CLAYTON et al. ( 1989), dot-and-dash curves are after the combined data from hydrothermal experiments by MATSUHISA et al. ( 1979) and dotted curves are ...
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Gmhimica et Cosmochimica Acta Vol. 57, pp. 1079-1091 Copyright 0 1993 Pergamon Press Ltd. Printed in U.S.A.
+ IN
Calculation of oxygen isotope fractionation in anhydrous silicate minerals YONG-FEI ZHENG* Geochemical Institute, University of GSttingen, Goldschmidtstrasse 1, D-3400 GGttingen, Germany (Received ~e~e~~~~ 30, 199 1; accepted in r#jsed~r~
August 25, 1992 )
Abstract-Thermodynamic oxygen isotope factors for anhydrous silicate minerals have been calculated by means of the modified increment method. The obtained order of ‘*O enrichment in common rockforming minerals is quartz > albite z K-feldspar > sillimanite 2 leucite > andalusite > jadeite > kyanite > anorthite ;r cordierite > diopside > wollastonite > zircon = garnet > olivine. Two sets of self-consistent fractionation factors between quartz and the silicate minerals and between the silicate minerals and water have been respectively obtained for a tempemture range of 0 to 1200°C. The present results on the quartz-mineral systems are in good agreement with hip-tem~rature data derived from semi-empirical calibrations and calcite-exchange experiments, demonstrating that the present calculated fractionation factors for mineral pairs are applicable to isotopic geothermometry and as a test of disequilibrium in natural mineral assemblages over all temperature ranges of geological interest. The silicate-water fractionations obtained from the present calculations also match those from hydrothermal experiments (except 3-isotope exchange results). The present calculations provide a potential insight into the qu~titative dependence of oxygen isotope fractionation upon chemical com~sition and structural state of minerals. Minerals may be depleted in “0 with increasing pressure as a result of the change in crystal structures. be explored. Precise theoretical calculations can provide information on fractionation at low temperatures where experimental study is diI%uh. Calculations of oxygen isotopic partition function ratios have been carried out for several condensed phases using statisticomechanical methods (e.g., O’NEIL et al. 1969; SHIRO and SAKAI, 1972; BECKERand CLAYTON, 1976; KAWABE, 1979; KIEFFER, 1982; HA~ORI and HALAS, 1982). In such calculations, it has been nece%uy to assume approximate frequency distributions for isotopitally light and heavy minerals in order to account for the contributions of lattice vibration to the partition function ratios. The most common approach to this problem has been one in which detailed lattice dynamics models are formulateed, and force constants for the isotopically light compounds are evaluated from spectroscopic and elastic-wave velocity data. Various models have been used to predict the ~bmtion~ frequencies of isotopically heavy species. These allow detailed treatment of individual minerals but are limited in application by their complexity. KIEFFER ( 1982) formulated a model intermediate between detailed spectroscopic calculations and less detailed Si-0 bond models. She assumed that lattice vibrations spectra of isotopically light minerals can be approximated from spectroscopic and elastic data. Rather than approximating the spectra of a series of Einstein oscillators, she employed a refinement of her model for predicting thermodynamic functions from available elastic, structural, and spectroscopic data on minerals, in which the spectra of each mineral are subdivided into various groups of vibrational modes characteristic of the minerals. A hypothetical spectrum for the isotopically heavy minerals was then generated from a set of rules for describing the expected frequency shifts for different types of vibrational modes upon substitution of a heavy isotope into mineral structure. KIEFFER ( 1982) derived a set of fractiona~on factors for silicate minerals from her calculations. The predicted order of relative “0 enrichment is for the most part similar
INTRODUCTION STUDIESOF THE EQUILIBRIUMoxygen isotope properties of solid minerals were initiated p~nci~ly because of their application to the solution of geological problems. For example, the temperature-dependent isotope fractionation between pairs of cogenetic minerals often provides a sensitive indicator of the temperature of rock formation (e.g., BOTTINGAand JAVOY, 1973; CLAYTON, 1981; SHEPPARD, 1984). In order to interpret the natural data quantatively, it is necessary to determine the equilibrium oxygen isotope fractionation factors between minerals in the laboratory. The most common practice was oxygen isotope exchange measurements between mineral and water (e.g., O’NEIL and TAYLOR, 1967; CLAYTON et al., 1972; MATSUHISAet al., 1979; MA?‘THEWSet al., 1983). Equilib~um fmctionation factors for mineral pairs may then be derived from combining the different mineraiwater fractionation data. A significant advance in the experimental calibration of oxygen isotope fractionation factors for solid minerals was made by CLAYTONet al. ( 1989), who developed a new experimental technique which used calcium carbonate rather than water as the exchange medium, to obtain a set of high-tem~rature fractionation factors for some common rock-forming minerals (CHlBA et al., 1989). However, the experimental determination of fractionation factors by this approach has been limited to relatively high temperatures (above 6OO’C) where isotopic exchange is sufficiently rapid for equilibrium to be attained. ~quilib~um isotope data for sofid minerals also provide a basis upon which methods of calculating isotopic fractionation factors for structurally complex condensed phases may
* Presenf address: Institut fdr Mineralogie, Petrologic, und Geechemie, Universitiit Tiibingen, Wilhemstrasse 56, D-7400 Tiibingen 1, Germany. 1079
1080
Y.-F. Zheng
to that either observed in nature or in laboratory experiments. The partition function ratios calculated by her have been used to fit the experimental data of CLAYTONet al. ( 1989) and CHIBA et al. ( 1989) by applying a small “adjustment factor” and to extrapolate the data to temperatures beyond the experimentally accessible range (CLAYTONand KIEFFER, 199 1) . However, a number of significant discrepancies exist, which cannot be understood at the present time (e.g., the rutile-water system; see Fig. 4 in ZHENG, 199la). Based on heat capacity data calculated from the Debye function, BROECKERand OVERSBY( 197 1) calculated a sequence of “0 enrichment in minerals at room temperature, which is qualitatively consistent with obse~ations in igneous rocks. Recently, PATEL et al. ( 199 1) utilized an atomistic model to calculate the fractionation factors of oxygen isotope partitioning reactions between silicates through evaluating the free energy of isotopically distinct silicates as a function of temperature. Their results, however, are poorly comparable with existing experimental data and not better than the results derived by I&FFER ( 1982). On the other hand, from the theoretical considerations of published experimental data for mineral-water fractionations, BOTTINGAand JAVOY( 1973) derived a set of semi-empirical calibrations for oxygen isotope fractionation in quartz, feldspar, muscovite, magnetite, and water at temperatures between 500 and 800°C. In addition to rederiving fractionation expressions from the experimental data, a number of mineral systems (pyroxene, olivine, garnet, biotite, amphibole, ilmenite) were thus “calibrated” in the absence of laboratory data by BOTTINGA and JAVOY ( 1975) on the basis of the observed fmctionation systematics among natural mineral assemblages. Their results have been widely applied to igneous and metamorphic rocks, because the calculated isotopic temperatures seem geologically reasonable and a relatively high degree of concordance has been observed among the isotopic temperatures calculated from the different mineral-pair fractionations. As noted by CLAYTON ( 1981) and SHEPPARD ( 1984), however, the mines-water fractionation relations