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REE diffusion in calcite
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Earth and Planetary Science Letters 160 (1998) 273–287
REE diffusion in calcite D.J. Cherniak * Department of Earth and Environmental Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA Received 24 July 1997; revised version received 19 February 1998; accepted 9 March 1998
Abstract Chemical diffusion of four rare-earth elements (La, Nd, Dy and Yb) has been measured in natural calcite under anhydrous conditions, using rare-earth carbonate powders as the source of diffusants. Experiments were run in sealed silica capsules along with finely ground calcite to ensure stability of the single-crystal samples during diffusion anneals. Rutherford backscattering spectroscopy (RBS) was used to measure diffusion profiles. The following Arrhenius relations were obtained over the temperature range 600–850ºC: DLa D 2:6 ð 10 14 exp. 147 š 14 kJ mol 1 =RT ) m2 s 1 , DNd D 2:4 ð 10 14 exp. 150 š 13 kJ mol 1 =RT ) m2 s 1 , DDy D 2:9 ð 10 14 exp. 145 š 25 kJ mol 1 =RT ) m2 s 1 , DYb D 3:9 ð 10 12 exp. 186 š 23 kJ mol 1 =RT ) m2 s 1 . In contrast to previous findings for refractory silicates (e.g. zircon), differences in transport rates among the REE are not pronounced over the range of temperature conditions investigated in this study. Diffusion of the REE is significantly slower than diffusion of the divalent cations Sr and Pb and slower than transport of Ca and C at temperatures above ¾650ºC. Fine-scale zoning and isotopic and REE chemical signatures may be retained in calcites under many conditions if diffusion is the dominant process affecting alteration. 1998 Elsevier Science B.V. All rights reserved. Keywords: rare earths; diffusion; calcite
1. Introduction Carbonate minerals can be major constituents of sediments and sedimentary rocks. They incorporate a number of minor and trace elements, including the REEs, that provide invaluable information about the environment and processes that influence mineral formation and growth, as well as the circumstances characterizing subsequent alteration. The REEs, while to some degree chemically similar to one another because they all possess the same number and type of valence electrons in their outermost shells, do exhibit varying geochemical behavior. This is to a great extent a consequence of the Ł Fax:
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decreasing size of REE ionic radii with increasing atomic number, a function of the enhanced attraction between 4f subshell electrons and the nucleus as the respective charges increase. Hence, the REE are useful in tracing and interpreting kinetic processes. In the case of diffusion, the influence of these differences in ionic radii can be pronounced. In zircon [1], for example, quite dramatic decreases in diffusion rates (and concomitant increases in activation energies for diffusion) are observed in measurements across the lanthanide series from heavy to light REE. Calcite commonly displays zoning of trivalent and divalent cations on the scale of micrometers to tens of micrometers. While zoning in Mn2C is most widely reported both because of the ubiquity of the element and its characteristic orange luminescence,
0012-821X/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 0 8 7 - 9
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zoning of Fe, Y and Sr has been observed in analyses with PIXE [2]. Several of the REE, notably Sm3C , Dy3C , Tb3C , and Eu in both trivalent and divalent states, are also activators in cathodoluminescence (CL) spectroscopy (e.g. [3,4]) of carbonates. Activation is more commonly observed in vein calcites and carbonatites rather than in sedimentary carbonates [4] because of the relatively high REE contents of the former. REE zoning has been observed in calcite with CL (e.g. [5]), and zoning patterns tend to be resistant to thermal alteration, as calcites heated to temperatures up to 490ºC show little evidence of change in REE distributions [5]. In the present study, we investigate diffusion rates of a range of rare earths in calcite. Knowledge of such transport rates, as noted above, may assist in the determination of the extant character of chemical environments during calcite growth and alteration and permit better understanding of constraints on the formation and retention of trivalent cation zoning in carbonates. In addition, by measuring transport of light, intermediate, and heavy rare earths, we may assess the degree of dependence (if any) of diffusion on REE ionic radii. Whether such trends are common among minerals or are more nearly a function of specific crystal–chemical characteristics of zircon —e.g. low ionic porosity, cf. [6–8], small size of Zr4C with respect to substituent cations— remains to be determined. With further systematic studies of diffusion of the REEs in other minerals, it may be possible to elucidate these observations and develop general predictive models for REE transport.
2. Experimental procedure The experiments were performed on natural calcite from Mexico. Compositional information for N the calcite is presented in Table 1. Natural f1014g cleavage surfaces were used in all diffusion anneals. Powder XRD of a representative specimen indicated the presence of no phases other than calcite. Other orientations were not investigated, although another study [9] suggests that cation diffusion in calcite is not strongly anisotropic. Rare-earth carbonate powder sources were used for all experiments. A single REE (La, Nd, Dy or Yb) was used in each experiment in order to preclude
Table 1 Bulk composition of calcite specimen used in study CaO Fe2 O3 MnO MgO TiO2 Cr2 O3 Na2 O K2 O Al2 O3 SiO2 P2 O5 Be B Sc V Co Ni Cu Zn Ge As Se Br Rb Sr Y Zr Nb Mo Ag Cd Sb Cs Ba La Ce Nd Sm Eu Tb Yb Lu Hf Ta W Ir Pb Th U
55.9 0.05 0.05 <0.01 <0.001 <0.01 <0.01 <0.01 <0.01 <0.01 >0.01 <1 <10 0.08 <2 1.0 <1 <0.5 <0.5 <10 <1 <1 4.5 <10 198 15 <10 18 <2 <0.2 <1 0.1 <0.5 <10 <0.5 <1 <3 0.02 0.18 <0.1 <0.20 <0.05 <0.2 <0.5 5 <0.005 <2 <0.2 <0.1
Be, B, V, Ni, Cu, Zn, Ge, Ag, Cd and Pb were measured on the bulk sample by ICP at XRAL Laboratories. Sc, Cr, Co, As, Se, Br, Mo, Sb, Cs, the REEs, Hf, Ta, W, Ir, U and Th were measured by neutron activation. All other elements were measured by XRF at XRAL. Oxides are wt%, other elements are in (wt) ppm.
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interferences from signals of the other REEs in the RBS spectra. The carbonates were dried thoroughly in a drying oven at ¾120ºC, then placed in Pt capsules (3 mm od, welded at one end) with a cleaved calcite specimen. The prepared capsules were then left in the drying oven overnight. After removal from the drying oven, Pt capsules were sealed under vacuum in silica glass tubes (6 mm od, 4 mm id). A small amount of CaCO3 powder was also sealed in the silica glass tubing with the Pt capsules to ensure calcite sample stability (by generation of some gaseous CO2 in the capsule environment) throughout the diffusion anneals. The silica capsules were annealed in 1-atm vertical tube furnaces for times ranging from 1 day to 3 months at temperatures from 600º to 850ºC. Temperatures in the furnaces were monitored with chromel-alumel (type K) thermocouples. Temperature uncertainties were typically š2ºC. After diffusion anneals, the sample capsules were simply quenched by removing them from the furnace and permitting them to cool in air. The capsules were then opened and samples removed and freed of residual source material clinging to surfaces by ultrasonic cleaning in ethanol. Sources of diffusant selected were easily removed from sample surfaces and samples displayed no evidence of surface reaction following diffusion anneals. A ‘zero-time’ experiment was also run to determine whether there might be rapid initial non-diffusional uptake of the diffusing species or other difficulties with the experimental protocol. For this experiment, a capsule was prepared as above, brought up to run temperature, and immediately quenched.
3. RBS analyses The RBS analyses were performed at the 4 MeV Dynamitron accelerator at the University at Albany – SUNY. A beam of 2 MeV 4 HeC ions was used, with backscattered ions detected by a silicon surface barrier detector. Beam spot size for analysis was typically about 1 mm2 . For each sample, a number of brief analyses was collected at several spots on the sample surface to test for reproducibility and to determine whether unusual conditions (e.g. the presence of large numbers of cracks) might exist on a region of the sample that would produce anomalous
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profiles. Following such reconnaissance, RBS spectra were taken with longer acquisition times (typically 15 to 50 min). The spectra (counts vs. channel, collected in a multichannel analyzer, MCA) were converted to concentration profiles with computer code involving a number of steps. MCA channel number was first related to detected particle (4 HeC ) energy through calibration with standards (typically SiO2 glass and thin-film metal targets). A depth scale was then generated by calculating the rate of energy loss .dE=dx/ for the ions traveling through the calcite before and after the scattering events. These energy-loss rate values, or stopping powers, were calculated for calcite using analytical polynomial expressions for elemental stopping powers [10] and by weighting the contribution of each element to the total stopping power by considering its atomic concentration in the matrix. Particle yields were converted into REE concentrations by taking into account the probability of scattering events for the relevant atomic species at corresponding depths in the samples. Further details on the RBS technique [10] and analytical procedures employed (e.g. [11,12]) are outlined elsewhere. Typical diffusion profiles and their inversions through the error function are shown in Fig. 1. Surface concentrations measured for the REE were typically on order of 0.1–1.0 atomic percent. Depth profile lengths ranged from 40 to 400 nm. Uncertainties in diffusivities extracted from depth profiles were determined by the uncertainties in measurements of concentration and depth. The former is a function primarily of counting statistics in the RBS spectra (i.e. 1¦ error proportional to N 1=2 , where N is the number of counts in a particular channel), while the latter is determined mainly by the energy resolution of the surface barrier detector used to detect the backscattered particles and by the energy spread of the ions as they travel in and out of the sample.
