indicated by the theory (see sect. 3.2).  Further i t was assumed  In K = x T  that the f r a c t i o n a t i o n factor f o r systems not involving water would become unity at high temperatures.  This i s because i n systems involving  water the "cross over" phenomenon i s bound to occur (see sect. 3.2). F i n a l l y they took f o r granted that the minerals quartz, c a l c i t e and hematite which appeared to be cogenetic i n some of t h e i r samples, were also i n thermodynamic equilibrium. deduce eqns. 5.2 and  This provided enough information to  5.3.  In addition to t h i s they could p l o t also In  vs In  for their  samples and obtain the relationship  = 1.388 In K. QH  In K, CH  where KQJJ stands for the f r a c t i o n a t i o n factor of the system quartzhematite . The convenient  equation  5.5  -58-  IOOO m  K  =  A B  where  A  -  .  S  AB  S  A  B  i s generally employed to give a r e l a t i o n s h i p between fractionation factor.  & values and the  This eqn. i s e a s i l y derived ( 3 3 ) .  K  [ o AB  1  / ^ A  8  1  [O /O1 ]B 1 8  "  6  1  +  A/1000  +  B  /  1 0 0 0  = 1 + ( i - «S)/iooo k  For oxygen exchange reactions  ^  B  1.04  thus  % = i + m K. AB  By means of eqn. 5.5 the following r e l a t i o n s could be deduced  In K Q  In K  H  C H  = 3216 T~  = 2317 T~  2  5.6  2  5.7  -2 In K  H W  = 413 T  - 0.00256  5.8  -59-  In the empirical derivation of eqn. 5.5 Clayton and Epstein (32, 33) used the data shown i n table 5.1.  TABLE 5.1  Cogenetic quartz - c a l c i t e - haematite valuesv  Sample  So 17.3  0.3  18.0  12.8  -2.8  34  112.. 3  8.2  2.2  35  10.4  7.4  1.6  6.8  6.5  3.3  32  24.4  33  i.s.C)  /  •  (*) I.S. i s a oogenetic quartz - c a l c i t e magnetite sample from Iron Springs. The f r a c t i o n a t i o n factor f o r the system magnetite - haematite was believed to be very small. (**)' A l l 6 values are with respect to SMOW as reported i n (32, 33).  From data In table 5.1 the temperatures  shown i n table 5.2 may be  deduced f o r each of the oogenetic mineral p a i r s .  -60-  TABLE 5.2 Temperatures of freezing i n of the O^/O  16  r a t i o of  three cogenetic mineral p a i r s  t  Sample  *  t  °C  CH  °C  °C  32  87  94  97  33  147  119  113  34  195  293  350  35 .  277  331  359  I.S.  1244  684  593  (*) tQQ stands for the temperature derived from the Rvalues of the cogenetic mineral pair quartzcalcite. Equation 5.5 was determined by means of a l e a s t square f i t f o r the graph of In KQ^J vs In K Q  H  (graph 5.1).  The l e a s t square method  presupposes that errors are distributed at random. here.  This i s not the case  In general high temperature data w i l l be more questionable than  low temperature ones.  Therefore, i t seems preferable to assume that  sample 32 i s a l l r i g h t and that.the graph In K Q through the o r i g i n (see graph 5.1).  H  vs In K  One obtains then  C H  w i l l pass  -61-  .IS  J  1 4  I  I  1  l  5  6  7  8  i  i  i  l  |  i  I  I  9 10 11 12 13 14 15 16 17 1000 In K Graph 5.1 - Relationship between quartz - haematite fractionation and c a l c i t e - haematite f r a c t i o n a t i o n i n quartz - c a l c i t e haematite rocks. CH  -62-  in K  and  Q H  = 1.404 In K  5.9  C H  subsequently  In K Q = 3124 T"  2  5.10  In K  2  5.11  H  C  H  = 2225 T"  In KHW = 505 T"  In the derivation of eqn. 5.9 the culated.  &  - 0.00256  2  5.12  values of table 5.1 were r e c a l -  This was necessary because Clayton and Epstein ( 3 2 ) used the  formula  £  /„„«,,•= 1-0399 £ + 39.9 x/SMOW x/PDB  5.13  to convert t h e i r measurements with respect to PDB, to values with respect to SMOW. Equation 5.13 i s based on the i n d i r e c t  determined  & value f o r Hawaiian sea water (taken to be the same as SMOW i n ( 3 2 ) ) namely  £„  A  W  A  I  I  A  N  S  E  A  W  A  T  E  R  /  P  D  B  = - 38.4.  But l a t e r i n 1958 Compston  and Epstein ( 3 9 ) reported f o r the reaction  1 2  16 .18 1 „ 1 8 2 2° =2 2 2° A  C 0  <^  +  H  = 1.0407  C 0  .16  + H  at t = 2 5 ° C  -63-  Therefore eqn. 5.13 should be modified to  ^x/SMOW  because  h g^ow/poES ~ ° '  w  ^  =  e n  1  -°  4 0 1  ^x/PDB  " ^ Q-^»^s t  ie  +  '  4 0  7  5  8  ratio for  16  Applying eqns. 5.9, 5.10, 5.11 and 5.12  one obtains the r e s u l t tabulated i n table 5.3.  TABLE 5.3 Modification of table 5.2 Temperatures of freezing i n of the 0 / 0 1 8  1 6  ratios for  three cogenetic mineral p a i r s  Sample  t  Q  t  C  o _C  o  Q  t  H  C  o •  C  H  C  32  89  89  89  33  150  116  104  34  205  285  331  35  287  325  342  1487  673  562  I.S.  1 4  neglected (see Craig (41)).  Equation 5.14 i s i n agreement with the absolute atomic 0 ^ / 0 SMOW as published by Craig (42).  '  -64-  Although the data of table 5.3 are not overwhelmingly impressive, they are somewhat more consistent than those presented i n table 5.2.  The  question i s now, what causes these temperatures to be so d i f f e r e n t and what may one deduce from t h i s . Experimentally  &  can be measured with an accuracy of - 0.2  (presently even better accuracy i s obtained).  The errors due to accuracy  l i m i t a t i o n s become appreciable at high temperature; t h i s w i l l be evident from an inspection of graphs 5.2 and 5.3. how a certain error i n &  In these graphs i t i s shown  measurement ( A ^  ) f o r a p a r t i c u l a r mineral  p a i r corresponds to a c e r t a i n temperature difference ( A t ) f o r a given temperature of freezing i n of the 0  /Or  ratio.  I f one assumes that the  samples 32, 33, 34, and 35 were p r e c i p i t a t e d from aqueous solutions, which can be treated as. pure water, then the various solutions can be evaluated (table 5.4).  £  values f o r these  Of course t h i s i s only possible  i f the isotopic composition of the solution remained constant as long as appreciable exchange took place. r  These are not unreasonable assumptions  when one takes i n consideration the low s o l u b i l i t y of quartz, c a l c i t e and haematite. To explain the r e s u l t s presented i n table 5.4 one may invoke the following mechanisms: - s o l i d state d i f f u s i o n ; - nonequilibrium p r e c i p i t a t i o n ; - m i n e r a l p a i r s were not t r u l y cogenetic; - changes i n isotopic composition of the hydrothermal solutions. Assuming that: -The  18 16 0 /Or r a t i o of the hydrothermal solutions remained constant as  -65-  100  200  300  400  500  600  700  Temperature of freezing i n of the Cr /Cr- r a t i o i n degrees Celcius 8  6  •h  Graph 5.2 - Errors i n calculated temperatures, due to errors i n S measurements, f o r the mineral p a i r s quartz - c a l c i t e (Q-C), quartz - haematite (Q-H) and c a l c i t e - haematite (C-H).  800  -66-  "I  100  I  200  I  300  I  400  I  I  500  600  ,  I  700  I  800  Temperature of freezing i n of the Q18 16 /0  ratio i n degrees Celsius. Graph 5 . 3 - Errors i n calculated temperatures, due to errors i n measurements, f o r e q u i l i b r i a quartz - water (Q-W), c a l c i t e - water (C-W) and haematite - water (H-W).  -67-  27 _  AQC,  ACH  Graph 5.4 - Fractionation relationships between the mineral p a i r s quartz - c a l c i t e ( Q C ) , c a l c i t e - haematite ( C - H ) and quartz - haematite ( Q - H ) .  -68-  TABLE 5.4 values f o r hydrothermal solutions with respect to PDB  Sample  Temp. °C  Mineral pair  ^  w  from Q ( * )  ^  w  from C  ^  W  from H  -39.3  -39.3  -39.3  Q-c  -38.3  -38.3  -41.3  116  Q-H  -41.8  -41.3  -41.8  33  104  C-H  -43.3  -42.0  -42.0  34  205  Q-C  -39.4  -39.5  -36.0  34  285  Q-H  -3513  -36.4  -35.4  34  331  C-H  -33.6  -35.2  -35.2  35  287  Q-C  -37.1  -37.0  -35.9  35  325  Q-H  -35.8  -36.1  -35.7  35  342  C-H  -35.2  -35.7  -35.7.  32  89  33  150  33  W from Q stands f o r the  . •  O value of the hydrothermal  solution calculated by means of eqn. 5.2.  -69-  long as appreciable exchange of oxygen took place.  This assumption  i s necessitated by lack of additional information. - The simplest mechanism which can provide a p h y s i c a l l y and geologically acceptable explanation i s most l i k e l y the main cause of the observed pattern of l v a l u e s . The data of table 5.4 are explained here i n the following way: Sample No.  32  The consistency of r e s u l t s i s forced by the i n i t i a l assumption that t h i s sample represented cogenetic quartz- - c a l c i t e - haematite p a i r s which are i n thermodynamical equilibrium.  Graph 5.1 was based on t h i s  and i t had as a consequence the modification of eqn. 5.5 to eqn. But even when one applies eqns. 5.6, 5.11,  and 5.12  5.7,  5.9.  and 5.8 instead of eqns.  5.10,  the consistency f o r t h i s sample i s f a r better than f o r any  of the other samples.  A t h i n section study revealed a. sequence of  c r y s t a l l i z a t i o n , the large equigranualar quartz was  formed f i r s t followed  successively by haematite, c a l c i t e , dendritic haematite and fine grained * quartz. Sample No.  33  The three d i f f e r e n t temperatures f o r t h i s sample may  be explained by  d i f f u s i o n of oxygen i n the c a l c i t e , by isotopic disequilibrium p r e c i p i t a t i o n of the quartz, or by the p o s s i b i l i t y that the quartz was formed at a somewhat higher temperature than the c a l c i t e and haematite.  In the l a s t  The author f e e l s i t may be concluded the quartz c a l c i t e and haematite used by Clayton and Epstein (32) were cogenetic. Professor H. James of the University of Minnesota was so kind as to provide samples 32, 34 and 35. Professors K. McTaggart and J . V. Ross of the Geology Department of the University of B r i t i s h Columbia determined the order of c r y s t a l l i z a t i o n of the minerals under consideration by examining t h i n sections of these samples.  -70-  two cases S Q w i l l be too low, while i n the f i r s t case high.  w i l l be too  I f oxygen d i f f u s i o n i n the c a l c i t e occurred then t q ^ ( i . e . the tem-  perature as derived from eqn. 5.10)  should be r i g h t .  