- Email: [email protected]
Limits on the effect of pressure on isotopic fractionation
Notes
MARLANDG. (1975) The stability of CaCO, .6H,O (ikaite). Geochim. C&m&him. Acta 39, 83-91. _ _ MAR~CHNERH. (1969) Hydrocalcite (CaCOa.H,O) and nesquehonite (MgCO, .3H,O) in’ carbonate scales. Science 165, 1119-1120. ROBIE R. A. and WALDBAUM D. R. (1968) Thermodynamic properties of minerals and related substances at 298.15” K (250°C) and one atmosphere (1.013 bars) pressure and at higher temperature. LI.S. Geol. Suru. Bull. 1259, 256 pp. SAFQZHNIKOV D. G. and TSVETKOVA. L. (1960) Precipitation of hydrous calcium carbonate on the bottom-of Lake Issyk Kul. Dokl. Akad. Nauk SSSR Earth Sci. 124, 131-133.
1197
SEMENOV
E. I. (1964) Hydrated carbonates of sodium and calcium. Soviet Phys. ~Cryst. 1964, 88-90. STAAVELEY L. A. K. and LINDFORDR. G. (1969) The heat capacity and entropy of calcite and aragonite, and their interpretation. J. Chem. Thermodynamics, 1, l-11. TURNBULLA. G. (1973) A thermochemical study of vaterite. Geochim. Cosmochim. Acta 37, 1593-1602. VAN TASSEL R. (1962) Carbonatniederschllge aus calcium-magnesiumchloridliisungen. Z. gemischten Anorg. Allgem. Chem. 319, 107-112. ZEN E. (1966) Construction of pressure-temperature diagrams for multi-component systems after the method of Schreinemakers-a geometric approach. U.S. Geol. Surv. Bull. 1225, 56 pp.
Geochimica et Cosmochimica Acta. 1975, Vol. 39, pp. I197 to 1201. Pergamon Press. Printed in Great Brrtain
NOTE
Limits on the effect of pressure on isotopic fractionation ROBERT N. CLAYT~N,*~$ JULIAN R. GOLDSMITH,~KARIN J. KAREL,$$ TOSHIKO K. MAYEDA* and ROBERT C. NEWToNt Enrico Fermi Institute,* Department of Geophysical Sciences,? and Department of Chemistry,$ The University of Chicago, 5630 Ellis Avenue, Chicago, Illinois 60637, U.S.A. (Received 27 August 1974; accepted in revised
form 9 December
1974)
Abstract-The equilibrium distribution of oxygen isotopes between calcium carbonate and water was determined at 500°C at pressures from 1 to 20 kbar and at 700°C at pressures of 0.5 and 1 kbar. At both temperatures, the pressure-dependence of the fractionation’factor was below the limit of detection. The experimental results are consistent with theoretical estimates of the volume change due to isotope substitution. Application of the theory to silicate systems leads to the conclusion that pressure effects on oxygen isotopic fractionation between silicates are <02x, at pressures of tens of kilobars. Thus the observed large variations of O1*/O’6 ratio in kimberlitic eclogites cannot be attributed to the effect of pressure. INTRODUCTION
of stable isotope geothermometry that the effect of pressure on isotopic fractionation is negligible. This assumption is based on the fact that isotopic substitution makes only a minute change in the molar volume of solids and liquids. However, neither theoretical calculations nor prior experiments have ruled out the possibility that measurable pressure effects might exist at pressures of tens or hundreds of kilobars, with significant consequences for the isotopic compositions of mantle rocks
IT IS A basic assumption
and mantle-derived
rocks.
4 Present address: Department of Chemistry, Princeton University, Princeton, N.J., U.S.A.
The effect of pressure on oxygen isotope fractionation between calcium carbonate and water has been estimated theoretically (JOY and LIBBY, 1960). If their treatment were correct, isotopic fractionations in the lower crust and upper mantle would be dominated by pressure effects rather than temperature effects. The only published experimental search for pressure effects on isotopic fractionation was carried out on the reaction between water and dissolved bicarbonate ion (HOERING, 1961). The fractionation factor at 4 kbar was not measurably different from that at one bar. In only one instance have isotopic pressure effects been adduced to account for observed oxygen isotope abundance in rocks (GARLICK et al., 1971). The authors concluded that crystal-liquid fractionations
119x
News
in basaltic-eclogitic
magma
must
increase
with
pres-
Oxygen isotopic fractionation between calcium bonate and water can be described by the exchange tion:
carrcac-
sure. THEORETICAL
CONSIDERATIONS
I ,3CaCO”’3 + H z 0’” s Ii3 CaC0183 + H,O’”
(1)
for which K = (O”;O”‘)
CaCOJ(0”
‘0”‘) H,O.
