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Oxygen isotopes in geology. Bottinga, Jan 1963

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OXYGEN ISOTOPES IN GEOLOGY by J A N B O T T I N G A B . S c . , U n i v e r s i t y o f T o r o n t o , 1961 A THESIS SUBMITTED IN P A R T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t o f PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA F e b r u a r y , 1963 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics  The University of British Columbia, Vancouver 8, Canada. Date February 22, 1963 - i i -ABSTRACT A c r i t i c a l survey has been conducted on the research done in oxygen isotopes. Only those aspects are considered which are of interest to the earth scientists. Oxygen isotopes have been used for geothermometric purposes and for rock genesis problems. The physical principles underlying these two lines of research are stressed. Assumptions which are usually implied are expl i c i t l y stated. It i s shown that the influence of pressure on the equilibrium constant of oxygen isotope exchange reactions i s only a minor one in comparison with the temperature influence. The significance of determined temperatures i s discussed in the light of possible oxygen diffusion in silicates and carbonates. It i s concluded that diffusion i s usually neglected without justification. As far as data are available i t i s shown that diffusion can be responsible for many discrepancies between oxygen isotope temperatures and' temperatures derived by other means. Studies on the origin of rocks by means of oxygen isotopes are discussed. Attention i s focussed on the Southern Californian batholith. The results of Taylor and Epstein's preliminary study of this batholith are interpreted here as evidence in favour of a metamorphic origin of this huge rock body. - x i -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 this thesis; especially he is grateful to Professor W. F. Slawson, who assisted him in general practical matters. To Professor R. D. Russell, the writer i s In particular indebted for the way in which he made i t possible for the author to switch from geology to the study-of physics, and for the suggestion of this research. Thanks are due to the staff of the Science Division of the Library, who have aided the author frequently in obtaining valuable references and foreign periodicals, and to Miss N. Bernan who typed this thesis. The author would l i k e to express his appreciation for a bursary and a studentship from the National Research Council of Canada. - i i i -TABLE OF CONTENTS ABSTRACT i i LIST OF GRAPHS v i i LIST OF TABLES ix ACKNOWLEDGMENT . xi INTRODUCTION 1 CHAPTER 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 Silicates 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 12 1.5 Reporting of 0 1 8/0 1 6 ratios 13 CHAPTER 2 ISOTOPIC EQUILIBRIUM THEORY 17 2.1 Introduction 17 2.2 Ideal gases 17 2.3 Limitations of the theoretical treatment 22 2.3.1 Ideal gas assumption 22 - i v -2.3.2 Anharmonicity 22 2.3.3 Intramolecular fractionation and the fractionation factor 25 2.3.4 Zero point energy 27 2.4 Liquids 28 2.5 Solids 29 2.6 Numerical example 30 CHAPTER 3 FACTORS INFLUENCING THE EQUILIBRIUM CONSTANT 35 3.1 Introduction 35 3.2 Temperature dependence 35 3.3 Pressure dependence 38 3.4 Thermodynamic activity 41 CHAPTER 4 PALAEOTHERMOMETRY 44 4.1 Introduction 44 4.2 Temperature formulae 46 4.3 O 1 8/^ 6 ratio of ocean water 47 4.4 Phosphate geothermometry 50 4.5 Vital effects 50 4.6 Insensitivity of the fractionation factor 51 4.7 Influence of pressure 51 4.8 Purification 53 4.9 Significance of measured temperatures 54 CHAPTER 5 HIGH TEMPERATURE GEOTHERMOMETRY 55 -V-CHAPTER 6 ISOTOPIC EXCHANGE REACTION KINETICS 74 6.1 Introduction 74 6.2 Homogeneous exchange reactions 74 6.3 Heterogeneous exchange reactions 78 CHAPTER 7 DIFFUSION 84 7.1 Introduction 84 7.2 Oxygen diffusion i n carbonates 86 7.3 Oxygen diffusion in quartz 89 7.4 Oxygen diffusion in silicates 92 CHAPTER 8 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 settling 98 8.3 Other possible separation processes 99 CHAPTER 9 O^/O16 RATIOS OF ROCKS 101 9.1 Igneous rocks 101 9.1.1 Southern Californian batholith-acidic rock 101 9.1.2 Basic rocks 112 9.2 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 - v i -9.2.5 The oxygen isotope ratio of the ocean 123 9.3 Metamorphic rocks 125 BIBLIOGRAPHY 127 - v i i -LIST OF GRAPHS Graph 5.1 Relationship between quartz-haematite fractionation and calcite-haematite fractionation i n quartz*-calcite haematite rocks 61 Graph 5.2 Errors in calculated temperatures, due to errors in & measurements, for the mineral pairs quartz-calcite, quartz-haematite and calcite-haematite 65 Graph 5.3 Errors in calculated temperatures, due to errors in measurements, for equilibria quartz-water, calcite-water and haematite-water 66 Graph 5.4 Fractionation relationships between the mineral pairs quartz-calcite, calcite-haematite and quartz-haematite 67 Graph 9.1 Fractionation relationships between mineral pairs in acidic rocks I 106 Graph 9.2 Fractionation relationships between mineral pairs in acidic rocks II 107 Graph 9.3 Fractionation relationships between mineral pairs in acidic rocks III 108 Graph 9.4 Variation diagram showing the relationship between chemical composition and oxygen isotope composition - v i i i -for various rocks 110 Graph 9.5 Fractionation relationships between mineral pairs in basic rocks 113 Graph 9.6 Oxygen isotope composition of various rock types 115 Graph 9.7 Relationships between 5 S io 2/ S M O W and ^ ( y s M O W for quartz and calcite, precipitated under equilibrium conditions from marine and fresh water and the temperature at which equilibrium i s attained 120 - i x -LIST OF TABLES Table 2.1 Normal vibrations of carbon dioxide and the water molecule 31 Table 2.2 Anharmonicity coefficients for C0 2 and H20 32 Table 2.3 Fractionation factors calculated for the systems water vapour-carbon 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 for different temperatures and frequencies 37 Table 4.1 Distribution of 0 1 8 in the hydrosphere at present 49 Table 5.1 Cogenetic quartz-calcite-haematite h values 59 Table 5.2 Temperatures of freezing in of the Q18/^6 ratio of three cogenetic mineral pairs 60 Table 5.3 Modification of table 5.2 63 Table 5.4 h values for hydrothermal solutions with respect to PDB 68 Table 6.1 Solutions of eqns. 6.17 and 6.18 83 Table 7.1 "Diffusion" of oxygen in calcite under wet conditions 87 -X-Table 7.2 Oxygen exchange between water and silicates 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 for the system orthosilicate ions - water 93 Table 9.1 S values with respect to Hawaiian sea water for various rocks and their constituent minerals 103 Table 9.2 O^/O 1 6 ratios for various quartzose rocks 116 18 16 Table 9.3 0 / 0 ratios of coexisting marine cherts and 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 interest to earth scientists. Meteorological aspects, snow and ice, are not considered. A knowledge of oxygen isotope distributions in 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 earth scientists are interested in oxygen isotopes. In this thesis attention i s mainly directed toward these two aspects. Other naturally occurring stable isotopes are in principle also suitable for investigation along this l i n e , but the great natural abundance of oxygen, the relatively large mass difference between O1^ and 0 1 6, and the well developed analytical procedures favour the usage of oxygen. The theory of isotopic equilibrium has been discussed by Urey (158) and by Bigeleisen and Mayer (15). It w i l l be assumed that the reader has a knowledge of these two important papers. Oxygen isotopes were reviewed by Dole (55) in 1952, by Ingerson (97) in 1953 and Rankama (129) in 1954. From 1951 to 1956 annual reviews (2) were published on isotopes in general. In 1959 Epstein (72) wrote a general paper about O^/O^6 ratio variations in nature. The last review published in the English language was by Mayne (114) in 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 this bibliography appeared for 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 1 8/0"^ ratios. It i s for, this reason that only data obtained by this method w i l l be considered here. Almost a l l of the abundance ratios have been deter-mined using a Nier type spectrometer, although some investigators (55, 119) have made modifications in the basic instrument. Two features normally employed for oxygen ratio determination are dual collection of the desired isotopes and provisions for 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 is not suitable because of "memory" effects (95). Water has the same disadvantage. Carbon monoxide has the problem of a quite large background in the mass range 28 and 30 due to the almost universal -4-presence of molecular nitrogen and hydrocarbons. Fortunately these adverse features can be obviated (26). On the other hand carbon monoxide has a number of distinct advantages. - In many processes in 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 is shorter than for carbon dioxide (105). - "Memory" effects for carbon monoxide are almost completely absent (105). Molecular oxygen has been used by Baertschi and Silverman (7). They mention the poss 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 fractionation and shorten the l i f e time of the filament. Carbon dioxide.has been used most frequently as a mass spectrometer gas for 0 / 0 determinations. Widely accepted standards of this gas are readily available (122). Craig (41) has given absolute abundance ratios for several carbon dioxide standards. He also has published correction factors for the mass spectrometrical analysis of this gas. 1.3 Methods of extracting oxygen To obtain accurate results, either the O-^/O16 ratio of the mass 1 8 1 spectrometer gas sample must be identical to the 0 /0 ratio of the rock sample, or the precise calculation of this latter ratio should be possible. Therefore, when the oxygen from a rock sample is 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 in process. - A l l possible precautions against oxygen contamination are taken. - The gas sample does not interact with the apparatus resulting in a fractionation of i t s 0 1 8/0 1 6 ratio. 1.3.1 Silicates and iron oxides Carbon reduction method. In 1952 Baertschi and Schwander (6) described a method in which the rock sample was reacted with carbon at 2000° C in a high vacuum resistance furnace. According to the reaction: MeSiOg + 6 C = MeC2 + SiC + 3 CO carbon monoxide was produced. By this method 60-80% of the oxygen in the s i l i c a t e was liberated. The carbon monoxide was used as the mass spectrometer gas. A detailed account and results are published by Schwander (137). Comparison with more recent results have shown that Schwanderfs method i s not free of fractionation. Possible causes for this are discussed by Clayton and Epstein (28, 32). In 1959 Dontsova (59) has described a very similar technique. She claimed an oxygen yield of 95-100%. Clayton and Epstein (28, 32) applied a modified form of this method in which the resistance furnace was replaced by an induction heater, and the carbon monoxide was converted to carbon dioxide over a nickel catalyst. They obtained yields of 90-100% for quartz, iron oxide and zircon. For a l l other minerals the oxygen -6-recovery was significantly less. However Russian workers (59, 166, 167) judged the carbon reduction method as successful for 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 fluorine. 3 Me 2Si0 4 + 8 C1F3 = 6 MeF2 + 3 S i F 4 + 4 C l 2 + 6 0 2 and Me 2Si0 4 + 4 F 2 = 2 MeF2 + S i F 4 + 2 0 2 The reaction was carried on at about 430° C, and oxygen yields were 80-100% for most minerals and rocks. A drawback of the method i s that everything which comes in contact with fluorine or chlorine trifl u o r i d e has to be made of nickel,ihconel or other inert materials. Taylor and Epstein (144, 147) used fluorine and found i t satisfactory for 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 his experimental technique and how to purify the fluorine, 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 nickel reaction chambers at 500° C, so this becomes a temperature l i m i t . The effect of this l i m i t may have been the reason why Taylor did not have any success with epidote, magnetite and garnet. Finally in 1962, Clayton and Mayeda (34) have refined the method - 7 -so that i t i s suitable for a l l minerals. They use bromine pentafluoride, which i s less reactive towards nickel, thus removing the limitation encountered by Taylor. They have described their apparatus and technique in f u l l detail (34). Oxygen yields of 100 ± 2%:,of the theoretical amount are obtained. Their isotopic reproducibility 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 trifluo r i d e for the quantitative deter-mination of oxygen in various metal oxides. They claim an accuracy of 0.4%. A l i s t of metal oxides which may be treated in this way i s given in 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 in general not applicable to carbonates. However i t has been used to determine the 0 1 8/0 1^ ratio in manganese carbonate (32). Thermal decomposition of carbonates has been attempted unsuccess-f u l l y . McCrea (115) states: "The kinetics of the decomposition of calcium carbonate thermally are such that carbon dioxide can not be obtained with the desired reproducibility of isotopic composition". Vedder (163) noticed that thermal decomposition readily takes place in an environment of 0.1 mm.Hg water vapour. The water vapour has a catalytic influence. However carbon dioxide obtained in this way can only be used for 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 + + + H20 + C0 2 It 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 fraction-ation between the reaction products. Oxygen exchange between the orthophosphate ion and carbon dioxide or the carbonate ion i s negligible. This i s shown by McCrea (115) and Ault (3). The reproducible fraction-ation ( CX') between the reaction products has been determined recently by Clayton (30). ( 018 / 016y in CO2 from acid decomposition of carbonate . (018/0 1 6) carbonate 1.1 = 1.00999 This i s for 100% phosphoric acid decomposition of calcium carbonate at 25° C. The O^/O^ ratio in the denominator of eqn. 1.1 was determined by means of the fluoride method (30). 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. McGrea's work (115) had already indicated that the CX's for calcium-, strontium-, and barium carbonate are virtu a l l y the same. - 9 -1.3.3 Phosphates Phosphates can be treated by bromine trifluo r i d e (155). A l l the oxygen i s released without fractionation and the precision i s claimed to be 0.15&,. There are several other methods, but usually not a l l of the oxygen is 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 Ag3P04 to 1000° C to give molecular oxygen ( l ) . Another method i s to heat KH2PO4 with Hg(CN)2 to produce carbon dioxide (87). Cohn and Drysdale (37) heated Ba 3(P0 4) 2 with carbon to 1350° C to produce carbon monoxide, while Boyer et a l . (20) thermally reacted with KH2P04 with guanidine hydrochloride and achieved in this way that two oxygens per KH2PO4 molecule were liberated as carbon dioxide. 