However i t i s  reasonable to suppose that no s i g n i f i c a n t oxygen d i f f u s i o n took place when one considers the quantitative information available about:' oxygen d i f f u s i o n i n c a l c i t e (see sect. 7.2).  Moreover samples 34 and 35  do riot show a pattern which could be caused by c a l c i t e s o l i d state diffusion.  I f the inconsistencies are caused by a too low value f o r  then t^jj should be r i g h t .  From graphs 5.1 and 5.4 i t may be  that & Q i s 1.3 too low. and using a  S  <5q  concluded  This can be checked by c a l c u l a t i n g t q ^ and t q ^  value f o r quartz of  tqQ .= tqjj = 104° C and a  S  <SQ  + 1.3.  This gives  value f o r the water as calculated from the  quartz of —42.0 with respect to PDB.  Geological evidence should decide  whether t h i s i s a case of disequilibrium formation of quartz, or that the quartz was  formed at a s l i g h t l y higher temperature.  I f the quartz  was  formed f i r s t , i t s temperature of c r y s t a l l i z a t i o n w i l l have been 114°  C.  Pure coincidence i s responsible f o r the equivalence of a ^ as calculated from quartz, and 150° C.  & W as calculated from c a l c i t e at a temperature of w  The coincidence i s caused by the f a c t that  d  CW  K  d T  / jJ^QC /  d T  150 - 114 ~ i50 - 104  i n the temperature i n t e r v a l 100 - 200° C. Sample No.  34  The d i f f e r e n t temperatures of table 5.4 may be explained by oxygen  -71-  d i f f u s i o n i n quartz and haematite or by a l a t e r c r y s t a l l i z a t i o n ' o f these minerals.  Russian r e s u l t s (56) give a q u a l i t a t i v e i n d i c a t i o n that i f  oxygen d i f f u s i o n i n quartz was s i g n i f i c a n t , i t should have been s i g n i f i cant i n haematite too. diffusion i n calcite.  The pattern can not be explained by oxygen I f d i f f u s i o n occurs, the c r y s t a l l i n e state can  reequilibrate with the hydrothermal solution at a lower temperature than the c r y s t a l l i z a t i o n temperature.  Haematite d i f f u s i o n w i l l not cause any  great changes since the f r a c t i o n a t i o n between water and haematite i s very small.  A l l data w i l l be i n harmony i f  - the quartz was formed at a s l i g h t l y lower temperature, - the quartz, because of s o l i d state d i f f u s i o n , reequilibrated with the hydrothermal solution at a temperature lower than i t s formation temperature, - the quartz exchanged just a part of i t s oxygen with the hydrothermal solution at a lower temperature. In a l l cases t^jj = 331° C should be about r i g h t and & y should be -35.2 with regard to PDB.  The temperature at which the quartz may have  c r y s t a l l i z e d or reequilibrated i s 290° C.  The order of c r y s t a l l i z a t i o n  as established from t h i n section study i s as follows:  carbonate, and  quartz and haematite simultaneously. Sample No. 35 Q u a l i t a t i v e l y the explanation i s the same as f o r sample No. 34. tCH = 342° C i s supposed to be the r i g h t temperature of c a l c i t e c r y s t a l lization.  The quartz C?~^/0^ r a t i o may have been frozen i n at 327° C  under equilibrium conditions.  Thin section evidence gives as order of  c r y s t a l l i z a t i o n carbonate, quartz, haematite.  -72-  A recent application of eqn. 5.3 i s reported by Schwarczet a l . (138), They have investigated Palaeozoic metamorphic rocks from Vermont and determined  the following temperatures: c h l o r i t e zone  200 - 250° C  b i o t i t e zone  250 - 350° C  garnet zone  275 - 4 5 0 ° C  s t a u r o l i t e zone:  320 - 550° C  Following the procedures of sect. 4.7, the influence of pressure w i l l be again i l l u s t r a t e d f o r the reaction:  | CaCOg + H 0 6  2  1 8  = |  CaCOg + H 0 8  1 6  2  At t = 200° C and a pressure of 1000 bars one finds a change i n f r a c t i o n a -4 t i o n f a c t o r of 3.7 x 10  i f pressure i s neglected which amounts to an  error i n temperature of approximately -7° C.  One should be aware that  the assumptions underlying t h i s method become worse at high  temperatures.  On the other hand, Clayton derived the equations 5.1 and 5.2 under pressurized conditions. F i n a l l y i t should be remarked that although the figures mentioned i n table 5.4 look very accurate, they are not necessarily accurate, because of uncertainties of pressure conditions and of a c t i v i t y c o e f f i c i e n t s . Moreover, the s t a t i s t i c a l basis f o r eqn. 5.5 i s p h y s i c a l l y not acceptable i n the author's opinion and t h i s basis i s absent f o r the alternative eqn. 5.9. From the above discussion i t should be clear that oxygen isotopes are very u s e f u l f o r geothermometric purposes.  However the i n t e r p r e t a t i o n  of the r e s u l t s i s not as straightforward as one could wish.  Specifically  high temperature geothermometry i s . i n comparison with carbonate low temperature palaeothermometry f a i r l y i n t r i c a t e , because of the possible occurrence of d i f f u s i o n and the uncertainties about the pressure and a c t i v i t y dependence of p( .  These three factors are r e l a t i v e l y  unimportant  i n low temperature palaeothermometry, but may play s i g n i f i c a n t roles i n :  high temperature geothermometry.  Under geological conditions high tempera  tures are usually concomitant with high pressures.  At high  temperatures  i t i s to be anticipated that the molecules are i n excited states (quantum mechanically) and thus the square root expectation value of x (eqn. w i l l increase and thus the, pressure dependence (see sect. 3.3) more s i g n i f i c a n t .  On the other hand i n eqn. 3.5  3.7)  w i l l become  there appears a tempera-  ture term i n the denominator which makes the pressure dependence at high temperatures  insignificant.  The thermodynamic a c t i v i t y of the hydro-  thermal solutions i s not known, hence t h i s factor cannot be evaluated. Diffusion becomes more pronounced at higher temperatures, measures freezing i n temperatures  of the C r ^ / O ^  hence one  r a t i o rather than tem-  peratures of c r y s t a l l i z a t i o n of a p a r t i c u l a r mineral.  I t should be  possible to evaluate t h i s e f f e c t , once the necessary d i f f u s i o n constants are known.  -74-  CHAPTER 6  ISOTOPIC EXCHANGE REACTION KINETICS  6.1  Introduction In t h i s chapter i s o t o p i c exchange reactions are discussed from a  k i n e t i c viewpoint.  The usual assumptions which are made i n the  derivation of rate equations are pointed out.  F i r s t the homogeneous  exchange reaction i s considered i n some d e t a i l , followed by the heterogeneous ones.  In the case of a heterogeneous exchange reaction three  possible rate determining steps are discussed, i . e . d i f f u s i o n i n phase I, d i f f u s i o n i n phase I I , and the surface reaction.  6.2  Homogeneous exchange reactions Returning to the reaction  w AX  V  + v BXJ = w AX#  the f r a c t i o n a t i o n f a c t o r may be defined as  + v  BX^  where •= t o t a l concentration of element X occurring i n compound AX  and A x |  y  i n gram atoms per unit volume.  cj| .= concentration of In calculations on how  X^.  the reaction proceeds, the following assumptions  are usually made i m p l i c i t l y or e x p l i c i t l y : (a)  cf  «  C  A  and  eg «  C  B  Assumption (a), i s always j u s t i f i e d i n oxygen studies because of the 18 r e l a t i v e r a r i t y of 0 (b)  .  The d i s t r i b u t i o n of X$ i n each of the molecular under equilibrium conditions. of the compounds.  species i s random  There are no X —-X  bonds i n either  This means that the p a r t i t i o n function of the  variously l a b e l l e d molecules obey "the rule of the geometric mean" (see also (158)). (c)  The rates of the forward and the reverse reaction are not a function of the i s o t o p i c nature of the molecule involved. i s j u s t i f i e d by a theorem due to Slater (142):  This assumption The rate of bond  rupture i s only dependent on the two atoms involved, and independent of the r e s t of the molecule.  Bigeleisen (12) concluded, consequently,  that i f t h i s were true f o r bond rupture, i t should also be true f o r bond formation. (d)  Assumption (b) i s v a l i d throughout the exchange process.  This i s  j u s t i f i e d by assumption ( c ) . (e)  The rates of the forward and the reverse reaction are s i m i l a r . Bunton et a l . (23) have shown that only a minor error i s introduced in this  way.'  -76-  (f)  A l l isotope e f f e c t s are neglected. previous assumptions.  This follows i n part from the  Due to the small mass difference between  and Cr^ and the small concentration of  , the errors introduced  i n t h i s way w i l l be only minor ones. Thus  d  A  d Cg  dt  ~ ~ dt  C  Cg "  C  B  c  - Cj  A  C  A  C| "  C  C  A  - eg  B  C  6.1  B  where R i s the gross rate of exchange. According to the material balance  The subscript oo  indicates the value of Cp^ when equilibrium i s reached.  Further  C#  C#  A  c -c # A  A  because there i s no isotope e f f e c t . Consequently  B  c -c # B  B  6. o  -77-  Using eqns. 6.1,  6.2,  6.3,  and  6.4  d C # A _ dt C C A  6.5 B  This integrates to  C  1 - F =  AJ  CJ  exp  -  C  ; -  # A  CJ  [-'dr* (c  L  6.6  + B) * C  B  where C# A  = the i n i t i a l value of  F•=  at t •= 0,  f r a c t i o n of exchange Which has  occurred.  For p r a c t i c a l purposes  r  A©o  r  Ao a " A o  1 - F• =  r  A  6.7  r  A  where  ,181 r  A  =  ,16  6.8 J  A  These.or s i m i l a r equations have been derived by several investigators (23, 89, 117,  118).  Bigeleisen (10) has derived formulae f o r the r a t i o of the rate constants  f o r the competitive  reactions of i s o t o p i c molecules.  The  -78-  problem was treated from the point of view of the "theory of absolute rates" (11, 83).  