derived by BOTTINGAand JAVOY( 1973, 1975) are different from those obtained by hydrothermal experiments, particularly by the 3-isotope exchange technique as discussed by BOTTINCA and JAVOY( 1987). TAYLORand EPSTEIN( 1962) and GARUCK (1966) pointed out that complex silicates show trends in oxygen isotope fractionation that can be explained from knowledge of the type of oxygen bonds, and they were able to estimate mineral 6 IgO values by linear combination of bond types. SAKAI and HONMA ( 1969) attempted to calculate mineral-water fractionation factors for ten minerals simply from examination of the Si-0 modes without detailed knowledge of the spectra. Isotopic fractionations in solid minerals depend primarily on the nature of the bonds between atoms of an element and the nearest atoms in the mineral crystal (e.g., O’NEIL, 1977, 1986). Therefore. the “0 enrichment in a mineral depends on the bond-type in the crystal structure. The masses of the bonding partners determine the isotopic effect of vibrational frequencies if I60 is su~titut~ by ‘*O, as also do the distances and 3dimensional configuration of all bonding-partners owing to their significant influence upon bond strength. The correlation between bond strength and oxygen isotopic frac-
tionation in silicate mineraIs was dealt with in SMVIYTH and CLAYTON( 1988) and SMYTH( 1989) in terms of electrostatic characterization of oxygen sites within the minerals. However, cation mass was not included as a variable in the calculation of oxygen site potential, although it is known to have an effect on oxygen isotope fractionation. SCHOTZEf 1980) took into account the effects of both bond strength and cation mass on isotopic substitution and developed an increment method for predicting oxygen isotope fractionation in silicate minerals. Although his calculations were semi-quantitative and his results were not directly applicable to natural fractionation systems, the method has indeed discovered a possibility of considering ~stallo~aphi~ pammeters in evaluating oxygen isotope fractionation in solid minerals. RICHTER and HOERNES ( 1988) applied the increment method to calculation of oxygen isotope fractionation factors between silicate minerals and water. Their results only in part match existing experimental calibrations for temperatures above -300°C. At temperatures below --25O”C, however, their results significantly deviate from the known data. The following deficiencies in their calculations limit the reliability of their results: ( 1) the same factor of 0.11 was used to multiply the IsOincrement of weakly bonded cations, an assumption which is not unive~~ly valid for different structures of silicate minerals; (2) the values of both IO3 In PWw, and IO3 In (Y,+~_,,_~~~ were obtained by averaging literature data, leading to a significant loss of accuracy in calculated fractionation factors. The increment method has been modified by ZHENG ( 199la) for calculating the the~odynamic isotope factors of oxygen in metal oxide minerals. In the new version of the increment method, the parameters of crystal chemistry have fully been used for calculating the ‘80-increment of given minerals with no empirical factor. The ionic radii of both cation and oxygen in different coordination sites have been applied to calculation of bond strength. The transport property of matter has been taken into account in order to correct for the departure of thermodynamic oxygen isotope factors at low temperatures. And a term for mass normalization has been added to the calculation of the I-“0 index of the minerals in question, referring to the transitional contribution in isotopic partitioning. These modifications rationalize the trends in oxygen isotope fractionation in terms of simple crystallographical parameters. Furthermore, the reduced partition function ratios of quartz which were calculated by KJEFFER ( 1982) and corrected by CLAYTON et al. ( 1989) have directly been used as the @-factors of the reference mineral. The reduced partition function ratios of water listed by HATTORI and HALAS( 1982) based on the c~c~ation of RICHET et al. ( 1977) for water vapor have been applied to the calculation of oxygen isotope fractionation factors between mineral and water. Using the modified increment method ZHENG ( 199la) has theoretically obtained a first approximation to oxygen isotope fractionation in metal oxides of geochemical interest over a temperature range of 0 to 1200°C. The obtained results are in fair agreement with existing experimental and/or empirical calibrations. An application of the calculated fractionation factors between quartz and hematite to isotopic
Oxygen isotope fractionation in anhydrous silicates geothermometry has been presented by ZHENG and SIMON ( 199 1) for metamorphic iron-formations. The theoretical calibration of the futile-water system has been confirmed by the low-tem~rature experiments of BIRD et al. ( 1993). Additionally, the modified increment method has been adapted to evaluate oxygen isotope fractionation in wolframite, demonstrating that the quartz-wolframite mineral pair is suitable as an isotopic geothermometer in hydrothermal tungsten mineralizations ( ZHENG, 1992). These successes are encouraging in continuing to apply the method to silicate minerals, recognizing well that we are only gradually building complexity and rigour into the quantitative evaluation of isotopic partitioning. This paper presents the calculations on anhydrous silicate minerals. CALCULATION METHOD AND RESULTS
The present calculations follow the modified increment method of ZHENG ( 199 la) for calculating oxygen isotope fractionations in metal oxides. In principle, the degree of the I80 enrichment of a mineral can be quantified by the oxygen isotope index of the mineral (I-“0) relative to a reference mineral. The I- “0 index is determined by the effects of cation-oxygen bond strength (C,.,) and cation mass on isotopic substitution (WC,.,), which can be quantified by the i80-increment of cation-oxygen bonds in different structural sites of the mineral. The cation-oxygen bond strength is defined as a function of cation oxidation state (V), coordination number (CN,) and co~esponding ionic radii (r,, + rO). Generally, bonds with great bond strength and reduced mass, producing high vibrational frequencies, tend preferentially to incorporate heavy isotopes. The ‘80-increment essentially results from a marriage of crystal chemistry with the relationship between vibrational frequency and reduced mass. The thermodynamic oxygen isotope factors for the mineral in question (@-factors) can then be calculated by multiplying the I-i80 index with the p-factors of the reference mineral. Consequently, the relationship of temperature to oxygen isotope fractionation between two minerals can be obtained through the relation: lo3 In oXmy= lo3 In PX - lo3 In &.
(1)
Unlike the simple cation-oxygen bonds in the metal oxides, silicates contain significant complex anions of silicate (e.g., [ SiO,] 4-) or aluminosilicate (e.g., [ AlSi308] ‘-) bound to different complex cations. As a result, silicates have two kinds of vibrational frequencies: an internal one of complex anions and an external one between complex cations and oxygen. Apparently, the bonds in the complex anions contribute the major part of ‘80-increment to the I-‘8O index of silicate minerals. For this reason, the calculation of normalized r80increment for cation-oxygen bonds (i’,*,) in silicates is different from that in the metal oxides, i.e., &,, = (Lo/ &i-o)@
(2)
where, besides q which wili be defined in next paragraph, i,*., is the “O-increment of a cation-oxygen blood and isi+ is the ‘80-increment of Si-0 bond in quartz (the reference mineral) . The method of calculating the “0 increments has been described by ZHENC ( 1991a) in detail and is not repeated
Table Bond Si’+-0 Si‘+-0 Si’+-0 Si’*-0 Ala+-0 AIs+Ala+-0 Ala+-0 AP+-0 AP+-0 Fe3+-0 ?G3+-0 Fez+-0 Fea+-0 Fes+-O M$+-0 M$+-0 Mga+-0 MI?+-0 MI?+-0 Mn2+-0 Ca*+-0 Ca*+-0 CP+-0 Caa+-0 Ca2+-0 Ba?+--0 K’*-0 K’+-0 K’+-0 K’+-0 Na’+-0 Na’+-0 Na’+-0 Li**-0 Be”+-0 zr?+-0 w+-0 Ni*+-0 TV+-0 Sn*+-0 Th4+-0 ua+-() ?P+ -0 HP+-0
1.