1.3.4 Water The older method of measuring the density of water (104) i s not considered here. Equilibration with carbon dioxide i s most often used at present. A measured volume of water i s put in a flask together 1 8 16 with a certain amount of carbon dioxide whose 0 / 0 ratio i s known. The temperature of the flask 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 for the exchange reaction H 20 1 8(1) + \ C0 2 1 6(g) = H 20 1 6(1) + \ C0 2 1 8(g) -10-at 25° C i s known, the 0 1 8/0 1 6 ratio of the water can be deduced. This fractionation factor was measured by Compston and Epstein (39) . (O^/O 1 6) in C0 2 Ck = 1 L L ^ = 1.04070 1.2 (O 1 8/© 1 6) in H20 at 25° C. The rate of this reaction i s pH dependent (121). To obtain equilibrium in a reasonable time interval i t i s necessary that the water is acidic (pH = 5-6) because the oxygen, exchange between water and carbon dioxide i s due to reversible hydration of the carbon dioxide C0 2 + H20 ^ H 2C0 3 ^ H + HCOg""^ 2 H + + COg ~~ and no direct exchange occurs between the bicarbonate ion and the water. The experimental procedure has been described by Epstein and Mayeda (77). Craig (41) gives correction formulae for this procedure and Dansgaard (46) also provides particulars. To assure that isotopic equilibrium i s established Hoering (95) added the enzyme carbonic anhydrase to the water. Disadvantages of the equilibration method are that i t takes at least 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 in the liquid phase. Dostrovsky and Klein (60) reduced the equilibration from hours to minutes by speeding up the reaction. This i s done by the catalysing action of a hot platinum wire. Unfortunately this procedure does not yield reproducible results with different equilibration 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 in about one half 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 ratio 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 in 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 H20 = Fe 30 4 + 4 H 2 Fe 30 4 + 4 C = 4 CO + 3 Fe The water vapour i s reduced at 500° C by a.mixture of iron and carbon; at this 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 con-verted to carbon dioxide over a nickel catalyst. 1.3.5 Inorganic compounds According to Finikov (81), many oxygen containing solids can be treated with K 4Fe(CN) 6 at temperatures lower than 600° C. Oxygen i s released without fractionation as carbon dioxide. Finikov analysed successfully A1 20 3, L i 2 S 0 4 , BaS04, Ba 3(P0 4) 2, and NaW04. -12-1.3.6 Organic compounds Organic compounds can be analysed in different ways, depending on the type of compound. The Untersaucher (157), method i s often used. In this method the compound is pyrolysed on a carbon surface, carbon monoxide i s formed, and subsequently converted to carbon dioxide. For f u l l particulars see (24,54). A variety of organic compounds can be treated with O-phenylendiamine monohydrochloride; the oxygen i s con-verted quantitatively to water in this 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 is dis-cussed briefly. This effect i s in 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. A similar observa-tion i s published by Mills and Hindin (121). They sealed water enriched in 0 1 8 in pyrex vessels and maintained the temperature at 105° C for periods up to four days. The same i s done with 0.1 N . alkaline solutions at 100° C for 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 in agreement with this. 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 16 When carbon dioxide or molecular oxygen i s used and 0 /0 ratios are mentioned, one means more often than not the 0 1 8 0 1 6 / 0 1 6 0 1 ratio. The latter i s the ratio which is actually measured. The oxygen isotopic ratio i s usually given as a ^ value ( ( 0 1 8 0 1 6 / 0 1 6 0 1 6 ) sample 1 - 1 t 1000 1.3 (OlSnlS /o l^O 1 6) standard During the last 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 ratios of various standards are given by Craig (41). When carbon monoxide or water are employed as a mass spectrometer 1 ft i ft gas, true 0 /0 ratios are reported. It i s only in rare cases when authors state whether they record their results as the 0 1 8 0 1 6 / 0 1 6 0 1 6 ratio or as the 0 /0 ratio. It 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 for 17 0 while Baertschi and Dansgaard apply this correction. -14-The Russian analogue for the O value i s o. _ [ (O l 8/0 1 6) sample _ ± 1 | ( O 1 8 / ^ 6 ) standard J 100 Among the Russian standards are - River water (58) ° atmo spheric oxygen/river water 3.2 1.4 Atmospheric oxygen i s f a i r l y uniform in i t s isotopic composition. Nier (125) gives 0 1 8 0 1 6 -5 U " = 408.8 x l O S 1.5 016 016 for atmospheric oxygen. Hence Russian river water has the ratio 0 1 8 0 1 6 -5 = 396 x 10 b 1.6 016Q16 and thus £ - -47 ° river water/PDB 1.7 < -9 °river water/SMOW = - Quartz from the Neroika deposit from the Artie Urals (165). 1.1 7? 1 Nier made a small numerical error in the percentage calculation of 0 X O for atmospheric oxygen j this should be 0.20.35% instead of 0.2039%. -15-Absolute ratio of the quartz standard $1 = —2 0l6 487 Chupakhin (26) has described how this ratio was determined. Thus (W 6 quartz standard = 412 x IO" 5 1.9 and ^Neroika quartz/SMOW 3 0 2 , 0 In the calculation of eqns. 1.8 and 2.0 the [o180^'^/0160''"^]„w^r, ratio u SMOW as given by Craig (42) was used. The & value for the Neroika quartz i s far beyond the range of quartz S values measured by investigators in 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 direct cor-relation. Therefore, i t i s not possible to compare quantitatively the Russian results (165, 167) measured relative to Neroika quartz, with results obtained elsewhere. The Russian river water standard agrees better with similar measurements done outside the USSR. Not a l l investigators use the £ notation. Some notable exceptions are Rankama (129) and Dansgaard (46). Rankama records the data as the absolute or relative value of the O-^/O16 ratio. Dansgaard follows -16-the usage of tracer technique workers who report concentrations of the 18 rare isotope i n parts.per million. Dar.sgaard records the 0 content as parts per million of the total oxygen content of the sample with respect to the Danish standard. He has correlated his Danish standard with American standards. In this survey the American practice i s followed; wherever C T ^ / O ^ ratios are mentioned, the molecular 0 l 8 o 1 6 /O^O^ ratio i s meant. -17-CHAPTER 2 ISOTOPIC EQUILIBRIUM THEORY 2.1 Introduction This chapter deals with the calculation of the equilibrium constant for isotopic exchange reactions, from spectroscopic data. It i s assumed that the reader i s familiar 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 AXtt + v BX v w 2.1 The superscript # denotes the presence of the heavy (usually the rarer) isotope. The compounds AXy and BX,^  are ideal gases. By definition K eq (AXj) ( B Xwl 2.2 Theoretically successful calculations of Ke^ have been, performed only -18-for ideal 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 energy, R .= gas constant, T • = absolute temperature. The free energy i s related to the partition function Q according to Qe F = - RT In -7 2.4 N where e = base of natural logarithme, N = Avogadro's number. To a.very good approximation the potential energy functions are the same for isotopically different molecules. Therefore i t i s justified to take as the reference datum for the energies appearing in the partition function, the hypothetical vibrationless state of the molecule. For normal chemical reactions this procedure i s not followed, the ground state of the molecule i s taken as reference lev e l , and the zero point energy i s neglected. However, since i t i s mainly the difference in zero -19-point energies which make isotopically substituted molecules behave differently, i t i s essential not to neglect the zero point energy. Thus zero point energy is included in the energy appearing in the partition function. For reaction 2.1 B X W AX. BX w - RT In w / rQBx#) [«AxJ / V - V M ) - ' C „ H - VBX )] P v v w w 2.5 where ^AX = v ° l u m e °f molecule AXy in the ground state, v P = pressure. Usually the change in volume due to isotopic substitution i s neglected, because i t s influence on K eq i s only a minor one. Therefore K eq 2.6 Under nonextreme conditions the partition function may be approximated by -20-Q = Q t r Q v i b %ot 2.7 where Q^ tr .= translational partition function, Q v£k = vibrational partition function, Q r o t = rotational partition function. Using this approximation the partition function ratio becomes # J i # i # irf r #-i 3 / 2 •Sc ly 1 z hF_J I x xy " e - U i / 2 1 - e 1 e 2.8 where I I I •Lx'-Ly x z u. = I i s = symmetry number, the three principal moments of inertia, h S)±/kT, 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 I# j# jtt" x y z *X *y *z -, 1. 2 3/2 fml M . 3n/2 u i u? l 2.9 -21-one obtains I Q p — ni 3n/2 s = s# e * 1-e  u i l - e u ? e " u i / 2 2.10 where n = number of isotopic atoms being exchanged, m,m = atomic weights of the two isotopes. Following Bigeleisen and Mayer (15) one defines Q# rm^3n/2 f = Q :\m# 2.11 as the reduced partition function ratio. Thus K eq 2.12 and " # -uf/2 u i e 1 . u i -u,/2 / 1 - e " u i i e i ' 2.13 Substituting u.. = uY + & u.. into eqn. 2.13 and expanding the result, one obtains # In 1 e 1 .2u# 2 " 2! (I - eu|) 2J A u. -uf „-2u}l r i i _ e~ u i - e - " u i " Wf2 " 3 1 (1 - e " ? ) 3 2.14 -22-Vojta (169) gives a detailed account of this expansion. When A-uj i s small, the higher powers of eqn. 2.14 may be neglected. Put G(u,) = i - -4 + — T r i 2.15 Eqn. 2.13 becomes now In f .= In ^  + Q(u±) A u.. 2.16 s i Except for the case of very ligh t atoms (Hydrogen), A u.. w i l l be small enough to make this approximation a good one. Values for the function G(u^) are calculated' and tabulated conveniently by Bigeleisen and Mayer (15). These tables are reproduced in (56). The equilibrium constant i s given by In K = w eq In J# + E G(u.) A U j j - v In ^  + X G(u.) A u. 1 L S • — AXV 1 B 2.17 Higher accuracy may be obtained by including the second term of eqn. 2.14 in the calculations for K . eq When one defines u i 1 u i e S K ) = n 2.18 u i ( e u i - l ) 2 an alternative equation for In f i s obtained -23-ln f •+ 2~S(u.)(A U i ) 2 / 2 u i 2.19 i i This development i s due to Bigeleisen (13, 14) who has also published tabulated values for the function S(u^) (13). 2.3 Limitations of the theoretical treatment 2.3.1 Idea gas assumption Eqns. 2.17 and 2.19 are only valid for ideal gases. In applying them to condensed phases one neglects the influence of the presence of other molecules on the internal vibrations of the molecule under consideration. 2.3.2 Anharmonicity In the derivation of eqn. 2.17 the vibrational partition function for the harmonic oscillator was used. At moderate temperatures this w i l l be adequate, but anharmonicity becomes more pronounced when the tempera-ture increases. The usual procedure i s to correct only the zero point vibrational energy for anharmonicity. Thus 2.20 where -24-Then the correction for f w i l l be " I 4 ? k hcAT (xf-: - *ij) 2.21 because the anharmonicity contribution to the partition function i s -\ he AT X ,\ X i , -Qanh = e 1 3 2' 2 2 Therefore in f . i n 'if + I G f u ^ - £ I T (x - x t j ) Normally the anharmonicity constants for the isotopically substituted molecule are not known. But these constants can be calculated, provided they are known for the nonsubstituted molecule With respect to eqn. 2.24, Herzberg (91) remarks that i t has not been rigorously proven, but that results justify i t , i.e. i t agrees with the experimentally determined values. At low temperature the influence of anharmonicity i s unimportant. One may also consider the influence of anharmonicity on the total vibrational energy. According to Vojta (170) this correction would amount to 0.1% to 1% of the anharmonicity correc-tion for the zero point energy at about 273° K. It would increase to -25-0.5% to 5% at about 500 K. The correction for the anharmonicity can be evaluated theoretically when one uses a semi-empirical potential energy function l i k e the Morse potential, instead of the Hooke's law potential, in the wave functions for the oscillator. 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 fractionation and the fractionation factor Generally i t i s assumed that the distribution of the isotope X in the molecular species AXy i s governed only by the symmetry numbers of the various isotopic configurations of the species AXV. In other words the heavy isotope w i l l be distributed at random through the assemblage of molecules of a certain species. For example 18 + C0 2 =2 CO 0" 2.25 K 2.26 eq Because when eqn. 2.17 i s applied one finds that 2.27 -26-However eqn. 2.27 represents an idealization and observations (116) have shown that for reaction 2.25 The discrepancy of 0.017 i s due to intramolecular fractionation caused by the presence of the heavy isotope. The presence of the heavy isotope has changed the vibrational frequencies of the molecule. In this case tration and the effect i s not of practical importance as long as a l l oxygen atoms occupy structurally equivalent positions in the molecule. Intramolecular fractionation can be evaluated only i f one knows a l l zero order vibrational frequencies of the differently substituted molecules. In the course of numerical evaluation of the equilibrium constant (see sect. 2.6) i t i s implicitly assumed that there w i l l be no intra-molecular fractionation. One takes for granted that a l l atoms which can be exchanged have equal probabilities of doing so, provided they are in structurally equivalent positions. The fractionation factor i s defined as K, eq = 3.983 the concentration of 018 i s very sm ll with respect to the 0 concen-for the reaction CO2 + 2 H20' .18 C07 + 2 H90' 2 2 .16 (*) With regard to the usage of 0 /0 X O ratios see sect. 1.5. -27-while now ^ 2 [ c o ^ + [co 1 6o 1 8] / f e ) 1 8 ] " ^ O 1 ^ 1 8 ] + 2 [CO^6] / [H 20 1 6] eq provided eqn. 2.26 i s valid. Hence the relation , vw K = CN 2.28 eq for the reaction 2.1 i s also an idealization. 2.3.4 Zero point energy For the calculations of Ke^ one must use zero order frequencies. From empirical formulae for the molecular energy levels 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 for an isotopic exchange reaction between a gas and l i q u i d phase i s easily evaluated provided information i s available about the vapour pressure of the normal and of the isotopic li q u i d . Let 0^^ be the fractionation factor for the reaction \ CO^Cg) + H 20 1 8(1) = \ C0"(g) + H 20 1 6(1) and i s the fractionation factor for the corresponding reaction h C0 2 6(g) + H 20 1 8(g) = \ C o f (g) + H 20 1 8(g) then P H 20l6 ,18 2.29 where P^ ^ g = vapour pressure of H20 Theoretical calculations of vapour pressures of isotopic liquids are not t r i v i a l and have been successfully undertaken only for argon, neon, etc. But there are experimental equations available to calculate the vapour pressure ratio. Riesenfeld and Chang (132) found experimentally P 16 H20J' 2.74 log — t = _ 0.0056 2.30 PH 018 T -29-Zhavoronkov et a l . (179) derived from an independent set of experimental data P h^" 3.449 l o g - ~ = - 0.00781 2.31 P 18 T H 20 1 8 Eqns. 2.30 and 2.31 give the same result at room temperatures, but differ slightly for high and low temperatures. Devyatekh et a l . (53) derived the equation l n __92-l = i - i i - 0.0610 2.32 P 18 T CO But usually such equations are not available. Waldmann (174) gives the following rule of thumb: the phase in which the molecule or atom group has the most vibrational degrees of freedom, w i l l be enriched i n the heavy isotope. 