6.3  Heterogeneous exchange reactions Zimens (180, 181) has treated heterogeneous exchange reactions  kinetically. may be rate  In t h i s kind of exchange one of the following'three  processes  determining:  - oxygen d i f f u s i o n i n phase I, - oxygen d i f f u s i o n i n phase I I , - surface reaction by which the exchange of'oxygen isotopes between phase I and II takes place. Consider the reaction  w AXy ( s o l i d ) + v BxJ ( l i q u i d ) = w Axf (solid) + v BX„ ( l i q u i d )  and define n = t o t a l mass of exchangeable atoms, i n gram atoms n^ = t o t a l mass of atoms X^, i n gram atoms :  C ,= concentration of exchangeable atoms (gram atoms/unit volume) = concentration of X  C r r  _ "  n# _ C# n" "  F  A = abbreviation f o r compound AX  ( s o l i d state)  V  B = abbreviation f o r compound BX ( l i q u i d state) W  n  A  + nB  V = volume S = surface area Dg = d i f f u s i o n constant of X#. or X i n X B  W  -79-  Assume that i n i t i a l l y ( t = 0):  n # = C# = 0 A  A  then,  n # + n # = ng# . o B  A  further when equilibrium i s attained ( t =  0  n #  0  )  ~ B n  or  r  A ^ " Boc" r  Hence  ~> O0 = BB (1 - -q)  rL  Xr  _  6  o  -  9  Although the s i t u a t i o n w i l l not be very common i n geology, i t i s possible that the d i f f u s i o n of  i n the adhesive layer of B surround-  ing A i s rate determining f o r the exchange.  The steady state concentra-  t i o n gradient i n the adhesive layer w i l l be l i n e a r . plays an important r o l e i n the Nernst-Brunner dissolution.  This layer also  (22) theory of  I t i s much thicker than an absorbed f i l m .  I t may be  i d e n t i f i e d with the boundary layer i n hydrodynamic theory.  This theory  gives f o r i t s approximate thickness  'US N  p-\r  6.10  -80-  where  = v i s c o s i t y of the f l u i d , p  = density of the f l u i d ,  % = l i n e a r dimension of the surface of the s o l i d , ~IT = v e l o c i t y of the f l u i d , L = thickness of adhesive layer. # For the d i f f u s i o n of X and X d n# B  I n t h i s layer one can apply Ficks law  = S • "  %  A  dt  C  "  r  " <A) L  B  rB  B  u  6.11  where r ., . = r B(A) B  n  at the s o l i d - l i q u i d interface. H  Assuming that d i f f u s i o n i n the adhesive layer i s rate determining  r  B(A)  ~  r  A  Hence  r  B  ~  r  B(A)  = \  (  r  "  B  r  oc)  _ *oo - A . r  6.12  1-q i s obtained by combining eqns. 6.9 and 6.11. Therefore  cws  r  -  r  A  r  1 - F =  B  ~  r e  *°  = r  ° °  = exp  r  S  A  B  %  "  Q  ;  t  6.13  -81-  for the case that d i f f u s i o n i n the adhesive layer i s rate determining. I t i s also possible that the surface reaction i s the rate determining step.  When one considers the exchange between the f l u i d and  the  # s o l i d phase only, then the number of atoms X and X  which pass the  interface i n one d i r e c t i o n i s equal to the number that pass i n the opposite  direction.  ft - number of exchangeable atoms which pass one  cm  of the i n t e r f a c e i n one d i r e c t i o n per second. - ^ ! = S  Applying  eqn.  6.12  A  " ( r  B  -  r  A  )  one obtains a f t e r integration  1 - F = exp  .ft  S  A  6.15  t  when the surface reaction i s rate determining. Most l i k e l y i t i s the s o l i d state d i f f u s i o n of X and X  17  rate determining.  which i s  Solid state d i f f u s i o n has been treated by several  authors; among the more recent of these are Crank (44) and Jost  (99).  The solution of t h i s problem i s the solution of the d i f f u s i o n equation  ^  D  ^  f i t t e d to the proper boundary conditions. I f the s o l i d has the shape of a slab and the l i q u i d phase i s present at both sides of the slab then  2  -82-  1 - F=  -c cJ -c# A. i*  ©o  4r' 7"  TT "  2  L  — — 2p+l p^O  e  *P  6.17  - (P 2  where h i s the thickness of the slab. When the. s o l i d has the shape of a cube  F =  , 512  z  L=o  2 exp ( - (2p+l)  (2p+l)'  "if A 2D  t  6.18  P  where h i s the: length of a side of the cube.  Anisotropy i n solids can  be dealt with by varying h f o r the d i f f e r e n t crystallographic directions. When the s o l i d has the shape of a sphere Oo  2 exp  P  2  T  2  D  A  t  P=l  where h i s the radius of the sphere. In the derivation of eons. 6.17, 6.18, and 6.19 i t was assumed that at t = 0 the s o l i d phase had the uniform concentration  .  Instantaneously,  a f t e r t = .0 the surface of the s o l i d phase r e e q u i l i b r a t e d and acquired the concentration CA  . Compared with the slowness of s o l i d state  d i f f u s i o n the r e e q u i l i b r a t i o n of the surface layer of the s o l i d i s instantaneous.  . Urey et a l . (161) give some numberical r e s u l t s f o r eqn. 6.18,  These simplify considerably the process of c a l c u l a t i n g the d i f f u s i o n constant from, a set of experimental  data.  -83-  TABLE 6.1 Solutions of eqns. 6.17 and 6.18  D  Af  2  h  1 -F  t  2  •  for the slab  Ref. (161)  1 -F f o r the cube  .0.773  0.461  0.05  0.839  0.590  0.01  0.926  0.795  0.005  0.949  0.854  0.001  0.971  0.915  0.0001  0.988  0.964  0.00001  0.991  0.972  0.1  The theory developed i n t h i s chapter, especially the d i f f u s i o n equation, i s the background f o r the material presented i n chapter 7.  -84-  CHAPTER 7  DIFFUSION  7.1  Introduction As f a r as homogeneous exchange reactions - are concerned, Brodsky (21)  has given general rules f o r the r e l a t i v e exchange v e l o c i t i e s . f o r reactions between water and other compounds. reactions f o r oxygen have been described  Many homogeneous exchange (see Dole (55)).  Publications  about heterogeneous oxygen isotope exchange reactions are r e l a t i v e l y rare and only a few,of d i r e c t i n t e r e s t to earth s c i e n t i s t s are known to the author. Cameron et a l . (25) have investigated the systems vanadium pentoxide ( s o l i d ) - water - oxygen (gaseous) and vanadium.pentoxide oxygen.  This i s one of the few papers i n which surface reactions as well  as s o l i d state d i f f u s i o n are considered.  They found that the oxygen  exchange i n the system vanadium pentoxide - water - oxygen.between 400° and 550°  C was about 25 times f a s t e r than exchange i n the system  vanadium pentoxide - oxygen, under s i m i l a r conditions.  They also found  that whether the exchange rate was surface or d i f f u s i o n controlled depended on the surface/volume r a t i o and on the c r y s t a l l i n i t y of the  -85-  vanadium pentoxide.  High s p e c i f i c surface values and an amorphous phase  favoured a surface reaction controlled exchange rate; while f o r c r y s t a l l i n e s o l i d s and f o r low s p e c i f i c surface values•a d i f f u s i o n controlled rate i s most l i k e l y .  In the case of a d i f f u s i o n controlled rate one  finds that i n i t i a l l y the rate of exchange i s r e l a t i v e l y high, but drops as exchange proceeds.  When the surface becomes saturated .the exchange  rate drops under the controlling, influence of s o l i d state d i f f u s i o n . Johnston et a l . (98) have reported e s s e n t i a l l y the same thing f o r the oxygen exchange between uranium oxides and water. are  known f o r the most simple compounds only.  Diffusion mechanisms  Hence, i t i s not astonish-  ing that the c a t a l y t i c action of water i s not yet explained.  Haul and  Stein (90). noticed that water also speeded up the carbon exchange between gaseous carbon dioxide and c a l c i t e . was smaller than 50  .  The size of t h e i r c r y s t a l l i n e grains  They found that even at 20° C measurable exchange  occurred when water was present, while no measurable exchange occurred under dry conditions. That amorphous, material exchanges i t s oxygen.more rapidly than c r y s t a l l i n e i s shown too by Dontsova (58).  She performed a series of  exchange experiments i n which quartz, sphene, a l b i t e , mica, and diatomite exchanged t h e i r oxygen with the gaseous carbon dioxide.  Unfortunately,  these e s s e n t i a l l y very i n t e r e s t i n g experiments have q u a l i t a t i v e  signifi-  cance only, since the grain sizes used were very small ( 1 2 ^ ) and the e f f e c t of water on the exchange rates was neglected. Experiments by Hutchinson (96) on oxygen isotope exchange between s i l i c a , water and oxygen have shown that no exchange takes place at 1000° C when the system i s dry. . However, the exchange between s i l i c a  -86-  and water i s r e l a t i v e l y rapid. reaction i s 47 minutes.  At 960° C the h a l f time of t h i s exchange  At 750° C the h a l f time i s 100  minutes.  Hutchinson believes that the reaction at 960° C i s a homogeneous phase reaction between dissolved s i l i c a and water, while at 75,0° C the exchange rate i s controlled by a surface reaction.  That no exchange takes place  i n the dry system s i l i c a glass - oxygen i s confirmed by Bank (8). t h i s should not be generalized.  However,  Kingery and Lecron (102) have shown that  i s o t o p i c exchange between carbon dioxide and glass occurs, and that the chemical composition of the glass plays an important p a r t . The evidence these l a s t two investigators have presented to show that the exchange rate i s s o l i d state d i f f u s i o n controlled i s unsatisfactory i n the author's opinion.  As i s done very often, they based their-conclu-  sion concerning the rate determining step s o l e l y upon the exponential 18 v a r i a t i o n with time of 0  concentration i n the gas phase.  However t h i s  exponential v a r i a t i o n does not uniquely indicate a d i f f u s i o n process as the rate determining step.  The surface reaction controlled rate of  18 exchange shows a similar exponential decay f o r the 0 the gas phase ( c f . eqns. 6.19  and 6.15).  