(2,
the carbonate ion. the (‘-0’” bond should be only I.6 x IO A A shorter than the C-Olh bond [Fig. l(b)]. This decrease in carbon-oxygen bond length results in a decreased ionic radius of the carbonate ion and hence a decrcasc of molar volume of the CaCO, crystal. The fractional change of molar volume is then approximately equal to three times the fractional change in cation-anion distance. Taking the Cd?‘--C distance to be 3.2& we estimate the fractional change in molar volume (AVIV) to hc I.5 X 10-4. which leads to a difference of 5.6 x IO 3 cm’.‘molc between CaCOih and CaCOAs. The change of molar volume on O’* substitution in H,O is considerably smaller. since the oxygen atom displacements
and ,A = IGWln h From the pressure phase:
dependence
(:I
of free cnerpq
for each
g -.95 and the relationship between standard free energy change:
equilibrium
constant
and
it follows that
/
/
/
4.05
1.00
I
4.40
I
4.45
R(B) where AC’ is the volume change per molt for the rcactlon as written. An effect of pressure on the equilibrium constant will result if AV for the exchange reaction is not zero. It is known both from theory and from experiment that isotopic substitution does have an effect on molecular dimensions, with substitution of a heavier isotope leading to shorter bonds. It may be instructive to consider. as a model. the methane molecule, for which experimental and theoretical studies exist (KUCHITSU and BAKTELI.. 1962a. h). In a molecule of methane in the gas phase, even though the potential energy curves for CH, and CD, arc the same, the equilibrium bond lengths (R,) are different due to the anharmonicity of the vibrations. and the fact that C’H 1 has a larger zero-point energy. KWHITSC and BAKTLLI (1962a) calculated the mean value of the C D bond length to be about 0.004A less than that of the C-H bond, based on a quantum mechanical treatment of the anharmonic oscillator. A very similar estimate of the bond lengths can be obtained simply by taking the value of the bond-lengths equal to the mean of the two limits of the corresponding classical vibration. as illustrated in Fig. l(a), A similar difference in bond length has been observed between D,O and Hz0 (KC’CHITW and BAKTELI.. 1962b). The differences in bond lengths lead to differences of about 0.3 per cent in the molar volumes between liquid hydrocarbons and deutcrocarbons (BAK.TELL and ROSK~S. 1966). By the same methods, the volume change on substitution of 0” for OLh in the carbonate ion can be cstimatcd by approximating the potential energy curve by a Morse function (MORSE. 1929), and calculating the difference in the mean C-O bond length due to anharmonicity. Fol
4.25
4.30
4.35
4.40
R (8) Fig. I. Morse curves for CH, (a) and CO:(b). approximated as diatomic molecules. Parameters used are as follows: bond dissocation energy D = 104 kcal/mole for methane. I I I kcal/mole for carbonate ion: minimum in potential curve R,. = I%5 A for methane, l.3OOA for carbonate ion: stretching force constant k = 4.88 x lo5 dyne/ cm for methane, X.50 x IO” dyne/cm for carbonate ion. Energy levels shown arc zero-point energies for the labeled isotopic species. E is potential energy relative to dissociated hond. It is not implied that the absolute values of R,,. the equilibrium bond lengths. are known to 5 or 6 significant ligures. Only the cl~yu m R, on isotopic substitution contributes to the estimate of At!
Notes are very small in the vibrations of the water molecule, resulting in very small zero-point energy differences betweenH,016 and H,O’*. ThuH, for the o&all exchange reaction (11 in which l/3 mole of CaCOl is involved. an upper limit of about 1.9 x 10e3 cm3/mole may be estimated for AK The corresponding upper limit on the pres-
Table 1. CaCOs-HZ0 Run I
PreSSWe (kb)
Tine (days)
1199
sure effect on the calcitewater O.O3”%Jkbar.
fractionation
EXPERIMENTAL
METHODS
Isotopic equilibration experiments were carried out by holding a mixture of calcium carbonate and distilled water
fractionations at 500°C
6 watd' (inithl)
A@
A meaH=
Fraction of equlllbrium @
Material balan&%.)
1
1
31
0
1.34
-0.12
2
1
31
+15
1.27
-0.12
3
1
31
+2a
1.39
+0.42 1.33f.04
4
2
46
0
1.00
+0.17
5
2
46
0
0.68
+0.03
6
2
46
+2a
1.32
-0.03
7
2
46
+2a
0.88
+a.23
8
2
46
0
0.78
-0.24
9
2
46
-10
1.23
-0.29
10
2
30
+28
0.77
-0.07
11
2
30
0
1.05
-0.05 0.96t.19
12
8
1
0
1.07
13
8
1
+28
1.29
14
a
1
0
1.58
15
8
1
+28
0.81
0.98
Nl.21 -0.35 w.41 -0.11
1.18f.23 16
11
4
0
1.80
17
11
4
+28
1.09
-0.80 0.00 .23
18
13
4
0
19
13
4
+2a
1.23
-0.22
1.22,
w.04 .23
20
20
1
0
21
20
1
+2a
at 5C!O”Cis
1.45
+0.24
1.w
(1) Isotopic composition of water in ¬ation, relative to SMOW (CRAIG, 1961). The reagent calcite used in all experiments has 6 = +24.67& so that in experiments in which Gwater < +23.4y&,, the equilibrium A is approached from above and in experiments in which Gwater > +23.4%,, the equilibrium A is approached from below. (2) Measured A value for individual experiment, determined from isotopic compositions of run products. (3) Mean A’s for experiments at 1 and 2 kbar are arithmetic means of individual A’s. For experiments at 8 kbar and above, mean A’s are weighted in inverse proportion to distance from equilibrium of starting materials to take account of incomplete equilibration (NORTHROPand CLAYTON,1966). Assigned error is mean deviation of observations. (4) Determined by method of NORTHROPand CLAYTON(1968). (5) Difference between measured isotopic composition of products and that of reactants, as a check on quality of run. For an ideal experiment, value should be 0 k 0.2 (combined error of four isotopic analyses). Occasional values beyond these limits may be due to evaporation of water during sealing of capsule, which would not seriously affect final A if equilibrium is closely approached. (6) Final water lost; its isotopic composition was calculated assuming material balance.
