A study of strontium diffusion in apatite using Rutherford backscattering spectroscopy and ion implantation

0016-703?/93j$66.00

Geochimica et Cosmochimica Acla Vol. 57, pp. 4653-4662 Copyright Q 1993 Pergamon Press Ltd. Printed in U.S.A.

+ .I0

A study of s~ontium diffusion in apatite using Rutherford backscattering spectroscopy and ion implantation D. J. CHERNIAK~and F. J. RYERSON’ ‘Departmentof Earth and Environmentaf Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA 21nstitute of Geophysics and Planetary Physics, Lawrence Livermore Laboratory, University of California, Livermore, CA 94550, USA (Received July 24, 1992; accepted in revisedfirm April 1, 1993)

Abstract-Strontium diffusion in Durango fluorapatite has been measured under anhydrous conditions using a combination of techniques. Diffusants were introduced into the apatite by two methods: ( 1) ion implan~tion of Sr, and (2) immersion in a strontium oxide reservoir. Resulting diffusion profiles were measured by Rutherford Backscattering Spectrometry (RBS) and fit to the appropriate solutions of the diffusion equation to obtain diffusion coefficients. Previous determinations of Sr diffusion in apatite obtained under hydrous conditions ( FARVERand GILETTI, 1989) indicate that a decrease in activation energy occurs at approximately 1000°C. In contrast, diffusivities obtained in the present work may be described by a simple Arrhenius relationship: D = 2.7 X 1O-3 exp

65000 + 2200 cal/mol RT

for diffusion perpendicular to c over the temperature range 700- 1050°C. Similar results are obtained for transport parallel to c. As in the case of Pb diffusion in apatite ( CHERNIAKet al., 199 1 ), the results of the present study lie on the down-temperature extrapolation of diffusion coefficients determined under dry conditions at higher temperatures (WATSON et al., 1985 ) . Radiation damage induced by ion implan~tion may, in some cases, enhance or otherwise a&ct dif%tsion parameters. To assess the significance of such effects in apatite, the Sr results obtained by ion implantation were compared with those from a set of experiments in which Sr was introduced by immersion of the crystals in strontium oxide powder. Excellent agreement of diffusion coefficients from the two data sets indicates that radiation damage does not adversely affect these measurements of Sr diffusion in apatite made under anhydrous conditions. The measured diffusivities suggest that strontium isotope ratios in the cores of apatite crystals entrained in felsic magmas or n&dual to crustal anatexis may be unaffected by the Strontium isotopic compositions of their surroundings for the temperatures and durations typical of these events. INTRODUCIION

these factors can be used to simply determine if geochemical information characteristic of the source is preserved in the mineral core for a particular history and mineral grain size. It may, with continued improvement in secondary ion mass spectrometry (SIMS), eventually be possible to measure concentration profiles in restitic accessory minerals, yielding more detailed thermal histories. In this respect, diffusion parameters for elements such as Sr in accessory minerals are necessary for this application as well as in the now familiar method of determining closure temperatures (DODSON,

DURINGEPISODESOFCRUSTAL anatexis, radiogenicisotopes, and trace elements contained within the mineral phases comprising a source rock are redistributed, and the geochronologic (radiogenic isotopes “Sr 206,207Pb,‘43Nd, ‘76Hf) and geochemical information (e.g., KEEs) within each mineral phase may be significantly affected. This information is lost if the mineral is totally consumed during partial melting, or if diffusion of the element of interest within the rest&c fraction of the mineral is sufficiently rapid to allow ~uilib~tion on the time scale of the partial melting event. Alternatively, restitic minerals may be transported from the source region by the departing melt. Under certain circumstances, they then carry not only information characteristic of the source region, but may also retain information reflecting the time-temperature history of crustal melting and transport. The relatively high concentrations of xadiogenic isotopes and trace elements in accessory minerals make them particularly useful in this regard. Whether or not insoluble accessory phases retain anatectic andlor source region information depends upon the integrated time-ornate history of melting and transport and the relevant diffusion parametem In a first-order application,

1973).