concentration of  To distinguish the two  processes one should very the surface area across which the exchange takes place. Solid state d i f f u s i o n as a cause of i s o t o p i c f r a c t i o n a t i o n has been treated by Senftle and Bracken  (140).  They concluded that generally the  e f f e c t was only of minor importance. 7.2  Oxygen d i f f u s i o n i n carbonates Diffusion constants f o r the carbonate ion.in carbonates have been  ^87-  estimated by Urey et a l . (161) f o r several temperatures (15° - 160° C ) showing a v a r i a t i o n from 4.4 x 10  2  3  cm^sec  -1  to 1.9 x 1 0 " ^ c m s e c . 2  -1  Haul and Stein (90) have measured a d i f f u s i o n constant f o r carbon i n -4 c a l c i t e under dry conditions. 2 exp - 58000/RT  They obtained D Q = 4.5 x. 10  -1  cm sec  . The a c t i v a t i o n energy i s expressed i n c a l o r i e s .  Haul and Stein did not reach a conclusion about the mechanism by which the d i f f u s i o n took plaqe.  They considered three d i f f u s i n g units:  - carbonate ions, the oxygen- d i f f u s i o n should be about three times as large as D Q , - c a r b o n dioxide, D Q should be about twice D Q , - carbon atoms. Urey et a l . ' s (161) estimations of D Q appear to be too high when compared to the Haul and Stein measurements under dry conditions.  But from two  preliminary experiments also reported by Haul and Stein one may obtain an estimate of D Q under wet conditions at temperatures of 300° C and 20° C. I t i s r e a l i z e d that i t may not be proper to c a l l these constants, d i f f u s i o n constants. Assuming that D Q = 2 D Q , the following estimates were made. TABLE 7.1 " D i f f u s i o n " of oxygen i n c a l c i t e under wet conditions Temperature °C  20 300  Diffusion constant D Q 2 -1 cm sec 3 x TO"" 5 x 10~  24  2 2  -88-  These values resemble those of Urey et a l . quite c l o s e l y .  However the  :  speculative nature of these values can not be overstressed. Urey et a l . (161) have calculated, on the basis of t h e i r estimation of D Q , that a c a l c i t e c r y s t a l of 1 mm. dimensions w i l l r e t a i n 96.4% of 18 i t s original 0 concentration, r e l a t i v e to the equilibrium concentration +8 of a changed environment f o r 7 x 10 remained at 20° C during t h i s period.  years, provided the  temperature  I f the temperature was raised to  100° C t h i s period would be only 64000 years.  These figures do certainly  not contradict the available empirical evidence. I t i s found that coarse c r y s t a l l i n e material retains i t s o r i g i n a l Ql8yQl6 ^ very well. Beartschi (5) has measured a change i n ^ value r a t  0  of 5 over a distance of 1 cm i n a large c a l c i t e c r y s t a l of unknown age. Urey e t a l . (161) have observed thataJurassic belemnite guard maintained i t s d i f f e r e n t O-^ concentrations due to seasonal temperature  variations,  while the O^/O''" r a t i o of the chalk i n which the belemnite was embedded 6  was not preserved. O^/O  16  Compston (38) has measured, variations of 0.5% i n the  r a t i o f o r d i f f e r e n t portions of a Permian brachiopod s h e l l . . As  f a r as the author knows no occurrences have been published of preservation 18 i of 0 /0  f\  r a t i o s by f o s s i l s older than the Carboniferous.  Compston (38)  reported on one questionable Devonian sample. Engel et a l . (71) have published data on the metamorphism and 18 0  16 /0  r a t i o s of the Leadville limestone.  They noticed the coarse cry-  s t a l l i n e dolomite showed a l i n e a r v a r i a t i o n of i t s Near the Gilman ore from the ore  value with distance.  S> coarse dolomite = + 16.5 and at 10,000 feet away  Scoarse  dolomite = + 23.  But the dense fine grained  dolomite which occurred together with the coarse material does not show  -89-  t h i s l i n e a r v a r i a t i o n ; i t has e s s e n t i a l l y the same and at 10,000 feet away from i t :  ^  value at the ore  dense f i n e grained dolomite = + 23.  This suggests solutions came up v i a the Gilman ore conduit and moved r a d i a l l y away from i t .  A temperature gradient was  negative away from the ore.  established which was  This gradient was. maintained long enough so  that a l l dolomite could equilibrate with the solution.  Subsequently  the  temperature dropped, the drop was rapid enough that only the f i n e grained dolomite could exchange i t s oxygen with the cooler solutions. pened at the temperature characterized by  I t hap-  £ = 23 ( i t i s assumed the  &  of the solution was constant) the exchange became n e g l i g i b l e , because of the exponential decrease of the d i f f u s i o n constant with temperature. o r i g i n a l gradient i s best r e f l e c t e d by the most coarse material.  The  This  explanation i s not a unique one, but i t s e s s e n t i a l features are i n agreement with the general i n t e r p r e t a t i o n of the Gillman ore and i t s surrounding as given by Loyering and Tweto (107).  7.3  Oxygen d i f f u s i o n i n quartz The amount of s o l i d state d i f f u s i o n data available on quartz i s D Q along the c axis of quartz was estimated to be  very small. 3 x 10  1 1  cm sec 2  _1  at 500° C by Verhoogen (164).  on e l e c t r i c a l conductivity studies. d u c t i v i t y was  This value i s based  Verhoogen assumed that the con-  caused by migrating oxygen ions.  This i s not self-evident.  From exchange experiments done by Wyart et a l . (178) a few D Q values f o r quartz were calculated by the author (table 7.2).  These calculations  indicate Verhoogen's value f o r D Q could be too high by about two orders of magnitude.  Wyart et a l . ' s experiments are the only set of exchange  -90-  data published which allow some quantitative conclusions and which have a d e f i n i t e bearing on geological circumstances.  TABLE 7.2  Oxygen exchange between water and s i l i c a t e s period of 24 hours.  Grain size  Sample  '  Temp. °C  during a  Ref. (178)  Press, bars  D (**) 2 -1 cm sec 0  F(*)  -14  Quartz  60  360  170  0.10  7.6x10  Quartz  60  ,445  250  0.14  1.7xl0~  Quartz  60  610  350  0.16  2.4x10  Microcline  25  690  400  0.37  2.8xl0~  Granite  -  800  500  0.26  -  Granite (fused)  -  800  1800  0.72  -  xo  13  ( * ) - f r a c t i o n of exchange which has occurred. (**) because of the small values of F , the r e l i a b i l i t y of the calculated DQ i s small. F  The importance  of these data w i l l be evident from the following  hypothetical example.  Assume an amount of quartz i s p r e c i p i t a t e d at  600° C from an aqueous solution under equilibrium conditions. The 18 0  16 /0  r a t i o of the solution remains constant, while the temperature  drops to 500° C.  How long w i l l i t take before a given amount of  -91-  i s o t o p i c exchange has occurred between the aqueous solution at 500 and the quartz p r e c i p i t a t e d at 600° C?  C  For sake of s i m p l i c i t y the  quartz i s supposed to have a cubic shape and to be i s o t r o p i c .  Using  eqn. 6.18 and data of table 6.1, the calculations are r e a d i l y performed. The r e s u l t s are tabulated i n table 7.3.  TABLE 7.3  Oxygen exchange between water and quartz at t = 500° C  h  v  = o.i  'cm IO"  5xl0  1  hours  5.5 days  - 2  10" 5xl0  5  2  21  days  1.5 years  _ 1  f=  0.2 1.3 days 33  days  130  days  9  years  0.5  11. 6 days 289  days  3. 2 years 79  years  (*) h = side of the cube. (**)  A  the average change of o value f o r the c r y s t a l .  A o = 0.1 i s about the present-day accuracy f o r measuring values. = 0.2 means an error i n temperature determination of 10° C at t .=• 500° C. 0.5 means an error i n temperature determination of 30° C at t = 500° C.  -92-  These r e s u l t s indicate that d i f f u s i o n i s a r e a l problem i n high temperature geothermometry.  The temperatures measured i n t h i s way represent  only freezing, i n temperatures of the  ratio.  Of course, i f the  quartz i s p r e c i p i t a t e d from a dry melt, the measured temperatures w i l l be nearer to the true c r y s t a l l i z a t i o n temperatures because water catalyses the exchange considerably.  7.4  Oxygen d i f f u s i o n i n s i l i c a t e s The c h i l l e d gabbroic.margins of the Skaergaard i n t r u s i o n have  3.7 which i s nearly 2 . 5 % l i g h t e r than normal o l i v i n e basalt. 0  Taylor and  Epstein (144, 149) have t r i e d to explain t h i s by postulating that the minerals i n the c h i l l e d margin have equilibrated with meteoric water supposedly present i n the country rock. explanation i s advanced.  Here a somewhat d i f f e r e n t  According t o Kennedy (101) the cooled edges  of the i n t r u s t i o n w i l l have been enriched i n water. indicated by Wager (172).  This i s also  From the example given i n sect. 7.3 i t i s  p l a u s i b l e that at 900° C the exchange of oxygen between s i l i c a t e s and water, i s rapid.  I t i s supposed that at about t h i s temperature the  c h i l l e d margins s o l i d i f i e d . To evaluate the f r a c t i o n a t i o n factors f o r the oxygen exchange reaction between the o r t h o s i l i c a t e group and water one has to know the normal modes of the i n t e r n a l vibrations of the o r t h o s i l i c a t e group. These are known but not too accurately because of the d i f f i c u l t i e s i n assigning force constants f o r the o r t h o s i l i c a t e group.  The T e l l e r -  Redlich product rule (91) makes i t possible to calculate the frequencies  -93-  18 of two of the four normal modes of the 0 substituted o r t h o s i l i c a t e group.  The frequencies  of the remaining two normal modes of the  substituted o r t h o s i l i c a t e group were estimated i n such a way that the Teller-Redlich product rule was s a t i s f i e d .  Following  the procedures  outlined i n section 2.2, the f r a c t i o n a t i o n factor f o r the reaction  U ]" 1 6  H  2  0 «  +  i  was approximated f o r various temperatures.  