Notes
I200
at a known
temperature and pressure for a period of l40days. followed by oxygen isotopic analysis of both phases. Most of the experiments were carried out at 500°C. over the pressure range l--20 kbar. Some equilibrations were done at 7oO’C. at pressures of 0.5 and I kbar. For pressures of 2 kbar or less, cold-sea1 bombs were used; for higher pressures. a solid medium piston-cylinder apparatus was used. The pressure medium was talc. The samples were brought to the final desired pressure in the cold state and then heated to the final temperature of 500°C. In doing so. the pressure gauge rose by ll2 per cent. This rise was considered to counterbalance the frictional pressure loss in the solid pressure medium and the initial pressure setting was recorded as the run pressure. This assumption can be checked by comparing the pistoncylinder runs on the calciteearagonite transition of GOLDSMITH and NEWTON (1969) which were done in a manner identical to those of the present piston-cylinder runs, with the gas-apparatus runs of JOHANNES and PUHAN (1971) in which pressures were measured with a manganin gauge. The piston-cylinder determination agrees within two to three hundred bars with the gas apparatus result. Thus a pressure uncertainty estimate of k 400 bar for the present runs is considered appropriate. Temperatures were measured with chromel-P-alumel thermocouples in direct contact with the sample capsules. The temperature difference across the small capsules could not have exceeded IO’C. No correction was made for the effect of pressure on thermocouple e.m.f. 4 typical charge consisted of 7~~IO mg of reagent calcite and 7 IO mg of distilled water. Several water samples of known oxygen isotopic composition were available so that equilibrium could be approached from opposite directions, The charge was sealed by welding into a gold or platinum tube l-2 mm in diameter, and IO mm long. After equilibration, the furnaces were quenched rapidly. and the capsule reweighed to verify that no leakage had occurred. The capsule was then placed inside a highvacuum system where it was punctured by a steel needle. The water was completely distilled into a tube for reaction with bromine pentafluoride to liberate oxygen. which was converted to COz for analysis. The capsule was then removed from the vacuum system and cut open. The carbonate was removed and treated with 100 per cent H,PO, to liberate CO] for isotopic analysis.
RESULTS
AND
DISCUSSION
The results of experiments conducted at SOO’C are in Table 1. At pressures of 8 kbar and above, isotopic exchange was rapid, >98 per cent of equilibrium being attained in one day. The data obtained from runs at 2 kbar are more scattered than expected, but not apparently due to lack of equilibration. The value of A = I.33 at I kbar is in reasonable agreement with the value of 1.50 k 0.12 measured by O’NEIL rt al. (1971). The difference. if real. may be due to the fact that the earlier experiments were done with 0.6M NH,Cl solutions, rather than distilled water. The experimental data plotted in Fig. 2 show no trend of isotopic fractionation with pressure from 1
2
I
I calcite
I
1 /
oroqonite
oo-------J 5
10
P kilobors
45
20
Fig 2. Isotopic fractionation between CaCOs and water at 500 ‘C as a function of pressure. Relow I2 kbar, calcite is stable; above 12 kbar. aragonite is stable. Error bars show mean deviations from mean at each pressure. 20 kbar. all values falling in the range: A = 1.2 k O.?“,,,,. Not only is there no observable effect of pressure. there is also no measurable effect due to the calcite-aragonite phase change which occurs between the I I and 13 kbar experiments, Because of the apparent small difference between data at I and 2 kbar. a search was made for a pressure effect in the IOM.pressure region which might come about in a hydrothermal system due 70 the change of density of the fluid phase with pressure. Above 5 kbar, the specific volume of water changes rather slowly with pressure: below 5 kbar the specific volume changes rapidly with pressure Thus, the fluid is more liquid-like at high pressure and more vaporlike at low pressure. and might give different crystal fluid isotopic fractionations as a result. Due to the relative slowness of the calcite-water exchange reaction at low pressures, it was considered unlikely that equilibrium could be reached at 500 . and pressures less than 1kbar. in reasonable time. Hence. a search for a low pressure effect was conducted at 7OOC. The results are presented in Table 2. Although there is a difference in density of water by a factor of 2 between the two experiments, the fractionation factors are equal. within experimental error. to
CONCLUSIONS
presented
No measurable change in oxygen isotopic fractionation factor between calcium carbonate and water Table
2. CaCO,
Hz0
fractionations
at 700 C