4. Results 4.1. Arrhenius relations The REE diffusion results are presented in Table 2 and plotted in Fig. 2. The Nd data de-
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Fig. 1. Typical REE diffusion profiles. The (a) Yb and (c) Nd diffusion data are plotted with complementary error function curves. The (b) Yb and (d) Nd data are inverted through the error function. Slopes of the lines are equal to .4Dt/ 1=2 .
fine an Arrhenius relation with activation energy 150 š 13 kJ mol 1 (35:8 š 3:2 kcal mol 1 ) and pre-exponential factor 2:38 ð 10 14 m2 s 1 (log Do D 13:624 š 0:678). Diffusivities among the rare earths do not differ dramatically, but the data do fall along somewhat different trends. The activation energy for La diffusion, 147 š 14 kJ mol 1 (35:2 š 3:3 kcal mol 1 ), agrees within uncertainty with that for Nd, and the pre-exponential factor is similar but a bit larger at 2:57 ð 10 14 m2 s 1 (log Do D 13:590 š 0:693), yet again well within uncertainty. A somewhat higher activation energy of 186 š 23 kJ mol 1 (44:4 š 5:4 kcal mol 1 ) is measured for Yb diffusion along with a larger pre-exponential factor of 3:86 ð 10 12 m2
s 1 (log Do D 11:413 š 1:151). The Dy diffusion data exhibit a bit more scatter than the others, and have an activation energy of 145 š 25 kJ mol 1 (34:5 š 6:0 kcal mol 1 ) and pre-exponential factor of 2:87 ð 10 14 m2 s 1 (log Do D 13:542 š 1:284). 4.2. Time-series and ‘zero-time’ experiments In order to ascertain whether the profiles measured represent volume diffusion and not some other process, we conducted both time-series experiments for Nd diffusion anneals and a zero-time experiment using the Yb carbonate source. For the time series, a set of experiments was run at fixed temperature (800ºC) for times ranging from one day
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Table 2 REE diffusion in calcite T (ºC)
Time (s)
D (m2 s
La diffusion CCLa-4 CCLa-3 CCLa-2 CCLa-1 CCLa-6 CCLa-5
650 700 750 800 826 850
6.57 ð 106 2.74 ð 106 1.28 ð 106 6.32 ð 105 5.72 ð 105 8.42 ð 105
1.92 ð 10 5.08 ð 10 2.48 ð 10 1.05 ð 10 3.83 ð 10 6.99 ð 10
22
Nd diffusion CCNd-9 CCNd-4 CCNd-5 CCNd-8 CCNd-6 CCNd-10 CCNd-12 CCNd-11 CCNd-14 CCNd-13
597 650 701 750 801 800 800 800 829 853
7.24 ð 106 4.27 ð 106 2.19 ð 106 2.40 ð 106 3.46 ð 105 1.21 ð 106 6.91 ð 105 9.36 ð 104 5.80 ð 105 5.19 ð 105
5.46 ð 10 5.12 ð 10 2.15 ð 10 3.31 ð 10 5.68 ð 10 9.72 ð 10 8.08 ð 10 9.85 ð 10 2.69 ð 10 4.81 ð 10
23
Dy diffusion CCDy-6 CCDy-5 CCDy-4 CCDy-3 CCDy-7
650 700 749 798 825
6.58 ð 106 2.74 ð 106 1.28 ð 106 6.32 ð 105 2.52 ð 105
3.26 ð 10 6.52 ð 10 7.43 ð 10 1.52 ð 10 1.34 ð 10
22
Yb diffusion CCYb-5 CCYb-4 CCYb-3 CCYb-2 CCYb-7 CCYb-6
650 700 751 803 826 852
6.56 ð 106 2.74 ð 106 1.20 ð 106 7.85 ð 105 5.90 ð 105 6.05 ð 105
1.72 ð 10 4.31 ð 10 8.25 ð 10 3.26 ð 10 3.63 ð 10 1.60 ð 10
22
to two weeks. Fig. 3 indicates that diffusivities for the investigated temperature are fairly consistent for diffusion times ranging over more than an order of magnitude. The result of a zero-time experiment at 800ºC using the Yb source is shown in Fig. 4. The RBS spectrum of this sample differs little from that of an untreated specimen, showing little sign of REE uptake. The results of both zero-time and time-series anneals suggest that the dominant process being measured is indeed volume diffusion.
log D
C=
1)
22 22 21 21 21
23 22 22 22 22 22 22 21 21
22 22 21 20
22 22 21 21 20
21.717 21.294 21.606 20.981 16.417 20.156
0.117 0.186 0.115 0.101 0.091 0.132
22.263 22.291 21.668 21.480 21.246 21.012 21.093 21.007 20.570 20.318
0.190 0.164 0.203 0.218 0.211 0.211 0.179 0.273 0.233 0.125
21.487 21.186 21.129 20.818 19.873
0.141 0.128 0.094 0.179 0.175
21.765 21.365 21.084 20.487 20.440 19.796
0.124 0.071 0.103 0.050 0.142 0.064
5. Discussion 5.1. Comparison of REE transport in calcite and among other minerals While diffusivities among the REE do not differ substantively, there appear to be small variations and trends which may be attributed to REE ionic radii. The Arrhenius lines plotted in Fig. 5 illustrate these behaviors. La3C and Nd3C , which are most ˚ larger similar in size to Ca2C (0.032 and 0.017 A and smaller than Ca2C , respectively, in six-fold co-
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Fig. 2. Arrhenius plots of (a) La and Nd, and (b) Dy and Yb diffusion data for calcite. The following Arrhenius parameters are derived from least-squares fits to the data. La: activation energy 147 š 14 kJ mol 1 (35:2 š 3:3 kcal mol 1 ), pre-exponential factor 2:57 ð 10 14 m2 s 1 (log Do D 1:359 ð 101 š 0:69); Nd: activation energy 150 š 14 kJ mol 1 (35:8 š 3:2 kcal mol 1 ), pre-exponential factor 2:38 ð 10 14 m2 s 1 (log Do D 1:362 ð 101 š 0:68); Dy: activation energy 145 š 25 kJ mol 1 (34:5 š 6:0 kcal mol 1 ), pre-exponential factor 2:87 ð 10 14 m2 s 1 (log Do D 1:354 ð 101 š 1:28); Yb: activation energy 186 š 23 kJ mol 1 (44:4 š 5:4 kcal mol 1 ), pre-exponential factor 3:86 ð 10 12 m2 s 1 (log Do D 1:141 ð 101 š 1:15).
Fig. 3. Time series of diffusion anneals at 800ºC for Nd. Measured diffusivities are generally quite consistent for anneal times ranging over nearly an order of magnitude.
ordination; [13]), diffuse at comparable rates. Dy3C and Yb3C , the REEs yet smaller (0.088 and 0.132 ˚ smaller than Ca2C , respectively; [13]), generally A diffuse more rapidly at the temperatures explored in this study. The smallest, Yb, also exhibits a relatively high activation energy compared with that of the other REE and earlier measurements of the divalent cations Pb and Sr [14], suggesting the pos-
sibility of a different transport mechanism for Yb. However, given the relatively large uncertainties in diffusion parameters due to the limited temperature range over which diffusivities may be reasonably measured in calcite, it is perhaps incautious to place great emphasis on this observation. Clearly, however, the pronounced differences among REE transport rates observed in zircon [1] are not noted in calcite. In zircon, diffusion coefficients might differ by as much as three orders of magnitude when comparing the lightest and heaviest REEs. Variations in transport rates in calcite across the spectrum of lanthanides are at most about half a log unit (Fig. 5) over the temperature range investigated in this study. There are a number of possible explanations for these disparities in REE diffusion behavior between these minerals. Zircon has a much smaller ionic porosity than does calcite (values of 28.8 and 43.7, respectively, where each value is essentially the ‘free space’ in the crystal unoccupied by cations or anions; [8]). Therefore, small differences in ionic radii among the rare earths may more drastically influence transport in the less open zircon structure than in calcite. The greater deviation of the REEs from the size of Zr ion for which they substitute in zircon [1,15] may also contribute to
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Fig. 4. Results of a ‘zero-time’ experiment, compared with the RBS spectra of an untreated calcite sample and a Yb diffusion anneal. Little evidence of REE uptake may be seen in the zero-time experiment.
Fig. 5. Arrhenius plot summarizing trends for REE diffusion in calcite. Diffusion of the heavier rare earths with smaller ionic radii tends to be a bit faster, but differences among REE transport rates are at most about half a log unit over the investigated temperature range.
this more pronounced dependence. All of the REE are significantly larger than the Zr4C cation in eightfold coordination [13], with differences ranging from
˚ for Lu3C to 0.320 for La3C . Clearly, the ‘fit’ 0.137 A of the REE on the Zr4C site in zircon is much poorer than that for REEs on the Ca2C site in calcite; the LREE will be less well accommodated on the Zr site and their ability to migrate through the zircon structure may be diminished. The REEs in calcite are incorporated on the Ca2C site [16], likely charge compensated by NaC (if present in the system), or through the relation 2REE3C C ! 3Ca2C (i.e. one Ca2C site vacancy for every two REE3C introduced). Given the source materials employed in this study, the latter process seems most likely in the present case. Under certain circumstances, other univalent cations may also play charge compensating roles. For example, HC may be a compensating species facilitating REE uptake, as has been shown in the case of the incorporation of Pb into zircon [17]. However, it is not clear that the inclusion of such species will enhance transport rates. Cation diffusion rates in calcite appear to be little influenced by the presence of water, although oxygen diffusion is significantly enhanced under hydrothermal conditions [18,19].