4 S i0  4  18 -4 H 0 " 2  +  |  \_  The r e s u l t s are tabulated  i n table 7.4.  TABLE 7.4 Fractionation factors f o r the system o r t h o s i l i c a t e ions - water  t°  c  c<  0  0.9897  100  0.9859  150  0.9856  200  0.9857  250  0.9862  300  0.9869  500  0.9894  700  0.9919  900  0.9935  1100  0.9948  -94-  18 According to table 7.4 water i s enriched i n 0 with regard t o the o r t h o s i l i c a t e ion. These fractionation factors should not be taken too seriously, since a l l s o l i d state e f f e c t s were neglected.  But, since  the i n t e r n a l vibrations of the o r t h o s i l i c a t e ion are mainly responsible for the f r a c t i o n a t i o n , i t seems l i k e l y that the calculations are q u a l i tatively significant. The extremely low  values found f o r the c h i l l e d margin of the  Skaergaard rocks may be the r e s u l t of e q u i l i b r a t i o n of the s i l i c a t e s with water from the i n t r u s i o n i t s e l f and from water released by the country rock.  Assuming the calculated f r a c t i o n a t i o n factors to be  s a t i s f a c t o r y , then at 900° C water with a i s o t o p i c equilibrium with o l i v i n e with equilibrium conditions  ^/  =  +  7  g M 0 W  ^SMOW  =  +  2  -  T  w i l l be i n ^  i s r  e  f  e  r  s  t  o  though i t i s noticed by Taylor and Epstein (144,  149) that the c h i l l e d marginal o l i v i n e gabbro i s not i n isotopic equilibrium;  p l a g i o c l a s e " ^clinopyroxene = - 1 - 3 while t h i s value i s  p o s i t i v e under equilibrium conditions.  Due to the rapid rate of cooling  d i f f u s i o n became n e g l i g i b l e before equilibrium was reached.  Besides i t  i s to be anticipated that the oxygen d i f f u s i o n constants are d i f f e r e n t f o r plagioclase and pyroxene. that above 220° C, HgO pressure.  18  Further one should take into account  i s more v o l a t i l e than H 0 , under 1 atmosphere  This may cause a somewhat anomalous  the c h i l l e d margins.  To recapitulate, the low  1 6  2  %  value of the water i n  & value of the c h i l l e d .  border rock i s due to e q u i l i b r a t i o n between water (from the wall rock and the i n t r u s i v e ) and the c h i l l e d border rock.  But a low i n i t i a l  S  value f o r the water i s not postulated, as was done by Taylor and Epstein, because i t i s believed here the f r a c t i o n a t i o n factors f o r oxygen exchange  -95-  between s i l i c a t e s and water are close t o unity or smaller than unity at 900° C. low  &  This i s p h y s i c a l l y l i k e l y and may explain the exceptionally  values of the c h i l l e d borders.  The c a t a l y t i c action of water on exchange reactions i s also evident from the gneissic inclusions which are found i n the Northern border group of the Skaergaard i n t r u s i o n .  Notwithstanding these i n c l u -  sions are fused by the i n t r u s i o n , they have e s s e n t i a l l y the same & value as the country rock, while of i n t r u s i o n .  ^"  c o u n t r v  r o c  k  i  s  v  e  r  v  u n  l i k e the  value  The Skaergaard melt was apparently very dry (101) and  consequently no s i g n i f i c a n t exchange occurred.  Likewise clinopyroxene  from the f a y a l i t e - ferro gabbro contains more or l e s s the o r i g i n a l 0  1 8  /0  1 6  r a t i o of wollastonite from which the clinopyroxene i s an  inversion product (149). In conclusion, i t i s suggested here  that under wet high  conditions s o l i d state oxygen d i f f u s i o n can be important.  temperature  -96-  CHAPTER 8  OTHER PROCESSES BY WHICH OXYGEN ISOTOPES MAY  8.1  The Rayleigh d i s t i l l a t i o n process  BE SEPARATED  (130)  The derivation of the Rayleigh equation comes from consideration of an i s o l a t e d quantity of l i q u i d c r y s t a l l i z i n g at constant temperature. An assumption  i s made that no i s o t o p i c exchange takes place between  the c r y s t a l l i n e phase and the melt.  Using the symbols defined as  follows: n = t o t a l mass of exchangeable  atoms i n gramatoms,  n^ = t o t a l mass of i s o t o p i c atoms, f - indicates the l i q u i d phase, s - indicates the s o l i d phase,  r =•«* n  And the i n i t i a l conditions of t = 0 sec, n  g  = 0 an a r b i t r a r y stage of  the s o l i d i f i c a t i o n process can be described as;  n^  17  = n^ r ^  Hence, dn^  =  rif  d r f + r ^ dn^  8.1  -97-  and  dn ^ •= - drif* = - r g  where r  s  i s the value of r  factor  g  dn  8.2  f  f o r the quantity dn^.  g  The f r a c t i o n a t i o n  i s given by  r' CX* = _§.  8.3  Therefore,  dr.c  —L r  dn^ _ i) — £ n  = f  8.4  f  which integrates to  r  = r  f r  (<* - 1) F/ J  f  o  r  8.5  which i s the Rayleigh equation. Where,  F o and n.c  o  i s the i n i t i a l value of n^.  To obtain a value f o r r  r  g  (this i s the average value f o r the t o t a l amount  of p r e c i p i t a t e at any moment),  n  f  r 0  f  = 0  n  s s r  +  n  f f r  8.6  -98-  ns  and  i s given by eqn. 8.5,  =  n  f  8.7  " f n  o  thus  r,s  1 - Ff Q  8.8  1 - Ff  I t i s c r u c i a l that the f r a c t i o n a t i o n f a c t o r remains constant during the process.  Therefore the following requirements should be  - The temperature -The  met:  remains constant during the t o t a l process.  pressure remains constant (less important than the temperature).  - The structure of the l i q u i d does not change. - The chemical composition of the l i q u i d does not change. -The  s o l i d phase does not exchange oxygen with the remaining l i q u i d .  -The  system i s closed.  I t i s clear that these stringent requirements are never met under the usual capricious geological conditions.  Semiquantitative useful results  may be obtained as i s demonstrated by Dansgaard (46) f o r water evaporat i o n , and by Taylor and Epstein (151) f o r the s o l i d i f i c a t i o n of the Skaergaard  8.2  intrusion.  Gravitational One may  settling  envision that g r a v i t a t i o n a l forces may  separation of l i g h t and heavy isotopes i n a melt.  cause a measurable Using Stokes'  formula,  8.9  -99-  one may  estimate the v e l o c i t y v, at which the two i s o t o p i c a l l y d i f f e r e n t  flow units w i l l be separated.  tyj = v i s c o s i t y of the melt, a = c h a r a c t e r i s t i c dimension of the flow u n i t , M = weight i n grams of the flow u n i t , g = g r a v i t a t i o n a l acceleration. I t i s u n l i k e l y that the melt i s a continuous medium with respect to the flow units.  Hence s t r i c t l y Stokes' formula can not be applied.  Further  i t i s by no means established what the flow unit i s i n s i l i c a t e melts. But following the time honoured p r a c t i c e of neglecting those aspects of the problem which can not be evaluated, one can proceed with the calculations. Estimating that the c h a r a c t e r i s t i c radius "a" of a flow unit equals 1.5 x 10  8  cm, one finds v = 9 x 10  17  i n the flow unit i s replaced by 0 . 18  separation of 1 cm would be obtained.  cm sec  —1  i f only one oxygen atom  Hence i n 3 x 1 0  1 2  years a  A value of 21 poise was  as the v i s c o s i t y f o r the melt at 1450° C.  selected  The Handbook of physical  constants (16) gives v i s c o s i t i e s f o r melts of natural occurring rocks which are much greater than the value used.  Hence i t seems that t h i s  mechanism i s not s i g n i f i c a n t .  8.3  Other possible separation processes When a thermal gradient exists i n a melt the Soret e f f e c t w i l l be  operative, i . e . heavy molecules w i l l i n e f f e c t migrate towards cool regions and l i g h t molecules towards warm regions. mechanism use i s made of the Soret e f f e c t .  In the Clusius-Dickel  By means of a system of  -100-  convection currents the heavy isotopes migrate e f f e c t i v e l y towards the cool wall and are concentrated at the bottom of the system while the l i g h t isotopes are concentrated at the top. be important i n nature.  These mechanisms could c e r t a i n l y  But unfortunately not enough molecular data are  available to make even rough calculations at present.  The d i f f i c u l t y i s  the estimation of the thermal d i f f u s i o n constants f o r oxygen i n s i l i c a t e melts. The mechanism of s o l i d d i f f u s i o n can not produce s i g n i f i c a n t i s o t o p i c separation as was Grant (85).  shown by Senftle and Bracken (140) and by  The reason f o r t h i s i s the extraoridinary smallness of s o l i d  state d i f f u s i o n constants.  -101-  CHAPTER 9  0  9.1  18  /O  1 ft  RATIOS OF ROCKS  Igneous rocks Unfortunately the extensive work done by Vinogradov et a l . (166,  167) and by Schwander (137) could not be considered i n t h i s  review.  As remarked e a r l i e r Vinogradov's work can not be correlated with r e s u l t s obtained by other investigators (see sect. 1.5). clusions are at variance with present-day  Schwander's con-  observations; t h i s i s  attributed to a systematic error i n h i s measurements (28, 32,  9.1.1  144).  Southern C a l i f o r n i a n b a t h o l i t h - Acidic rocks The b a t h o l i t h has been described by Larsen (104) and the oxygen  isotopic work on i t has been done by Taylor and Epstein (144, 147,.148). Their data are reproduced 9.1,  9.2,  ^A ~ tSg dependent.  and 9.3. = ^  AB.  i n table 9.1 and form the basis of graphs  I t was  shown i n chapter 5 that 1000 In K ^  =  Hence A AB i s e s s e n t i a l l y only temperature  In graphs 9.1,  9.2  and 9.3 the  p a i r s are p l o t t e d respectively against ^ /\ K feldsp. - b i o t i t e . temperature dependent.  A  values of various mineral  Q - C,^Q  - K f eldsp.,  These r e l a t i o n s h i p s are e s s e n t i a l l y only  and  -102-  i f the p a i r s under consideration are i n equilibrium.  The i n c l i n e d l i n e s  give the s t r a i g h t l i n e relationships between 2 p a i r s of minerals; these l i n e s have not been calculated, but are drawn by eye.  