Notes has been found at 500” from 1 to 20 kbar, and at 700” from 0.5 to 1 kbar. From the experiments at 500”, it is possible to place an upper limit on the change of volume in the exchange reaction (I), as follows. If a value of 1.0004 is taken as an upper limit on the ratio of K at 20 kbar to K at 1 kbar (corresponding to an upper limit for the A difference of 0.4x0), then the upper limit on AV is 1.3 x 10-4cm3/mole. This result is compatible with that given in the section ‘Theoretical Considerations’ above, but is much smaller than the value 0.14cm3/ mole estimated by JOY and LIBBY (1960). The principal difference between our calculations of the isotopic size effect and that of JOY and LIBBY (1960) is that we have estimated the change in the mean value- of the C-O bond length, which results from anharmonicity of the vibrational potential, whereas Joy and Libby estimated the change in the root-meansquare value of the C-O distance, which depends on vibrational amplitudes, and does not require anharmonicity. In condensed phases, it is the mean atomic positions which determine the forces on neighbouring ions and hence determine the molar volume of the condensed phase. It was pointed out by JOY and LIBBY (1960) that the carbonate-water system is a good candidate for exhibiting an isotopic pressure effect, since, in one species in the exchange reaction (CaCO& oxygen atoms have relatively large vibrational amplitudes (and hence isotopic size effects) and in the other species (H,O) the oxygen atoms have small vibrational amplitudes. Thus the decrease in volume of CaC03 in reaction (1) is not offset by an equal increase in volume of HzO. This situation would not hold for an exchange reaction between two silicates, where the vibrational motions of oxygen are likely to be similar, so that the decrease in molar volume of one phase would be largely offset by the increase in volume of the other. In such cases, which correspond to most applications of oxygen isotopes to igneous and metamorphic rocks, the upper limit for the change of volume on isotopic substitution may be reduced by a further factor of 5 or 10. Thus we may safely conclude that pressure effects on oxygen isotopic fractionation Eactors are very small (<0,2x,) even at pressures of tens of kilobars. GARLICK et al. (1971) noted variations of more than 576, in O’s/O’6 in eclogite xenoliths from kimberlite, and attributed these relatively large effects to a pressure dependence of the crystal-liquid isotopic fractionation factors. The present experimental results would appear to rule out such an explanation, and
1201
alternative mechanisms must be sought to account for the observations on eclogites. It was noted during the course of these experiments that the rates of isotopic exchange and recrystallization were much greater at several kilobars than at 1 kbar. This fact, plus the observation that pressure effects on the equilibrium state are negligible, suggest that studies of isotopic equilibrium.in the laboratory can be carried out over a broader range of temperatures, and applied to less reactive minerals, by using higher pressures than have been used in most such studies to date. Acknowledgements-Financial support for this work was provided by the National Science Foundation through a grant to the Materials Research Laboratory and through grants GA-2271 1 (Clayton), GA-35164 (Goldsmith) and GA-22904 (Newton). REFERENCES BARTELLL. S. and ROSKOSR. R. (1966) Isotope effects on molar volume and surface tension: simple theoretical model and experimental data for hydrocarbons. J. Chem. Phys. 44, 451-463.
CRAIG H. (1961) Standard for reporting concentrations of deuterium and oxygen-18 in natural waters. Science 133, 1833-1834. GARLICKG. D., MACGREGORI. D. and VOGELD. E. (1971) Oxygen isotope ratios in eclogites from kimberlites. Science 172, 1025-1027. GOLDSMITHJ. R. and NEWTONR. C. (1969) The P-T-X relations in the system CaC03-M&O3 at high temperatures and pressures. Amer. J. Sci. 267A, 16&190. HOERINCT. C. (1961) The effect of-physical changes on isotopic fractionation. Annual Report of the Director of the Geophysical Laboratory, Carnegie Institution of Washington, pp. 201-204. JOHANNES W. and PUHAN D. (1971) The calcite-aragonite transition, reinvestigated. Contrih. Mineral. Petrol. 31, 28-29. JOY H. W. and LIBBY W. F. (1960) Size effects among isotopic molecules. J. Chem. Phys. 33, 1276. KUCHITSUK. and BAR~LL L. S. (1962a) Effect of anharmanic vibrations on the bond lengths of polyatomic molecules. I: Model of force field and application to water. J. Chem. Phys. 36, 246C-2469. KUCHITSUK. and BARTELLL. S. (1962b) Effect of anharmanic vibrations on the bond lengths of polyatomic molecules. II: Cubic constants and equilibrium bond lengths in methane. J. Chem. Phys. 36, 247@2481. MORSEP. M. (1929) Diatomic molecules according to the wave mechanics-II. Vibrational levels. Pkys. Reu. 24, 57-64. NORTHROPD. A. and CLAYTONR. N. (1966) Oxygen-isotope fractionation in systems containing dolomite. J. Geol. 74, 174-196. O’NEIL J. R., CLAYTONR. N. and MAYEDAT. K. (1971) Oxygen isotope fractionation in divalent metal carbonates. J. Chem. Phys. 51, 5547-5558.