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Fig. 6. Arrhenius plot summarizing results for cation and anion diffusion in calcite. Sources for diffusion data: oxygen (dry) and carbon [19]; oxygen (hydrothermal) [18]; Ca [9]; Sr and Pb [14]; REE (this study).
The study of Ca self-diffusion by Farver and Yund [9] suggests a much higher activation energy for diffusion (382 kJ mol 1 , 91 kcal mol 1 ; Fig. 6) than the values for REE chemical diffusion measured here. However, diffusivities of the REE and Ca are comparable at temperatures between 680º and 695ºC, and REE diffusion is more than two orders of magnitude slower at the highest temperature investigated (850ºC). It is not surprising that REE transport might be slower than Ca, given the strong dependence of diffusion rates on cation charge observed in other mineral systems, including zircon [1,15], and the feldspars (e.g. [11,12,20–22]). However, it should be understood that with the differences in activation energies for diffusion of Ca and the REEs, Ca diffusion will be slower than that of the REEs under most geologically applicable circumstances. It is not clear why the discrepancies in activation energies exist if the REEs occupy the Ca2C site. It is possible that the REE do not move solely on the Ca site; perhaps some interstitial paths are dominant. The similarity of Sr and Pb activation energies [14] for diffusion in calcite with those of the REE measured here suggests the possibility of a similar transport mechanism for these cations. Both Sr and Pb do, however, diffuse at a rate considerably faster than
Fig. 7. Summary of REE diffusion data for various minerals. Diffusion of the REEs have lower activation energies than the other minerals for which diffusion data exist. Diffusivities over the investigated temperature range are relatively fast when compared with those for the silicates, but are comparable to transport rates in apatite. Sources for REE diffusion data: apatite [25,26]; calcite (this study); diopside [28]; titanite [27]; garnet [23,24]; zircon [1]; YAG [46].
that of the REE; Sr transport is approximately two orders of magnitude faster than Nd transport (Fig. 6). The slowness of REE diffusion with respect to Sr2C ˚ and Pb2C despite ionic radii smaller (i.e. 1.03 A ˚ for La3C and Yb3C , respectively, in sixand 0.87 A fold coordination; [13]) than either Sr or Pb (1.18 ˚ , respectively, in six-fold coordination; and 1.19 A [13]) is also not unexpected for the reasons cited above. Activation energies for REE diffusion in calcite are considerably smaller than those for REE diffusion in most other minerals for which data exist (Fig. 7). The exceptions are the data for garnet [23,24]. However, given the experimental conditions reported in the garnet studies, it is possible that instability of the samples during diffusion anneals may have affected transport properties and thus diffusion coefficients extracted through analysis of the distributions of diffusing species. Such effects would most significantly impact the shortest diffusion profiles in
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the former study. REE diffusivities in calcite (Fig. 7) are also generally higher than in most minerals, with the exception of Sm diffusion in apatite [25,26]. For example, at 800ºC, diffusion of Nd is about four orders of magnitude faster than Nd in titanite [27] and Sm in diopside [28], and twelve orders of magnitude faster than Sm in zircon [1]. Although Yb diffusion in zircon is significantly faster than that of Sm, it is fully eight orders of magnitude slower than Yb diffusion in calcite. Interestingly, some general correlations, albeit based on a limited data set, appear to exist between mineral properties and REE diffusion parameters. These are revealed in Fig. 8. Lower activation energies and smaller pre-exponential factors for diffusion are correlated with increasing ionic porosity [6,7] of mineral structures (e.g. [8]), for all minerals
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for which diffusion data exist save aluminosilicate garnets. The reasons for nonconformity of the aluminosilicate garnets to these trends may stem from earlier-outlined difficulties in the cited experiments. Mineral elastic moduli also appear to be correlated with diffusion parameters; materials with greater moduli of elasticity exhibit generally higher activation energies and larger pre-exponential factors for REE diffusion. Again, however, the aluminosilicate garnets do not adhere to these trends, but this is perhaps so for the reasons above. However, a recent study of REE diffusion in YAG (Cherniak, unpubl. results), yields diffusion parameters for aluminate garnet consistent with the trends mentioned above. Similar broad trends have been noted for Pb diffusion in minerals [8] and in metals (e.g. [29,30]), and theoretical bases for correlations between activation
Fig. 8. Plots of diffusion parameters for REE transport in various minerals vs. mineral ionic porosities (a) and (b), and bulk moduli (c) and (d). There appears to be at least some degree of correlation of both activation energy of diffusion and the log of the pre-exponential factor with these two mineral properties among all but the garnets. Ionic porosities were obtained from Refs. [6–8]. Bulk moduli values were obtained from Refs. [42,43]. For minerals for which data were unavailable, moduli were estimated using the relationships derived in Ref. [44].
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energy for diffusion, and bulk moduli and atomic volume have been established (e.g. [30,31]). Blundy and Wood [32] have noted differences in partitioning behavior corresponding to variations in elastic moduli among the feldspars; with the more flexible sodic plagioclase accommodating Sr and Ba ions more easily than the more rigid calcic plagioclases. They have further extended these arguments to a predictive model [33] to determine partition coefficients as a function of Young’s Moduli and cation size and charge. Similar treatments might be applicable to diffusion if we presume that a more flexible (i.e. smaller elastic modulus) structure would also permit easier cation migration. Clearly, however, such simple correlations provide only first-order information as they do not consider defect structures that may influence diffusion, or the added complexities of the exchange process when other chargecompensating species are involved. More diffusion data on trivalent cations (especially the REE) are warranted to better understand such systematic behaviors should they exist. It is important to consider also that the diffusion parameters themselves (i.e. activation energies and pre-exponential factors) may be correlated through the Meyer–Neldel or ‘compensation’ effect (e.g. [34–36]). A detailed discussion of this phenomenon with respect to diffusion in minerals is beyond the scope of this paper, but will be presented elsewhere (Cherniak, in prep.). 5.2. Applications 5.2.1. REE closure temperatures A summary of REE closure temperatures as functions of effective diffusion radii (for a cooling rate of 10ºC per million years) is plotted in Fig. 9. In correspondence with the diffusivities above, closure temperatures for the REEs in calcites are fairly low. For example, closure temperatures for calcites of 100 µm effective diffusion radii are 495º and 523ºC for Nd and Yb, respectively. These values are 25º to 50ºC lower than that for Sm in apatite, the next-lowest closure temperature. However, closure temperatures for the REE in zircon, titanite, and diopside are all higher by a considerable margin. It seems clear that calcites are much more likely to experience REE exchange at low temperatures than most other minerals for which diffusion data exist, but the sequence
Fig. 9. Closure temperatures of the REE as a function of effective diffusion radius. Closure temperatures are calculated using the expression from Ref. [45] and the diffusion parameters from the sources cited in Fig. 7.
of closure is complicated by variations in effective diffusion radii among minerals and the influence of modal abundances on the REE reservoir. We consider two geologic scenarios for which closure temperature calculations may be relevant: (1) cooling of marbles in regional metamorphism; and (2) cooling of carbonatites. The first case involves slow cooling from modest temperatures. If we consider a moderate metamorphic temperature of 550ºC and cooling rates as above, REE information will be largely retained (provided changes in REE composition are affected only by diffusion) since diffusivities are sufficiently slow over the temperature range that 100 µm grains will close to diffusional exchange before significant loss has occurred. Slower cooling will depress closure temperatures (they will be about 60ºC lower for a cooling rate an order of magnitude slower, i.e. 1ºC per million years), but diffusivities over this temperature range are such that complete REE alteration will not occur before diffusional exchange effectively ceases. Finer-grained material, however, will be much less retentive.
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The latter case involves relatively rapid cooling from much higher temperatures (1000–1100ºC). More rapid cooling will elevate closure temperatures (by about 70ºC for an order of magnitude increase in cooling rate; very rapid cooling rates, however, render the construct of closure temperature invalid), but REE diffusivities are sufficiently high above 700ºC that calcite is unlikely to retain the REE composition reflective of conditions of its crystallization. 5.2.2. REE zoning According to the model of Watson and Liang [37], the formation of growth zoning is related to the volume diffusion rate .D/ of the zoned element within the mineral crystal lattice as well as the growth rate .V / of the crystal. The model considers volume diffusion in the crystal as the determining factor in transport kinetics. Regions of perturbed chemical potential of a trace element, due to its incorporation at the surface of a growing crystal, can only be eliminated by lattice diffusion of this element. Thus, fast lattice diffusion would lead to equilibrium growth, and slow lattice diffusion would result in disequilibrium growth. Watson and Liang [37] suggest that a ‘critical value’ of the dimensionless parameter V l=D (where l is the half-width of the enriched-surface growth layer, the latter assumed to be a monolayer) is a determining factor in the development of sector zoning: when this parameter is above ¾0.5 to 3, the development of sector zoning during growth is unavoidable in crystals that exhibit selective enrichment of the element on specific growth faces. In Fig. 10, minimum growth rates for calcite that would result in Nd and Yb zoning, calculated using this model, are plotted as a function of temperature. For example, at 500ºC, growth rates faster than ¾10 15 m=s would result in sector zoning with respect to Nd or Yb. At 200º and 30ºC, rates would be ¾10 21 and 10 30 m=s, respectively, for Nd, and ¾10 23 and 10 35 m=s for Yb. Paquette and Reeder [38] report laboratory growth rates of 1– 5ð10 10 m=s at 30ºC. Given this result and other calcite growth rates reported under various conditions, sector zoning with respect to the REE is quite likely (if these cations are in fact preferentially incorporated at some growth faces). Zoning of the REE has been reported [5] in laboratory-grown calcites, a result also consistent with the low REE diffusivities expected at room temperature.