The  vertical  l i n e s marked with c a p i t a l l e t t e r s , connect the various mineral p a i r s belonging to the same rock sample.  From these graphs i t can be seen that  the Rubidoux Mountain leucogranite shows the highest temperature of freezing i n of Cr- /0  r a t i o s followed i n order by Shakeflat  monzonite, Rock Creek pegmatite and Bonsai t o n a l i t e .  quartz  The l a s t two forma-  tions show approximately the same temperature (see graph 9.1).  Further  i t i s clear that the minerals of the Woodson Mountain granodiorite are not i n i s o t o p i c equilibrium. I t i s also evident from the graphs that the minerals are not i n complete equilibrium but are approaching i t . expected on grounds of s o l i d state d i f f u s i o n .  This feature could be But t h i s i s also explain-  able when one considers the c r y s t a l l i z a t i o n process somewhat more c l o s e l y . This i s done by Taylor and Epstein (148) who  focussed t h e i r attention on  the following two possible sequences: - During c r y s t a l l i z a t i o n only the outer portions of the c r y s t a l s are i n continuous equilibrium with the melt.  The inner parts of the c r y s t a l  do not r e e q u i l i b r a t e . Zoning i n plagioclases i s explained i n t h i s  way.  This i s considered a Rayleigh : process by Taylor and Epstein. - The c r y s t a l i s at a l l times i n i s o t o p i c equilibrium with the melt, because continuous exchange between melt and c r y s t a l takes place. The possible r e l a t i o n s h i p r e s u l t i n g from these two processes  i s shown  graphically by Taylor and Epstein (148) f o r a simple binary system from which minerals A and B c r y s t a l l i z e .  18 A i s deficient i n 0 with regard  -103-  TABLE 9.1  Values with respect to Hawaiian sea water(*) for various rocks and t h e i r constituent minerals.  •P  s o £>  O 4->OJ T •H3 •rl U CU a  CU •cH C J C •H XCU > O • H U >> H O OH  Ref.  (147)  T3  o  -P  C •p CO H C U O cu C C Ol p c f co  o u co o  c  CO  H co  •H O CU ,£>  3 CO Q bo  co bD  quartz  10.2  plagioclase  7.5  6.6  7.4  K. feldspar biotite muscovite 6.5  hornblende clinopyroxene  5.9  6.3  orthopyroxene  6.4  olivine  5.1  6.6 5.1  apatite  9.1  magnetite  1.6 2.1  ilmenite  t o t a l rock  S  5.9  5.2  Hawaiian sea water  6.0  SMOW  6.6  —  7.0  0  6.3  -104-  TABLE 9.1 (continuation)  •  CD  C P •P »H  CN O H U H ,0 L O  cC O  CD  O co )H H Xi L O CO O  quartz plagioclase  6.8  6.7  4->  H -H cC H CO res C  C  o o m -P  o co  CD  P  O 'rl •"3 H C C O  2  h o  O 03  co o  O T3 O  CO C  U  DJO  10.3  9.7  9.5  8.5  8.0  8.5  5.4  5.2  '4.4  6.9  6.6  7.9  7.8  8.6  K. feldspar biotite muscovite hornblende clinopyroxene  5.6  orthopyroxene  5.6  olivine  4.5  5.7  apatite  6.7  magnetite ilmenite  t o t a l rock  6.0  5.8  8.3  -105-  TABLE'9.1 . (continuation)  S X  3  -P  «H rH O «H  to CU r-l -P HH  'rl  o-o •no  rOco  3 JH psbo  q cuo  ro  c  rCO co 6  quartz  9.9  10.3  plagioclase  8.8  8.9  K. feldspar  9.1  biotite  6.6  A! C  O CU  -P -p rH *H ^3  ro  H M woo  CU CU CU+J rH ' H CJ-P  co  o  5c  ocu Pi On  cu  +J 'H COP  ceo  Bob  cocu QZ Cu  11.9  10.5  9.4  10.3  8.6  9.0  8.4  10.5  8.8  5.4  4.7  7.1  muscovite  7.3  hornblende  6.4  clinopyroxene orthopyroxene olivine apatite magnetite ilmenite  t o t a l rock-  2.8  9.2  9.1  8.5  10.9  9.4  -106-  Q  - Bi  feldsp - B i LEGEND  lag - Bi  Q Plag Bi Hbl  -  quartz plagioclase Biotite hornblende  A Q _ K feldsp A Q - Bi 0 A K feldsp - Plag + A K feldsp - B i A plag - Hbl A plag - B i  - K feldsp  F G  Woodson Mtn. granodiorite Rubidoux Mtn. leucogranite Shake f l a t monzonite Rock Creek pegmatite San Jose tonalite Bonsai t o n a l i t e Ramona pegmatite  - Plag 0.5  1.0  1.5  2.0  AQ - Plag Graph 9.1 - Fractionation relationships between mineral p a i r s i n a c i d i c rocks (see text) I. 1  -107Q - Bi K feldsp - B i  Plag - B i  •H CQ  I  <l  LEGEND A A  •rt  03 I  Q - Bi K feldsp - B i  A Plag - B i  U CO CL,  co T3  i—I  AQ  - Plag  AK  feldsp - Plag  <D  Woodson Mtn. granodiorite Rubidoux Mtn. leucogranite Shake f l a t monzonite Rock Creek pegmatite Elberton granite  •rt  CQ  «  i—I  CK  <I DO CO H  eu i o* CN  DX) CO  l—I  t CH CO T3  i—I CD  K feldsp - Plag  0.5  1.0 AQ-K feldsp  T7T  Graph 9.2 - Fractionation relationships between mineral p a i r s i n a c i d i c rocks I I .  -1085.0 LEGEND A. Q - B i  4.5 x *  A Plag - B i A Q - Plag A Q _ K feldsp K feldsp - Plag A  4.0  3.5  A B C D H  Woodson Mtn..granodiorite Rubidoux Mtn. leucogranite Shake f l a t monzonite Rock Creek pegmatite Elberton granite  3.0  2.5  2.0 Q - Bi  1.5  1.0  0.5 _  (-0.6)6 0.5  1.0  1.5  2.0  2.5  3.0  A K feldsp - B i Graph 9.3 - Fractionation relationships between, mineral p a i r s i n a c i d i c rocks I I I .  3.5  -109-  to the melt and B i s enriched i n 0  .  C r y s t a l l i z a t i o n s t a r t s with the  formation of A, and B does not begin to c r y s t a l l i z e u n t i l l a t e r . then shown that the f i n a l  It i s  value of A w i l l be somewhat smaller than i t s  equilibrium value and the f i n a l average  £> value of B w i l l be somewhat  larger than i t s equilibrium value i f the Rayleigh; process takes place. By means o f eqn. 8.5 Taylor and Epstein calculated the 018 relationships between the melt and the formed c r y s t a l s . According t o Larsen (104) the Southern C a l i f o r n i a n Batholith was emplaced by magmatic stoping i n the following sequence:  San Marcos gabbro,  Bonsai t o n a l i t e , Woodson Mountain granodiorite, Rubidoux leucogranite, and other minor granite bodies.  Aptly Taylor and Epstein (144, 147, 148),  remark that four samples are most c e r t a i n l y not s u f f i c i e n t to explain the o r i g i n o f the batholith.  Notwithstanding t h i s they have observed:  ... " t h i s (oxygen isotope) evidence adds to the growing accumulation of data which suggests that the various rock types of the batholith are of magmatic o r i g i n , are intimately related and come from a well mixed source". As evidence f o r t h i s conclusion they present a v a r i a t i o n diagram, which i s reproduced here as graph 9.4.  San Marcos gabbro, Bonsai t o n a l i t e ,  Woodson Mountain granodiorite and Rubidoux Mountain leucogranite are p l o t t e d by Taylor and Epstein. author.  The other three rocks are added by the  The information f o r these three rocks i s obtained from Taylor  and Epstein (144, 147). From graph 9.4 i t can be seen that a straight l i n e on a v a r i a t i o n diagram does not uniquely indicate a monomagmatic genetic r e l a t i o n s h i p . Taylor and Epstein (144, 147, 148) consider i t compatible with the i s o t o p i c data that the leucogranite and the granodiorite are d i f f e r e n t i a t i o n products of the Bonsai t o n a l i t e magma.  But the same i s o t o p i c data  -110-  I  1  I  7  8  I  ,  6-  9  I  10  __]  11  Rock  Graph 9.4 - Variation diagram showing the r e l a t i o n s h i p between chemical composition and oxygen isotope composit i o n f o r various rocks. A - San Marcos gabbro B - Bonsai t o n a l i t e C - Woodson Mtn. granodiorite D - Rubidoux Mtn. leucogranite 1 - San Jose t o n a l i t e 2 - Gabbro N 36-8 3 - Elberton granite  -Ill-  indicate that the freezing i n temperature of the 0l8 16 /0  r a t i o f o r the mineral p a i r quartz plagioclase i s f a r lower f o r the Bonsai t o n a l i t e than f o r the Woodson Mountain and the Rubidoux Mountain formation. Whether t h i s implies that the Woodson Mountain granodiorite has also a higher temperature  of s o l i d i f i c a t i o n than the Bonsai t o n a l i t e i s d i f f i c u l t  to ascertain, since the granodiorite i s non-equilibrium assemblage.  How-  ever the Rubidoux Mountain leucogranite most l i k e l y has a higher s o l i d i f i c a t i o n temperature b i o t i t e and  A. quartz -  than the Bonsai t o n a l i t e because  A plagioclase - b i o t i t e are smaller f o r the leucogranite  than f o r the t o n a l i t e .  This appears t o contradict Taylor and Epstein's  deduction. I f , as Larsen proposed, the parent magma i s gabbroic then i t should have a  & value of about 7 (see graph 9.6).  formed from t h i s gabbroic parent magma have  But a l l rocks which are & values greater than 7.  What happened t o the excess 016 r e s u l t i n g from t h i s fractionation? postulated existence of a huge unexposed mafic body with a between 5 and 6 would be a suitable deus ex machina.  The  S value  I t i s impossible  to hold the 3 or 4% o r i g i n a l water content of the magma responsible f o r carrying away the excess Cr^. A simple but tedious c a l c u l a t i o n w i l l show that i f the o r i g i n a l magma contained 3% water and the the o r i g i n a l magma was 7, then the have been -15.  S  value of  £ value of the escaping water should  The i m p o s s i b i l i t y of t h i s w i l l be evident (see also  sect. 7.4). Again i t i s emphasized that four samples picked at random can not invalidate Larsen's conclusions, which were made a f t e r an intensive and c a r e f u l analysis of the geological evidence.  I t i s only demonstrated  -112-  what could be done with oxygen isotopes i f s u f f i c i e n t data were available. When c r y s t a l f r a c t i o n a t i o n i s responsible f o r the d i f f e r e n t i a t i o n of a magma, which was  a closed system as f a r as oxygen i s concerned, then  the l a s t minerals to be formed should be enriched i n Cr^.  The  reason  18 f o r t h i s i s feldspars and quartz are always enriched i n 0  with respect  to the melt from which they p r e c i p i t a t e and these two minerals contain more oxygen than a l l other minerals p r e c i p i t a t e d from t h i s melt.  That the  l a s t minerals formed i n a system where c r y s t a l f r a c t i o n a t i o n has been operating are enriched i n CrA i s observed i n the Skaergaard i n t r u s i o n (144, 149).  