2.5 Solids As w i l l be shown in the numerical example of isotopic exchange between gaseous carbon dioxide and water (sect. 2.6), the calculated values are slightly different from the experimental ones. The d i f f e r -ence in the example i s only 2.2% but i t i s s t i l l far greater than the present day experimental accuracy. This discrepancy between theoretical and experimental values w i l l increase when one applies the calculations of sect. 2.2 to solids. The reason being that the assumptions become worse and the spectroscopic data less dependable. Only two cases of isotopic exchange calculations involving solids are reported in the -30-recent literature. Grant (85) assumed that the isotopic exchange of silicon isotopes in s i l i c a t e s i s exclusively governed by the internal vibrations of the orthosilicate ion. By means of this approximation the problem was reduced to an ideal gas case. McCrea (115) tried to determine the temperature dependence of the fractionation factor for H 20 1 8(1) + | CaC0g 6(calcite) .= H 2 0 1 6 ( l ) + | CaCO*^calcite) He assumed that the internal vibrations remained unchanged and he tried to evaluate the contribution of the l a t t i c e motions to the fractionation. The acoustical mode of the calcite l a t t i c e was approximated by a Debye function, while the optical modes and the rotation of the COg ion were expressed as Einstein functions. Because of several ad hoc assumptions, necessitated by lack of data and the complexities of the problem, McCrea's treatment could not be expected to give quantitatively correct results. However qualitatively the agreement between McCrea's calcula-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 results from the inherent d i f f i c u l t i e s in the interpretation of Raman and Infrared spectra. 2.6 Numerical example The theoretical calculation of the equilibrium constant for the exchange reaction -31-\-C02 + H 2 0 1 8 = \ C 0 2 8 + H20 i s performed to various degrees of accuracy (table 2.3). Table 2.1 gives the vibrational wave numbers which were used. TABLE 2.1 Normal vibrations of the carbond dioxide and the water molecule Normal vibrations < cm - 1 cm - 1 H 2 0 1 6 cm x V 1 ' cm"1 w i 1351.20 1273.9 3825.32 3815.5 ^ 2 672.2o(x) 661.94^x) 1633.91 1647.8 ^ 3 2396.4 2359.81 3935.59 3919.4 ^ The OJ^ vibration i s twice degenerate for carbon dioxide. A l l data are from Urey (158). For H20 the symmetry numbers s and are always unity. For C0 2 the ratio 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 coefficients of table 2.2 were used. -32-TABLE 2.2 Anharmonicity coefficients for C0 2 and H20. Ref. (158) Anharmonicity coefficient < cm--'-< cm-"*" cm-"'" H / 8 -1 cm x l l - 0.3 - 0.27 - 43.89 - 43.66 x22 - 1.3 - 1.26 - 19.5 -'19.36 x33 -12.5 -12.12 - 46.37 - 45.99 x12 + 5.7 + 5.29 - 20.02 - 19.89 x13 -21.9 -20.33 -155.06 -154.03 x23 -11.0 -10.67 - 19.81 - 19.66 From data given in tables 2.1 and 2.2 the following fractionation factors are calculated (table 2.3). -33-TABLE 2.3 Fractionation factors calculated for the systems water vapour - carbon dioxide and water - carbon dioxide at 25.1° C and 1 atmosphere pressure System water vapour - carbon dioxide o4 (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 refining the calculations the accuracy may be increased, provided the basic information (vibrational frequencies and anharmonicity coefficients) allows this. If eqn. 2.17 is used to 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 rapidly, 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. By means of eqn. 2.21 the anharmonicity correction can be evaluated. Line (c) in table 2.3 gives thus the best value of Oi. for the system water vapour - carbon dioxide. Applying eqn. 2.29 one obtains the fractionation factor for the system water -carbon dioxide. It i s generally f e l t that the experimental value i s more accurate than the theoretically derived one. However i t should be noted that the actual difference between the two oi. Ts (lines (d) and (e)) i s f a i r l y small, when one considers a l l the approximations used to arrive at the theoretically derived o^. In conclusion one may say that theoretically derived ^ 's are only of value for semi-quantitative purposes. However a theoretical calculation of ' w i l l provide insight about the phenomena one may anticipate, because i t illustrates 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 in some detail. Formulae for the temperature and pressure dependence are derived. 3.2 Temperature dependence When s =. s^, eqn. 2.17 becomes 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). In K eq Z G(u.) A u 4] BXw -36-• TABLE 3.1 Comparison between G(u.) and u./12 U./12 G( U i) ui/12 - G( U i) % difference 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 At high temperatures u.. becomes small enough to justify the approximation l n Keq = 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 Uj i s large, at low temperatures, KQ(^ i s better approximated by ln K e q = | + s 3.2 where x, y, r and s are constants. T i s the absolute temperature. -37-Most polyatomic oxygen containing compounds have vibrational frequencies of the order of 1000 cm-1. But 0-H bonds have vibrational frequencies of about 4000 cm - 1. TABLE 3.2 Values of u for different temperatures and frequencies Temperature °K U> = 1000 cm 1 u U)= 4000 cm - 1 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 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 in eqn. 3.1 become less good. The anharmonicity becomes more pronounced. The ri g i d rotator assumption does not hold any longer, because of stretching of the molecule by i t s own centrifugal force, and therefore one finds -38-an increase in the difference between the average moment of inertia of the molecule in an excited vibrational state and that of the molecule in the ground state. The usage of the Teller-Redlich product rule becomes less justifiable. At very high temperatures a l l partition functions have their classical value and no isotopic fractionation w i l l take place. Cross over temperature It i s f a i r l y common that a phase which concentrates the light isotope at low temperatures, w i l l concentrate the heavy isotope at high temperatures. This phenomenon i s called "cross-over". It may happen phase A i s enriched in the heavy isotope at low temperature and has lower vibrational frequencies than phase B, which i s enriched in the light isotope at that low temperature. Phase A w i l l have more vibrational degrees of freedom than phase B in this case. The occurrence of "cross over" under these circumstances follows directly from eqn. 2.17 and from the fact that G(u;[) i s a monotonically increasing function of u^ (see table 3.1) for which dG(uj) tends to zero when u^ increases. dui 3.3 Pressure dependence Returning to eqn. 2.5 one obtains for the equilibrium constant K. eq e -P(wAVA - v AV B)/RT 3.3 where V v - 39 -and 3 In K_n -T- - q = -(w*V A -VAV B)/RT 3.4 O P since d In K e q d P 3 K 1 - (wAV A - VAV B)/RT 3.5 9 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 fractional volume change on isotopic substitution i s about equal to the cube of the fractional change i n the distance from the centre of the molecule to the furthest position of any constituent atom in the course of normal vibrations of the molecule in the ground state. . Also i t i s assumed that the bonds are harmonic oscillators. The bond length i t s e l f w i l l not be affected by isotopic substitution, however, the root mean square distance between the atom's position and i t s equilibrium site w i l l change as a result of the substitution. The wave function for the groundstate of the harmonic oscillator i s 4Tn>ml4 -2^2-Vmx2/h " 3.6 -40-The root mean square expectation value of x 4 ? = I 2 8TT2V nj 3.7 and 21 M f m 3.8 where y - vibration frequency of the harmonic oscillator, f = force constant, m = reduced mass. Only the stretching mode ( i s considered i n the calculation of the change in distance on isotopic substitution. &r = 4'7 - \ l x * 2 .4s he \ 2 f stretching 3.9 (*) and 3 A R V " r 3.10 The distance r may be calculated from the molecular volume or may be (*) The corresponding formula as given in (100) i s in error, see also (106). -41-put equal to half of the distance between the centres of neighbouring molecules in the solid state. The vibration frequency of the stretching mode of the isotopically substituted molecule can be calculated by. means of the product rule. Hoering (94) has asserted that the maximum effect of pressure on the equilibrium constant can be derived from the anharmonicity correction to the ratio of the vibrational p a r t i t i t i o n functions. This i s based on the following line of reasoning: If chemical bonds are harmonic oscillators, then the effect of isotopic substitution w i l l be only a change in fre-quency, the amplitude and hence the volume of the molecule w i l l be constant. But actually, chemical bonds are anharmonic oscillators, thus the amplitude w i l l change as a result of isotopic substitution. Therefore, the anhar-monicity correction i s a measure of the maximum influence of pressure on the equilibrium constant. It is true that classically the amplitude pf any harmonic oscillator depends only on the i n i t i a l conditions, and i s thus mass independent. However the same i s true for the anharmonic oscillator. Quantum mechanically the concept of amplitude i s empty, but the root mean square expectation value for x (eqn. 3.7) i s mass dependent for a harmonic oscillator. In section 4.7 i t will' be shown that the pressure dependence in carbonate palaeothermometry i s relatively insignificant. 3.4 Thermodynamic activity Besides the temperature and the pressure, the thermodynamic activity of the components of the system w i l l influence the equilibrium constant. Thus for the reaction -42-C o J 8(g) + H 20 1 8(1) = C0 1 60 1 8(g) + H 0 1 6 ( i ) co2/ / ra#i .a JH 20 C 016 Q18 / ko 1 8l jr. co2 _ C 0 2 1 6 / _r. H20 H2O"J 3.11 where a = thermodynamic activity, ^ = activity coefficient, o*- = fractionation factor for the system with activity coefficient ratios equal to unity, f( ^) = function of the activity coefficients, cJv ' = actual measured fractionation factor. Hoering (94) has measured the change in r^,' when one replaces the pure water by a 10 molar aqueous lithium chloride solution. It i s believed that the lithium chloride interacts solely with the water, therefore only the ratio ( ^ # / ^ ) H 2 0 i s affected. Taking f( ^ ) = 1.000 for the system with pure water Hoering has observed f ( ^ ) = 1.0008 for the lithium chloride solution. He attributes this to selective solvation of the lithium ions by water, so that the solvent becomes enriched in 0 16 -43-Unfortunately l i t t l e i s known about activity coefficients of hydrothermal solutions. It should be noted that Hoering's solution i s quite con-centrated. Thus for natural occurring aqueous solutions one may anticipate that the activity dependence of K gq i s only of secondary importance. -44-CHAPTER 4 PALAEOTHERMOME TRY 4.1 Introduction Palaeothermometry u t i l i z e s the temperature dependence of the equi-librium constant for the oxygen isotope exchange reaction between calcite and water. Urey (158) suggested that palaeotemperatures could be deter-mined in this way. In 1948 he published some preliminary results (159). Experimentally one does not determine the constant Ke^ but the fractionation factor dL . McCrea has grown calcium-carbonate very slowly from an aqueous solution at different temperatures. In this way he determined the temperature dependence of e>(. . The fractionation factor could not be evaluated because of the constant fractionation occurring when calcite i s treated with acid to produce CO2 (see sect. 1.3.2). The 18 1 r. CO2 i s used to measure the 0 /0 1 ratio of the calcite mass spectrometrically. By comparing McCrea's inorganic results with organically precipitated calcite one can conclude whether the biogenic calcite was precipitated in thermodynamical equilibrium with the water or not. This has been done by Epstein et a l . (73). Marine calcareous shelled invertebrates were -45-grown at known temperatures and their shells were analysed. Because of d i f f i c u l t i e s in the purification of biogenic calcite, Epstein et a l . (74) had to publish a revision of their 1951 paper (73). A temperature "I o "I £ relationship was established between the 0 /0 ratios of the water and of the calcite. This relationship i s in virtual 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 in isotopic equilibrium with the Upper Cretaceous ocean. This assumption has with-stood the test of internal consistency of results. They also assumed the habitat of belemnites was characterised by a salinity of 34.8%0, that of the present ocean, and a ^sea water/PDB = -0.47. The absolute tempera-ture measured in this way may not be too significant because of the uncertainty in the 0 /0 ratio of the sea water. But their tentative conclusions about temperature trends during the Upper Cretaceous have been later confirmed by Lowenstam and Epstein ( i l l ) . Emiliani and Epstein (68) have shown that certain recent foraminifera form their tests in isotopic equilibrium with their surroundings. This has been the start of the Pleistocene temperature work. Once the pioneering papers (73, 74, 161) were published a great many publications appeared dealing with Pleistocene, Tertiary, Cretaceous, Jurassic and Permian temperatures. The majority of them are li s t e d by Samuel and Steckel (135, 136). Among the papers published in 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 & 2 4.1 where t = temperature in °C at which the carbonate i s formed, £> = the per mil difference between the O ^ / O ^ ratio of COv, obtained from the sample and a standard C02. 