1081
Celculetion of 180-increments for silicatea
CNd
CN,
4 4 4 6 4 4 4 5 6 6 6 6 6 6 8 6 6 8 6 6 8 6 6 7 8 8 9 6 9 10 12 6 8 8 6 4 4 6 6 6 6 8 8 8 8
2
3 4 3 2 3 4 3 3 4 3 4 3 4 4 3 4 4 3 4 4 3 4 3 3 4 3 3 3 3 3 3 3 4 3 3 3 4 4 3 3 3 3 3 3
r&d%) 1.61 1.62 1.64 1.76 1.74 1.75 1.77 1.84 1.89 1.91 1.96 1.98 2.06 2.08 2.16 2.08 2.10 2.25 2.11 2.13 2.31 2.36 2.38 2.42 2.48 2.50 2.80 2.74 2.90 2.92 2.96 2.38 2.52 2.54 2.10 1.63 1.96 1.995 2.07 1.965 2.05 2.40 2.38 2.20 2.19
md
Wd-.
&t-o
k-0
28.09 28.09 28.09 28.09 26.98 26.98 26.98 26.98 26.98 26.98 55.85 55.85 65.85 55.85 55.85 24.31 24.31 24.31 54.94 54.94 54.94 40.08 40.08 40.08 40.08 40.08 137.34 39.10 39.10 39.10 39.10 22.99 22.99 22.99 6.94 9.01 65.37 52.00 58.71 47.90 118.69 232.04 238.03 91.22 178.49
1.03748 1.03748 1.03748 1.03748 1.03690 1.03690 1.03690 1.03690 1.03690 1.03690 1.04631 1.04631 1.04631 1.04631 1.04631 1.03537 1.03537 1.03537 1.04613 1.04613 1.94613 1.04234 1.04234 1.04234 1.04234 1.04234 1.05381 1.04205 1.04205 1.04205 1.04205 1.03454 1.03454 1.03454 1.01729 1.02064 1.04798 1.04551 1.04674 1.04455 1.05300 1.05655 1.05665 1.05090 1.05525
0.62112 0.61728 0.60976 0.37881 0.43103 0.42861 0.42373 0.32612 0.26455 0.26178 0.25541 0.25253 0.16181 0.16064 0.11574 0.16026 0.15873 0.11111 0.15798 0.15649 0.10823 0.14124 0.14006 0.11806 0.10081 0.10000 0.07937 0.06283 0.03831 0.03425 0.02815 0.07003 0.04960 0.04921 0.07937 0.30675 0.25510 0.25063 0.16103 0.33927 0.32520 0.20833 0.21008 0.22727 0.22831
0.02285 0.02271 0.02244 0.01394 0.01562 0.01553 0.01535 0.01182 0.00959 0.00949 0.01156 0.01126 0.00733 0.00728 0.00524 0.00557 0.00552 0.00386 0.00712 0.00706 0.00488 0.00586 0.00581 0.00489 0.00418 0.00415 0.00416 0.00251 0.00158 0.00141 0.00116 0.00238 0.00168 0.00167 0.00136 0.00627 0.01196 0.01115 0.00736 0.01479 0.01679 0.01146 0.01158 0.01128 0.01228
here. Table 1 lists the parameters used and the calculated I80 increment of cation-oxygen bonds in silicate minerals for this paper. The ionic radii are from MULLER and ROY ( 1974). In cases where the ionic radii of cations occur in high spin and low spin states, a mean value is taken in calculation. The parameter q, which is newly introduced here into the calculation of normalized 180-increment by Eqn. 2, is based on the consideration that, besides the bond strength, different types of cation-oxygen bonds in silicate minerals can differentially contribute “O-increments to I-r80 indices. Therefore, the q is a weight which is defined by q=
vk,
k=
-1,0,+1
(3)
where Vis the oxidation state of the cation; k = - 1 is assumed for strongly bonded cations such as those in the complex anions (e.g., A13+ and Si4+ in feldspar), k = + 1 is assumed for weakly bonded complex cations (e.g., Na ‘+ and Ca2+ in feldspar), and k = 0 is assumed for the other complex cations (e.g., Fe2’ and Mg*+ in garnet), Essentially, these assumptions
Y.-F. Zheng
1082
imply that the 180-increment of weakly bonded cations constitutes the least part of I-l80 index in silicate minerals, whereas the “O-increment of strongly bonded cations contributes the dominant part to the I-‘*0 index. The assumption of k = - 1 for the cation-oxygen bonds in complex anion and k = +I for complex cation-oxygen bonds has successfully been applied to wolframite ( ZHENG, 1992). Implicitly, k = 0 was assumed by ZHENG ( 199 1a) in the calculation of normalized ‘*O-increment for cation-oxygen bonds in the metal oxides (i.e., an equivalent contribution of cation-oxygen bonds to the I- ‘*O index of oxide minerals). Apparently, K is a coupling coefficient in this context. Tables 2,3, and 4 list the chemical formulae of anhydrous silicate minerals in question, with the coordination number CN denoted by romanized superscripts. The crystal structure of the silicate minerals is after JAFFE ( 1988), SMYTH and BISH ( 1988 ), and SMYTH ( 1989). In calculation of norrnalized ‘*O increments, besides k = -1 for tetrahedrally coordinated cations in the complex anions, the following conventions or rules are developed for work with different structures of silicates: 1) for feldspars and feldspathoids, k = + 1 is assumed for complex cations; 2) for pyroxenes and olivines, k = 0 is assumed for complex cations in M2 sites wheres k = - 1 is assumed for complex cations in M 1 sites. and the same for titanite group; 3) for garnets, k = -1 is assumed for 6-fold coordinated trivalent complex cations, whereas k = 0 is assumed for 8fold coordinated divalent complex cations; 4) for AlzSiOs polymorphs, k = -1 is assumed for all of the cations; 5) for zircon group, willemite group, wollastonite, beryl, and cordierite, k = 0 is assumed for all the complex cations. Constraints on the rules have been set by the nature of cation-oxygen bonds in the anhydrous silicate minerals and by known data from the experimental and semi-empirical calibrations. The advantage of these rules is that they can be uniformly applied with individual groups (the same structural types and compositional series) of silicate minerals and to similar structures. The set of thermodynamic oxygen isotope factors thus obtained is internally consistent. The disadvantage of these rules is that they could introduce systematical errors in the thermodynamic isotope factors between the different groups of silicate minerals. The reasonably good agree-
ment between isotopic fractionation factors derived from the present calculations and the known experimental and/or semi-empirical data, as shown in the next section, demonstrates that the principal assumptions of the rules are adequate. In this context, it is suggested that the modified increment method provides a framework in which relative trends of “0 enrichment in silicate minerals can be rationalized and may serve as a basis for more fundamental models for the calculation of isotopic fractionation in solid minerals. If this approach may be extended to the prediction of isotopic partitioning of other elements, it could ultimately prove to be a powerful tool to guide the extrapolation of experimental results outside measured temperature ranges. Following the procedures above and those described by ZHENG( lQQla), I-‘*0 indices and lo3 In 0 values ofcommon silicate minerals are calculated as presented in Tables 2, 3, and 4. The quartz lo3 In /3 values used are regressed from the reduced partition function ratios of quartz listed by CLAYTONet al. ( 1989) based on the calculation of KIEFFER ( 1982). A slightly different regression program is used in this study to obtain the minimum intercept of fractionation curves at infinite temperature. Table 5 gives the fractionation factor equations for quartz-mineral and mineral-water systems. The water lo3 In B values used are those listed by HATTORI and HALAS ( 1982) based on the calculation of RICHET et al. ( 1977) for water vapor. Unlike the previous calculations of fractionation factors for the mineral-water systems by Eqn. 1, a term of P-factors for mineral/ water interaction is added according to the translational contribution in isotopic partitioning, i.e., lo3 ln