The upper parts of t h i s l a c c o l i t h which s o l i d i f i e d l a s t  show progressive enrichment i n Cr^. 9.1.2  Basic rocks Oxygen isotope data f o r basic rocks are even more scanty than f o r  a c i d i c rocks. 0  1 8  /0  1 6  Graph 9.5  i s s i m i l a r to 9.1,  9.2,  and 9.3.  A l l the  measurements used have been published by Taylor and Epstein  (144, 147, 148, 149).  A few points are suggested by t h i s graph:  - The minerals of the four gabbros form i s o t o p i c equilibrium assemblages. - The f r a c t i o n a t i o n f a c t o r f o r the mineral p a i r s clinopyroxene  -  magnetite and plagioclase - magnetite do not approach unity i n a simple way  at high temperatures as i s the case f o r the mineral p a i r s  considered i n graphs 9.1,  9.2,  and 9.3.  This i s not astonishing since  the f r a c t i o n a t i o n between water and magnetite i s very small and i t i s known that "cross-over" occurs i n systems where water i s present - The temperature at which i s o t o p i c exchange becomes n e g l i g i b l e i s highest f o r the hypersthene - o l i v i n e gabbro followed by the  (30).  -113-  0  0.5  1.0  1.5 A  ...  Plag -  2.0  2.5  Cpx  Graph 9.5 - Fractionation relationships between mineral p a i r s i n basic rocks.  -114-  hortonolite - f e r r o gabbro, the Duke Island gabbro and the San Marcos gabbro. The composition of the upper mantle (taking the Mohorovicic discontinuity as the upper boundary of the mantle) i s suggested to be p e r i d o t i t e (92, 171).  The measured  &  range from 5.2 to 6 (144, 147, 148).  values f o r dunite and p e r i d o t i t e B a l s a l t s which are supposed to be  products of p a r t i a l melting of the p e r i d o t i t e have  l v a l u e s from 6 to 7.  Assuming that t h i s difference i s real> one faces the question of what happened to the excess 0 ^ peridotite.  created i n the process of p a r t i a l melting of  For the time being the question w i l l remain unanswered,  again due to lack of s u f f i c i e n t information about oxygen isotope d i s t r i b u t i o n i n rocks. 18 Graph 9.6 summarizes the information available about 0  16 /0  ratios  i n d i f f e r e n t rock types. 9.2 9.2.1  Sedimentary rocks General In the weathering process and during the erosion of igneous rocks  the minerals w i l l i n general exchange t h e i r oxygen with the hydrosphere when they undergo chemical a l t e r a t i o n . atmosphere i s of no importance  Isotopic exchange with the  (see also Dontsova (58)).  I f the igneous  rocks are reduced to d e t r i t a l fragments without chemical a l t e r a t i o n , exchange i s l e s s l i k e l y to happen (see table 9.2). from Silverman's data (141).  This can be seen  :  " — ~ l —  I  I  I  I I  I  1  I  I  1  I  I  1  |  Ref. (33.8)  5,52 5 5,52 38,52  Marine Limestones Calcareous Tufa Calcareous Sinter Fresh water Limestones  5 5  Vein Carbonates Carbonatites  5 5 146 146 147  Intrusive Carbonates Metamorphic Carbonates D e t r i t a l Sed. Rocks Meta Sed. Rocks Metamorphic Rocks  147  Granitic  147 147 147 147  Granites and Granodiorites Tonalites Anorthosites Gabbros and Basalts  147,141 148 141 146  Peridotites and Dunites Skaergaard Meteorites Tektites  Pegmatites  i 0  l 2  l 4  1 6  i  8  i 10  | 12  i  i  14  16  i  18  i  20  i  22  i  24  i 26  Graph 9.6 - Oxygen isotope composition of various rock types, a l l c5 values with respect to SMOW.  i  28  i 30  -116-  TABLE 9.2 Q18 16 /0  r a t i o s f o r various quartzose rocks  Sample  St. Peter sandstone 46  11.0  0  Basal breccia  45  15.7  10-15  Wishart orthoquartzite F--75  15.9  20  (*) ' v  % secondary s i l i c a !  c o • values are with respect to SMOW from Glayton and Mayeda (34).  Hydrothermal solutions usually have a higher 0 / C r ^ r a t i o than 18  the hydrosphere, besides f r a c t i o n a t i o n factors at lower temperatures are greater ( d i f f e r more from unity) than those at igneous temperatures. Thus the net r e s u l t i s that minerals which are p r e c i p i t a t e d from the hydrosphere usually have a higher parts. b  S  value than t h e i r igneous counter-  This i s shown f o r quartz and can also be seen when carbonatite  values are compared with those of sedimentary limestones. Because fresh water has lower  ttl values than marine water,  sediments equilibrated with fresh water should have a lower  &  value  than sediments equilibrated with marine water, at comparable  temperatures.  This i s the basis f o r distinguishing marine and nonmarine carbonates and cherts by means of the 0  1 8  /0  1 6  r a t i o s (see 31, 52).  This method i s  -117-  quite powerful when one i s dealing with post Palaeozoic sediments.  Older  marine sediments become l e s s d i s t i n c t because of exchange with ground 18 water which has lower 0  16 /0  values than marine water (50).  Often the  exchange takes place by means of a r e v e r s i b l e hydration mechanism, as i s the case f o r carbonates, thus the exchange reaction w i l l be f a s t e r i f the c i r c u l a t i n g ground water has a pH ^ 6 (120).  The grainsize of the sediment  i s of prime importance (see chapt.7) as f a r as exchange i s concerned. was shown by Urey et a l . (161) and also by Gross (86).  This  Other factors are  pressure and temperature, which may promote dissolution and r e p r e c i p i t a t i o n , during which exchange most l i k e l y occurs.  Graf (84) published recently a  compilation of 0l8 16 /0  r a t i o s f o r sedimentary carbonates. 9.2.2  Origin of chert Degens and Epstein (52) have t r i e d to establish the o r i g i n of chert.  To t h i s end they have measured the O*- /0^ r a t i o s of coexisting carbonates 8  and cherts of marine and fresh water o r i g i n .  From t h e i r data (table  9.3)  some, i n t e r e s t i n g conclusions may be drawn. I f one assumes the  value f o r ocean water has been more or l e s s  constant and approximately equal to zero since the Cambrian, then the S value f o r ground water w i l l have been approximately -10.  Supposing  the carbonate was formed i n equilibrium with sea water and that oceanic temperatures have always been l e s s than 50° C, then judging from Degens' and Epstein"s work a l l Precretaceous marine carbonates have exchanged t h e i r oxygen to some degree with percolating ground water.  A Permian and  a Jurassic sample are the only exceptions among the 18 Precretaceous samples under consideration.  Clayton and Degens (31) report on  -118-  TABLE 9.3 18 1 0 /Cr r a t i o s o f coexisting marine cherts and limestones fi  Sample No.  Age  ^  Si0  2/SM0W  ^  CaC0  3/SM0W  Locality  1  Danian  32.6  28.4  Denmark  ,..4  Danian  30.1  27.2  Denmark  6  Maastrichtian  32.9  28.6  Germany  9  Santonian  32.5  26.7  England  11  Campanian  32.5  27.3  Germany  12  Turonian  33.8  27.8  France  13  Jurassic  32.7  27.3  Greece  14  Jurassic  28.7  23.7  Germany  15  Jurassic  28.6  25.2 .  Germany  16  Permian  28.8  27.7  Texas  17  Permian  25.7  23.3  Arizona  18  Permian  24.2  23.2  Arizona  19  Pennsylvanian  27.7  27.7  Utah  20  Pennsylvanian  26.6  22.1  Arizona  21  Mississippian  25.9  24.3  Arizona  22  Devonian  26.3  23.0  Pennsylvania  23  Devonian  26.0  21.3  Pennsylvania  ' 24  Silurian  25.6  22.9  Nevada  25  Silurian  24.7  21.5  Nevada  -119-  (continuation of table 9.3)  Sample No.  2/SM0W  Sl0  Age  s CaC0  Locality  3/SM0W  26  Ordovician  25.8  20.4  Pennsylvania  . 27  Ordovician  25.0  20.7  Pennsylvania  28  Ordovician  24.2  21.2  Pennsylvania  29  Cambrian  24.2  20.4  Pennsylvania  30  Cambrian  22.7  21.4  Pennsylvania  eleven Precretaceous marine carbonate samples, which a l l confirm the above mentioned conclusion.  The PostJurassic marine carbonates seem t o  have retained t h e i r o r i g i n a l 0  1 8  /0  1 6  r a t i o s f a i r l y well. 18  permian marine chert samples (52) have 0  A l l Post-  16 /0  r a t i o s which indicate  that they may have equilibrated with ground water.  The e q u i l i b r a t i o n  temperature w i l l have been between 15° - 20° C, i f the ground water had a  S value o f -10.  This can be deduced from graph 9.7.  But a l l  Prejurassic marine cherts (only one Permian exception)- either have exchanged t h e i r oxygen with ground water with a to -15, or they have experienced a temperature hood o f a temperature evidence.  approximately equal  of 45° C. The l i k e l i -  r i s e t o 45° C i s d i f f i c u l t to judge without more  The samples under consideration here are from Nevada,  Arizona and Pennsylvania; a lowering of the  $> value f o r ground water  to -15 over so large an area may mean an i s o t o p i c change i n composition of the ocean.  Unfortunately the PreJurassic carbonates do not seem t o  -12048 46 44 Si0  precipitated i n marine water ( o = 0)  2  42 40 38 36 34 32  SiO  p r e c i p i t a t e d infresh water ( c> = -10)  30 28 26  CaCOg p r e c i p i t a t e d i n . , marine water ( o - 0)  24 22  CaCOg p r e c i p i t a t e d i n fresh water ( £ = -10)  20 18 16 14 12 A  Si0  2  - CaCO,  10 8 10  20  30  40  50  "50  ^0  Temperature °C Sraph 9.7 - Relationships between &> S1O2/SMOW * ^ CaC03/SM0W f ° guartz and calcite,. p r e c i p i t a t e d under equilibrium conditions from narine ( h = 0) and fresh water ( c> - -10) and the temperature at vhich equilibrium i s attained. an(  r  -121-  be i n i s o t o p i c equilibrium with percolating ground water and hence they do not provide much information.  This nonequilibrium feature i s  obvious when A chert - carbonate values are inspected. temperatures of over 100° C.  They indicate  The Degens-Epstein paper does not mention  any evidence f o r such high temperatures. 18 As f a r as the o r i g i n of the chert i s concerned, the 0  16 /0  ratios  indicate that the supposed change from marine p r e c i p i t a t e d s i l i c a to chert takes place i n a fresh water environment.  