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 in South Carolina. Equation 4.1 i s only applicable when ^ sea water /PDB ~ " " ^ . l (see Craig (41)). To avoid confusion, this value - 0.1 i s the & value of the carbon dioxide, equilibrated with mean ocean water at 25° C. It was realized that locally the ocean water O - ^ / O 1 6 ratio may vary appreciably from the ratio for mean ocean water (76) and thus eqn. 4.1 was changed to 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 refers to the 0 /0 ratio of the carbonate and A equals the & value for the water in which the sample•carbonate precipitated. Equations 4.1 and 4.2 are based on data in 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 - 2 - 0.00256 4.3 K = fractionation factor for the water - calcite system. Clayton's nomenclature i s followed here. T = absolute temperature in degrees Kelvin. Since Clayton used Epstein's low temperature results eqns. 4.2 and 4.3 give practically the same result in the interval 0 - 30° C. 18 16 4.3 0 /0 ratio of ocean water Epstein and Mayeda (76) have analysed 93 marine water samples and found that the 0 18 / 016 ratio 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 is more-salty and enriched in 0 1 8, while fresh water i s enriched in O1^. The reason for this i s the higher vapour pressure of P^O1^, as compared to H^O18, under meteoro-logical conditions. In palaeotemperature work i t i s often assumed that the ocean i n the past had the same CP-S/O16 ratio as the ocean has presently, i.e. A = 0 i n eqn. 4.2. Emiliani (64) approximates the -48-Ql8yol6 ratio of the ocean in the past by taking the weighted average of this ratio for the present day hydrosphere. This i s , of course, for nonglacial times. For glacial times he assumes that the glacier ice in the past had the same average 0^/0^ ratio as at present. By estimating 18 16 the extent of past glaciations one can deduce the 0 /Cr ratio of the ocean during these glaciations. In this way he arrives at the following values for A: - at maximum glaciation: A = + 0.4, • corresponding to a temperature correction of + 1.7° C. - at nonglacial times: A = - 0.3, corresponding to a temperature correction of - 1.3° C. 6 3 Emiliani (64) has taken for the present day volume of ice 18.8 x 10 km with an average & = - 25. Both values seem to be underestimated i n the ligh t of recent measurements. Information given by Epstein and Benson (77). for ice from Antarctica and Greenland indicates that the average S> value for glacier ice at present i s approximately - 35. Donn et a l . (57) report two estimates on the present world ice volume which are given in table 4.1. These estimates have been used to calculate weighted average & ' s for the hydrosphere (these are possible values of A) and corres-ponding temperature corrections for nonglacial times (see table 4.1). The suggestion that the isotopic composition of the ocean has been constant for a significant part of the geological history i s attractive and positive evidence for this hypothesis i s available (see also sect. 9.2.5). -49-TABLE 4.1 18 Distribution of 0 in the hydrosphere at present volume ' 10"6km3 II volume 10 _ 6km 3 /^SMOW ocean 1360.0 1360.0 - 0.1 ice 30.6 25.0 -35 fresh water 0.5 0.5 - 7 total hydrosphere 1391.1 1385.5 £ , /SMOW hydrosphere ("A" for nonglacial times) -0.87 -0.73 temperature correction for nonglacial times -3.6°C -3.1°C (*) columns I and II are different because of the different present day glacier ice 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 ice as 0.88 gram/cm3. -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 ratio of the ocean-in the past can perhaps be circumvented. Urey (159) suggested in 1948 that probably use could be made of the temperature dependence of the fractionation factor for the hypothetical exchange reaction between cogenetic phosphate and carbonate in shells. Although this attractive pos s i b i l i t y existed, i t was not un t i l 1960 that Tudge (155) published a method, accurate enough, for extracting oxygen from orthophosphates. Oxygen isotope exchange does not take place directly between the solid phosphate and the solid carbonate. But i t may be possible that equilibrium i s established between these two substances, via the water in which the animal live s . Unfortunately there is.apparently no oxygen exchange between water and orthophosphate under inorganic conditions. The extent to which this i s also true for organic conditions i s not yet known. Hence i t i s not certain whether this line of approach w i l l be successful. 4.5 V i t a l effects The subject of biological fractionation has been reviewed by Bowen (18). It w i l l be obvious that the biogenic carbonate used for palaeo-temperature 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 their body fluids are in isotopic equilibrium -51-with the water. Lowenstam and Epstein (111) have reported in their study of recent marine invertebrate skeletal material, that only exoskeletons seem to be formed in isotopic equilibrium. Recent echinoderms secrete their skeleton not i n equilibrium with the water. Nonequilibrium pre-cipitation i s also indicated for shoal water corals and some algae (112). According to Emiliani (64), isotopic exchange between the oxygen liberated by Zooxanthella and the algal- and coral carbonate i s the cause of this phenomenon. Zooxanthella i s a symbiotic organism l i v i n g in the tissue of the corals and algae under consideration. 4.6 Insensitivity of the fractionation factor The fractionation factor for 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 in pH and/or ionic strength appear to be of no importance. Epstein (72) reports that also small amounts of magnesium and/or strontium ions in the carbonate l a t t i c e do not affect in a measur-able way the fractionation factor. Moreover, the crystal symmetry (rhombohedral calcite or orthohombic aragonite) does not have a signi-ficant influence. The physical reason for the last two points i s that the fractionation i s mainly dependent on the internal vibrations of the carbonate ion; these vibrations appear to be influenced only in a minor way by crystal symmetry and small amounts of impurities. 4.7 Influence of pressure The pressure dependence of the fractionation factor seems to be unimportant in carbonate thermometry. This w i l l be illustrated by an example | CaCO^6 (calcite).+ H 20 1 8 (l) = | CaCO^8 (calcite) + H 20 1 6 (1) To estimate the influence of pressure the following simplifying assumptions are made: - A l l molecules involved in the exchange are in the groundstate. - The molar volume of the water molecule does not change upon oxygen isotopic substitution. Because of the central position of the oxygen atom in the water molecule, this assumption should be reasonably good. - The effective volume of the carbonate ion i s spherically shaped. Applying eqn. 3.10, one obtains AV •= \J 36Tf V 2 A r 4 Insert this into eqn. 3.6 and put VB = 0 3 K _ _• 1 ^  ?P 3 \ 36 T I V2 AT RT 4 -1 (Ref. 91). Molecular volume of calcite = 6.179 x 10 -23 ,3 cm' -53-Thus A V = - 0.043 cm mole -1 and = 6 x 10 -7 atm -1 -5 Therefore, at depth of 1 km i n the ocean K w i l l be increased by 6 x 10 . This would cause an error of less than 1° C, which i s not significant 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). They roast the sample in a platinum boat for 30 minutes. During this process a continuous flow of purified helium gas sweeps away the volatile decomposition products of the heated organic compounds and provides an inert 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 liquid nitrogen trap f i l l e d with activated charcoal, to purify the helium. Craig (41) has checked this procedure by treating in 18 16 the same manner a sample of Ticino marble and measuring i t s 0 /0 ratio before and after the treatment. He did not detect a difference between the two measurements. Russian workers (123, 151) use a simplified version of this process. -54-4.9 Significance of measured temperatures The interpretation of the measured data requires that the s t r a t i -graphic range, the habitat and the growth characteristics of the f o s s i l material used are known. The stratigraphic range of many fos s i l s i s well established, but the habitat of most fo s s i l s i s only crudely known. For instance, i t i s known that a certain animal is pelagic, but i t i s usually not known in what depth range the animal lived. This i s important because marine water temperatures change considerably with depth. The surface temperature in the Eastern equatorial Pacific 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) for pelagic foraminefera. Further the 18 1 ft habitat may be characterized by a certain 0 /Cr ratio different from SMOW. Only limited information i s available about the growth character-i s t i c s of most f o s s i l s . It appears that the growth of many invertebrates is chiefly confined to a particular season (see for example (84)). Thus, generally one determines the temperature of the growth season of the animal. Epstein and Lowenstam (75, 111) have investigated this. One may conclude that the carbonate thermometer i s a powerful tool in palaeothermometry. Its weakest spots are the uncertainties about the 0l8 / 016 ratio of the ocean in 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 after 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 pairs, because the melt or hydrothermal solutions from which minerals were precipitated are not available anymore. Obviously, the oogenetic pairs should be in thermodynamic equilibrium. Whether this i s the case or not can be shown to various degrees of conclusiveness. not in equilibrium, because i f equilibrium were established quartz are would be enriched in Q I S with regard to the calcite, according to the experimentally obtained eqn. 5.2 - The o Q and ^ c of equilibrium pairs precipitated from hydrothermal solutions with approximately the same 0l8 / 016 ratio are related i n a simple linear fashion (28, 33). -56-- If there are three cogenetic minerals, the three possible pairs should give consistent results. - If the quartz and the calcite are in equilibrium with the same solution, then the S values calculated for this solution from ^ Q and &^  should be identical. Clayton (29, 30) has measured the fractionation factor for the system o o calcite - water over the temperature range 190 - 750 C under pressure of 1000 atmospheres. In K p w = 2730 T"2 - 0.00256 5.1 where Co 1 8/0 1 6 3 CaC03  K ° W = [pl8/0 1 6] H20 The low temperature data of Epstein et a l . (74) are incorporated in eqn. 5.1. The water was replaced by a dilute aqueous ammonium chloride solution in Clayton's experiments. In 1961 O'Neil and Clayton (127) have reported a similar relationship for the system quartz - water. In K = 3629 T"2 - 0.00256 5.2 QW Equation 5.2 was derived from experiments done in the range 380° - 700° C under 1000 bars pressure. This time the water was replaced by a dilute aqueous sodium fluoride solution. From eqns. 5.1 and 5.2 one can deduce the relationship -57-In K, = 899 T' ,-2 5.3 •QC for the oxygen isotope exchange between quartz and calcite. 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 as was indicated by the theory (see sect. 3.2). Further i t was assumed that the fractionation factor for systems not involving water would become unity at high temperatures. This i s because in systems involving water the "cross over" phenomenon i s bound to occur (see sect. 3.2). Finally they took for granted that the minerals quartz, calcite and hematite which appeared to be cogenetic in some of their samples, were also in thermodynamic equilibrium. This provided enough information to deduce eqns. 5.2 and 5.3. In addition to this they could plot also In vs In for their samples and obtain the relationship In K = x T -2 5.4 - y In K. QH = 1.388 In K, CH 5.5 where KQJJ stands for the fractionation factor of the system quartz-hematite . The convenient equation -58-IOOO m K A B = where A - S . S AB A B is generally employed to give a relationship between & values and the fractionation factor. This eqn. i s easily derived (33). K AB [ o 1 8 / ^ A 1 + A/1000 [ O 1 8 / O 1 6 ] B " 1 + B / 1 0 0 0 = 1 + ( ik - «SB)/iooo For oxygen exchange reactions ^ 1.04 thus % = i + m K. AB By means of eqn. 5.5 the following relations could be deduced In KQ H = 3216 T~ 2 5.6 In K C H = 2317 T~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 in table 5.1. TABLE 5.1 Cogenetic quartz - calcite - haematite valuesv / Sample So 32 24.4 • 17.3 0.3 33 18.0 12.8 -2.8 34 112.. 3 8.2 2.2 35 10.4 7.4 1.6 i.s.C) 6.8 6.5 3.3 (*) I.S. i s a oogenetic quartz - calcite -magnetite sample from Iron Springs. The fractionation factor for the system magnetite - haematite was believed to be very small. (**)' A l l 6 values are with respect to SMOW as reported in (32, 33). From data In table 5.1 the temperatures shown in table 5.2 may be deduced for each of the oogenetic mineral pairs. -60-TABLE 5.2 Temperatures of freezing in of the O^/O 1 6 ratio of three cogenetic mineral pairs Sample t * tCH °C °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 quartz-calcite. Equation 5.5 was determined by means of a least square f i t for the graph of In KQ^J vs In KQ H (graph 5.1). The least square method presupposes that errors are distributed at random. This i s not the case here. 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 right and that.the graph In KQ H vs In K C H w i l l pass through the origin (see graph 5.1). One obtains then -61-. I S J 1 I I 1 l i i i l | i I I 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1000 In K C H Graph 5.1 - Relationship between quartz - haematite fractionation and calcite - haematite fractionation in quartz - calcite haematite rocks. -62-i n K Q H = 1.404 In K C H 5.9 and subsequently In KQ H = 3124 T" 2 5.10 In K C H = 2225 T" 2 5.11 In KHW = 505 T" 2 - 0.00256 5.12 In the derivation of eqn. 5.9 the & values of table 5.1 were recal-culated. This was necessary because Clayton and Epstein (32) used the formula £ /„„«,,•= 1-0399 £ + 39.9 5.13 x/SMOW x/PDB to convert their measurements with respect to PDB, to values with respect to SMOW. Equation 5.13 is based on the indirect determined & value for Hawaiian sea water (taken to be the same as SMOW in (32)) namely £ „ A W A I I A N S E A W A T E R / P D B = - 38.4. But later in 1958 Compston and Epstein (39) reported for the reaction 1 16 .18 1 „ A18 .16 2 C 0 2 + H 2 ° = 2 C 0 2 + H 2 ° <^ = 1.0407 at t = 25° C -63-Therefore eqn. 5.13 should be modified to ^x/SMOW = 1 - ° 4 0 1 ^x/PDB + 4 0 ' 7 5 ' 1 4 because h g^ow/poES ~ ° ' w ^ e n " t^ i e Q-^»^s neglected (see Craig (41)). Equation 5.14 i s i n agreement with the absolute atomic 0^ 8/0 1 6 ratio for SMOW as published by Craig (42). Applying eqns. 5.9, 5.10, 5.11 and 5.12 one obtains the result tabulated in table 5.3. TABLE 5.3 Modification of table 5.2 Temperatures of freezing in of the 0 1 8/0 1 6 ratios for three cogenetic mineral pairs Sample t Q C t Q H t C H o o o _ C C • C 32 89 89 89 33 150 116 104 34 205 285 331 35 287 325 342 I.S. 1487 673 562 -64-Although the data of table 5.3 are not overwhelmingly impressive, they are somewhat more consistent than those presented in table 5.2. The question i s now, what causes these temperatures to be so different and what may one deduce from this. Experimentally & can be measured with an accuracy of - 0.2 (presently even better accuracy i s obtained). The errors due to accuracy limitations become appreciable at high temperature; this w i l l be evident from an inspection of graphs 5.2 and 5.3. In these graphs i t i s shown how a certain error in & measurement ( A ^ ) for a particular mineral pair corresponds to a certain temperature difference ( A t ) for a given temperature of freezing in of the 0 /Or ratio. If one assumes that