amineral-water
=
-
lo3
In
lo3
In
Bmined
LL,,
In
Bmineral~water
(4)
As a result, the fractionation factors for the mineral-water systems calculated by Eqn. 4 are systematically greater than those calculated simply by Eqn. 1 for the minerals having I“0 > 0 .5. The purpose of introducing the mineral/water interaction term is to reconcile the discrepancy between theoretically calculated and experimentally measured frac-
Chemical formula
I-'80
A
B
C
Stishovite
0.90786 0.90786
1.0000 0.8837
6.673 6.457
10.398 8.523
-4.78 -4.00
K-feldspar Albite Anorthite Calsian
0.91941 0.91481 0.91955 0.93932
0.9075 0.9147 0.8279 0.8065
6.511 6.526 6.312 6.249
8.897 9.011 7.668 7.347
-4.16 -4.21 -3.64 -3.51
Leucite Kalsilite Nepheline
0.92286 0.92866 0.92507
0.8815 0.8202 0.8255
6.451 6.290 6.305
8.489 7.552 7.632
-3.99 -3.60 -3.63
Beryl Cordierite
0.90734 0.91431
0.7828 0.8199
6.173 6.289
6.999 7.547
-3.36 -3.59
Quartz
lo3
in which
Table 2. Oxygen isotope indices and p-factors of framework silicates (1031np = Ax lOe/p + B x 103/T + C) Mineral
+
1083
Oxygen isotope fra~ionation in anhydrous silicates Table 3. Oxygen isotope indices and b-factors Mineral
Chemical formula
Diopeide Hedenbergite Johannwnite En&at&e Ferroeilite Jadeite Acmite Ureyite Spodumene Wollastonite Rbodonite
tionation factors for the silicate-water system and to bring them into the best available agreement. The introduction of such a term, nevertheless, does not sig~~~n~y change the fractionations between metal oxides and water calculated by ZHENG ( 199 la), because the I-l80 indices of the metal oxides are close to 0.5 (0.40-0.69). Table 5 lists the fractionation factor equations for the anhydrous silicate-water systems. Also listed in Table 5 are those for calcite-mineral systems based on the calcite 1031n/3 values calculated by KIEFFER ( 1982). By combining the 1031n@values for different silicates in Tables 2-4, the fractionation factors between silicate pairs can be deduced.+ Figure 1 depicts the relationship of oxygen isotope fmctionations between quartz and some common silicate minerals to temperature. The error ~nt~but~ to the fractionation relations involving the silicate minerals by the modified increment method is estimated to be within -2% (i.e., 10 + 2 or 100 & 2%0), as previously given by ZHENG ( 199 la) for the metal oxides. Jn terms of the size of I-‘*0 indices, the order of “0 enrichment in the anhydrous silicate minerals can be predicted as follows: quartz > albite 2 K-feldspar > stishovite r sillimanite z leucite > andalusite > jadeite > kyanite > anorthite 2 cordierite > beryl s diopside > zirgon = garnet > fayalite > for&e&e. It is inte~sting to note for mineral ~lymo~hs that the hid-pr~sure form of SiO2, stishovite, is signifi~ntly depleted in “0 relative to the common form quartz (Table
+ Because of common occurrence of calcite and CO2 in nature, the fractionations involving calcite or CO2 can be derived from the combination of 10’ in fl values. The 10’ in a values for calcite can be expressedby
of anhydrous chain silicates
(Ka/Mu) 311 I_“0 0.92229
0.03160 0.93137 0.91662 0.03547 0.01714 0.02685 0.02560 0.91053 0.92’724 0.93505
A
B
C
0.7643 0.7684 0.7673
6.111 6.125 6.121
6.730 6.780 6.774
-3.25 -3.27 -3.27
0.7791 0.7876
6.161 6.180
6.945 7.060
-3.34 -3.39
0.8483 0.8511 0.8499
6.368 6.376 6.373
7.077 8.020 8.001
-3.77 -3.79 -3.79
0.8653
6.412
8.238
-3.88
0.7335 0.7452
5.999 6.292 -3.06 6.043 6.457 -3.13
2). So is the high-pressure form of A12SiOS, kyanite, with respect to the low-pressure form, andalusite, and the hightem~rature form, sillimanite (Table 4). Evidently, the minerals having the same chemical composi~on can have different oxygen isotope behaviors due to the differences in their crystal structure. The present results on the anhydrous silicates (Fig. 1) and the previous results on the metal oxides (Fig. 1 in ZHENG, 199 1a) indicate that the curves of both thermodynamic isotope factors for solid minerals and isotopic fractionation factors between them are radially divergent from the origin to varying slopes and curvatures and are zero at infinite temperature. This implies that neither crossover nor intersection can occur between the fractionation curves of different mineral-mineral systems, somewhat differing from the results of KIEFFER ( 1982) and PATEL et al. (1991). Additionally, the present results confirm that a linear relationship fails to describe the effect of temperature on oxygen isotope fractionation in silicates over the temperature range of 0 to 12OO”C, similar to previous recognization for the metal oxides by ZHENG ( 199 1a). Calculations of oxygen isotope fractionation factors between gases by STERNet al. ( 1968), SPINDELet al. ( 1970), and RICHETet al. ( 1977) even revealed several types of unusual tem~mture dependencies. At high temperatures (above 5~-6~OC), nevertheless, the shape of isotopic fmctionation curves involving solid minerals can generally be approximated by a simple linear relationship between 10 3 In a! and 1/ T*, as suggested by BOTTINGA and JAVOY ( 1973). For the mineral-water systems, however, it is apparent that fractionation curves often pass through a minimum (i.e., the negative value for lo3 In (w)before approaching the origin.
- 4.78 lo3 In && = 6.207 x 106/T2+ 10.499 X 103,'T
COMPARISON WITH KNOWN DATA
which has been regressed from the theoretical results of KIEFFER ( 1982) as listed by CLAYTON et al. (1989). The lo3 in /3 values for
In order to test the accuracy of the present calculations, comparison between the calculated fm~tionations and known experimental and/or semi-empirical calibrations can be made in one of two ways: ( 1) mineral-pair systems or ( 2) mineralwater systems. The present data will not be compared with the previous results calculated by KIEFFER ( 1982) and PATEL et al. ( 199 1 ), because much larger uncertainties have been associated with their data relative to the present results, nor with the results of RICHTER and HOERNES ( 1988) because of the following defects in their calculations: ( 1) the departure of mineral @-factors at low temperatures, (2) the abuse of
COz are derived from RICHET et al.( 1977): IO3 In @co, = 4.494 X 106/TZ + 20.506 X lO'/T- 8.23.
Consequently, we obtain the best available theoretical calibrations on oxygen isotope fractionation in the COz-calcite system and the CO*-Hz0 system, respectively, over the temperature range of O1200°C: IO3In ~~~~~~~~~ = -1.71 X 106/Tz + 10.01 X I03/T- 3.45 lo-’ In DcOrH2,,= 2.30 x 106fT2-I5.34 X lO'/T- 3.51.