In this paper, we present data on the difision of Sr in apatite under dry, one-atmosphere conditions. Two different methods are used to introduce the difisant: ( 1) ion implantation of Sr and (2) immersion of the apatite crystals in a SrO powder reservoir. The first technique has been used with some success in q study of Pb diffusion in apatite f CHERNIAK et al., 199 1) and silica glass ( CHERNIAKet al., 1990). However, as noted in these studies, radiation damage induced by ion implantation may influence diffusion under some circumstances. For instance, measurements obtained from zircon in which an implanted Pb source was used yieid dill&on coefficients that are several orders of magnitude higher than those inferred from geochronologic data (CHERNIAK et al., 4653

3654

I>. J. Cherniak

To assess the significance

1991).

experiments eliminated

in which (i.e.,

also performed

the

the SrO and

results

of such

source

effects

of radiation

powder

source

compared

Energy

in apatite. damage

experiments)

with those

and F. J. Ryerson

2.2

was

---.-

from

c,;

the Sr

SJ1 “lnll t-1

REE

50

0

850

900

950

d

Channel

Preparation

The diffusion experiments were performed on samples of natural fluorapatite from Durango, Mexico. Its chemical composition, as reported by YOUNG et al. ( 1969) is Gag s3NaoosSro.o,REo.os(POd)5.87-

FIG. I. Expanded regions of RBS spectra of Sr-implanted (solid symbols) and unimplanted (open symbols) apatite, showing the Sr peak and rare-earth background. The location of the sample surface with respect to the Sr peak is indicated by the vertical dashed lint.

Although

there can be significant chemical variation in individual specimens of this apatite, RBS analyses indicated that the samples used in this study all had very similar major element and total REE compositions. Apatite crystals were sectioned with a low-speed saw and cut parallel or perpendicular to the c-axis. Samples used in the study had surface areas ranging from IO to 30 mm2 and were typically about 1 mm thick. All samples cut perpendicular to c and some cut parallel to c were polished to 0.3 Km AlzOl and ultrasonically cleaned to remove residual grit and material. The remainder of the samples cut parallel to c had clean natural growth faces and required no further surface preparation. Ion Implantation

2.8

. ‘mpS0r.e j,S ,,i, Lr(.-

100

PROCEDURE

(S0~)o.o~(Si0~)o.~(As04)0.o1(C03)~~1F1.~C1~.1~(OH)~.01.

-.__ _ ___

.. ..* ”

800

Sample

2.6

were

ion implantation experiments. In both cases, concentration profiles were obtained using Rutherford Backscattering Spectrometry (RBS). This method permits us to make diffusion measurements in a temperature range (700-1050°C) that is directly applicable to high-grade metamorphism and crustal anatexis. These data also augment previously determined high-temperature ( 1050-1250°C) I-atm data OfWATSON et al. ( 1985). In addition, we consider the effect of orientation on Sr transport and compare our results to the hydrothermal experiments of FARVER and GILETT~ ( 1989). EXPERIMENTAL

(Add)

2.4

Experiments

Prepared samples were implanted at room temperature with a beam of 70 keV Sr+ ions produced from a SrF2 powder source in a Danfysik I50 kV ion implanter. The nominal dose delivered to the samples was 3 X lOI Sr cm-‘. This is three times the ion dose used in an earlier study of Pb diffusion in apatite employing the same technique (CHERNIAK et al., 1991). The higher dose is necessary in order to resolve the Sr peak from the background signal produced by the rare earth elements (Fig. 1 ). In addition, RBS is less sensitive to Sr than to Pb, as the probability of a backscattering event is proportional to Z *. Because it is a lighter ion with lower Z, however, the Sr implantation should result in levels of radiation damage similar to that for the Pb implantation, despite the difference in dose ( MOREHEAD and CROWDER, 197 I: CHERNIAK, 1990). Beam currents during implantation were typically on order of 0.1 to 0.5 /*A. Sample heating and surface sputtering due to the ion beam were minimal under the conditions used in implantation. The implanted samples were placed in silica glass boats and annealed in air in a silica glass tube furnace. The furnace temperature was monitored with a chrome]-alumel thermocouple and varied by no more than -+2”C during runs. SrO Powder Source Experiments Prepared apatite samples were loaded into 8 mm Pt crucibles and surrounded by strontium oxide powder. The crucibles were annealed in air in vertical tube furnaces. Temperatures were monitored with chrome]-alumel thermocouples and varied by no more than rt2’C during anneals. After annealing, the samples were removed from the crucibles and cleaned ultrasonically in distilled water and alcohol. In some cases, the powder adhered to the sample surface and could not be removed without more aggressive means which would have damaged the sam-