Fig. 10. Minimum growth rates to produce sector zoning of the REEs in calcite as a function of temperature. Curves are calculated using the model of Ref. [37]. See text for further explanation.
Once present, REE compositional zoning is likely to persist under many circumstances. A simple model illustrates this point. Zones in calcite are modeled as plane sheets of thickness l; adjacent planes have different concentrations of the diffusing species. Only diffusion in the x direction (i.e. normal to the planar interface) is considered. We evaluate two different (arbitrary) criteria for changes in zones due to diffusion: (i) ‘blurring’ of these regions, defined by a compositional change of 10% of the way into the zone; and (ii) ‘disappearance’ of zones, defined by a compositional change of 10% in the center of a zone. For condition (i), the dimensionless parameter Dt=l 2 is equal to 1:8 ð 10 3 ; for condition (ii) the value for this parameter is 3:3 ð 10 2 . Fig. 11 shows curves constraining the time–temperature conditions under which Nd and Dy zoning of various dimensions (1 and 100 µm) will be retained given the above criteria. At temperatures of 300ºC, 1 µm regions of Nd zoning would be ‘blurred’ in 65,000 years and ‘lost’ in 1.2 million years, zones of 100 µm dimensions would be ‘blurred’ in 650 million years and ‘lost’ in 1.2 billion years. Some 1 µm Nd zoning would be retained in calcite heated to 170ºC for times in excess of the age of the earth. Coarser zoning of 100 µm would be retained to some degree over this time scale at temperatures of 340ºC. At 500ºC, the time for ‘blurring’ of 10 µm zones is about 2000
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diffusion between chemically distinct zones during such events, we evaluate the integral of the diffusion coefficient as a function of time, i.e.: Z t D.t 0 / dt 0 Deff t D 0
Fig. 11. Preservation of REE zoning in calcite during isothermal events. Curves represent maximum time–temperature conditions under which 1 and 100 µm scale zoning would be preserved in calcite, assuming alteration of zone compositions only through volume diffusion. For conditions above the upper curves in each group, well-defined zoning will be lost. For conditions below the lower curves, zones may be ‘blurred’ but still retain initial composition in zone center. The model used to calculate trends of curves is described in the text.
years, loss of zones occurs in 42,000 years. For 1 µm and 100 µm zoning, times would be two orders of magnitude shorter or longer, respectively. Dy zoning would require shorter time than Nd at a given temperature for loss or blurring. For example, at 300ºC, the time necessary to ‘blur’ 1 µm Dy zones is 29,000 years, loss of zones occurs in 540,000 years. For 100 µm zones, the values for blurring and loss are 290 million years and 5.4 billion years, respectively. Clearly, however, the simple case of isothermal heating is rarely reflective of geologic conditions. We consider the more realistic diagenetic=metamorphic circumstance of heating of sediments as a consequence of burial. A geothermal gradient of 30ºC per km (a normal continental gradient) is assumed, with depositional rates on order of 10–20 m per million years, e.g. [39,40]. Typical heating rates are then on order of 0.3–0.6ºC per million years, with burial depths from 4 to 10 km and maximum temperatures of 150–250ºC (starting from a surface temperature of 20ºC). In order to determine the extent of inter-
Interestingly, simple numerical integration reveals that Deff is roughly an order of magnitude smaller than D.t/ (for maximum T greater than ¾50ºC). It should be noted that this simple relationship applies to the range of conditions (heating rates and activation energies for diffusion) considered here. A more comprehensive treatment taking into account a broader range of conditions is beyond the scope of this paper, and will be elsewhere addressed (Cherniak and Watson, in prep.). We again return to the simple criteria outlined above for the preservation of zoning, i.e. Dt=l 2 equal to 1:8 ð 10 3 and 3:3 ð 10 2 for ‘blurring’ and loss of zones, respectively. Instead of assuming a constant D, however, we substitute Deff t (determined by numerically integrating the expression for D.t 0 / over time given a heating rate of 0.5ºC per million years and the diffusion parameters for Nd) for Dt in the relations. Fig. 12 shows plots of zone width as functions of burial depth and maximum temperature of heating as a consequence of burial. It is clear from the figure that even zoning on the scale of tens of micrometers will be to some extent preserved under most of these diagenetic conditions. 5.2.3. Isotopic=chemical equilibration of REEs in calcite We can also use the diffusion data to determine the extent that calcite grains of more homogeneous composition will isotopically or chemically equilibrate with their external environment during a thermal event, noting that the model that follows applies strictly under conditions in which diffusion is the dominant mechanism of exchange. Clearly, however, solution=reprecipitation provides a more expeditious means of exchange in many natural settings. We consider the simple model in which a calcite grain is a sphere of radius a and initial uniform concentration of diffusant C1 ; it is exposed to an external medium with concentration of diffusant Co . The solution to the diffusion equation given these conditions is
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Fig. 12. Preservation of REE zoning during heating as a consequence of burial. Curves represent minimum zone dimension and that will be preserved given a heating rate of 0.5ºC per million years. The abscissas are burial depth and maximum temperature, with assumptions of reasonable (and constant) deposition rates and a typical continental geothermal gradient of 30ºC per km. Further detail is included in the text.
presented in Crank ([41]; p. 91). When the dimensionless parameter Dt=a 2 (where D is the diffusion coefficient, t is the time at elevated temperature) is less than or equal to 0.03, the concentration of diffusant at the center of the sphere is unchanged from its initial value. Above 0.03, the concentration at the grain center is affected by the externally imposed concentration Co . In Fig. 13, we plot curves representing Dt=a 2 D 0:03 for La and Yb in calcite given a 1 mm effective diffusion radius. These curves define time– temperature conditions limits for which La and Yb isotopic information in the calcite grain will be retained. For times and temperatures below the curves, Yb and La isotopic ratios at crystal cores will be preserved. Above the curves, they will be influenced by external La and Yb compositions. At 500ºC, centers of 1 mm calcite grains will retain their initial La compositions for nearly 340 million years, while Yb compositions will be retained for nearly 900 million years. La and Yb
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Fig. 13. Preservation of REE composition in calcite grains. The curves correspond to values of 0.03 for the dimensionless parameter Dt=a 2 for Yb and La, and represent maximum time– temperature conditions under which the centers of grains of 1 mm effective size will preserve their original REE isotopic or chemical signatures, again assuming volume diffusion of the REE as the dominant mechanism facilitating exchange. For conditions above the curves, this information will be lost.
compositions will be preserved over times in excess of the age of the earth at temperatures of 400º and 450ºC, respectively. Information on initial REE compositions will persist for a few million years even for temperatures in excess of 700ºC. Preservation of REE isotope and chemical information is therefore quite possible under a broad range of conditions if REE contents are altered only by diffusion.
Acknowledgements I thank Rich Reeder for inspiring and encouraging the undertaking of these calcite diffusion studies. Both he and Bruce Watson provided invaluable suggestions and discussion during the course of this investigation. Insightful review comments by F.M. Richter and S.M. Fortier assisted immeasurably in improving the final version of the manuscript. This work was supported through grant EAR-9406916 from the National Science Foundation (to E.B. Watson). [CL]
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[17] E.B. Watson, D.J. Cherniak, J.M. Hanchar, T.M. Harrison, D.A. Wark, The incorporation of Pb into zircon, Chem. Geol. 141 (1997) 19–31. [18] J.R. Farver, Oxygen self-diffusion in calcite: dependence on temperature and water fugacity, Earth Planet. Sci. Lett. 121 (1994) 575–587. [19] A.K. Kronenberg, R.A. Yund, B.J. Giletti, Carbon and oxygen diffusion in calcite: effects of Mn content and pH2 O, Phys. Chem. Mineral 11 (1984) 101–112. [20] B.J. Giletti, J.E.D. Casserly, Sr diffusion kinetics in plagioclase feldspars, Geochim. Cosmochim. Acta 58 (1994) 3785–3793. [21] B.J. Giletti, T.M. Shanahan, Alkali diffusion in plagioclase feldspars, Chem. Geol. 139 (1997) 3–20. [22] K.A. Foland, Alkali diffusion in orthoclase, in: A.W. Hofmann, B.J. Giletti, H.S. Yoder Jr., R.A. Yund (Eds.), Geochemical Transport and Kinetics, Carnegie Institution of Washington, 1974, pp. 77–98. [23] R.A.N. Coughlan, Studies in Diffusional Transport: Grain Boundary Transport of Oxygen in Feldspars, Strontium and the REEs in Garnet, and Thermal Histories of Granitic Intrusions in South-Central Maine using Oxygen Isotopes. Ph.D. thesis, Brown University, Providence, RI, 1990. [24] W.J. Harrison, B.J. Wood, An experimental investigation of the partitioning of REE between garnet and liquid with reference of the role of defect equilibria, Contrib. Mineral. Petrol. 72 (1980) 145–155. [25] D.J. Cherniak, F.J. Ryerson, Diffusion of Sr and Sm in apatite, Eos 72 (1991) 309. [26] E.B. Watson, T.M. Harrison, F.J. Ryerson, Diffusion of Sr, Sm and Pb in fluorapatite, Geochim. Cosmochim. Acta 49 (1985) 1813–1823. [27] D.J. Cherniak, Diffusion of Sr and Nd in titanite, Chem. Geol. 125 (1995) 219–232. [28] M. Sneeringer, S.R. Hart, N. Shimizu, Strontium and samarium diffusion in diopside, Geochim. Cosmochim. Acta 48 (1984) 1589–1608. [29] H. Bakker, Tracer diffusion in concentrated alloys, in: G.E. Murch, A.S. Nowick (Eds.), Diffusion in Crystalline Solids, Academic Press, Orlando, FL, 1984, pp. 189–254. [30] D.L. Beke, Theoretical background of empirical laws for diffusion, Defect Diffusion Forum 66–69 (1989) 127–156. [31] P.A. Varotsos, K.D. Alexopoulos, Thermodynamics of Point Defects and their Relations with Bulk Properties, NorthHolland, Amsterdam, 1986. [32] J.D. Blundy, B.J. Wood, Crystal–chemical controls on the partitioning of Sr and Ba between plagioclase feldspar, silicate melts, and hydrothermal solutions, Geochim. Cosmochim. Acta 55 (1991) 193–210. [33] J. Blundy, B. Wood, Prediction of crystal–melt partition coefficients from elastic moduli, Nature 372 (1994) 452– 454. [34] W. Meyer, H. Neldel, Beziehungen zwischen der energiekonstanten ε und der mangenkonstanten a in der leitwerts-temperaturformel bei oxydischen halbleitern, Z. Tech. Phys. 12 (1937) 588–593.