I084
Y.-F. Zheng Table 4. Oxygen isotope indices and &factors
Mimed
of orthosilicates
@WMm) 31” I-‘8O
Chemical formula
A
B
C
Almardine mope SpeaeartiUe Grossular Andradite Uvarovite
0.93166 0.91674 0.93130 0.92493 0.93298 0.93201
0.7226 0.7194 0.7190 0.7161 0.7206 0.7208
5.958 5.946 5.944 5.933 5.950 5.951
6.140 6.095 6.090 6.049 6.112 6.114
-2.99 -2.98 -2.97 -2.96 -2.98 -2.98
Fay&e Forsterite Tsphroite Liebenbergite Monticellite Kirschsteinite
0.94388 0.92040 0.94340 0.94534 0.92794 0.93941
0.6911 0.6717 0.6871 0.6916 0.6681 0.6788
5.831 5.748 5.814 5.833 5.732 5.779
5.707 5.447 5.652 5.713 5.398 5.540
-2.81 -2.69 -2.78 -2.81 -2.67 -2.74
Titanite Malay&e
0.92810 0.94631
0.7333 0.7527
5.999 6.070
6.289 6.564
-3.06 -3.18
Wiiemite Phenacite
0.94847 0.90014
0.7284 0.6419
5.980 5.612
6.221 5.054
-3.03 -2.52
Thorite Coffinite zircon H&on
0.96409 0.96472 0.93793 0.95927
0.7048 0.7083 0.7222 0.7283
5.888 5.902 5.957 5.980
5.894 5.942 6.134 6.219
-2.89 -2.91 -2.99 -3.03
Sillimaoite
0.91940 0.91940 0.91940
0.8828 0.8589 0.8416
6.455 6.396 6.350
8.509 8.139 7.874
4.00 -3.84 -3.73
Andalueite Kyanite
Table 5. Oxygen isotope fiactionations in anhydrous Glicate minerals (1031ncr = A x lob/T? + B x 103/T + C) Quartz-Mineral Mineral
Miner&Water
Calcite-Mineral
I-180 A
B
C
A
B
C
A
B
C
Stishovite
1.0000 0.8837
0.22
1.88
-0.78
4.48 4.26
-4.77 -6.64
1.71 2.08
-0.47 -0.25
0.10 1.98
0 -0.78
K-feldspar Albite Anorthite
0.9075 0.9147 0.8279
0.16 0.15 0.36
1.50 1.39 2.73
-0.62 -0.57 -1.14
4.32 4.33 4.12
-6.27 -6.15 -7.50
2.00 1.98 2.24
-0.30 -0.32 -0.11
1.60 1.49 2.83
-0.62 -0.57 -1.14
Leucite Nepheline
0.8815 0.8255
0.22 0.37
1.91 2.77
-0.79 -1.15
4.26 4.11
-6.67 -7.53
2.08 2.24
-0.24 -0.10
2.01 2.89
-0.79 -1.15
Diop=side Enstatite Hsdenbergite Ferrwilite
0.7643 0.7791 0.7684 0.7876
0.56 0.51 0.55 0.48
3.67 3.45 3.61 3.33
-1.53 -1.44 -1.51 -1.39
3.92 3.97 3.93 3.99
-8.43 -8.22 -8.37 -8.09
2.40 2.37 2.40 2.35
0.10 0.05 0.08 0.02
3.78 3.55 3.71 3.43
-1.53 -1.44 -1.51 -1.39
Jsdeite Acmite
0.8483 0.8511
0.31 0.30
2.42 2.38
-1.01 -0.99
4.17 4.18
-7.19 -7.14
2.18 2.17
-0.16 -0.17
2.52 2.45
-1.01 -0.99
Wollastonite Hbodonite
0.7335 0.7452
0.67 0.63
4.11 3.94
-1.72 -1.65
3.81 3.85
-8.87 -8.71
2.49 2.46
0.21 0.16
4.21 4.04
-1.72 -1.65
Beryl Cordierite
0.7828 0.8199
0.50 0.38
3.40 2.85
-1.42 -1.19
3.98 4.10
-8.16 -7.62
2.34 2.26
-0.03 -0.08
3.50 2.95
-1.42 -1.19
Almandine Pyrope Spessartine Grossular Andrsdite Uvarovite
0.7226 0.7194 0.7190 0.7161 0.7206 0.7208
0.72 0.73 0.73 0.74 0.72 0.72
4.26 4.30 4.31 4.35 4.29 4.28
-1.79 -1.80 -1.81 -1.82 -1.80 -1.80
3.76 3.75 3.75 3.74 3.76 3.76
-9.02 -9.07 -9.07 -9.11 -9.05 -9.05
2.52 2.52 2.52 2.52 2.52 2.52
0.25 0.26 0.26 0.27 0.26 0.26
4.36 4.40 4.41 4.45 4.38 4.39
-1.79 -1.80 -1.81 -1.82 -1.80 -1.80
Titanite Malayaite
0.7333 0.7527
0.67 0.60
4.11 3.83
-1.72 -1.60
3.81 3.88
-8.87 -8.60
2.49 2.43
0.21 0.14
4.21 3.94
-1.72 -1.60
Zircon Thorite
0.7222 0.7048
0.72 0.79
4.26 4.50
-1.79 -1.89
3.76 3.69
-9.03 -9.27
2.52 2.55
0.25 0.32
4.37 4.61
-1.79 -1.89
Fayalite Forsterite Tephroite
0.6911 0.6717 0.6871
0.84 0.93 0.86
4.69 4.95 4.75
-1.97 -2.09 -2.00
3.64 3.55 3.62
-9.46 -9.72 -9.51
2.59 2.64 2.60
0.38 0.46 0.39
4.79 5.05 4.85
-1.97 -2.09 -2.00
Willemite Phenacite
0.7284 0.6419
0.69 1.06
4.18 5.34
-1.75 -2.26
3.79 3.42
-8.94 -10.11
2.50 2.70
0.23 0.60
4.28 5.45
-1.75 -2.26
Sillimanite And&site Kyanite
0.8828 0.8589 0.8416
0.22 0.28 0.32
1.89 2.26 2.52
-0.78 -0.94 -1.05
4.26 4.20 4.16
-6.65 -7.02 -7.29
2.07 2.15 2.20
-0.25 -0.19 -0.14
1.99 2.36 2.63
-0.78 -0.94 -1.05
Quartz
1085
Oxygen isotope fractionation in anhydrous silicates 4
16
1-This dwlalion P-Clayton et al. (1989) 3Matsuhisa et al. (1979) 4-BotIinga 8 Javoy (1973)
3
8 c2 n0 F
1
2 Oo.II
21 II 4
11
11
OL
1110 1 12I
400
I
I
I
600 Ternpe~ure
I
I
I
I
1200 ;:;
1 0+TZ8
FIG. 1. Oxygen isotope fractionation factors between quartz and the common rock-forming minerals indicated vs. 1/ T*.
the empirical factor 0.1 I, and ( 3 ) the mischoice of 10 3 In p values for the reference systems. It appears that the present I- ‘*O indices for the anhydrous silicate minerals are considerably different from those calculated by RICHTER and HOERNES (1988).
FIG. 2. Comparison of oxygen isotope fractionations between quartz and feldspar. Solid curves are after the present calculations, dashed curves are after the calcite-exchange experimental results of CLAYTON et al. ( 1989), dot-and-dash curves are after the combined data from hydrothermal experiments by MATSUHISAet al. ( 1979) and dotted curves are after the semi-empirical calibrations of BOTTINGA and JAVOY(1973).
6n
FELDSPAR Isotopic fractionation curves for quartz-feldspar systems derived from the present calculations are shown in Fig. 2, together with those obtained from semi-empirical calculations by BOTTINGA and JAVOY ( 1973), combination of hydro-
thermal experimental data by MATSUHISAet al., 1979), and combination of calcite-exchange experimental data by CLAYTONet al. ( 1989). The results for the quartz-anorthite system from the four different approaches are virtually identical with each other. However, the result for the quartz&bite system from hydrothermal exchange experiments by MATSUHISAet al. ( 1979) is significantly lower than the other three data sets. As depicted in Fig. 3, the present calculations on the plagioclase-water systems well match the hydrothermally experimental results of MATSUHKA et al. ( 1979) and O’NEIL and TAYLOR ( 1967) as well as the semi-empirical calibrations of BOTTINGAand JAVOY( 1973 ). O’NEIL and TAYLOR ( 1967) assumed that isotopic fractionations involving plagioclase are linearly related to the mole fraction of anorthite. The present calculations confirm their assumption. Therefore, the quartz-plagioclase and plagioclase-diopside fractionation curves derived from the present calculations for the temperature range of 1200 to 0°C can be expressed by lo3 ln
aQz_p/
+
=
(0.15
+
0.21.x)
x
106/T2
(1.39 + 1.34x) X 103/T - (0.57 + 0.57x)
(6)
6
1-This calculation P-Matauhisa et al. (1979) 3-Bottinga & Javoy (1973) 4-O’Neil & Taylor (1967)
FIG. 3. Comparison of oxygen isotopic fractionation between feldspar and water. Solid curves are after the present calculations, dotand-dash curves are after the hydrothermal experiments of MATSUHISA et al. ( 1979). dotted curves are after the semi-empirical calibrations of BOTTINGAand JAVOY( 1973), and dashed curves are after the hydrothermal experiments of O’NEIL and TAYLOR( 1967).