ple surface itself. However, on most samples, the powder residue clung only to isolated regions and there was sufficient clear surface area available for RBS analysis. CYGAN and LASAGA ( 1985 ) observed similar behavior with the deposition of magnesium salts as isotopic tracers on garnet surfaces. Rutherford

Backscattering

Spectrometry

(RBS)

As previously noted above, RBS was used to obtain concentration profiles. This technique is based on the measurement of energies of light ions which are elastically scattered from atoms in a target material. A mono-energetic beam of ions, produced in a linear accelerator, bombards the sample, and the ions scattered from target atoms are detected. A spectrum of particle yields as a function of energy is collected in a multichannel analyzer. The energies of detected ions depend upon the mass of the target atoms and the depth within the material at which they are located. In the case of a thick (at least several pm) multi-elemental target, the energy spectrum is the sum of contributions of the spectra from each constituent atom. Hence. the spectrum consists of a series of steps whose edges correspond to scattering events at the sample surface. Target atoms can be identified by the energies at which these edges occur. Particles with lower energies (when considering only contributions to the RBS spectrum from a particular target element) result from scattering events at depth in the material, as the ingoing (before scattering) and outgoing (after scattering) ions lose energy as they travel through it. The number of detected ions at a given energy is directly related to the concentration of the atomic species and the probability of a scattering event occurring. The latter factor is proportional to the square of the atomic number of the target atom, resulting in greater detection sensitivities for high-i! atoms. Hence, the energy spectrum of the scattered particles provides information on the type, concentration, and depth disnibution of atoms in the target material. Further information on this technique may be found in CHU et al. ( 1978). The RBS analysis was performed on the 4 MV Dynamitron accelerator at SUNY-Albany. A beam of 2 or 3 MeV ‘He+ ions was used, with backscattered ions detected by a silicon surface barrier detector. Beam size was typically about 1 mm’. The MCA spectra were converted from counts vs. channel to concentration profiles as follows: MCA channel number was first related to detected particle energy through calibration with standards (typically Si02 glass and metal targets). A depth scale was then determined by calculating the rate of energy loss (dE/dx) for the ions travelling through the material before and after scattering events. These energy loss rate values, or stopping powers, were calculated for apatite using analytical polynomial expressions for elemental stopping powers (CHU et al., 19%)

4655

Diffusion of Sr in apatite and weighting the contribution to the total stopping power of each element according to its abundance in the material, also taking into consideration the effectsof changes in material composition and ion energies on stopping powers. Particle yields were converted to concentrations by taking into account the probabilitiesof scatteringevents for the relevant atomic species (Sr) at various depths in the sample.

DATA ANALYSIS The concentration profiles derived from the RBS spectra were fit with models to determine the diffusion coefficient D. The different initial and boundary conditions imposed in the ion implantation and powder source experiments consequently result in dissimilar solutions to the diffusion equation. However, in both cases, we can describe the process as one dimensional (concentration independent) diffusion. The model used for the ion implantation experiments assumes an initial Gaussian distribution of Sr ( RYSSELand RUGE, 1986; CHERNIAKet al., 199 1): C(x, 0) = sexp[-e],

/

I

I

:: : :. f\: *

1

: .‘\ /I :: ::H !I

.:

1 :

:I \: 1s 1t

.

unannealed

-.-

15 mip

-..-

1 hr

-

4 hr

- -

16 hr

---

64 hr

-1 0.05

0.10

0.15

Depth

(microns)

0.20

0.25

FIG. 2. Time evolution of the diffusion model for ion-implanted samples (Eqn. 2), usin the parameters I X lo-l6 cm* set-’ for D, 275 li for R, and 130 x for AR.