D.J. Cherniak / Earth and Planetary Science Letters 160 (1998) 273–287 [35] P. Winchell, The compensation law for diffusion in silicates, High Temp. Sci. 1 (1969) 200–215. [36] S.R. Hart, Diffusion compensation in natural silicates, Geochim. Cosmochim. Acta 45 (1981) 279–291. [37] E.B. Watson, Y. Liang, A simple model for sector zoning in slowly grown crystals: Implications for growth rate and lattice diffusion, with emphasis on accessory minerals in crustal rocks, Am. Mineral. 80 (1995) 1179–1187. [38] J. Paquette, R.J. Reeder, Relationship between surface structure, growth mechanism, and trace element incorporation in calcite, Geochim. Cosmochim. Acta 59 (1995) 735–749. [39] C.H. Moore, Carbonate Diagenesis and Porosity, Elsevier, Amsterdam, 1989. [40] J.W. Morse, F.T. Mackenzie, Geochemistry of Sedimentary Carbonates, Elsevier, Amsterdam, 1990. [41] J. Crank, The Mathematics of Diffusion (2nd ed.), Oxford
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REE diffusion in calcite D.J. Cherniak * Department of Earth and Environmental Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA Received 24 July 1997; revised version received 19 February 1998; accepted 9 March 1998
Abstract Chemical diffusion of four rare-earth elements (La, Nd, Dy and Yb) has been measured in natural calcite under anhydrous conditions, using rare-earth carbonate powders as the source of diffusants. Experiments were run in sealed silica capsules along with finely ground calcite to ensure stability of the single-crystal samples during diffusion anneals. Rutherford backscattering spectroscopy (RBS) was used to measure diffusion profiles. The following Arrhenius relations were obtained over the temperature range 600–850ºC: DLa D 2:6 ð 10 14 exp. 147 š 14 kJ mol 1 =RT ) m2 s 1 , DNd D 2:4 ð 10 14 exp. 150 š 13 kJ mol 1 =RT ) m2 s 1 , DDy D 2:9 ð 10 14 exp. 145 š 25 kJ mol 1 =RT ) m2 s 1 , DYb D 3:9 ð 10 12 exp. 186 š 23 kJ mol 1 =RT ) m2 s 1 . In contrast to previous findings for refractory silicates (e.g. zircon), differences in transport rates among the REE are not pronounced over the range of temperature conditions investigated in this study. Diffusion of the REE is significantly slower than diffusion of the divalent cations Sr and Pb and slower than transport of Ca and C at temperatures above ¾650ºC. Fine-scale zoning and isotopic and REE chemical signatures may be retained in calcites under many conditions if diffusion is the dominant process affecting alteration. 1998 Elsevier Science B.V. All rights reserved. Keywords: rare earths; diffusion; calcite
1. Introduction Carbonate minerals can be major constituents of sediments and sedimentary rocks. They incorporate a number of minor and trace elements, including the REEs, that provide invaluable information about the environment and processes that influence mineral formation and growth, as well as the circumstances characterizing subsequent alteration. The REEs, while to some degree chemically similar to one another because they all possess the same number and type of valence electrons in their outermost shells, do exhibit varying geochemical behavior. This is to a great extent a consequence of the Ł Fax:
C1 (518) 276-8627; E-mail: [email protected]
decreasing size of REE ionic radii with increasing atomic number, a function of the enhanced attraction between 4f subshell electrons and the nucleus as the respective charges increase. Hence, the REE are useful in tracing and interpreting kinetic processes. In the case of diffusion, the influence of these differences in ionic radii can be pronounced. In zircon [1], for example, quite dramatic decreases in diffusion rates (and concomitant increases in activation energies for diffusion) are observed in measurements across the lanthanide series from heavy to light REE. Calcite commonly displays zoning of trivalent and divalent cations on the scale of micrometers to tens of micrometers. While zoning in Mn2C is most widely reported both because of the ubiquity of the element and its characteristic orange luminescence,
0012-821X/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 0 8 7 - 9
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zoning of Fe, Y and Sr has been observed in analyses with PIXE [2]. Several of the REE, notably Sm3C , Dy3C , Tb3C , and Eu in both trivalent and divalent states, are also activators in cathodoluminescence (CL) spectroscopy (e.g. [3,4]) of carbonates. Activation is more commonly observed in vein calcites and carbonatites rather than in sedimentary carbonates [4] because of the relatively high REE contents of the former. REE zoning has been observed in calcite with CL (e.g. [5]), and zoning patterns tend to be resistant to thermal alteration, as calcites heated to temperatures up to 490ºC show little evidence of change in REE distributions [5]. In the present study, we investigate diffusion rates of a range of rare earths in calcite. Knowledge of such transport rates, as noted above, may assist in the determination of the extant character of chemical environments during calcite growth and alteration and permit better understanding of constraints on the formation and retention of trivalent cation zoning in carbonates. In addition, by measuring transport of light, intermediate, and heavy rare earths, we may assess the degree of dependence (if any) of diffusion on REE ionic radii. Whether such trends are common among minerals or are more nearly a function of specific crystal–chemical characteristics of zircon —e.g. low ionic porosity, cf. [6–8], small size of Zr4C with respect to substituent cations— remains to be determined. With further systematic studies of diffusion of the REEs in other minerals, it may be possible to elucidate these observations and develop general predictive models for REE transport.
2. Experimental procedure The experiments were performed on natural calcite from Mexico. Compositional information for N the calcite is presented in Table 1. Natural f1014g cleavage surfaces were used in all diffusion anneals. Powder XRD of a representative specimen indicated the presence of no phases other than calcite. Other orientations were not investigated, although another study [9] suggests that cation diffusion in calcite is not strongly anisotropic. Rare-earth carbonate powder sources were used for all experiments. A single REE (La, Nd, Dy or Yb) was used in each experiment in order to preclude
Table 1 Bulk composition of calcite specimen used in study CaO Fe2 O3 MnO MgO TiO2 Cr2 O3 Na2 O K2 O Al2 O3 SiO2 P2 O5 Be B Sc V Co Ni Cu Zn Ge As Se Br Rb Sr Y Zr Nb Mo Ag Cd Sb Cs Ba La Ce Nd Sm Eu Tb Yb Lu Hf Ta W Ir Pb Th U
55.9 0.05 0.05 <0.01 <0.001 <0.01 <0.01 <0.01 <0.01 <0.01 >0.01 <1 <10 0.08 <2 1.0 <1 <0.5 <0.5 <10 <1 <1 4.5 <10 198 15 <10 18 <2 <0.2 <1 0.1 <0.5 <10 <0.5 <1 <3 0.02 0.18 <0.1 <0.20 <0.05 <0.2 <0.5 5 <0.005 <2 <0.2 <0.1
Be, B, V, Ni, Cu, Zn, Ge, Ag, Cd and Pb were measured on the bulk sample by ICP at XRAL Laboratories. Sc, Cr, Co, As, Se, Br, Mo, Sb, Cs, the REEs, Hf, Ta, W, Ir, U and Th were measured by neutron activation. All other elements were measured by XRF at XRAL. Oxides are wt%, other elements are in (wt) ppm.
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interferences from signals of the other REEs in the RBS spectra. The carbonates were dried thoroughly in a drying oven at ¾120ºC, then placed in Pt capsules (3 mm od, welded at one end) with a cleaved calcite specimen. The prepared capsules were then left in the drying oven overnight. After removal from the drying oven, Pt capsules were sealed under vacuum in silica glass tubes (6 mm od, 4 mm id). A small amount of CaCO3 powder was also sealed in the silica glass tubing with the Pt capsules to ensure calcite sample stability (by generation of some gaseous CO2 in the capsule environment) throughout the diffusion anneals. The silica capsules were annealed in 1-atm vertical tube furnaces for times ranging from 1 day to 3 months at temperatures from 600º to 850ºC. Temperatures in the furnaces were monitored with chromel-alumel (type K) thermocouples. Temperature uncertainties were typically š2ºC. After diffusion anneals, the sample capsules were simply quenched by removing them from the furnace and permitting them to cool in air. The capsules were then opened and samples removed and freed of residual source material clinging to surfaces by ultrasonic cleaning in ethanol. Sources of diffusant selected were easily removed from sample surfaces and samples displayed no evidence of surface reaction following diffusion anneals. A ‘zero-time’ experiment was also run to determine whether there might be rapid initial non-diffusional uptake of the diffusing species or other difficulties with the experimental protocol. For this experiment, a capsule was prepared as above, brought up to run temperature, and immediately quenched.