Y.-F. Zheng
1086
IO3 In c+/.~~= (0.42 - 0.21x) x 106/T2 + (2.28 -
1.34x) X 10)/T - (0.96 - 0.57x)
(7)
where x is the mole fraction of anorthite in plagioclase. The fractionation curve for the albite-anorthite system in the temperature range of 1200 to 0°C can be expressed by lo3 In aAh_An= 0.21 X 106/T2
+ 1.34 X 103/T - 0.57.
(8)
As shown in Table 2, the calculated I-l80 index is 0.9075 for K-feldspar, 0.9147 for albite and 0.8279 for anorthite. Theoretically, K-feldspar can therefore be slightly depleted in “0 relative to albite due to the effect of cation mass. But as seen from the present calculations, the difference between the I- I80 indices of K-feldspar and albite is so small (0.0072) that the simple replacement of K by Na in alkali feldspar has no measurable isotopic consequences at high temperatures within the experimental errors. The I-‘8O index of anorthite is significantly smaller than that of albite, indicating that the replacement of CaAl by NaSi considerably affects the fractionation behavior of plagioclase. These theoretical results are in reasonable agreement with those obtained by O'NEIL and TAYLOR( 1967) from cation exchange experiments and by SCHWARCZ( 1966) from natural assemblages. PYROXENE AND OLIVINE The determination of oxygen isotope fractionation factors among pyroxene, olivine, and calcite is very important for the interpretation of oxygen isotope data on metamorphic rocks, mantle and lunar samples. Figure 4 depicts isotopic fractionation curves for the calcite-forsterite and calcitediopside systems derived from the present calculations, to-
600
600
1000
Temperature
1200
(‘X)
FIG. 4. Comparison of oxygen isotope fractionations between calcite, forsterite and diopside derived from the present calculations (solid curve) with the experimental calibrations (dashed curve) of CHIBA
et al. (1989).
gether with those from the direct exchange experiments of al. ( 1989 ). The theoretical fractionation factors are in excellent agreement with the experimental ones. The diopside-forsterite fractionation curve derived from the present calculations is shown in Fig. 5, along with other empirical ( KYSER et al., 198 I), semi-empirical ( BOTTINGA and JAVOY, 1975) and experimental (CHIBA et al., 1989) calibrations. The present results lie between the semi-empirical data of BOTTINGA and JAVOY ( 1975) and the experimental values OfCHIBA et al. ( 1989). The diopside-forsterite fractionation curve derived from the present calculations can be expressed by
CHIBA et
IO3 In ~l~,.~,,= 0.36 x 106/T2+
1.28 X 10)/T-0.56
(9)
Figure 6 depicts isotopic fractionation curves for the pyroxene-water systems derived from the present calculations, together with data from the 3-isotope exchange experiments of MATTHEWSet al. ( 1983) and the semi-empirical calibrations of BOTTINGAand JAVOY ( 1975). The present results on the jadeite-water system are at variance with the experimental data of MATTHEWSet al. ( 1983); those on the diopside-water and wollastonite-water systems deviate from the experimental ones. As shown in Table 3, the I- ‘*O index is 0.7643 for diopside, 0.7684 for hedenbergite, and 0.7630 for johannsenite, indicating that mutual substitution of Mg*+, Fe2+, and Mn*+ mto the octahedral sites have little or negligible effect on isotopic fractionations in the pyroxenes. In contrast, jadeite has significantly greater I- I80 index (0.8483), suggesting that replacement of CaFe by NaAl has significant effect on isotopic partitioning between hedenbergite and jadeite. Additionally, wollastonite is depleted in “0 relative to diopside because of its smaller I-“0 index (0.7335). These theoretical results are in concordance with the observations by MATTHEWSet al. ( 1983) from high-pressure hydrothermal experiments. As depicted in Fig. 7, the fractionations for the quartz-diopside system derived from the present calculations are consistent with those from the calcite-exchange experiments of CHIBA et al. ( 1989) and the semi-empirical calibrations of BOT-I-INCAand JAVOY ( 1975). However, the fractionations between quartz and pyroxenes derived by MATTHEWSet al. ( 1983) from combining hydrothermal experimental data are systematically lower than those obtained from the present calculations, and thus correspond to lower temperatures when applied to isotopic geothermometry in petrology. Figure 8 shows fractionation curves for the plagioclase (An = 60)-diopside system, where the present calculation gives the results identical to those from BOTTINGA and JAVOY ( 1975), but also considerably larger than the combined data by MATTHEWSet al. (1983) from the hydrothermal experiments. In natural pyroxenes, the Si in the tetrahedral sites has been found to be replaced by Al up to an Si:Al ratio of 3:1 (BERRY et al., 1983). As a result, a decrease in the I-‘*0 index can occur for pyroxenes with tetrahedral Al replacement, leading to a depletion in “0 relative to pyroxenes without the Al replacement. Thus, an analysis of mineral composition and structure is desirable in the interpretation of oxygen isotope data. Zircon has the similar structure to olivine. From Table 4 it can be seen that zircon has the I- I80 index of 0.7222 which
Oxygen isotope fractionation in anhydrous silicates
l-Thiscalculation P-Chibaetal.(1989)
.i i -i
3-Kyser et al. (1981) 4-Bottinga &Javoy (1975)
i
i
8
1087
._._._-.-
Quartz-Woilastonite
-
Quartz-Diopside
. ______-- Quartz-Jadeite i
i-This
cakx~latton
P-Chiba et al. (iSt?S) 3-Matthew et al. (lSS3) 4-eottinga & Javoy (1975)
600
800
1000
1200
Temperature (“C)
Temperature (Oc) FIG. 5. Oxygen isotope fractionations between diopside and forsterite.
is greater than that of olivines (0.69 1l-0.67 17), indicating a considerable difference of oxygen isotope fractionations between zircon and olivines, with a significant ‘*O enrichment
: : :
i
l-This cablstion : :
:
P-Matthews
et al. (1983)
3-Bofflnga
& Javoy (1975)
1
FIG. 7. Comparison of oxygen isotope fractionations between quartz and pyroxenes. Solid curves denote the quartzdiopside system, dashed curves denote the qua~z-jadei~e system, and dot-and-dash curves denote the qua~z-wollastonite system.
in zircon. When applying the present calibration on quartzzircon fractionation as expressed by IO3 In CQ~_~~ = 0.72 X lob/T2 + 4.26 X 103/T-
1.79 (IO)
to natural mineral assemblages, the fractionations of 2.4 to 4.1 %Odetermined by KERRICH( 1987) for granites correspond
1
a
6
cO 0
XT F
-1
-2 2 1
-9100 :OO I
FIG. 6. Comparison of oxygen isotope fractionations between pyroxene and water. Curves lab&led 1are after the present calculations; 2 with points are after the hydrothe~al ex~~ments of MATTHEWS et al. ( 1983) where squares denote the jadeite-water system (dashed curves), circles denote the diopside-water system {solid curve) and triangles denote the wollastonite-water system (dot-and-dash curve); 3 is after the semi-empirical calibrations of BOTTINGA and JAVOY (1975).