the samples 32, 33, 34, and 35 were precipitated from aqueous solutions, which can be treated as. pure water, then the various £ values for these solutions can be evaluated (table 5.4). Of course this i s only possible i f the isotopic composition of the solution remained constant as long as appreciable exchange took place. These are not unreasonable assumptions r when one takes i n consideration the low solubility of quartz, calcite and haematite. To explain the results presented in table 5.4 one may invoke the following mechanisms: - solid state diffusion; - nonequilibrium precipitation; -mineral pairs were not truly cogenetic; - changes in isotopic composition of the hydrothermal solutions. Assuming that: 18 16 -The 0 /Or ratio of the hydrothermal solutions remained constant as -65-100 200 300 400 500 600 700 800 Temperature of freezing in of the Cr8/Cr-6 ratio in degrees Celcius •h Graph 5.2 - Errors in calculated temperatures, due to errors in S measurements, for the mineral pairs quartz - calcite (Q-C), quartz - haematite (Q-H) and calcite - haematite (C-H). -66-" I I I I I I , I I 100 200 300 400 500 600 700 800 Temperature of freezing in of the Q18 / 016 ratio in degrees Celsius. Graph 5.3- Errors in calculated temperatures, due to errors in measurements, for equilibria quartz - water (Q-W), calcite - water (C-W) and haematite - water (H-W). -67-27 _ A Q C , A C H Graph 5.4 - Fractionation relationships between the mineral pairs quartz - calcite ( Q C ), calcite - haematite ( C - H ) and quartz - haematite ( Q - H ) . -68-TABLE 5.4 values for hydrothermal solutions with respect to PDB Sample Temp. °C Mineral pair ^ w from Q(*) ^ w from C ^ W from H 32 89 -39.3 -39.3 -39.3 33 33 33 150 116 104 Q-c Q-H C-H -38.3 -41.8 -43.3 -38.3 -41.3 -42.0 -41.3 -41.8 -42.0 34 34 34 205 285 331 Q-C Q-H C-H -39.4 -3513 -33.6 . • -39.5 -36.4 -35.2 -36.0 -35.4 -35.2 35 35 35 287 325 342 Q-C Q-H C-H -37.1 -35.8 -35.2 -37.0 -36.1 -35.7 -35.9 -35.7 -35.7. W from Q stands for 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 is necessitated by lack of additional information. - The simplest mechanism which can provide a physically 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 in the following way: Sample No. 32 The consistency of results i s forced by the i n i t i a l assumption that this sample represented cogenetic quartz- - calcite - haematite pairs which are i n thermodynamical equilibrium. Graph 5.1 was based on this and i t had as a consequence the modification of eqn. 5.5 to eqn. 5.9. But even when one applies eqns. 5.6, 5.7, and 5.8 instead of eqns. 5.10, 5.11, and 5.12 the consistency for this sample is far better than for any of the other samples. A thin section study revealed a. sequence of crystallization, the large equigranualar quartz was formed f i r s t followed successively by haematite, calcite, dendritic haematite and fine grained * quartz. Sample No. 33 The three different temperatures for this sample may be explained by diffusion of oxygen in the calcite, by isotopic disequilibrium precipi-tation of the quartz, or by the possibility that the quartz was formed at a somewhat higher temperature than the calcite and haematite. In the last The author feels i t may be concluded the quartz calcite 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 British Columbia determined the order of crystallization of the minerals under consideration by examining thin sections of these samples. -70-two cases S Q w i l l be too low, while in the f i r s t case w i l l be too high. If oxygen diffusion in the calcite occurred then tq^ (i.e. the tem-perature as derived from eqn. 5.10) should be right. However i t i s reasonable to suppose that no significant oxygen diffusion took place when one considers the quantitative information available about:' oxygen diffusion in calcite (see sect. 7.2). Moreover samples 34 and 35 do riot show a pattern which could be caused by calcite solid state diffusion. If the inconsistencies are caused by a too low value for <5q then t^jj should be right. From graphs 5.1 and 5.4 i t may be concluded that & Q i s 1.3 too low. This can be checked by calculating tq^ and tq^ and using a S value for quartz of <SQ + 1.3. This gives tqQ .= tqjj = 104° C and a S value for the water as calculated from the quartz of —42.0 with respect to PDB. Geological evidence should decide whether this i s a case of disequilibrium formation of quartz, or that the quartz was formed at a slightly higher temperature. If the quartz was formed f i r s t , i t s temperature of crystallization w i l l have been 114° C. Pure coincidence i s responsible for the equivalence of a ^ as calculated W from quartz, and & w as calculated from calcite at a temperature of 150° C. The coincidence i s caused by the fact that d KCW / jJ^QC 150 - 114 d T / d T ~ i50 - 104 in the temperature interval 100 - 200° C. Sample No. 34 The different temperatures of table 5.4 may be explained by oxygen -71-diffusion in quartz and haematite or by a later crystallization'of these minerals. Russian results (56) give a qualitative indication that i f oxygen diffusion in quartz was significant, i t should have been s i g n i f i -cant in haematite too. The pattern can not be explained by oxygen diffusion in calcite. If diffusion occurs, the crystalline state can reequilibrate with the hydrothermal solution at a lower temperature than the crystallization temperature. Haematite diffusion w i l l not cause any great changes since the fractionation between water and haematite i s very small. A l l data w i l l be in harmony i f - the quartz was formed at a slightly lower temperature, - the quartz, because of solid state diffusion, 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 right and & y should be -35.2 with regard to PDB. The temperature at which the quartz may have crystallized or reequilibrated i s 290° C. The order of crystallization as established from thin section study i s as follows: carbonate, and quartz and haematite simultaneously. Sample No. 35 Qualitatively the explanation i s the same as for sample No. 34. tCH = 342° C i s supposed to be the right temperature of calcite crystal-l i z a t i o n . The quartz C?~^/0^ ratio may have been frozen in at 327° C under equilibrium conditions. Thin section evidence gives as order of crystallization carbonate, quartz, haematite. -72-200 - 250° C 250 - 350° C 275 -450° C 320 - 550° C 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: chlorite zone biotite zone garnet zone staurolite zone: Following the procedures of sect. 4.7, the influence of pressure w i l l be again illustrated for the reaction: | CaCOg6 + H 20 1 8 = | CaCOg8 + H 20 1 6 At t = 200° C and a pressure of 1000 bars one finds a change in fractiona--4 tion factor of 3.7 x 10 i f pressure i s neglected which amounts to an error in temperature of approximately -7° C. One should be aware that the assumptions underlying this method become worse at high temperatures. On the other hand, Clayton derived the equations 5.1 and 5.2 under pres-surized conditions. Finally i t should be remarked that although the figures mentioned in table 5.4 look very accurate, they are not necessarily accurate, because of uncertainties of pressure conditions and of activity coefficients. Moreover, the s t a t i s t i c a l basis for eqn. 5.5 is physically not acceptable in the author's opinion and this basis i s absent for the alternative eqn. 5.9. From the above discussion i t should be clear that oxygen isotopes are very useful for geothermometric purposes. However the interpretation of the results i s not as straightforward as one could wish. Specifically high temperature geothermometry is. in comparison with carbonate low tem-perature palaeothermometry f a i r l y intricate, because of the possible occurrence of diffusion and the uncertainties about the pressure and activity dependence of p( . These three factors are relatively unimportant in low temperature :palaeothermometry, but may play significant roles in 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 in excited states (quantum mechanically) and thus the square root expectation value of x (eqn. 3 .7) w i l l increase and thus the, pressure dependence (see sect. 3 .3) w i l l become more significant. On the other hand in eqn. 3.5 there appears a tempera-ture term in the denominator which makes the pressure dependence at high temperatures insignificant. The thermodynamic activity of the hydro-thermal solutions i s not known, hence this factor cannot be evaluated. Diffusion becomes more pronounced at higher temperatures, hence one measures freezing in temperatures of the C r ^ / O ^ ratio rather than tem-peratures of crystallization of a particular mineral. It should be possible to evaluate this effect, once the necessary diffusion constants are known. -74-CHAPTER 6 ISOTOPIC EXCHANGE REACTION KINETICS 6.1 Introduction In this chapter isotopic exchange reactions are discussed from a kinetic viewpoint. The usual assumptions which are made in the derivation of rate equations are pointed out. F i r s t the homogeneous exchange reaction i s considered in some detail, followed by the hetero-geneous ones. In the case of a heterogeneous exchange reaction three possible rate determining steps are discussed, i.e. diffusion in phase I, diffusion in phase II, and the surface reaction. 6.2 Homogeneous exchange reactions Returning to the reaction w AXV + v BXJ = w AX# + v BX^ the fractionation factor may be defined as where •= total concentration of element X occurring in compound AXy and A x | in gram atoms per unit volume. cj| .= concentration of X^. In calculations on how the reaction proceeds, the following assumptions are usually made implicitly or explicitly: (a) cf « C A and eg « C B Assumption (a), i s always just i f i e d in oxygen studies because of the 18 relative rarity of 0 . (b) The distribution of X$ i n each of the molecular species i s random under equilibrium conditions. There are no X —-X bonds in either of the compounds. This means that the partition function of the variously labelled 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 isotopic nature of the molecule involved. This assumption i s justified by a theorem due to Slater (142): The rate of bond rupture i s only dependent on the two atoms involved, and independent of the rest of the molecule. Bigeleisen (12) concluded, consequently, that i f this were true for bond rupture, i t should also be true for bond formation. (d) Assumption (b) i s valid throughout the exchange process. This i s just i f i e d by assumption (c). (e) The rates of the forward and the reverse reaction are similar. Bunton et a l . (23) have shown that only a minor error i s introduced in this way.' -76-(f) A l l isotope effects are neglected. This follows in part from the previous assumptions. Due to the small mass difference between and Cr^ and the small concentration of , the errors introduced in this way w i l l be only minor ones. Thus d CA d Cg dt ~ ~ dt 6.1 Cg c A - Cj C| C B - eg " CB CA " CA C 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 CA# CB# 6 . o c A - c A # c B - c B # because there i s no isotope effect. Consequently -77-Using eqns. 6.1, 6.2, 6.3, and 6.4 d C # A _ dt C AC B 6.5 This integrates to 1 - F = C A J - C A # C J ; - C J exp [-'dr(c* L B + C B ) * 6.6 where CA# = the i n i t i a l value of at t •= 0, F•= fraction of exchange Which has occurred. For practical purposes where 1 - F • = rA©o rA rA " rA Aoa o 6.7 ,181 r A = ,16 JA 6.8 These.or similar equations have been derived by several investigators (23, 89, 117, 118). Bigeleisen (10) has derived formulae for the ratio of the rate constants for the competitive reactions of isotopic 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. In this kind of exchange one of the following'three processes may be rate determining: - oxygen diffusion in phase I, - oxygen diffusion i n phase II, - surface reaction by which the exchange of'oxygen isotopes between phase I and II takes place. Consider the reaction w AXy (solid) + v BxJ (liquid) = w Axf (solid) + v BX„ (liquid) and define n = total mass of exchangeable atoms, in gram atoms n^ := total mass of atoms X^, in gram atoms C ,= concentration of exchangeable atoms (gram atoms/unit volume) C = concentration of X r _ n# _ C# r " n" " F A = abbreviation for compound AXV (solid state) B = abbreviation for compound BX W (liquid state) n A + nB V = volume S = surface area Dg = diffusion constant of X#. or X in XB W -79-Assume that i n i t i a l l y (t = 0): nA# = CA# = 0 then, nB# + nA# = ng# . o further when equilibrium i s attained (t = 0 0 ) n # ~ nB or rA ^ " r B o c " Hence r~> = rB (1 - -q) 6 - 9 LO0 _ XB o Although the situation w i l l not be very common i n geology, i t i s possible that the diffusion of i n the adhesive layer of B surround-ing A i s rate determining for the exchange. The steady state concentra-tion gradient in the adhesive layer w i l l be linear. This layer also plays an important role in the Nernst-Brunner (22) theory of dissolution. It i s much thicker than an absorbed film. It may be identified with the boundary layer in hydrodynamic theory. This theory gives for i t s approximate thickness 'US 6.10 N p-\r -80-where = viscosity of the f l u i d , p = density of the f l u i d , % = linear dimension of the surface of the solid, ~IT = velocity of the f l u i d , L = thickness of adhesive layer. # For the diffusion of X and X In this layer one can apply Ficks law d nB# = S A % C B r B " r B<A) 6.11 dt • " " u L where r ., . = r n at the solid - li q u i d interface. B(A) B H Assuming that diffusion in the adhesive layer i s rate determining r B ( A ) ~ r A Hence r B ~ r B ( A ) = \ ( r B " r o c ) _ *oo - rA . 1 - q is obtained by combining eqns. 6.9 and 6.11. Therefore rcws - r A r B ~ r e * ° 1 - F = = r ° ° r B Q " 6.12 S A % t = exp ; 6.13 -81-for the case that diffusion in the adhesive layer is rate determining. It i s also possible that the surface reaction i s the rate determin-ing step. When one considers the exchange between the f l u i d and the # solid phase only, then the number of atoms X and X which pass the interface in one direction i s equal to the number that pass in the opposite direction. ft - number of exchangeable atoms which pass one cm2 of the interface in one direction per second. - ^ ! = S A " ( r B - r A ) Applying eqn. 6.12 one obtains after integration .ft S A 1 - F = exp t 6.15 when the surface reaction i s rate determining. Most l i k e l y i t i s the solid state diffusion of X and X17 which is rate determining. Solid state diffusion has been treated by several authors; among the more recent of these are Crank (44) and Jost (99). The solution of this problem i s the solution of the diffusion equation ^ D ^ f i t t e d to the proper boundary conditions. If the solid 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 -82-1 - F = i * - c cJ -c# A.