3. RBS analyses The RBS analyses were performed at the 4 MeV Dynamitron accelerator at the University at Albany – SUNY. A beam of 2 MeV 4 HeC ions was used, with backscattered ions detected by a silicon surface barrier detector. Beam spot size for analysis was typically about 1 mm2 . For each sample, a number of brief analyses was collected at several spots on the sample surface to test for reproducibility and to determine whether unusual conditions (e.g. the presence of large numbers of cracks) might exist on a region of the sample that would produce anomalous
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profiles. Following such reconnaissance, RBS spectra were taken with longer acquisition times (typically 15 to 50 min). The spectra (counts vs. channel, collected in a multichannel analyzer, MCA) were converted to concentration profiles with computer code involving a number of steps. MCA channel number was first related to detected particle (4 HeC ) energy through calibration with standards (typically SiO2 glass and thin-film metal targets). A depth scale was then generated by calculating the rate of energy loss .dE=dx/ for the ions traveling through the calcite before and after the scattering events. These energy-loss rate values, or stopping powers, were calculated for calcite using analytical polynomial expressions for elemental stopping powers [10] and by weighting the contribution of each element to the total stopping power by considering its atomic concentration in the matrix. Particle yields were converted into REE concentrations by taking into account the probability of scattering events for the relevant atomic species at corresponding depths in the samples. Further details on the RBS technique [10] and analytical procedures employed (e.g. [11,12]) are outlined elsewhere. Typical diffusion profiles and their inversions through the error function are shown in Fig. 1. Surface concentrations measured for the REE were typically on order of 0.1–1.0 atomic percent. Depth profile lengths ranged from 40 to 400 nm. Uncertainties in diffusivities extracted from depth profiles were determined by the uncertainties in measurements of concentration and depth. The former is a function primarily of counting statistics in the RBS spectra (i.e. 1¦ error proportional to N 1=2 , where N is the number of counts in a particular channel), while the latter is determined mainly by the energy resolution of the surface barrier detector used to detect the backscattered particles and by the energy spread of the ions as they travel in and out of the sample.
4. Results 4.1. Arrhenius relations The REE diffusion results are presented in Table 2 and plotted in Fig. 2. The Nd data de-
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Fig. 1. Typical REE diffusion profiles. The (a) Yb and (c) Nd diffusion data are plotted with complementary error function curves. The (b) Yb and (d) Nd data are inverted through the error function. Slopes of the lines are equal to .4Dt/ 1=2 .
fine an Arrhenius relation with activation energy 150 š 13 kJ mol 1 (35:8 š 3:2 kcal mol 1 ) and pre-exponential factor 2:38 ð 10 14 m2 s 1 (log Do D 13:624 š 0:678). Diffusivities among the rare earths do not differ dramatically, but the data do fall along somewhat different trends. The activation energy for La diffusion, 147 š 14 kJ mol 1 (35:2 š 3:3 kcal mol 1 ), agrees within uncertainty with that for Nd, and the pre-exponential factor is similar but a bit larger at 2:57 ð 10 14 m2 s 1 (log Do D 13:590 š 0:693), yet again well within uncertainty. A somewhat higher activation energy of 186 š 23 kJ mol 1 (44:4 š 5:4 kcal mol 1 ) is measured for Yb diffusion along with a larger pre-exponential factor of 3:86 ð 10 12 m2
s 1 (log Do D 11:413 š 1:151). The Dy diffusion data exhibit a bit more scatter than the others, and have an activation energy of 145 š 25 kJ mol 1 (34:5 š 6:0 kcal mol 1 ) and pre-exponential factor of 2:87 ð 10 14 m2 s 1 (log Do D 13:542 š 1:284). 4.2. Time-series and ‘zero-time’ experiments In order to ascertain whether the profiles measured represent volume diffusion and not some other process, we conducted both time-series experiments for Nd diffusion anneals and a zero-time experiment using the Yb carbonate source. For the time series, a set of experiments was run at fixed temperature (800ºC) for times ranging from one day
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Table 2 REE diffusion in calcite T (ºC)
Time (s)
D (m2 s
La diffusion CCLa-4 CCLa-3 CCLa-2 CCLa-1 CCLa-6 CCLa-5
650 700 750 800 826 850
6.57 ð 106 2.74 ð 106 1.28 ð 106 6.32 ð 105 5.72 ð 105 8.42 ð 105
1.92 ð 10 5.08 ð 10 2.48 ð 10 1.05 ð 10 3.83 ð 10 6.99 ð 10
22
Nd diffusion CCNd-9 CCNd-4 CCNd-5 CCNd-8 CCNd-6 CCNd-10 CCNd-12 CCNd-11 CCNd-14 CCNd-13
597 650 701 750 801 800 800 800 829 853
7.24 ð 106 4.27 ð 106 2.19 ð 106 2.40 ð 106 3.46 ð 105 1.21 ð 106 6.91 ð 105 9.36 ð 104 5.80 ð 105 5.19 ð 105
5.46 ð 10 5.12 ð 10 2.15 ð 10 3.31 ð 10 5.68 ð 10 9.72 ð 10 8.08 ð 10 9.85 ð 10 2.69 ð 10 4.81 ð 10
23
Dy diffusion CCDy-6 CCDy-5 CCDy-4 CCDy-3 CCDy-7
650 700 749 798 825
6.58 ð 106 2.74 ð 106 1.28 ð 106 6.32 ð 105 2.52 ð 105
3.26 ð 10 6.52 ð 10 7.43 ð 10 1.52 ð 10 1.34 ð 10
22
Yb diffusion CCYb-5 CCYb-4 CCYb-3 CCYb-2 CCYb-7 CCYb-6
650 700 751 803 826 852
6.56 ð 106 2.74 ð 106 1.20 ð 106 7.85 ð 105 5.90 ð 105 6.05 ð 105
1.72 ð 10 4.31 ð 10 8.25 ð 10 3.26 ð 10 3.63 ð 10 1.60 ð 10
22
to two weeks. Fig. 3 indicates that diffusivities for the investigated temperature are fairly consistent for diffusion times ranging over more than an order of magnitude. The result of a zero-time experiment at 800ºC using the Yb source is shown in Fig. 4. The RBS spectrum of this sample differs little from that of an untreated specimen, showing little sign of REE uptake. The results of both zero-time and time-series anneals suggest that the dominant process being measured is indeed volume diffusion.
log D
C=
1)
22 22 21 21 21
23 22 22 22 22 22 22 21 21
22 22 21 20
22 22 21 21 20
21.717 21.294 21.606 20.981 16.417 20.156
0.117 0.186 0.115 0.101 0.091 0.132
22.263 22.291 21.668 21.480 21.246 21.012 21.093 21.007 20.570 20.318
0.190 0.164 0.203 0.218 0.211 0.211 0.179 0.273 0.233 0.125
21.487 21.186 21.129 20.818 19.873
0.141 0.128 0.094 0.179 0.175
21.765 21.365 21.084 20.487 20.440 19.796
0.124 0.071 0.103 0.050 0.142 0.064
5. Discussion 5.1. Comparison of REE transport in calcite and among other minerals While diffusivities among the REE do not differ substantively, there appear to be small variations and trends which may be attributed to REE ionic radii. The Arrhenius lines plotted in Fig. 5 illustrate these behaviors. La3C and Nd3C , which are most ˚ larger similar in size to Ca2C (0.032 and 0.017 A and smaller than Ca2C , respectively, in six-fold co-
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Fig. 2. Arrhenius plots of (a) La and Nd, and (b) Dy and Yb diffusion data for calcite. The following Arrhenius parameters are derived from least-squares fits to the data. La: activation energy 147 š 14 kJ mol 1 (35:2 š 3:3 kcal mol 1 ), pre-exponential factor 2:57 ð 10 14 m2 s 1 (log Do D 1:359 ð 101 š 0:69); Nd: activation energy 150 š 14 kJ mol 1 (35:8 š 3:2 kcal mol 1 ), pre-exponential factor 2:38 ð 10 14 m2 s 1 (log Do D 1:362 ð 101 š 0:68); Dy: activation energy 145 š 25 kJ mol 1 (34:5 š 6:0 kcal mol 1 ), pre-exponential factor 2:87 ð 10 14 m2 s 1 (log Do D 1:354 ð 101 š 1:28); Yb: activation energy 186 š 23 kJ mol 1 (44:4 š 5:4 kcal mol 1 ), pre-exponential factor 3:86 ð 10 12 m2 s 1 (log Do D 1:141 ð 101 š 1:15).