500 I 600 700
1
800 900 1000
Temperature(%)
FIG. 8. Oxygen isotope fractionations between quartz and garnet and between plagioclase (An = 60) and diopside. Sohd curves are after the present calculations, dashed curves are after the semi-empirical calibration of BOTTINGA and JAVOY ( 1975), dot-and-dash curve is after the hydrothermal experiments of MA-ITHEWS et al. (1983).
Y.-F. Zheng
1088
to isotopic temperatures of 890 to 590°C which can be regarded as petrologically reasonable temperatures. GARNET Oxygen isotope fractionations between garnet and water have been experimentally investigated by TAYLOR and O’NEIL (1977) and LICHTENSTEINand HOERNES (1992). Figure 9 shows a comparison of their results with the present calculations. It is noted that the experimental values of LICHTENSTEINand HOERNES( 1992) are rather scattered and significantly greater than the calculated ones. As depicted in Fig. 8 for the quartz-garnet system, the present calculations give slightly larger fractionation factors than the semi-empirical calibrations of BOTTINGAand JAVOY ( 1975), and thus correspond to slightly higher temperatures when applied to isotopic geothermometry in metamorphic rocks. As listed in Table 4, I-l80 index of garnets varies within a very small range with an average of 0.7 198 f 0.003 1, indicating that the substitution of complex cations in either 6or 8-fold coordinated sites has no significant effect on oxygen isotopic partitioning in garnet. This is consistent with the experimental results of LICHTENSTEINand HOERNES( 1992), but contrary to those of TAYLOR and O’NEIL ( 1977) who obtained a relatively large fractionation of 1.77~ between grossular and andradite at 600°C which was attributed to the mass effect of substitution of A13+-0 by Fe3+-0 bonds in octahedral sites. However, it is noteworthy that grossular commonly contains combined water as a result of the partial substitution of [ OH ] :- for [ SiO,] 4- in the structure (BERRY et al., 1983). In this case, grossular with the [OH]:- substi-
1 1-This calculation 2-Lichtenstein & Hoernes (1992) 3-Taylor & O’Neil (1977) 0
-1 tl E 00 7
-2
-3
200
400
600
800
1000
Temperature (“C)
FIG. 9. Comparison of oxygen isotope fkactionations between garnet and water derived from the present calculations with the hydrothermal experimental measurements OfLICHTENSTEIN and HOERNE~ ( 1992) and TAYLORand O’NEIL (1977).
tution behaves isotopically unlike grossular without the [OH]:- substitution. Then an ‘80-enrichment in grossular could occur relative to andradite under the hydrothermal conditions. DISCUSSION ON APPLICATION TO GEOTHEkMOMETRY Application of newly calibrated fractionation curves to isotopic geothermometries for giving a set of internally consistent temperature values has been a classical subject in reporting the new calibration results. Inasmuch as the present calculations are in fair agreement with the semi-empirical calibrations of BOTTINGAand JAVOY (1973, 1975) and the experimental results of CLAYTONet al. ( 1989) and CHIBAet al. ( 1989), consistent temperature values can generally be anticipated when applying the new theoretical calibrations to natural mineral assemblages. It is thus considered redundant to list some examples for illustrating the application of the present geothermometers to selected igneous and metamorphic rocks. Instead, it would be useful to look at the applicability of all geothermometers available from different calibration approaches. As is well known, the application of isotopic geothermometry to natural mineral assemblages must take into account two necessary constraints: ( 1) isotopic equilibrium and (2) calibration of equilibrium fractionation factors. Demonstrating the attainment and preservation of isotopic equilibrium is more or less evident. The use of 6-6 diagram in presenting stable isotopic data for coexisting mineral pairs enables test of isotopic equilibrium by the biminerallic isotopic data themselves (e.g., GREGORY and CRISS, 1986; ZHENG, 199 1b). The remaining problem is that the isotope temperatures calculated can be different due to application of different calibration curves. The published literature contains many calibrations of oxygen isotopic geothermometers, some determined by laboratory measurements, some based on theoretical (semi-empirical) calculations and some determined by the analysis of coexisting minerals. Obviously, it is highly desirable to develop an internally consistent set of fractionation curves applicable to natural assemblages for as many mineral pairs as possible. This is now feasible, since we have had three sets of self-consistent fractionation factors for the mineral pairs of geological interest: ( 1) semi-empirical calibrations by BOTTINGAand JAVOY( 1973, 1975), (2) experimental measurements through carbonate-exchange technique by CLAYTONet al. ( 1989) and CHIBAet al. ( 1989), and (3) theoretical calculations by the modified increment method in the present study. The former two sets are limited in a high-temperature range above 500-600°C and only for some common rock-forming minerals. The present set is applicable over a temperature range of 1200 to 0°C and for mostly occurred minerals in igneous and metamorphic rocks. Therefore, it is advantageous to apply the present set of fractionation curves between minerals pairs to isotopic geothermometries with the best chance of insight into equilibrium or disequilibrium with respect to cooling and closure in natural mineral assemblages. As depicted in Figs. 6-8, the fractionation factors involving pyroxenes derived from the 3-isotope exchange experiments of MATTHEWSet al. ( 1983) are significantly different from the above mentioned three sets of calibration. The quartz-
Oxygen isotope fractionation in anhydrous silicates pyroxene and plagioclase-pyroxene fractionations obtained by combining the hydrothermal experimental data appear to be lower than the theoretical calibrations. It remains a puzzle why the discrepancies occur, though isotopic equilibrium has to be suspected (BOTTINGA and JAVOY, 1987). The laboratory hydrothermal equilibration experiments were conducted at pressures of 9 to 24 kbar, corresponding to gaseous water densities significantly higher than those at low pressures (KENNEDY and HOLSER, 1966). As pointed out by O’NEIL ( 1986), pressure effects might be expected for mineral-gas or melt-gas systems because the isotope properties of the gas might change drastically with big density changes, whereas those of the melts or minerals remain unaffected. At the high water densities, on the other hand, intermolecular interactions must be significant, so that mineral reactions can be catalyzed by aqueous fluids and the physicochemical properties of minerals could be modified. For example, water enhances mineral reactivity by promoting solution-reprecipitation processes (e.g., MATTHEWSet al., 1983). Experimental studies of oxygen diffusion in anorthite (ELPHKK et al., 1988) and in quartz (ELPHKK and GRAHAM, 1988) confirm the dramatic difference between oxygen diffusion under “wet” vs. ‘dry” conditions. The presence of water or one of its components clearly increases the diffusion rate, resulting in relatively lower closure temperature for oxygen diffusion. The introduction of the mineral/water interaction term in this study implies that the fractionation factors between two minerals cannot be simply derived from combining the calibrations of the two mineral-water systems. Congruence of oxygen isotope temperatures among different mineral pairs in metamorphic rocks, and consistency of these temperatures with those derived from alternative non-isotopic geothermometers, has been observed in nature (e.g., BOTTINGA and JAVOY, 1975; HOERNES and FRIEDRICHSEX,1978; SATIRet al., 1980). This implies that oxygen isotopic equilibrium among coexisting minerals in a metamorphic rock could be “frozen in” at the temperature of crystallization of the mineral assemblage, and that subsequent reequilibration of oxygen isotopes would have not occurred. This can be true in some situations. GILETTI ( 1986) pointed out that the rocks of yielding agreement in oxygen isotopic temperature for all sets of mineral pairs have either been quenched at high temperature or, if they are known to have cooled slowly, have probably had a complex history during, or subsequent to, cooling. On the other hand, data on oxygen diffusion in silicate minerals (e.g., FREER and DENNIS, 1982; GILETTI, 1986; GRAHAM and ELPHICK, 199 1) and evidence of isotopic disequilibrium among coexisting minerals (e.g., DEINES, i 977; GRAHAM, 198 1; GREGORYand CRISS, 1986) argue that postcrystallization oxygen isotopic exchange in mineral-mineral and mineral-fluid can continue during cooling. When kinetic data for oxygen diffusion in various minerals are available, the effect of oxygen diffusion during cooling can be evaluated as a cause for the discrepancies in isotopic temperature from different mineral pairs (e.g., JAVOY, 1977; GILLETI, 1986; FARVER, 1989). The relative order of oxygen isotope temperatures calculated from minerals pairs in an igneous or a me~mo~hic assemblage may provide info~ation about the relative oxygen diffusion rates in the constituent minerals,