MARLANDG. (1975) The stability of CaCO, .6H,O (ikaite). Geochim. C&m&him. Acta 39, 83-91. _ _ MAR~CHNERH. (1969) Hydrocalcite (CaCOa.H,O) and nesquehonite (MgCO, .3H,O) in’ carbonate scales. Science 165, 1119-1120. ROBIE R. A. and WALDBAUM D. R. (1968) Thermodynamic properties of minerals and related substances at 298.15” K (250°C) and one atmosphere (1.013 bars) pressure and at higher temperature. LI.S. Geol. Suru. Bull. 1259, 256 pp. SAFQZHNIKOV D. G. and TSVETKOVA. L. (1960) Precipitation of hydrous calcium carbonate on the bottom-of Lake Issyk Kul. Dokl. Akad. Nauk SSSR Earth Sci. 124, 131-133.
1197
SEMENOV
E. I. (1964) Hydrated carbonates of sodium and calcium. Soviet Phys. ~Cryst. 1964, 88-90. STAAVELEY L. A. K. and LINDFORDR. G. (1969) The heat capacity and entropy of calcite and aragonite, and their interpretation. J. Chem. Thermodynamics, 1, l-11. TURNBULLA. G. (1973) A thermochemical study of vaterite. Geochim. Cosmochim. Acta 37, 1593-1602. VAN TASSEL R. (1962) Carbonatniederschllge aus calcium-magnesiumchloridliisungen. Z. gemischten Anorg. Allgem. Chem. 319, 107-112. ZEN E. (1966) Construction of pressure-temperature diagrams for multi-component systems after the method of Schreinemakers-a geometric approach. U.S. Geol. Surv. Bull. 1225, 56 pp.
Geochimica et Cosmochimica Acta. 1975, Vol. 39, pp. I197 to 1201. Pergamon Press. Printed in Great Brrtain
NOTE
Limits on the effect of pressure on isotopic fractionation ROBERT N. CLAYT~N,*~$ JULIAN R. GOLDSMITH,~KARIN J. KAREL,$$ TOSHIKO K. MAYEDA* and ROBERT C. NEWToNt Enrico Fermi Institute,* Department of Geophysical Sciences,? and Department of Chemistry,$ The University of Chicago, 5630 Ellis Avenue, Chicago, Illinois 60637, U.S.A. (Received 27 August 1974; accepted in revised
form 9 December
1974)
Abstract-The equilibrium distribution of oxygen isotopes between calcium carbonate and water was determined at 500°C at pressures from 1 to 20 kbar and at 700°C at pressures of 0.5 and 1 kbar. At both temperatures, the pressure-dependence of the fractionation’factor was below the limit of detection. The experimental results are consistent with theoretical estimates of the volume change due to isotope substitution. Application of the theory to silicate systems leads to the conclusion that pressure effects on oxygen isotopic fractionation between silicates are <02x, at pressures of tens of kilobars. Thus the observed large variations of O1*/O’6 ratio in kimberlitic eclogites cannot be attributed to the effect of pressure. INTRODUCTION
of stable isotope geothermometry that the effect of pressure on isotopic fractionation is negligible. This assumption is based on the fact that isotopic substitution makes only a minute change in the molar volume of solids and liquids. However, neither theoretical calculations nor prior experiments have ruled out the possibility that measurable pressure effects might exist at pressures of tens or hundreds of kilobars, with significant consequences for the isotopic compositions of mantle rocks
IT IS A basic assumption
and mantle-derived
rocks.
4 Present address: Department of Chemistry, Princeton University, Princeton, N.J., U.S.A.
The effect of pressure on oxygen isotope fractionation between calcium carbonate and water has been estimated theoretically (JOY and LIBBY, 1960). If their treatment were correct, isotopic fractionations in the lower crust and upper mantle would be dominated by pressure effects rather than temperature effects. The only published experimental search for pressure effects on isotopic fractionation was carried out on the reaction between water and dissolved bicarbonate ion (HOERING, 1961). The fractionation factor at 4 kbar was not measurably different from that at one bar. In only one instance have isotopic pressure effects been adduced to account for observed oxygen isotope abundance in rocks (GARLICK et al., 1971). The authors concluded that crystal-liquid fractionations
119x
News
in basaltic-eclogitic
magma
must
increase
with
pres-
Oxygen isotopic fractionation between calcium bonate and water can be described by the exchange tion:
carrcac-
sure. THEORETICAL
CONSIDERATIONS
I ,3CaCO”’3 + H z 0’” s Ii3 CaC0183 + H,O’”
(1)
for which K = (O”;O”‘)
CaCOJ(0”
‘0”‘) H,O.