© o 4r' 7" — e*P T T 2 L— 2p+l " p^O - (2P where h i s the thickness of the slab. When the. solid has the shape of a cube F = , 512 z LP=o (2p+l)' exp ( - (2p+l) 2 " i f2 DA t 6.17 6.18 where h i s the: length of a side of the cube. Anisotropy i n solids can be dealt with by varying h for the different crystallographic directions. When the solid has the shape of a sphere Oo P=l 2 exp P 2 T 2 D A t 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 solid phase had the uniform concentration . Instantaneously, after t = .0 the surface of the solid phase reequilibrated and acquired the concentration CA . Compared with the slowness of solid state diffusion the reequilibration of the surface layer of the solid i s instantaneous. . Urey et a l . (161) give some numberical results for eqn. 6.18, These simplify considerably the process of calculating the diffusion constant from, a set of experimental data. -83-TABLE 6.1 Solutions of eqns. 6.17 and 6.18 Ref. (161) D A f 2 t 1 - F 1 - F h 2 • for the slab for the cube 0.1 .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 The theory developed i n this chapter, especially the diffusion equation, i s the background for the material presented in chapter 7. -84-CHAPTER 7 DIFFUSION 7.1 Introduction As far as homogeneous exchange reactions - are concerned, Brodsky (21) has given general rules for the relative exchange velocities.for reac-tions between water and other compounds. Many homogeneous exchange reactions for oxygen have been described (see Dole (55)). Publications about heterogeneous oxygen isotope exchange reactions are relatively rare and only a few,of direct interest to earth scientists are known to the author. Cameron et a l . (25) have investigated the systems vanadium pentoxide (solid) - water - oxygen (gaseous) and vanadium.pentoxide -oxygen. This i s one of the few papers in which surface reactions as well as solid state diffusion are considered. They found that the oxygen exchange in the system vanadium pentoxide - water - oxygen.between 400° and 550° C was about 25 times faster than exchange i n the system vanadium pentoxide - oxygen, under similar conditions. They also found that whether the exchange rate was surface or diffusion controlled depended on the surface/volume ratio and on the cr y s t a l l i n i t y of the -85-vanadium pentoxide. High specific surface values and an amorphous phase favoured a surface reaction controlled exchange rate; while for crystal-line solids and for low specific surface values•a diffusion controlled rate i s most l i k e l y . In the case of a diffusion controlled rate one finds that i n i t i a l l y the rate of exchange i s relatively high, but drops as exchange proceeds. When the surface becomes saturated .the exchange rate drops under the controlling, influence of solid state diffusion. Johnston et a l . (98) have reported essentially the same thing for the oxygen exchange between uranium oxides and water. Diffusion mechanisms are known for the most simple compounds only. Hence, i t i s not astonish-ing that the catalytic 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 calcite. The size of their crystalline grains was smaller than 50 . 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 crystalline i s shown too by Dontsova (58). She performed a series of exchange experiments in which quartz, sphene, albite, mica, and diatomite exchanged their oxygen with the gaseous carbon dioxide. Unfortunately, these essentially very interesting experiments have qualitative s i g n i f i -cance only, since the grain sizes used were very small (12^) and the effect 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 relatively rapid. At 960° C the half time of this exchange reaction i s 47 minutes. At 750° C the half 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 in the dry system s i l i c a glass - oxygen is confirmed by Bank (8). However, this should not be generalized. Kingery and Lecron (102) have shown that isotopic exchange between carbon dioxide and glass occurs, and that the chemical composition of the glass plays an important part. The evidence these last two investigators have presented to show that the exchange rate i s solid state diffusion controlled i s unsatisfactory in the author's opinion. As i s done very often, they based their-conclu-sion concerning the rate determining step solely upon the exponential 18 variation with time of 0 concentration in the gas phase. However this exponential variation does not uniquely indicate a diffusion process as the rate determining step. The surface reaction controlled rate of 1 8 exchange shows a similar exponential decay for the 0 concentration of the gas phase ( c f . eqns. 6.19 and 6.15). To distinguish the two processes one should very the surface area across which the exchange takes place. Solid state diffusion as a cause of isotopic fractionation has been treated by Senftle and Bracken (140). They concluded that generally the effect was only of minor importance. 7.2 Oxygen diffusion in carbonates Diffusion constants for the carbonate ion.in carbonates have been ^87-estimated by Urey et a l . (161) for several temperatures (15° - 160° C) showing a variation from 4.4 x 10 2 3 cm^sec - 1 to 1.9 x 10"^ cm 2sec - 1. Haul and Stein (90) have measured a diffusion constant for carbon in -4 calcite under dry conditions. They obtained DQ = 4.5 x. 10 2 -1 exp - 58000/RT cm sec . The activation energy i s expressed in calories. Haul and Stein did not reach a conclusion about the mechanism by which the diffusion took plaqe. They considered three diffusing units: - carbonate ions, the oxygen- diffusion should be about three times as large as D Q , -carbon dioxide, D Q should be about twice D Q , - carbon atoms. Urey et al.'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 DQ under wet conditions at temperatures of 300° C and 20° C. It i s realized that i t may not be proper to c a l l these constants, diffusion constants. Assuming that D Q = 2 D Q , the following estimates were made. TABLE 7.1 "Diffusion" of under wet oxygen in calcite conditions Temperature ° C Diffusion constant D Q 2 -1 cm sec 20 3 x TO""24 300 5 x 10~ 2 2 -88-These values resemble those of Urey et a l . quite closely. : However the speculative nature of these values can not be overstressed. Urey et a l . (161) have calculated, on the basis of their estimation of D Q , that a calcite crystal of 1 mm. dimensions w i l l retain 96.4% of 18 i t s original 0 concentration, relative to the equilibrium concentration +8 of a changed environment for 7 x 10 years, provided the temperature remained at 20° C during this period. If the temperature was raised to 100° C this period would be only 64000 years. These figures do certainly not contradict the available empirical evidence. It i s found that coarse crystalline material retains i t s original Ql8yQl6 r a t ^ 0 very well. Beartschi (5) has measured a change in ^ value of 5 over a distance of 1 cm in a large calcite crystal of unknown age. Urey et a l . (161) have observed thataJurassic belemnite guard maintained i t s different O-^  concentrations due to seasonal temperature variations, while the O^ /O''"6 ratio of the chalk in which the belemnite was embedded was not preserved. Compston (38) has measured, variations of 0.5% i n the O^/O 1 6 ratio for different portions of a Permian brachiopod shell. . As far as the author knows no occurrences have been published of preservation 18 i f\ of 0 /0 ratios by fo 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 16 0 /0 ratios of the Leadville limestone. They noticed the coarse cry-stalline dolomite showed a linear variation of i t s value with distance. Near the Gilman ore S> coarse dolomite = + 16.5 and at 10,000 feet away from the ore Scoarse dolomite = + 23. But the dense fine grained dolomite which occurred together with the coarse material does not show -89-this linear variation; i t has essentially the same value at the ore and at 10,000 feet away from i t : ^ dense fine grained dolomite = + 23. This suggests solutions came up via the Gilman ore conduit and moved radially away from i t . A temperature gradient was established which was negative away from the ore. 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 fine grained dolomite could exchange i t s oxygen with the cooler solutions. It hap-pened at the temperature characterized by £ = 23 ( i t i s assumed the & of the solution was constant) the exchange became negligible, because of the exponential decrease of the diffusion constant with temperature. The original gradient i s best reflected by the most coarse material. This explanation i s not a unique one, but i t s essential features are i n agree-ment with the general interpretation of the Gillman ore and i t s surround-ing as given by Loyering and Tweto (107). 7.3 Oxygen diffusion i n quartz The amount of solid state diffusion data available on quartz i s very small. D Q along the c axis of quartz was estimated to be 3 x 10 1 1 cm 2sec _ 1 at 500° C by Verhoogen (164). This value i s based on el e c t r i c a l conductivity studies. Verhoogen assumed that the con-ductivity was 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 for quartz were calculated by the author (table 7.2). These calculations indicate Verhoogen's value for D Q could be too high by about two orders of magnitude. Wyart et al.'s experiments are the only set of exchange -90-data published which allow some quantitative conclusions and which have a definite bearing on geological circumstances. TABLE 7.2 Oxygen exchange between water and sili c a t e s during a period of 24 hours. Ref. (178) Sample Grain size Temp. °C Press, bars F ( * ) D 0(**) 2 -1 cm sec Quartz 60 360 170 0.10 -14 7.6x10 Quartz 60 ,445 250 0.14 1.7xl0~ x o Quartz 60 610 350 0.16 2.4x10 Microcline 25 690 400 0.37 2.8xl0~ 1 3 Granite - 800 500 0.26 -Granite (fused) - 800 1800 0.72 -' (*) F - fraction 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. The importance of these data w i l l be evident from the following hypothetical example. Assume an amount of quartz i s precipitated at 600° C from an aqueous solution under equilibrium conditions. The 18 16 0 /0 ratio 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-isotopic exchange has occurred between the aqueous solution at 500 C and the quartz precipitated at 600° C? For sake of simplicity the quartz i s supposed to have a cubic shape and to be isotropic. Using eqn. 6.18 and data of table 6.1, the calculations are readily performed. The results are tabulated in table 7.3. TABLE 7.3 Oxygen exchange between water and quartz at t = 500° C h v 'cm = o . i 0.2 f= 0.5 IO" 2 5 hours 1.3 days 11. 6 days 5xl0 - 2 5.5 days 33 days 289 days 10" 1 21 days 130 days 3. 2 years 5 x l 0 _ 1 1.5 years 9 years 79 years (*) h = side of the cube. (**) A the average change of o value for the crystal. A o = 0.1 i s about the present-day accuracy for measuring values. = 0.2 means an error in temperature determination of 10° C at t .=• 500° C. 0.5 means an error in temperature determination of 30° C at t = 500° C. -92-These results indicate that diffusion i s a real problem in high tempera-ture geothermometry. The temperatures measured in this way represent only freezing, in temperatures of the ratio. Of course, i f the quartz i s precipitated from a dry melt, the measured temperatures w i l l be nearer to the true crystallization temperatures because water catalyses the exchange considerably. 7.4 Oxygen diffusion in silicates The chilled gabbroic.margins of the Skaergaard intrusion have 3.7 which i s nearly 2.5% 0lighter than normal olivine basalt. Taylor and Epstein (144, 149) have tried to explain this by postulating that the minerals i n the chilled margin have equilibrated with meteoric water supposedly present in the country rock. Here a somewhat different explanation i s advanced. According to Kennedy (101) the cooled edges of the intrustion w i l l have been enriched i n water. This i s also indicated by Wager (172). From the example given in sect. 7.3 i t i s plausible that at 900° C the exchange of oxygen between silicates and water, i s rapid. It i s supposed that at about this temperature the chilled margins s o l i d i f i e d . To evaluate the fractionation factors for the oxygen exchange reaction between the orthosilicate group and water one has to know the normal modes of the internal vibrations of the orthosilicate group. These are known but not too accurately because of the d i f f i c u l t i e s in assigning force constants for the orthosilicate group. The Teller-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 orthosilicate group. The frequencies of the remaining two normal modes of the substituted orthosilicate group were estimated in such a way that the Teller-Redlich product rule was satisfied. Following the procedures outlined in section 2.2, the fractionation factor for the reaction H 2 0 « + i U 1 6]" 4 - H 2 0 " + | 18 S i 0 4 \_ -4 was approximated for various temperatures. The results are tabulated in table 7.4. TABLE 7.4 Fractionation factors for the system orthosilicate 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 is enriched in 0 with regard to the orthosilicate ion. These fractionation factors should not be taken too seriously, since a l l solid state effects were neglected. But, since the internal vibrations of the orthosilicate ion are mainly responsible for the fractionation, i t seems l i k e l y that the calculations are quali-tatively significant. The extremely low values found for the chilled margin of the Skaergaard rocks may be the result of equilibration of the sil i c a t e s with water from the intrusion i t s e l f and from water released by the country rock. Assuming the calculated fractionation factors to be satisfactory, then at 900° C water with a ^ / g M 0 W = + 7 w i l l be i n isotopic equilibrium with olivine with ^SMOW = + 2- T ^ i s r e f e r s t o equilibrium conditions though i t i s noticed by Taylor and Epstein (144, 149) that the chilled marginal olivine gabbro i s not i n isotopic equi-librium; p l a g i o c l a s e " ^clinopyroxene = -1-3 while this value i s positive under equilibrium conditions. Due to the rapid rate of cooling diffusion became negligible before equilibrium was reached. Besides i t is to be anticipated that the oxygen diffusion constants are different for plagioclase and pyroxene. Further one should take into account that above 220° C, HgO18 i s more volatile than H 20 1 6, under 1 atmosphere pressure. This may cause a somewhat anomalous % value of the water in the chilled margins. To recapitulate, the low & value of the chilled . border rock i s due to equilibration between water (from the wall rock and the intrusive) and the chilled border rock. But a low i n i t i a l S value for the water i s not postulated, as was done by Taylor and Epstein, because i t i s believed here the fractionation factors for oxygen exchange -95-between sil i c a t e s and water are close to unity or smaller than unity at 900° C. This i s physically l i k e l y and may explain the exceptionally low & values of the chilled borders. The catalytic action of water on exchange reactions i s also evident from the gneissic inclusions which are found in the Northern border group of the Skaergaard intrusion. Notwithstanding these inclu-sions are fused by the intrusion, they have essentially the same & value as the country rock, while ^ " 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 of intrusion. The Skaergaard melt was apparently very dry (101) and consequently no significant exchange occurred. Likewise clinopyroxene from the fayalite - ferro gabbro contains more or less the original 0 1 8/0 1 6 ratio of wollastonite from which the clinopyroxene i s an inversion product (149). In conclusion, i t i s suggested here that under wet high temperature conditions solid state oxygen diffusion can be important. -96-CHAPTER 8 OTHER PROCESSES BY WHICH OXYGEN ISOTOPES MAY BE SEPARATED 8.1 The Rayleigh d i s t i l l a t i o n process (130) The derivation of the Rayleigh equation comes from consideration of an isolated quantity of li q u i d crystallizing at constant temperature. An assumption i s made that no isotopic exchange takes place between the crystalline phase and the melt. Using the symbols defined as follows: n = total mass of exchangeable atoms in gramatoms, n^ = total mass of isotopic atoms, f - indicates the li q u i d phase, s - indicates the solid phase, r =•«* n And the i n i t i a l conditions of t = 0 sec, n g = 0 an arbitrary stage of the so l i d i f i c a t i o n process can be described as; n^17 = n^ r ^ Hence, dn^ = rif drf + r ^ dn^ 8.1 -97-and dn g^ •= - drif* = - r g dn f 8.2 where r s i s the value of r g for the quantity dn^. The fractionation factor i s given by r' CX* = _§. 