Fig. 3. Time series of diffusion anneals at 800ºC for Nd. Measured diffusivities are generally quite consistent for anneal times ranging over nearly an order of magnitude.
ordination; [13]), diffuse at comparable rates. Dy3C and Yb3C , the REEs yet smaller (0.088 and 0.132 ˚ smaller than Ca2C , respectively; [13]), generally A diffuse more rapidly at the temperatures explored in this study. The smallest, Yb, also exhibits a relatively high activation energy compared with that of the other REE and earlier measurements of the divalent cations Pb and Sr [14], suggesting the pos-
sibility of a different transport mechanism for Yb. However, given the relatively large uncertainties in diffusion parameters due to the limited temperature range over which diffusivities may be reasonably measured in calcite, it is perhaps incautious to place great emphasis on this observation. Clearly, however, the pronounced differences among REE transport rates observed in zircon [1] are not noted in calcite. In zircon, diffusion coefficients might differ by as much as three orders of magnitude when comparing the lightest and heaviest REEs. Variations in transport rates in calcite across the spectrum of lanthanides are at most about half a log unit (Fig. 5) over the temperature range investigated in this study. There are a number of possible explanations for these disparities in REE diffusion behavior between these minerals. Zircon has a much smaller ionic porosity than does calcite (values of 28.8 and 43.7, respectively, where each value is essentially the ‘free space’ in the crystal unoccupied by cations or anions; [8]). Therefore, small differences in ionic radii among the rare earths may more drastically influence transport in the less open zircon structure than in calcite. The greater deviation of the REEs from the size of Zr ion for which they substitute in zircon [1,15] may also contribute to
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Fig. 4. Results of a ‘zero-time’ experiment, compared with the RBS spectra of an untreated calcite sample and a Yb diffusion anneal. Little evidence of REE uptake may be seen in the zero-time experiment.
Fig. 5. Arrhenius plot summarizing trends for REE diffusion in calcite. Diffusion of the heavier rare earths with smaller ionic radii tends to be a bit faster, but differences among REE transport rates are at most about half a log unit over the investigated temperature range.
this more pronounced dependence. All of the REE are significantly larger than the Zr4C cation in eightfold coordination [13], with differences ranging from
˚ for Lu3C to 0.320 for La3C . Clearly, the ‘fit’ 0.137 A of the REE on the Zr4C site in zircon is much poorer than that for REEs on the Ca2C site in calcite; the LREE will be less well accommodated on the Zr site and their ability to migrate through the zircon structure may be diminished. The REEs in calcite are incorporated on the Ca2C site [16], likely charge compensated by NaC (if present in the system), or through the relation 2REE3C C ! 3Ca2C (i.e. one Ca2C site vacancy for every two REE3C introduced). Given the source materials employed in this study, the latter process seems most likely in the present case. Under certain circumstances, other univalent cations may also play charge compensating roles. For example, HC may be a compensating species facilitating REE uptake, as has been shown in the case of the incorporation of Pb into zircon [17]. However, it is not clear that the inclusion of such species will enhance transport rates. Cation diffusion rates in calcite appear to be little influenced by the presence of water, although oxygen diffusion is significantly enhanced under hydrothermal conditions [18,19].
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Fig. 6. Arrhenius plot summarizing results for cation and anion diffusion in calcite. Sources for diffusion data: oxygen (dry) and carbon [19]; oxygen (hydrothermal) [18]; Ca [9]; Sr and Pb [14]; REE (this study).
The study of Ca self-diffusion by Farver and Yund [9] suggests a much higher activation energy for diffusion (382 kJ mol 1 , 91 kcal mol 1 ; Fig. 6) than the values for REE chemical diffusion measured here. However, diffusivities of the REE and Ca are comparable at temperatures between 680º and 695ºC, and REE diffusion is more than two orders of magnitude slower at the highest temperature investigated (850ºC). It is not surprising that REE transport might be slower than Ca, given the strong dependence of diffusion rates on cation charge observed in other mineral systems, including zircon [1,15], and the feldspars (e.g. [11,12,20–22]). However, it should be understood that with the differences in activation energies for diffusion of Ca and the REEs, Ca diffusion will be slower than that of the REEs under most geologically applicable circumstances. It is not clear why the discrepancies in activation energies exist if the REEs occupy the Ca2C site. It is possible that the REE do not move solely on the Ca site; perhaps some interstitial paths are dominant. The similarity of Sr and Pb activation energies [14] for diffusion in calcite with those of the REE measured here suggests the possibility of a similar transport mechanism for these cations. Both Sr and Pb do, however, diffuse at a rate considerably faster than
Fig. 7. Summary of REE diffusion data for various minerals. Diffusion of the REEs have lower activation energies than the other minerals for which diffusion data exist. Diffusivities over the investigated temperature range are relatively fast when compared with those for the silicates, but are comparable to transport rates in apatite. Sources for REE diffusion data: apatite [25,26]; calcite (this study); diopside [28]; titanite [27]; garnet [23,24]; zircon [1]; YAG [46].
that of the REE; Sr transport is approximately two orders of magnitude faster than Nd transport (Fig. 6). The slowness of REE diffusion with respect to Sr2C ˚ and Pb2C despite ionic radii smaller (i.e. 1.03 A ˚ for La3C and Yb3C , respectively, in sixand 0.87 A fold coordination; [13]) than either Sr or Pb (1.18 ˚ , respectively, in six-fold coordination; and 1.19 A [13]) is also not unexpected for the reasons cited above. Activation energies for REE diffusion in calcite are considerably smaller than those for REE diffusion in most other minerals for which data exist (Fig. 7). The exceptions are the data for garnet [23,24]. However, given the experimental conditions reported in the garnet studies, it is possible that instability of the samples during diffusion anneals may have affected transport properties and thus diffusion coefficients extracted through analysis of the distributions of diffusing species. Such effects would most significantly impact the shortest diffusion profiles in
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the former study. REE diffusivities in calcite (Fig. 7) are also generally higher than in most minerals, with the exception of Sm diffusion in apatite [25,26]. For example, at 800ºC, diffusion of Nd is about four orders of magnitude faster than Nd in titanite [27] and Sm in diopside [28], and twelve orders of magnitude faster than Sm in zircon [1]. Although Yb diffusion in zircon is significantly faster than that of Sm, it is fully eight orders of magnitude slower than Yb diffusion in calcite. Interestingly, some general correlations, albeit based on a limited data set, appear to exist between mineral properties and REE diffusion parameters. These are revealed in Fig. 8. Lower activation energies and smaller pre-exponential factors for diffusion are correlated with increasing ionic porosity [6,7] of mineral structures (e.g. [8]), for all minerals
281
for which diffusion data exist save aluminosilicate garnets. The reasons for nonconformity of the aluminosilicate garnets to these trends may stem from earlier-outlined difficulties in the cited experiments. Mineral elastic moduli also appear to be correlated with diffusion parameters; materials with greater moduli of elasticity exhibit generally higher activation energies and larger pre-exponential factors for REE diffusion. Again, however, the aluminosilicate garnets do not adhere to these trends, but this is perhaps so for the reasons above. However, a recent study of REE diffusion in YAG (Cherniak, unpubl. results), yields diffusion parameters for aluminate garnet consistent with the trends mentioned above. Similar broad trends have been noted for Pb diffusion in minerals [8] and in metals (e.g. [29,30]), and theoretical bases for correlations between activation
Fig. 8. Plots of diffusion parameters for REE transport in various minerals vs. mineral ionic porosities (a) and (b), and bulk moduli (c) and (d). There appears to be at least some degree of correlation of both activation energy of diffusion and the log of the pre-exponential factor with these two mineral properties among all but the garnets. Ionic porosities were obtained from Refs. [6–8]. Bulk moduli values were obtained from Refs. [42,43]. For minerals for which data were unavailable, moduli were estimated using the relationships derived in Ref. [44].
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energy for diffusion, and bulk moduli and atomic volume have been established (e.g. [30,31]). Blundy and Wood [32] have noted differences in partitioning behavior corresponding to variations in elastic moduli among the feldspars; with the more flexible sodic plagioclase accommodating Sr and Ba ions more easily than the more rigid calcic plagioclases. They have further extended these arguments to a predictive model [33] to determine partition coefficients as a function of Young’s Moduli and cation size and charge. Similar treatments might be applicable to diffusion if we presume that a more flexible (i.e. smaller elastic modulus) structure would also permit easier cation migration. Clearly, however, such simple correlations provide only first-order information as they do not consider defect structures that may influence diffusion, or the added complexities of the exchange process when other chargecompensating species are involved. More diffusion data on trivalent cations (especially the REE) are warranted to better understand such systematic behaviors should they exist. It is important to consider also that the diffusion parameters themselves (i.e. activation energies and pre-exponential factors) may be correlated through the Meyer–Neldel or ‘compensation’ effect (e.g. [34–36]). A detailed discussion of this phenomenon with respect to diffusion in minerals is beyond the scope of this paper, but will be presented elsewhere (Cherniak, in prep.). 5.2. Applications 5.2.1. REE closure temperatures A summary of REE closure temperatures as functions of effective diffusion radii (for a cooling rate of 10ºC per million years) is plotted in Fig. 9. In correspondence with the diffusivities above, closure temperatures for the REEs in calcites are fairly low. For example, closure temperatures for calcites of 100 µm effective diffusion radii are 495º and 523ºC for Nd and Yb, respectively. These values are 25º to 50ºC lower than that for Sm in apatite, the next-lowest closure temperature. However, closure temperatures for the REE in zircon, titanite, and diopside are all higher by a considerable margin. It seems clear that calcites are much more likely to experience REE exchange at low temperatures than most other minerals for which diffusion data exist, but the sequence
Fig. 9. Closure temperatures of the REE as a function of effective diffusion radius. Closure temperatures are calculated using the expression from Ref. [45] and the diffusion parameters from the sources cited in Fig. 7.
of closure is complicated by variations in effective diffusion radii among minerals and the influence of modal abundances on the REE reservoir. We consider two geologic scenarios for which closure temperature calculations may be relevant: (1) cooling of marbles in regional metamorphism; and (2) cooling of carbonatites. The first case involves slow cooling from modest temperatures. If we consider a moderate metamorphic temperature of 550ºC and cooling rates as above, REE information will be largely retained (provided changes in REE composition are affected only by diffusion) since diffusivities are sufficiently slow over the temperature range that 100 µm grains will close to diffusional exchange before significant loss has occurred. Slower cooling will depress closure temperatures (they will be about 60ºC lower for a cooling rate an order of magnitude slower, i.e. 1ºC per million years), but diffusivities over this temperature range are such that complete REE alteration will not occur before diffusional exchange effectively ceases. Finer-grained material, however, will be much less retentive.