(2,
the carbonate ion. the (‘-0’” bond should be only I.6 x IO A A shorter than the C-Olh bond [Fig. l(b)]. This decrease in carbon-oxygen bond length results in a decreased ionic radius of the carbonate ion and hence a decrcasc of molar volume of the CaCO, crystal. The fractional change of molar volume is then approximately equal to three times the fractional change in cation-anion distance. Taking the Cd?‘--C distance to be 3.2& we estimate the fractional change in molar volume (AVIV) to hc I.5 X 10-4. which leads to a difference of 5.6 x IO 3 cm’.‘molc between CaCOih and CaCOAs. The change of molar volume on O’* substitution in H,O is considerably smaller. since the oxygen atom displacements
and ,A = IGWln h From the pressure phase:
dependence
(:I
of free cnerpq
for each
g -.95 and the relationship between standard free energy change:
equilibrium
constant
and
it follows that
/
/
/
4.05
1.00
I
4.40
I
4.45
R(B) where AC’ is the volume change per molt for the rcactlon as written. An effect of pressure on the equilibrium constant will result if AV for the exchange reaction is not zero. It is known both from theory and from experiment that isotopic substitution does have an effect on molecular dimensions, with substitution of a heavier isotope leading to shorter bonds. It may be instructive to consider. as a model. the methane molecule, for which experimental and theoretical studies exist (KUCHITSU and BAKTELI.. 1962a. h). In a molecule of methane in the gas phase, even though the potential energy curves for CH, and CD, arc the same, the equilibrium bond lengths (R,) are different due to the anharmonicity of the vibrations. and the fact that C’H 1 has a larger zero-point energy. KWHITSC and BAKTLLI (1962a) calculated the mean value of the C D bond length to be about 0.004A less than that of the C-H bond, based on a quantum mechanical treatment of the anharmonic oscillator. A very similar estimate of the bond lengths can be obtained simply by taking the value of the bond-lengths equal to the mean of the two limits of the corresponding classical vibration. as illustrated in Fig. l(a), A similar difference in bond length has been observed between D,O and Hz0 (KC’CHITW and BAKTELI.. 1962b). The differences in bond lengths lead to differences of about 0.3 per cent in the molar volumes between liquid hydrocarbons and deutcrocarbons (BAK.TELL and ROSK~S. 1966). By the same methods, the volume change on substitution of 0” for OLh in the carbonate ion can be cstimatcd by approximating the potential energy curve by a Morse function (MORSE. 1929), and calculating the difference in the mean C-O bond length due to anharmonicity. Fol
4.25
4.30
4.35
4.40
R (8) Fig. I. Morse curves for CH, (a) and CO:(b). approximated as diatomic molecules. Parameters used are as follows: bond dissocation energy D = 104 kcal/mole for methane. I I I kcal/mole for carbonate ion: minimum in potential curve R,. = I%5 A for methane, l.3OOA for carbonate ion: stretching force constant k = 4.88 x lo5 dyne/ cm for methane, X.50 x IO” dyne/cm for carbonate ion. Energy levels shown arc zero-point energies for the labeled isotopic species. E is potential energy relative to dissociated hond. It is not implied that the absolute values of R,,. the equilibrium bond lengths. are known to 5 or 6 significant ligures. Only the cl~yu m R, on isotopic substitution contributes to the estimate of At!
Notes are very small in the vibrations of the water molecule, resulting in very small zero-point energy differences betweenH,016 and H,O’*. ThuH, for the o&all exchange reaction (11 in which l/3 mole of CaCOl is involved. an upper limit of about 1.9 x 10e3 cm3/mole may be estimated for AK The corresponding upper limit on the pres-
Table 1. CaCOs-HZ0 Run I
PreSSWe (kb)
Tine (days)
1199
sure effect on the calcitewater O.O3”%Jkbar.
fractionation
EXPERIMENTAL
METHODS
Isotopic equilibration experiments were carried out by holding a mixture of calcium carbonate and distilled water
fractionations at 500°C
6 watd' (inithl)
A@
A meaH=
Fraction of equlllbrium @
Material balan&%.)
1
1
31
0
1.34
-0.12
2
1
31
+15
1.27
-0.12
3
1
31
+2a
1.39
+0.42 1.33f.04
4
2
46
0
1.00
+0.17
5
2
46
0
0.68
+0.03
6
2
46
+2a
1.32
-0.03
7
2
46
+2a
0.88
+a.23
8
2
46
0
0.78
-0.24
9
2
46
-10
1.23
-0.29
10
2
30
+28
0.77
-0.07
11
2
30
0
1.05
-0.05 0.96t.19
12
8
1
0
1.07
13
8
1
+28
1.29
14
a
1
0
1.58
15
8
1
+28
0.81
0.98
Nl.21 -0.35 w.41 -0.11
1.18f.23 16
11
4
0
1.80
17
11
4
+28
1.09
-0.80 0.00 .23
18
13
4
0
19
13
4
+2a
1.23
-0.22
1.22,
w.04 .23
20
20
1
0
21
20
1
+2a
at 5C!O”Cis
1.45
+0.24
1.w
(1) Isotopic composition of water in ¬ation, relative to SMOW (CRAIG, 1961). The reagent calcite used in all experiments has 6 = +24.67& so that in experiments in which Gwater < +23.4y&,, the equilibrium A is approached from above and in experiments in which Gwater > +23.4%,, the equilibrium A is approached from below. (2) Measured A value for individual experiment, determined from isotopic compositions of run products. (3) Mean A’s for experiments at 1 and 2 kbar are arithmetic means of individual A’s. For experiments at 8 kbar and above, mean A’s are weighted in inverse proportion to distance from equilibrium of starting materials to take account of incomplete equilibration (NORTHROPand CLAYTON,1966). Assigned error is mean deviation of observations. (4) Determined by method of NORTHROPand CLAYTON(1968). (5) Difference between measured isotopic composition of products and that of reactants, as a check on quality of run. For an ideal experiment, value should be 0 k 0.2 (combined error of four isotopic analyses). Occasional values beyond these limits may be due to evaporation of water during sealing of capsule, which would not seriously affect final A if equilibrium is closely approached. (6) Final water lost; its isotopic composition was calculated assuming material balance.