8.3 Therefore, dr.c dn^ —L = _ i ) — £ 8.4 r f n f which integrates to (<* - 1) r f = r f F / J 8.5 r o r which i s the Rayleigh equation. Where, F o and n.c i s the i n i t i a l value of n^. o r To obtain a value for r g (this i s the average value for the total amount of precipitate at any moment), n f 0 r f 0 = n s r s + n f r f 8.6 -98-n s = n f " n f o 8.7 and i s given by eqn. 8.5, thus r, s 1 - Ff Q 1 - Ff 8.8 It i s crucial that the fractionation factor remains constant during the process. Therefore the following requirements should be met: - The temperature remains constant during the total process. -The 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 li q u i d does not change. -The solid phase does not exchange oxygen with the remaining liquid. -The system is closed. It i s clear that these stringent requirements are never met under the usual capricious geological conditions. Semiquantitative useful results may be obtained as is demonstrated by Dansgaard (46) for water evapora-tion , and by Taylor and Epstein (151) for the solidification of the Skaergaard intrusion. 8.2 Gravitational settling One may envision that gravitational forces may cause a measurable separation of l i g h t and heavy isotopes i n a melt. Using Stokes' formula, 8.9 -99-one may estimate the velocity v, at which the two isotopically different flow units w i l l be separated. tyj = viscosity of the melt, a = characteristic dimension of the flow unit, M = weight i n grams of the flow unit, g = gravitational acceleration. It i s unlikely 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 in s i l i c a t e melts. But following the time honoured practice of neglecting those aspects of the problem which can not be evaluated, one can proceed with the calculations. Estimating that the characteristic radius "a" of a flow unit equals 8 17 —1 1.5 x 10 cm, one finds v = 9 x 10 cm sec i f only one oxygen atom in the flow unit i s replaced by 0 1 8. Hence in 3 x 10 1 2 years a separation of 1 cm would be obtained. A value of 21 poise was selected as the viscosity for the melt at 1450° C. The Handbook of physical constants (16) gives viscosities for melts of natural occurring rocks which are much greater than the value used. Hence i t seems that this mechanism i s not significant. 8.3 Other possible separation processes When a thermal gradient exists in a melt the Soret effect w i l l be operative, i.e. heavy molecules w i l l in effect migrate towards cool regions and l i g h t molecules towards warm regions. In the Clusius-Dickel mechanism use i s made of the Soret effect. By means of a system of -100-convection currents the heavy isotopes migrate effectively towards the cool wall and are concentrated at the bottom of the system while the light isotopes are concentrated at the top. These mechanisms could certainly be important in nature. 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 diffusion constants for oxygen in s i l i c a t e melts. The mechanism of solid diffusion can not produce significant isotopic separation as was shown by Senftle and Bracken (140) and by Grant (85). The reason for this i s the extraoridinary smallness of solid state diffusion constants. - 1 0 1 -CHAPTER 9 18 1 ft 0 /O RATIOS OF ROCKS 9.1 Igneous rocks Unfortunately the extensive work done by Vinogradov et a l . (166, 167) and by Schwander (137) could not be considered in this review. As remarked earlier Vinogradov's work can not be correlated with results obtained by other investigators (see sect. 1.5). Schwander's con-clusions are at variance with present-day observations; this i s attributed to a systematic error in his measurements (28, 32, 144). 9.1.1 Southern Californian batholith - Acidic rocks The batholith 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 in table 9.1 and form the basis of graphs 9.1, 9.2, and 9.3. It was shown in chapter 5 that 1000 In K^ = ^A ~ tSg = ^ AB. Hence A AB i s essentially only temperature dependent. In graphs 9.1, 9.2 and 9.3 the A values of various mineral pairs are plotted respectively against ^ Q - C,^Q - K f eldsp., and /\ K feldsp. - biotite. These relationships are essentially only temperature dependent. -102-i f the pairs under consideration are in equilibrium. The inclined lines give the straight line relationships between 2 pairs of minerals; these lines have not been calculated, but are drawn by eye. The vertical lines marked with capital letters, connect the various mineral pairs 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 in of Cr- /0 ratios followed in order by Shakeflat quartz monzonite, Rock Creek pegmatite and Bonsai tonalite. The last 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 isotopic equilibrium. It is also evident from the graphs that the minerals are not i n complete equilibrium but are approaching i t . This feature could be expected on grounds of solid state diffusion. But this i s also explain-able when one considers the crystallization process somewhat more closely. This i s done by Taylor and Epstein (148) who focussed their attention on the following two possible sequences: - During crystallization only the outer portions of the crystals are in continuous equilibrium with the melt. The inner parts of the crystal do not reequilibrate. Zoning in plagioclases i s explained in this way. This i s considered a Rayleigh : process by Taylor and Epstein. - The crystal i s at a l l times in isotopic equilibrium with the melt, because continuous exchange between melt and crystal takes place. The possible relationship resulting from these two processes is shown graphically by Taylor and Epstein (148) for a simple binary system from 18 which minerals A and B crystallize. A i s deficient i n 0 with regard -103-TABLE 9.1 Values with respect to Hawaiian sea water(*) for various rocks and their constituent minerals. Ref. (147) s CU o -P £> •H •P CJ c O OJ C CU CO •p T3 4-> •H X C H •H •rl > O CU CO U a •H U cu CO CU H >> -p cfl O O H co o o u co o co bD T3 c CO H co •H O CU ,£> 3 CO Q bo quartz plagioclase K. feldspar biotite muscovite hornblende clinopyroxene orthopyroxene olivine apatite magnetite ilmenite 6.4 5.1 6.3 5.1 6.6 10.2 7.5 6.5 5.9 6.6 9.1 1.6 7.4 5.9 2.1 total rock S 5.2 Hawaiian sea water 6.0 6.6 7.0 6.3 SMOW — 0 -104-TABLE 9.1 (continuation) CN O H U H ,0 L O cC O O co )H H Xi L O CO O CD 4-> H -H cC H CO res C C o o m -P o C D co P O 'rl •"3 H C C O • C D C P •P »H 2 h o O 03 co o T3 C O O CO U D J O quartz plagioclase 6.8 K. feldspar biotite muscovite hornblende clinopyroxene 5.6 orthopyroxene 5.6 olivine 4.5 apatite magnetite ilmenite 6.7 5.7 10.3 8.5 5.4 6.9 6.7 9.7 8.0 5.2 6.6 9.5 8.5 '4.4 7.9 total rock 6.0 5.8 8.3 7.8 8.6 -105-TABLE'9.1 . (continuation) S «H -P A! rH to CU CU CU cu X O r-l -P C C U + J +J 3 «H HH 'rl O CU rH ' H ' H o - o q -P -p CJ-P C O P • n o c u o rH *H co c e o r O c o ro c ^3 ro o 5c B o b 3 JH r C O H M o c u cocu psbo co 6 w o o Pi On QZ Cu quartz 9.9 10.3 11.9 10.5 plagioclase 8.8 8.9 9.4 10.3 8.6 K. feldspar 9.1 9.0 8.4 10.5 8.8 biotite 6.6 5.4 4.7 7.1 muscovite 7.3 hornblende 6.4 clinopyroxene orthopyroxene olivine apatite magnetite ilmenite 2.8 total rock- 9.2 9.1 8.5 10.9 9.4 -106-Q - Bi feldsp - Bi lag - Bi - K feldsp LEGEND Q - quartz Plag - plagioclase Bi - Biotite Hbl - hornblende A Q _ K feldsp A Q - Bi A K feldsp - Plag A K feldsp - Bi A plag - Hbl A plag - Bi 0 + F G Woodson Mtn. granodiorite Rubidoux Mtn. leucogranite Shake f l a t monzonite Rock Creek pegmatite San Jose tonalite Bonsai tonalite Ramona pegmatite - Plag 0.5 1.0 1.5 2.0 AQ - Plag Graph 9.1 - Fractionation relationships between mineral pairs in acidic rocks (see text) I. 1-107-Q - Bi •H CQ I <l •rt 03 I U CO CL, co T 3 i—I <D •rt CQ « i—I CK <I DO CO H eu i o* CN DX) CO l—I t CH CO T 3 i—I CD K feldsp - Bi Plag - Bi LEGEND A Q - Bi A K feldsp - Bi A Plag - Bi A Q - Plag A K feldsp - Plag Woodson Mtn. granodiorite Rubidoux Mtn. leucogranite Shake f l a t monzonite Rock Creek pegmatite Elberton granite K feldsp - Plag 0.5 1.0 T7T A Q - K feldsp Graph 9.2 - Fractionation relationships between mineral pairs in acidic rocks II. -108-5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 _ x * A B C D H LEGEND A. Q - Bi A Plag - Bi A Q - Plag A Q _ K feldsp A K feldsp - Plag Woodson Mtn..granodiorite Rubidoux Mtn. leucogranite Shake f l a t monzonite Rock Creek pegmatite Elberton granite Q - Bi (-0.6)6 0.5 1.0 1.5 2.0 2.5 A K feldsp - Bi 3.0 3.5 Graph 9.3 - Fractionation relationships between, mineral pairs in acidic rocks III. -109-to the melt and B i s enriched in 0 . Crystallization starts with the formation of A, and B does not begin to crystallize u n t i l later. It i s then shown that the f i n a l 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 of eqn. 8.5 Taylor and Epstein calculated the 018 relationships between the melt and the formed crystals. According to Larsen (104) the Southern Californian Batholith was emplaced by magmatic stoping in the following sequence: San Marcos gabbro, Bonsai tonalite, Woodson Mountain granodiorite, Rubidoux leucogranite, and other minor granite bodies. Aptly Taylor and Epstein (144, 147, 148), remark that four samples are most certainly not sufficient to explain the origin of the batholith. Notwithstanding this they have observed: ... "this (oxygen isotope) evidence adds to the growing accumulation of data which suggests that the various rock types of the batholith are of magmatic origin, are intimately related and come from a well mixed source". As evidence for this conclusion they present a variation diagram, which i s reproduced here as graph 9.4. San Marcos gabbro, Bonsai tonalite, Woodson Mountain granodiorite and Rubidoux Mountain leucogranite are plotted by Taylor and Epstein. The other three rocks are added by the author. The information for these three rocks i s obtained from Taylor and Epstein (144, 147). From graph 9.4 i t can be seen that a straight lin e on a variation diagram does not uniquely indicate a monomagmatic genetic relationship. Taylor and Epstein (144, 147, 148) consider i t compatible with the isotopic data that the leucogranite and the granodiorite are differentia-tion products of the Bonsai tonalite magma. But the same isotopic data -110-I 1 I I I __] 7 8 , 9 10 11 6 - Rock Graph 9.4 - Variation diagram showing the relationship between chemical composition and oxygen isotope composi-tion for various rocks. A - San Marcos gabbro B - Bonsai tonalite C - Woodson Mtn. granodiorite D - Rubidoux Mtn. leucogranite 1 - San Jose tonalite 2 - Gabbro N 36-8 3 - Elberton granite - I l l -indicate that the freezing in temperature of the 0l8 / 016 ratio for the mineral pair quartz plagioclase i s far lower for the Bonsai tonalite than for the Woodson Mountain and the Rubidoux Mountain formation. Whether this implies that the Woodson Mountain granodiorite has also a higher temperature of solid i f i c a t i o n than the Bonsai tonalite 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 so l i d i f i c a t i o n temperature than the Bonsai tonalite because A. quartz -biotite and A plagioclase - biotite are smaller for the leucogranite than for the tonalite. This appears to contradict Taylor and Epstein's deduction. If, as Larsen proposed, the parent magma i s gabbroic then i t should have a & value of about 7 (see graph 9.6). But a l l rocks which are formed from this gabbroic parent magma have & values greater than 7. What happened to the excess 016 resulting from this fractionation? The postulated existence of a huge unexposed mafic body with a S value between 5 and 6 would be a suitable deus ex machina. It i s impossible to hold the 3 or 4% original water content of the magma responsible for carrying away the excess Cr^. A simple but tedious calculation w i l l show that i f the original magma contained 3% water and the S value of the original magma was 7, then the £ value of the escaping water should have been -15. The impossibility of this 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 after an intensive and careful analysis of the geological evidence. It i s only demonstrated -112-what could be done with oxygen isotopes i f sufficient data were available. When crystal fractionation i s responsible for the differentiation of a magma, which was a closed system as far as oxygen i s concerned, then the last minerals to be formed should be enriched i n Cr^. The reason 18 for this i s feldspars and quartz are always enriched in 0 with respect to the melt from which they precipitate and these two minerals contain more oxygen than a l l other minerals precipitated from this melt. That the last minerals formed in a system where crystal fractionation has been operating are enriched in CrA i s observed in the Skaergaard intrusion (144, 149). The upper parts of this laccolith which s o l i d i f i e d last show progressive enrichment in Cr^. 9.1.2 Basic rocks Oxygen isotope data for basic rocks are even more scanty than for acidic rocks. Graph 9.5 i s similar to 9.1, 9.2, and 9.3. A l l the 0 1 8/0 1 6 measurements used have been published by Taylor and Epstein (144, 147, 148, 149). A few points are suggested by this graph: - The minerals of the four gabbros form isotopic equilibrium assemblages. - The fractionation factor for the mineral pairs clinopyroxene -magnetite and plagioclase - magnetite do not approach unity in a simple way at high temperatures as i s the case for the mineral pairs considered i n graphs 9.1, 9.2, and 9.3. This i s not astonishing since the fractionation between water and magnetite i s very small and i t i s known that "cross-over" occurs in systems where water i s present (30). - The temperature at which isotopic exchange becomes negligible i s highest for the hypersthene - olivine gabbro followed by the -113-0 0.5 1.0 1.5 ... 