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The latter case involves relatively rapid cooling from much higher temperatures (1000–1100ºC). More rapid cooling will elevate closure temperatures (by about 70ºC for an order of magnitude increase in cooling rate; very rapid cooling rates, however, render the construct of closure temperature invalid), but REE diffusivities are sufficiently high above 700ºC that calcite is unlikely to retain the REE composition reflective of conditions of its crystallization. 5.2.2. REE zoning According to the model of Watson and Liang [37], the formation of growth zoning is related to the volume diffusion rate .D/ of the zoned element within the mineral crystal lattice as well as the growth rate .V / of the crystal. The model considers volume diffusion in the crystal as the determining factor in transport kinetics. Regions of perturbed chemical potential of a trace element, due to its incorporation at the surface of a growing crystal, can only be eliminated by lattice diffusion of this element. Thus, fast lattice diffusion would lead to equilibrium growth, and slow lattice diffusion would result in disequilibrium growth. Watson and Liang [37] suggest that a ‘critical value’ of the dimensionless parameter V l=D (where l is the half-width of the enriched-surface growth layer, the latter assumed to be a monolayer) is a determining factor in the development of sector zoning: when this parameter is above ¾0.5 to 3, the development of sector zoning during growth is unavoidable in crystals that exhibit selective enrichment of the element on specific growth faces. In Fig. 10, minimum growth rates for calcite that would result in Nd and Yb zoning, calculated using this model, are plotted as a function of temperature. For example, at 500ºC, growth rates faster than ¾10 15 m=s would result in sector zoning with respect to Nd or Yb. At 200º and 30ºC, rates would be ¾10 21 and 10 30 m=s, respectively, for Nd, and ¾10 23 and 10 35 m=s for Yb. Paquette and Reeder [38] report laboratory growth rates of 1– 5ð10 10 m=s at 30ºC. Given this result and other calcite growth rates reported under various conditions, sector zoning with respect to the REE is quite likely (if these cations are in fact preferentially incorporated at some growth faces). Zoning of the REE has been reported [5] in laboratory-grown calcites, a result also consistent with the low REE diffusivities expected at room temperature.
Fig. 10. Minimum growth rates to produce sector zoning of the REEs in calcite as a function of temperature. Curves are calculated using the model of Ref. [37]. See text for further explanation.
Once present, REE compositional zoning is likely to persist under many circumstances. A simple model illustrates this point. Zones in calcite are modeled as plane sheets of thickness l; adjacent planes have different concentrations of the diffusing species. Only diffusion in the x direction (i.e. normal to the planar interface) is considered. We evaluate two different (arbitrary) criteria for changes in zones due to diffusion: (i) ‘blurring’ of these regions, defined by a compositional change of 10% of the way into the zone; and (ii) ‘disappearance’ of zones, defined by a compositional change of 10% in the center of a zone. For condition (i), the dimensionless parameter Dt=l 2 is equal to 1:8 ð 10 3 ; for condition (ii) the value for this parameter is 3:3 ð 10 2 . Fig. 11 shows curves constraining the time–temperature conditions under which Nd and Dy zoning of various dimensions (1 and 100 µm) will be retained given the above criteria. At temperatures of 300ºC, 1 µm regions of Nd zoning would be ‘blurred’ in 65,000 years and ‘lost’ in 1.2 million years, zones of 100 µm dimensions would be ‘blurred’ in 650 million years and ‘lost’ in 1.2 billion years. Some 1 µm Nd zoning would be retained in calcite heated to 170ºC for times in excess of the age of the earth. Coarser zoning of 100 µm would be retained to some degree over this time scale at temperatures of 340ºC. At 500ºC, the time for ‘blurring’ of 10 µm zones is about 2000
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diffusion between chemically distinct zones during such events, we evaluate the integral of the diffusion coefficient as a function of time, i.e.: Z t D.t 0 / dt 0 Deff t D 0
Fig. 11. Preservation of REE zoning in calcite during isothermal events. Curves represent maximum time–temperature conditions under which 1 and 100 µm scale zoning would be preserved in calcite, assuming alteration of zone compositions only through volume diffusion. For conditions above the upper curves in each group, well-defined zoning will be lost. For conditions below the lower curves, zones may be ‘blurred’ but still retain initial composition in zone center. The model used to calculate trends of curves is described in the text.
years, loss of zones occurs in 42,000 years. For 1 µm and 100 µm zoning, times would be two orders of magnitude shorter or longer, respectively. Dy zoning would require shorter time than Nd at a given temperature for loss or blurring. For example, at 300ºC, the time necessary to ‘blur’ 1 µm Dy zones is 29,000 years, loss of zones occurs in 540,000 years. For 100 µm zones, the values for blurring and loss are 290 million years and 5.4 billion years, respectively. Clearly, however, the simple case of isothermal heating is rarely reflective of geologic conditions. We consider the more realistic diagenetic=metamorphic circumstance of heating of sediments as a consequence of burial. A geothermal gradient of 30ºC per km (a normal continental gradient) is assumed, with depositional rates on order of 10–20 m per million years, e.g. [39,40]. Typical heating rates are then on order of 0.3–0.6ºC per million years, with burial depths from 4 to 10 km and maximum temperatures of 150–250ºC (starting from a surface temperature of 20ºC). In order to determine the extent of inter-
Interestingly, simple numerical integration reveals that Deff is roughly an order of magnitude smaller than D.t/ (for maximum T greater than ¾50ºC). It should be noted that this simple relationship applies to the range of conditions (heating rates and activation energies for diffusion) considered here. A more comprehensive treatment taking into account a broader range of conditions is beyond the scope of this paper, and will be elsewhere addressed (Cherniak and Watson, in prep.). We again return to the simple criteria outlined above for the preservation of zoning, i.e. Dt=l 2 equal to 1:8 ð 10 3 and 3:3 ð 10 2 for ‘blurring’ and loss of zones, respectively. Instead of assuming a constant D, however, we substitute Deff t (determined by numerically integrating the expression for D.t 0 / over time given a heating rate of 0.5ºC per million years and the diffusion parameters for Nd) for Dt in the relations. Fig. 12 shows plots of zone width as functions of burial depth and maximum temperature of heating as a consequence of burial. It is clear from the figure that even zoning on the scale of tens of micrometers will be to some extent preserved under most of these diagenetic conditions. 5.2.3. Isotopic=chemical equilibration of REEs in calcite We can also use the diffusion data to determine the extent that calcite grains of more homogeneous composition will isotopically or chemically equilibrate with their external environment during a thermal event, noting that the model that follows applies strictly under conditions in which diffusion is the dominant mechanism of exchange. Clearly, however, solution=reprecipitation provides a more expeditious means of exchange in many natural settings. We consider the simple model in which a calcite grain is a sphere of radius a and initial uniform concentration of diffusant C1 ; it is exposed to an external medium with concentration of diffusant Co . The solution to the diffusion equation given these conditions is
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Fig. 12. Preservation of REE zoning during heating as a consequence of burial. Curves represent minimum zone dimension and that will be preserved given a heating rate of 0.5ºC per million years. The abscissas are burial depth and maximum temperature, with assumptions of reasonable (and constant) deposition rates and a typical continental geothermal gradient of 30ºC per km. Further detail is included in the text.
presented in Crank ([41]; p. 91). When the dimensionless parameter Dt=a 2 (where D is the diffusion coefficient, t is the time at elevated temperature) is less than or equal to 0.03, the concentration of diffusant at the center of the sphere is unchanged from its initial value. Above 0.03, the concentration at the grain center is affected by the externally imposed concentration Co . In Fig. 13, we plot curves representing Dt=a 2 D 0:03 for La and Yb in calcite given a 1 mm effective diffusion radius. These curves define time– temperature conditions limits for which La and Yb isotopic information in the calcite grain will be retained. For times and temperatures below the curves, Yb and La isotopic ratios at crystal cores will be preserved. Above the curves, they will be influenced by external La and Yb compositions. At 500ºC, centers of 1 mm calcite grains will retain their initial La compositions for nearly 340 million years, while Yb compositions will be retained for nearly 900 million years. La and Yb
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Fig. 13. Preservation of REE composition in calcite grains. The curves correspond to values of 0.03 for the dimensionless parameter Dt=a 2 for Yb and La, and represent maximum time– temperature conditions under which the centers of grains of 1 mm effective size will preserve their original REE isotopic or chemical signatures, again assuming volume diffusion of the REE as the dominant mechanism facilitating exchange. For conditions above the curves, this information will be lost.
compositions will be preserved over times in excess of the age of the earth at temperatures of 400º and 450ºC, respectively. Information on initial REE compositions will persist for a few million years even for temperatures in excess of 700ºC. Preservation of REE isotope and chemical information is therefore quite possible under a broad range of conditions if REE contents are altered only by diffusion.
Acknowledgements I thank Rich Reeder for inspiring and encouraging the undertaking of these calcite diffusion studies. Both he and Bruce Watson provided invaluable suggestions and discussion during the course of this investigation. Insightful review comments by F.M. Richter and S.M. Fortier assisted immeasurably in improving the final version of the manuscript. This work was supported through grant EAR-9406916 from the National Science Foundation (to E.B. Watson). [CL]
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