Notes
I200
at a known
temperature and pressure for a period of l40days. followed by oxygen isotopic analysis of both phases. Most of the experiments were carried out at 500°C. over the pressure range l--20 kbar. Some equilibrations were done at 7oO’C. at pressures of 0.5 and I kbar. For pressures of 2 kbar or less, cold-sea1 bombs were used; for higher pressures. a solid medium piston-cylinder apparatus was used. The pressure medium was talc. The samples were brought to the final desired pressure in the cold state and then heated to the final temperature of 500°C. In doing so. the pressure gauge rose by ll2 per cent. This rise was considered to counterbalance the frictional pressure loss in the solid pressure medium and the initial pressure setting was recorded as the run pressure. This assumption can be checked by comparing the pistoncylinder runs on the calciteearagonite transition of GOLDSMITH and NEWTON (1969) which were done in a manner identical to those of the present piston-cylinder runs, with the gas-apparatus runs of JOHANNES and PUHAN (1971) in which pressures were measured with a manganin gauge. The piston-cylinder determination agrees within two to three hundred bars with the gas apparatus result. Thus a pressure uncertainty estimate of k 400 bar for the present runs is considered appropriate. Temperatures were measured with chromel-P-alumel thermocouples in direct contact with the sample capsules. The temperature difference across the small capsules could not have exceeded IO’C. No correction was made for the effect of pressure on thermocouple e.m.f. 4 typical charge consisted of 7~~IO mg of reagent calcite and 7 IO mg of distilled water. Several water samples of known oxygen isotopic composition were available so that equilibrium could be approached from opposite directions, The charge was sealed by welding into a gold or platinum tube l-2 mm in diameter, and IO mm long. After equilibration, the furnaces were quenched rapidly. and the capsule reweighed to verify that no leakage had occurred. The capsule was then placed inside a highvacuum system where it was punctured by a steel needle. The water was completely distilled into a tube for reaction with bromine pentafluoride to liberate oxygen. which was converted to COz for analysis. The capsule was then removed from the vacuum system and cut open. The carbonate was removed and treated with 100 per cent H,PO, to liberate CO] for isotopic analysis.
RESULTS
AND
DISCUSSION
The results of experiments conducted at SOO’C are in Table 1. At pressures of 8 kbar and above, isotopic exchange was rapid, >98 per cent of equilibrium being attained in one day. The data obtained from runs at 2 kbar are more scattered than expected, but not apparently due to lack of equilibration. The value of A = I.33 at I kbar is in reasonable agreement with the value of 1.50 k 0.12 measured by O’NEIL rt al. (1971). The difference. if real. may be due to the fact that the earlier experiments were done with 0.6M NH,Cl solutions, rather than distilled water. The experimental data plotted in Fig. 2 show no trend of isotopic fractionation with pressure from 1
2
I
I calcite
I
1 /
oroqonite
oo-------J 5
10
P kilobors
45
20
Fig 2. Isotopic fractionation between CaCOs and water at 500 ‘C as a function of pressure. Relow I2 kbar, calcite is stable; above 12 kbar. aragonite is stable. Error bars show mean deviations from mean at each pressure. 20 kbar. all values falling in the range: A = 1.2 k O.?“,,,,. Not only is there no observable effect of pressure. there is also no measurable effect due to the calcite-aragonite phase change which occurs between the I I and 13 kbar experiments, Because of the apparent small difference between data at I and 2 kbar. a search was made for a pressure effect in the IOM.pressure region which might come about in a hydrothermal system due 70 the change of density of the fluid phase with pressure. Above 5 kbar, the specific volume of water changes rather slowly with pressure: below 5 kbar the specific volume changes rapidly with pressure Thus, the fluid is more liquid-like at high pressure and more vaporlike at low pressure. and might give different crystal fluid isotopic fractionations as a result. Due to the relative slowness of the calcite-water exchange reaction at low pressures, it was considered unlikely that equilibrium could be reached at 500 . and pressures less than 1kbar. in reasonable time. Hence. a search for a low pressure effect was conducted at 7OOC. The results are presented in Table 2. Although there is a difference in density of water by a factor of 2 between the two experiments, the fractionation factors are equal. within experimental error. to
CONCLUSIONS
presented
No measurable change in oxygen isotopic fractionation factor between calcium carbonate and water Table
2. CaCO,
Hz0
fractionations
at 700 C