2.0 2.5 A Plag - Cpx Graph 9.5 - Fractionation relationships between mineral pairs in basic rocks. -114-hortonolite - ferro 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 peridotite (92, 171). The measured & values for dunite and peridotite range from 5.2 to 6 (144, 147, 148). Balsalts which are supposed to be products of p a r t i a l melting of the peridotite have l v a l u e s from 6 to 7. Assuming that this difference i s real> one faces the question of what happened to the excess 0^ created in the process of p a r t i a l melting of peridotite. For the time being the question w i l l remain unanswered, again due to lack of sufficient information about oxygen isotope distribution in rocks. 18 16 Graph 9.6 summarizes the information available about 0 /0 ratios in different rock types. 9.2 Sedimentary rocks 9.2.1 General In the weathering process and during the erosion of igneous rocks the minerals w i l l in general exchange their oxygen with the hydrosphere when they undergo chemical alteration. Isotopic exchange with the atmosphere i s of no importance (see also Dontsova (58)). If the igneous rocks are reduced to detrital fragments without chemical alteration, exchange i s less l i k e l y to happen (see table 9.2). This can be seen from Silverman's data (141). Ref. : " — ~ l — I I I I I I 1 I I 1 I I 1 | 5,52 Marine Limestones (33.8) 5 Calcareous Tufa 5,52 Calcareous Sinter 38,52 Fresh water Limestones 5 Vein Carbonates 5 Carbonatites 5 Intrusive Carbonates 5 Metamorphic Carbonates 146 Detrital Sed. Rocks 146 Meta Sed. Rocks 147 Metamorphic Rocks 147 Granitic Pegmatites 147 Granites and Granodiorites 147 Tonalites 147 Anorthosites 147 Gabbros and Basalts 147,141 Peridotites and Dunites 148 Skaergaard 141 Meteorites 146 Tektites i l l 1 i i | i i i i i i i i i 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Graph 9.6 - Oxygen isotope composition of various rock types, a l l c5 values with respect to SMOW. -116-TABLE 9.2 Q18 / 016 ratios for various quartzose rocks Sample % secondary silica! St. Peter sandstone 46 11.0 0 Basal breccia 45 15.7 10-15 Wishart orthoquartzite F--75 15.9 20 (*) c v ' o • values are with respect to SMOW from Glayton and Mayeda (34). Hydrothermal solutions usually have a higher 0 1 8/Cr^ ratio than the hydrosphere, besides fractionation factors at lower temperatures are greater (differ more from unity) than those at igneous temperatures. Thus the net result i s that minerals which are precipitated from the hydrosphere usually have a higher S value than their igneous counter-parts. This i s shown for quartz and can also be seen when carbonatite b 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 for distinguishing marine and nonmarine carbonates and cherts by means of the 0 1 8/0 1 6 ratios (see 31, 52). This method i s -117-quite powerful when one i s dealing with post Palaeozoic sediments. Older marine sediments become less distinct because of exchange with ground 18 16 water which has lower 0 /0 values than marine water (50). Often the exchange takes place by means of a reversible hydration mechanism, as i s the case for carbonates, thus the exchange reaction w i l l be faster i f the circulating ground water has a pH ^ 6 (120). The grainsize of the sediment i s of prime importance (see chapt.7) as far as exchange i s concerned. This was shown by Urey et a l . (161) and also by Gross (86). Other factors are pressure and temperature, which may promote dissolution and reprecipitation, during which exchange most l i k e l y occurs. Graf (84) published recently a compilation of 0l8 / 016 ratios for sedimentary carbonates. 9.2.2 Origin of chert Degens and Epstein (52) have tried to establish the origin of chert. To this end they have measured the O*-8/0^ ratios of coexisting carbonates and cherts of marine and fresh water origin. From their data (table 9.3) some, interesting conclusions may be drawn. If one assumes the value for ocean water has been more or less constant and approximately equal to zero since the Cambrian, then the S value for ground water w i l l have been approximately -10. Supposing the carbonate was formed in equilibrium with sea water and that oceanic temperatures have always been less than 50° C, then judging from Degens' and Epstein"s work a l l Precretaceous marine carbonates have exchanged their 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 fi 0 /Cr ratios of coexisting marine cherts and limestones No. Sample Age ^Si02/SM0W ^ C a C 03/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) No. Sample Age Sl02/SM0W s CaC03/SM0W Locality 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 to have retained their original 0 1 8/0 1 6 ratios f a i r l y well. A l l Post-18 16 permian marine chert samples (52) have 0 /0 ratios which indicate that they may have equilibrated with ground water. The equilibration temperature w i l l have been between 15° - 20° C, i f the ground water had a S value of -10. This can be deduced from graph 9.7. But a l l Prejurassic marine cherts (only one Permian exception)- either have exchanged their oxygen with ground water with a approximately equal to -15, or they have experienced a temperature of 45° C. The l i k e l i -hood of a temperature rise to 45° C i s d i f f i c u l t to judge without more evidence. The samples under consideration here are from Nevada, Arizona and Pennsylvania; a lowering of the $> value for ground water to -15 over so large an area may mean an isotopic change in composition of the ocean. Unfortunately the PreJurassic carbonates do not seem to 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 -120-Si0 2 precipitated in marine water ( o = 0) SiO precipitated in-fresh water ( c> = -10) CaCOg precipitated in., marine water ( o - 0) CaCOg precipitated in fresh water ( £ = -10) A Si0 2 - CaCO, 10 20 30 40 50 "50 0^ Temperature °C Sraph 9.7 - Relationships between &> S1O2/SMOW a n (* ^ CaC03/SM0W f ° r guartz and calcite,. precipitated under equilibrium conditions from narine ( h = 0) and fresh water ( c> - -10) and the temperature at vhich equilibrium i s attained. -121-be in isotopic 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. They indicate temperatures of over 100° C. The Degens-Epstein paper does not mention any evidence for such high temperatures. 18 16 As far as the origin of the chert i s concerned, the 0 /0 ratios indicate that the supposed change from marine precipitated s i l i c a to chert takes place in a fresh water environment. It i s implied that the system i s open for water and during the formation of chert the SiOv, equilibrates with the water. Alternatively,.it has been proposed that the s i l i c a of chert i s derived from diatomites. This lin e of reasoning was investigated by Degens and Epstein (52). Generally, the modern marine diatomites have 3 values which are very similar to the Postpermian marine cherts. If the chert i s just reorganized diatomite then during this reorganization process the system chert - diatomite has been closed for water, or no oxygen isotopic exchange has occurred, which suggests the reorganization does not proceed via dissolution and reprecipitation. - The diatomite skeleton i s not in equilibrium with sea water. This may be due to biological fractionation. However one would expect a diatomite skeleton, i n i t i a l l y not in equilibrium with sea water, would reequilibrate f a i r l y rapidly (c.f. sect. 7.1). - The fractionation factor for amorphous s i l i c a i s smaller than for crystalline s i l i c a . This i s physically acceptable. From the diatomites one may conclude that: or that: -122-Finally i f one suggests that the PreJurassic chert i s not in equilibrium with the ground water then one i s forced to postulate an even greater change in & value for the ground water or a greater change in temperature. 9.2.3 Origin of dolomite The origin of dolomite i s s t i l l controversial. Recently two important observations were made. 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 penecontem-poraneous replacement of pre-exisiting carbonate. Epstein and his associates (32, 71) noticed that A> quartz - dolomite values were always near to zero, for hydrothermal cogenetic pairs. Under those circumstances A quartz - calcite i s about 10. Degens and Epstein (51) investigated isotopically about 100 samples of coexisting dolomite and calcite. In some of the samples the calcite and the dolomite were of synsedimentary origin. They noticed that there was very l i t t l e difference 18 16 (max. 3°/oo in 0 /0 ratios between cogenetic calcites and "primary" dolomites. If there was a difference the dolomite was slightly enriched 18 19 in both 0 and Or*. They concluded that as the calcite changed to dolomite, almost no isotopic exchange occurred and roughly the dolomite inherited the O 1 8 / © 1 6 ratio 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 calcite. A year later Epstein et a l . (78) reported they had shown experimentally that hydrothermal dolomite had approximately the same ratio as quartz and this reflected the equilibrium d value for dolomite. -123-9.2.4 Origin of aragonite needles The origin of aragonite needles has been traced isotoptically. These needles occur in recent marine carbonate oozes of shallow water origin. It was held they have an inorganic origin. Lowenstam (108) found the needles could be derived from the disintegration of aragonitic calcifications of a great many algae. The algae produce needles which are very similar to those found in recent sediments. Lowenstam and of aragonitic carbonates such as needle secreting algae, oolites, grape-stones and sedimentary aragonite needles, from the Bahama Bank area. Their conclusions are that the oolites are most l i k e l y of inorganic origin, while the aragonite needles have an algal origin. However not everyone (35) seems to be convinced by their logical account. 9.2.5 The oxygen isotope ratio of the ocean The Cr^/Cr^. ratio of the ocean at present i s f a i r l y well known (76). But the same can not be said for the ocean in the past. This causes uncertainty in carbonate geothermometry. Moreover, a knowledge of the Q18/Q16 r a t £ 0 Qf o c e a n s £ n -the past could reveal something about their history. The variation in the oceanic C-^/O^ ratio due to the Pleistocene glaciation has already been treated (see sect. 4.3). Sedimentary carbonate deposits and O18^"*"6 ratios of belemnites make i t f a i r l y certain that the oceanic O^/0-l-6 ratio has not changed significantly from the Jurassic to the present. It i s claimed by Degens that the oceans have had a. constant isotopic composition since the Cambrian (47, 48). In another paper Degens (49) Epstein (112) have measured the range of oxygen and carbon, -124-attempts to show the <^  value of the ocean was +2 with respect to SMOW, 2500 x 10^ years ago. Notwithstanding Degens' positive assertions, the question i s s t i l l far from settled, for Degens' evidence (47, 48, 49) i s not firmly established. The ground for Degens' choice of & value +2 for the ocean 2.5 eons ago, i s a suggestion that ^ * - j u v e n : j j _ e w a t e r = + 2 ( 3 2 ) -However this suggestion was made before i t was realized how commong the "cross-over" phenomenon i s in 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 P P l i e d . Degens' claim of constant oxygen isotopic ratio for the ocean since the Cambrian is based on f o s s i l evidence as presented by Compston.(see next paragraph). But this f o s s i l evidence goes only as far back as the Permian. From there to the Cambrian i s a considerable extrapolation. Compston (38) has measured 0l8 / 016 ratios in Permian and Devonian brachiopods. He checked the shell microstructure of a l l his specimens. B^ggild (17) suggested that recrystallization of aragonitic shells to c a l c i t i c ones would destroy the microstructure. This suggestion has been used successfully (88, 143). In this process O^/O^ ratios would most l i k e l y not be preserved. Compston also checked carefully the amount of secondary calcite in his samples, because secondary calcite usually has a considerably different oxygen isotope ratio, compared with the ratio of the original shell carbonate. His results have produced Permian tem-peratures which are consistent and similar to present day oceanic temperatures. This i s certainly positive evidence for a constant 0l8 / 016 ratio for the oceans since the Permian. Unfortunately his Devonian samples did not f u l f i l the requirements of preserved microstructure and absence -125-of secondary calcite for being useful. This i s generally the case for Palaeozoic f o s s i l s . Lowenstam (109) has compared ratios, strontium and magnesium contents in recent and f o s s i l brachiopods. The uptake of strontium and magnesium i s determined by temperature, crystal chemistry and physiology 18 16 of the organism. Lowenstam has shown that the 0 /0 ratios, the SrCOg and MgCOg contents in certain f o s s i l s are compatible with those in recent counterparts of these f o s s i l s . He has concluded this can be best explained by accepting the Sr/Ca and (r^/Cp-^ ratios of the ocean have remained essentially unchanged since the late Palaeozoic. This problem can in principle also be solved by the method of "material balance". This line 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 / 016 ratios in 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 available for metamorphic rocks are summarized in graph 9.6. Because metamorphism is often a wet process i t can be anticipated that the minerals w i l l exchange their oxygen relatively fast. Diffusion constants and exchange rates w i l l be different for different minerals, hence different temperatures for the freezing in of the C?~^/(?~^ ratio should be expected. The coarsest fraction of the minerals w i l l indicate a temperature which i s nearest to the maximum temperature of metamorphism. From the -126-pattern of b values one may conclude whether the system was open to water or not. Equilibration with limited amounts of water may produce % values which l i e outside the normal range. If the system i s open to water then the S values for cogenetic mineral pairs should be related in a simple linear 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 i s published in papers (5, 32, 70, 71, 138, 141, 147, 148, 150). Not enough is known about equilibrium constants, their pressure and temperature dependences 18 16 and diffusion constants, to give any rules of thum for the 0 /Cr ratio in different types of metamorphic rocks. -127-BIBLIOGRAPHY 1. Anbar, M. et a l . , Determination of oxygen-18 in phosphate ion; Anal. Chem.. 32, 841, 1960. 2. Annual Reviews of Physical Chemistry 1951-1956. 3. Ault, W. , Oxygen isotope measurements in arctic cores; Geophysical Research papers 63, 159, 1959. 18 4. Baertschi, P., Uber die relativen UnterscMede im hVjO - Gehalt naturlicher Wasser; Helv. Chim. Acta 36, 1352, 1953. 5. Baertschi, P., Messung und Deutung relativer Haufigkeitsvariationen von O^8 und G 1 3 in Karbonatgesteinen und Mineralien; Schweiz. Min. Petr. Mitt. 37, 73, 1957: 6. Baertschi, P.. and Schwander, H., Ein neues Verfahren zur Messung der Unterschiedene im O^8 - Gehalt von Silikatgesteinen; Helv. Chim. Acta 35, 1748, 1952. 7. Baertschi, P. and Silverman, S. 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