I t i s implied that the  system i s open f o r water and during the formation of chert the SiOv, equilibrates with the water.  A l t e r n a t i v e l y , . i t has been proposed that  the s i l i c a of chert i s derived from diatomites. was investigated by Degens and Epstein (52).  This l i n e of reasoning  Generally, the modern  marine diatomites have 3 values which are very s i m i l a r to the Postpermian marine cherts.  I f the chert i s just reorganized  diatomite  then during t h i s reorganization process the system chert - diatomite has been closed f o r water, or no oxygen i s o t o p i c exchange has occurred, which suggests the reorganization does not proceed v i a d i s s o l u t i o n and reprecipitation. From the  diatomites one may conclude that:  - The diatomite skeleton i s not i n equilibrium with sea water.  This  may be due t o b i o l o g i c a l f r a c t i o n a t i o n . However one would expect a diatomite skeleton, i n i t i a l l y not i n equilibrium with sea water, would r e e q u i l i b r a t e f a i r l y r a p i d l y ( c . f . sect. 7.1). or that: - The f r a c t i o n a t i o n f a c t o r f o r amorphous s i l i c a i s smaller than f o r crystalline s i l i c a .  This i s p h y s i c a l l y acceptable.  -122-  F i n a l l y i f one suggests that the PreJurassic chert i s not i n equilibrium with the ground water then one i s forced to postulate an even greater change i n  &  value f o r the ground water or a greater change i n  temperature.  9.2.3  Origin of dolomite The o r i g i n of dolomite i s s t i l l controversial.  important observations were made.  Recently two  Wells (175) observed that dolomite  was formed on the upper parts of t i d a l f l a t s near Quatar, Persian Gulf. He did not establish whether the dolomite was primary or a penecontemporaneous replacement of p r e - e x i s i t i n g carbonate. associates (32, 71) noticed that  Epstein and h i s  A> quartz - dolomite values were  always near to zero, f o r hydrothermal cogenetic p a i r s . circumstances A  quartz - c a l c i t e i s about 10.  Under those  Degens and Epstein (51)  investigated i s o t o p i c a l l y about 100 samples of coexisting dolomite and calcite.  In some of the samples the c a l c i t e and the dolomite were of  synsedimentary o r i g i n . 18 (max.  3°/oo i n 0  They noticed that there was very l i t t l e  difference  16 /0  r a t i o s between cogenetic c a l c i t e s and "primary"  dolomites. I f there was a difference the dolomite was s l i g h t l y enriched 18 19 i n both 0  and Or*.  They concluded that as the c a l c i t e changed to  dolomite, almost no isotopic exchange occurred and roughly the dolomite inherited the O  1 8  /©  1 6  r a t i o from i t s c a l c i t i c progenitor.  This implies  sedimentary "primary" dolomite does not exist but a l l sedimentary dolomite i s derived from c a l c i t e .  A year l a t e r Epstein et a l . (78) reported they  had shown experimentally that hydrothermal dolomite had approximately the same f o r dolomite.  r a t i o as quartz and t h i s r e f l e c t e d the equilibrium  d value  -123-  9.2.4  Origin of aragonite needles The o r i g i n of aragonite needles has been traced i s o t o p t i c a l l y .  These needles occur i n recent marine carbonate oozes of shallow water origin.  I t was held they have an inorganic o r i g i n .  Lowenstam  (108)  found the needles could be derived from the d i s i n t e g r a t i o n of aragonitic c a l c i f i c a t i o n s of a great many algae.  The algae produce needles which  are very s i m i l a r to those found i n recent sediments.  Lowenstam and oxygen and  Epstein (112) have measured the range of  carbon,  of aragonitic carbonates such as needle secreting algae, o o l i t e s , grapestones and sedimentary aragonite needles, from the Bahama Bank area. Their conclusions are that the o o l i t e s are most l i k e l y of inorganic o r i g i n , while the aragonite needles have an a l g a l o r i g i n . everyone (35) seems to be convinced by t h e i r l o g i c a l  9.2.5  However not  account.  The oxygen isotope r a t i o of the ocean The Cr^/Cr^. r a t i o of the ocean at present i s f a i r l y w e l l known (76).  But the same can not be said f o r the ocean i n the past. uncertainty i n carbonate geothermometry. Q18/Q16  r a t  £  0  f  Q  their history.  o  c  e  a  n  s  £  n  This causes  Moreover, a knowledge of the  -the past could reveal something about  The v a r i a t i o n i n the oceanic C-^/O^ r a t i o due to the  Pleistocene g l a c i a t i o n has already been treated (see sect. 4.3). Sedimentary carbonate deposits and O ^"*" r a t i o s of belemnites make i t 18  6  f a i r l y c e r t a i n that the oceanic O^/0-l- r a t i o has not changed s i g n i f i c a n t l y 6  from the Jurassic to the present. I t i s claimed by Degens that the oceans have had a. constant i s o t o p i c composition since the Cambrian (47, 48).  In another paper Degens (49)  -124-  attempts t o show the <^ value of the ocean was +2 with respect to SMOW, 2500 x 10^ years ago.  Notwithstanding  Degens' p o s i t i v e assertions, the  question i s s t i l l f a r from s e t t l e d , f o r Degens' evidence (47, 48, 49) i s not f i r m l y established. The ground f o r Degens' choice of for the ocean 2.5 eons ago, i s a suggestion that ^ * - j  u v e n :  jj_  & value +2 e  w a  ter  =  +  2  ( )3 2  However t h i s suggestion was made before i t was r e a l i z e d how commong the "cross-over" phenomenon i s i n exchange reactions involving water (30). Since then i t has been clear that the high temperature extrapolation, used to estimate  ^ j u v e n i l e water  =  + 2  '  c  a  n n  o  t  ^  e  a  PPli  e d  .  Degens'  claim of constant oxygen i s o t o p i c r a t i o f o r the ocean since the Cambrian i s based on f o s s i l evidence as presented by Compston.(see next paragraph). But t h i s f o s s i l evidence goes only as f a r back as the Permian.  From  there to the Cambrian i s a considerable extrapolation. Compston (38) has measured 0l8 16 /0  r a t i o s i n Permian and Devonian brachiopods.  He checked the s h e l l microstructure of a l l h i s specimens.  B^ggild (17) suggested that r e c r y s t a l l i z a t i o n of aragonitic s h e l l s to c a l c i t i c ones would destroy the microstructure. used successfully (88, 143). l i k e l y not be preserved.  This suggestion has been  In t h i s process O^/O^  r a t i o s would most  Compston also checked c a r e f u l l y the amount of  secondary c a l c i t e i n h i s samples, because secondary c a l c i t e usually has a considerably d i f f e r e n t oxygen isotope r a t i o , compared with the r a t i o of the o r i g i n a l s h e l l carbonate.  His r e s u l t s have produced Permian tem-  peratures which are consistent and similar to present day oceanic temperatures.  This i s c e r t a i n l y p o s i t i v e evidence f o r a constant 0l8 16 /0  r a t i o f o r the oceans since the Permian. did not f u l f i l the requirements  Unfortunately h i s Devonian samples  of preserved microstructure and absence  -125-  of secondary c a l c i t e f o r being useful.  This i s generally the case f o r  Palaeozoic f o s s i l s . Lowenstam (109) has compared  r a t i o s , strontium and magnesium  contents i n recent and f o s s i l brachiopods.  The uptake of strontium and  magnesium i s determined by temperature, c r y s t a l chemistry and physiology 18 of the organism.  Lowenstam has shown that the 0  16 /0  r a t i o s , the SrCOg  and MgCOg contents i n certain f o s s i l s are compatible with those i n recent counterparts of these f o s s i l s .  He has concluded t h i s can be best  explained by accepting the Sr/Ca and (r^/Cp-^ r a t i o s of the ocean have remained e s s e n t i a l l y unchanged since the l a t e Palaeozoic. This problem can i n p r i n c i p l e also be solved by the method of "material balance".  This l i n e of approach has been followed by Degens  (48) and by Silverman (141).  However the calculations of these two  investigators should perhaps be judged as premature since there i s simply not enough information available about Q18 16 /0  r a t i o s i n various rock types, to warrant the use of any method based on s t a t i s t i c a l averages. 9.3  Metamorphic rocks The few measurements a v a i l a b l e f o r metamorphic rocks are summarized  i n graph 9.6.  Because metamorphism i s often a wet process i t can be  anticipated that the minerals w i l l exchange t h e i r oxygen r e l a t i v e l y f a s t . Diffusion constants and exchange rates w i l l be d i f f e r e n t f o r d i f f e r e n t minerals, hence d i f f e r e n t temperatures f o r the f r e e z i n g i n of the  C?~^/(?~^  r a t i o should be expected. The coarsest f r a c t i o n of the minerals w i l l i n d i c a t e a temperature which i s nearest to the maximum temperature of metamorphism.  From the  -126-  pattern of  b  water or not. %  values one may  conclude whether the system was open to  E q u i l i b r a t i o n with l i m i t e d amounts of water may produce  values which l i e outside the normal range.  to water then the  S  I f the system i s open  values f o r cogenetic mineral p a i r s should be  related i n a simple l i n e a r way.  In the case of dry metamorphism nearly  no exchange occurs, as i s shown by the Skaergaard inclusions (see sect. 7.4). A l l the work done on metamorphic rocks since 1950 papers (5, 32, 70, 71, 138, 141, 147, 148, 150).  i s published i n  Not enough i s known  about equilibrium constants, t h e i r pressure and temperature  dependences 18  and d i f f u s i o n constants, to give any rules of thum f o r the 0 r a t i o i n d i f f e r e n t types of metamorphic rocks.  16 /Cr  -127-  BIBLIOGRAPHY  1.  Anbar, M. et a l . , Determination of oxygen-18 i n phosphate ion; Anal. Chem.. 32, 841, 1960.  2.  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