Notes has been found at 500” from 1 to 20 kbar, and at 700” from 0.5 to 1 kbar. From the experiments at 500”, it is possible to place an upper limit on the change of volume in the exchange reaction (I), as follows. If a value of 1.0004 is taken as an upper limit on the ratio of K at 20 kbar to K at 1 kbar (corresponding to an upper limit for the A difference of 0.4x0), then the upper limit on AV is 1.3 x 10-4cm3/mole. This result is compatible with that given in the section ‘Theoretical Considerations’ above, but is much smaller than the value 0.14cm3/ mole estimated by JOY and LIBBY (1960). The principal difference between our calculations of the isotopic size effect and that of JOY and LIBBY (1960) is that we have estimated the change in the mean value- of the C-O bond length, which results from anharmonicity of the vibrational potential, whereas Joy and Libby estimated the change in the root-meansquare value of the C-O distance, which depends on vibrational amplitudes, and does not require anharmonicity. In condensed phases, it is the mean atomic positions which determine the forces on neighbouring ions and hence determine the molar volume of the condensed phase. It was pointed out by JOY and LIBBY (1960) that the carbonate-water system is a good candidate for exhibiting an isotopic pressure effect, since, in one species in the exchange reaction (CaCO& oxygen atoms have relatively large vibrational amplitudes (and hence isotopic size effects) and in the other species (H,O) the oxygen atoms have small vibrational amplitudes. Thus the decrease in volume of CaC03 in reaction (1) is not offset by an equal increase in volume of HzO. This situation would not hold for an exchange reaction between two silicates, where the vibrational motions of oxygen are likely to be similar, so that the decrease in molar volume of one phase would be largely offset by the increase in volume of the other. In such cases, which correspond to most applications of oxygen isotopes to igneous and metamorphic rocks, the upper limit for the change of volume on isotopic substitution may be reduced by a further factor of 5 or 10. Thus we may safely conclude that pressure effects on oxygen isotopic fractionation Eactors are very small (<0,2x,) even at pressures of tens of kilobars. GARLICK et al. (1971) noted variations of more than 576, in O’s/O’6 in eclogite xenoliths from kimberlite, and attributed these relatively large effects to a pressure dependence of the crystal-liquid isotopic fractionation factors. The present experimental results would appear to rule out such an explanation, and
1201
alternative mechanisms must be sought to account for the observations on eclogites. It was noted during the course of these experiments that the rates of isotopic exchange and recrystallization were much greater at several kilobars than at 1 kbar. This fact, plus the observation that pressure effects on the equilibrium state are negligible, suggest that studies of isotopic equilibrium.in the laboratory can be carried out over a broader range of temperatures, and applied to less reactive minerals, by using higher pressures than have been used in most such studies to date. Acknowledgements-Financial support for this work was provided by the National Science Foundation through a grant to the Materials Research Laboratory and through grants GA-2271 1 (Clayton), GA-35164 (Goldsmith) and GA-22904 (Newton). REFERENCES BARTELLL. S. and ROSKOSR. R. (1966) Isotope effects on molar volume and surface tension: simple theoretical model and experimental data for hydrocarbons. J. Chem. Phys. 44, 451-463.
CRAIG H. (1961) Standard for reporting concentrations of deuterium and oxygen-18 in natural waters. Science 133, 1833-1834. GARLICKG. D., MACGREGORI. D. and VOGELD. E. (1971) Oxygen isotope ratios in eclogites from kimberlites. Science 172, 1025-1027. GOLDSMITHJ. R. and NEWTONR. C. (1969) The P-T-X relations in the system CaC03-M&O3 at high temperatures and pressures. Amer. J. Sci. 267A, 16&190. HOERINCT. C. (1961) The effect of-physical changes on isotopic fractionation. Annual Report of the Director of the Geophysical Laboratory, Carnegie Institution of Washington, pp. 201-204. JOHANNES W. and PUHAN D. (1971) The calcite-aragonite transition, reinvestigated. Contrih. Mineral. Petrol. 31, 28-29. JOY H. W. and LIBBY W. F. (1960) Size effects among isotopic molecules. J. Chem. Phys. 33, 1276. KUCHITSUK. and BAR~LL L. S. (1962a) Effect of anharmanic vibrations on the bond lengths of polyatomic molecules. I: Model of force field and application to water. J. Chem. Phys. 36, 246C-2469. KUCHITSUK. and BARTELLL. S. (1962b) Effect of anharmanic vibrations on the bond lengths of polyatomic molecules. II: Cubic constants and equilibrium bond lengths in methane. J. Chem. Phys. 36, 247@2481. MORSEP. M. (1929) Diatomic molecules according to the wave mechanics-II. Vibrational levels. Pkys. Reu. 24, 57-64. NORTHROPD. A. and CLAYTONR. N. (1966) Oxygen-isotope fractionation in systems containing dolomite. J. Geol. 74, 174-196. O’NEIL J. R., CLAYTONR. N. and MAYEDAT. K. (1971) Oxygen isotope fractionation in divalent metal carbonates. J. Chem. Phys. 51, 5547-5558.