1089
The present calculations clearly demonstrate the dependence of oxygen isotopic partitioning on stoichiometry and structure in silicates, as illustrated for feldspar, pyroxene, and AlzSi05 polymorphs. Essentially, the size of the %-increment of cation-oxygen bonds (&) is a quantitative indicator of the ‘80-enrichment degree for them. As shown in Table 1, Si4+-0 bonds in tetrahedral positions have the greatest “Oincrement (0.02285-0.02244), A13+-0 bonds in tetrahedral positions are the next (0.0 1562-0.0 1535 ), and M *+-0 bonds (e.g., O&0733have generally the smaller “0-increment 0.00728 for Fe’+ in octahedral positions). This sequence of “0 enrichment in different cation-oxygen bonds is determined by the principles of increment method for the fractionation effects: the heavier isotope is preferentially incorporated into the substances with greater bond strengths. These theoretical results are consistent with the previous observations by TAYLOR and EPSTEIN( 1962 ) that the relative isotopic compositions in an equilibrium assemblage of silicates could be accounted for by counting the number of oxygen atoms in each of the following bonding arrangements: Si-0-Si, SiO-Al, and Si-O-M (where M is a divalent cation). Additionally, the substitution of cations between different structural sites has a much larger influence on the oxygen isotopic behavior than that within the same structural sites. Therefore, for those minerals which can have a large variation in chemical composition and structural state, the application of oxygen isotope geothermometry has to take into account the detailed information on the variation in order to deduce “realistic” fractionation curves for the natural mineral assemblages. Because the change in a molar volume of solids on isotopic substitution is small, typically hundreths to tenths of a percent, it has generally been assumed that the effect of pressure on isotopic fractionation between minerals is negligible for crustal rocks (CLAYTON,198 1; O’NEIL, 1986 ). However, JOY and LIBBY ( 1960) suggested that the oxygen isotope fractionation between CaC03 and Hz0 might be measurably pressure dependent at low temperatures. Pressure effects were invoked to explain unusual oxygen isotope compositions of some kimberlitic ecologites ( GARLICK and MACGREGOR, 1971) and olivine from a suite of ultramafic rocks (PINUS and DONTSOVA,197 1). Taking into account the possible involvement of fluids (CO2 and H20) in mantle and lower crustal processes, mineral-fluid systems could be sensitive to pressure effects because the isotopic substitution of oxygen atoms in CO2 or Hz0 would not produce a volume change sufficient to offset the volume change of the mineral. From another point of view, pressure effects can be expected in terms of the principles of the increment method for the minerals whose cation-oxygen bond strengths change as pressure changes. This is because the thermodynamic oxygen isotope factors for a mineral are proportional to the cation-oxygen bond strengths of the mineral, which are a function of the coordination numbers of cation-oxygen and interatomic distances within the mineral. This has been illustrated for SiOZ polymorphs (quartz and stishovite in Table 2) and A12SiOs polymorphs (sillimanite, andalusite and kyanite in Table 4). It appears that minerals in the lower crust and mantle could be depleted in 180 due to a decrease in the cation-oxygen bond strengths with increasing pressure. Furthermore, the
Y.-F. Zheng
1090
oxygen isotopic behavior of such minerals as pyroxene, garnet,
REFERENCES
and olivine can considerably change under the mantle conditions if the crystallographic parameters such as the coordination numbers of cation-oxygen and interatomic distances of the minerals change due to the significant change in pressure. Additionally, cation diffusion exchange with respect to pressure change (e.g., pressure-enhanced Al/Si diffusion in feldspar; GOLDSMITH, 1991) might exert an influence on oxygen isotope fractionation in minerals. Therefore, pressure effects may probably not be completely ignored in the application of oxygen isotope fractionation to geothermometry of igneous and metamorphic rocks.
BECKER R. H. and CLAYTON R. N. ( 1976) Oxygen isotope study of a Precambrian banded iron formation, Hamersley Range, Western Australia. Geochim. Cosmochim. Acta 40, 1153-I 165. BERRYL. G., MASONB., and DIETRICHR. V. ( 1983) Mineralogy: Concepts, Descriptions, and Determinations. W. H. Freeman and CO. BIRDM., LONGSTAFFE F. J., FYFEW. S., and BILDGENP. (1993) Oxygen-isotope systematics in a multiphase weathering system in Haiti. Geochim. Cosmochim. Acta 57, 2831-2838.
CONCLUSIONS The principles
of the increment
method developed by the difficulties in the semi-empirical calculations of oxygen isotope fractionation in solid minerals. This makes it possible to obtain a first approximation to thermodynamic oxygen isotope factors for anhydrous silicate minerals through appropriate modifications. A set of self-consistent fractionation factors for quartz-mineral and mineral-water systems has been acquired for temperatures from 0 to 1200°C. The mineralwater fractionations derived from the present calculations well match those from hydrothermal experiments (except the 3-isotope exchange results). The present data on the mineral-mineral fractionations are in good agreement with the semi-empirical calibrations of BOTTINGA and JAVOY ( 1973, 1975) and the experimental results OfCLAYTONet al. ( 1989) and CHIBA et al. ( 1989). This agreement is highly encouraging in applying the new calibrations to isotopic geothermometers over the all-temperature range of geological interest. In view of the relationship of isotopic partition to chemical composition and structural state within individual mineral groups, the present approach can be a powerful tool to deduce the equilibrium fractionation factors of a “realistic” mineral from the known theoretical or experimental data. The effect of pressure on the oxygen isotopic partitioning in minerals may be caused by the change in the mean cationoxygen distance and coordination numbers. In the absence of a structural change, the effect of compression on the cationoxygen distances, and hence on the mineral I- I80 index, is SCHUTZE (1980) have proven to be able to circumvent
relatively
small.
If a structural
change
takes place due to
polymorphic transformation on increasing pressure so that the coordination numbers of cations and anions increase, then the I- I80 index will significantly decrease. Consequently, minerals may considerably be depleted in ‘*O with increasing pressure due to the change in crystal structure. Additionally, taking into account the variations in mineral structure and chemical composition will inspire confidence in applicability of oxygen isotopic geothermometry. Acknowledgments-This study has benefited from the support of Prof. J. Hoefs during my work in Giittingen and of Profs. P. Metz and M. Satir during my w&k in Tiibingen within the framework of the DFGproject “Elemental Partitioning in Geological Systems”. Thanks are due to Profs. A. Matthews, J. R. O’Neil, and M. Thiemens as well as to an anonymous reviewer for constructive comments on an earlier draft of the manuscript. Editorial handling: F. Albarkde
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