C(x, t) =

&

sop

C(x’, 0)

x[exp[-VI-exp[-q]]f.lX’.

Substituting in Eqn. 1 for C(x), 0):

(1)

where x is the distance from the implanted surface, C(x, 0) is the initial ion concentration at x, Nimp is the implanted ion dose (ions cmm2), R is the distance between the peak maximum and the surface, and AR describes the width of the distribution of implanted ions about R. The latter factor, typically called range straggle, is a consequence of nonuniform energy loss rates among the individual ions comprising the implanted beam. The boundary conditions assumed in this case are ( 1) the concentration of diffusant goes to zero at the sample surface, C( 0, t) = 0, and (2) the medium is infinite in the positive x direction. These are the same boundary conditions as those in a study of Pb diffusion using this implantation technique ( CHERNIAK et al., 199 1). Since PbO is more volatile than SrO, one may question the validity of ( 1) as a suitable boundary condition. When the vapor pressures of these ele-

/

ments are compared, however, Sr is found to have values comparable to or higher than those for Pb in the temperature range of the diffusion anneals (NESMEYANOV,1963). The other possible surface boundary condition, that of no outdiffusion at the sample surface (i.e., X(x, c)/~x[~=~ = 0) would only be valid if the implanted species had negligible vapor pressure at the corresponding annealing temperature ( RYSSELand RUGE, 1986). The good fits of the data to the diffusion model derived from the above boundary conditions also provide empirical evidence that supports this choice. The general solution to the diffusion equation is then

-Figure 2 shows the time evolution of a concentration profile, determined by using Eqn. 2 and specific values for the parameters R , AR, D, and Nrmp.Diffusivities were determined with nonlinear fitting routines using Lever&erg-Marquardt (PRESS et al., 1987) and grid-search ( BEVINGTON,1969) algorithms. Fitting was first done on unannealed implanted samples to obtain values for R, AR, and Nrmp.These parameters were then held fixed when annealed samples were fit to determine D. Better fits were obtained when Nimp was permitted to vary by up to 20% to account for variations in initial implanted ion dose. The model occasionally underestimated peak heights, but changing the value of implant dose entered into the fitting program in order to better match the maximum peak height changed D values by at most a few percent, a factor much smaller than other contributions to error ( CHERNIAK, 1990). The values for R obtained by this fitting procedure were found to agree well with those calculated in the ion implantation simulation program TRIM (ZIEGLER et al., 1985). The values of AR were found to be much larger than the range straggle predicted by TRIM, but as pointed out in CHERNIAKet al. ( 1991), additional contributions to AR from detector resolution and straggle of the helium ion beam used for RBS analysis account for this discrepancy. Although Sr concentration goes to zero at x = 0 as illustrated by the model in Fig. 1, a number of counts (and, hence, a nonzero concentration) will be recorded in the RBS spectra in a position corresponding to the sample surface. This is

4656

D. J. Cherniak and F. J. Ryerson

because spatial resolution in RBS is limited by the detector and supporting electronics used to detect the backscattered ions, so concentration cannot be determined right at the surface. To obtain good fits, the diffusion model was convolved with a Gaussian representing the detector resolution. The AR term accounts for the straggling effects for both the implanted ions and the He ions used in RBS analysis. Figure 3 shows a set of Sr concentration profiles for various annealing conditions, with best fits to data using the above model. Errors in the fitting parameters were also obtained from the fitting routine by determining the curvature of the x2 function near its minimum with respect to the parameter of interest ( BEVINGTON, 1969). The uncertainties (at 14 level) for the RBS spectra (counts/channel) were assumed to be a function of both the number of counts in the Sr peak and the subtracted rare-earth background (i.e., (2N,, + N,) I’*, where Np is the number of counts in the Sr peak in a particular channel and Nb is the number of counts in the background). There was some concern that the implanted Sr redistributed itself during the first few minutes of the anneal due to radiation damage induced by implantation (GYULAI. 1988). As discussed in CHERNIAKet al. ( 199 I), overestimates of D could result if the implanted ion profile was broadened during such redistributions. Short-duration anneals of implanted apatite showed no significant change in the Sr profile, a result similar to that observed for Pb ( CHERNIAK et al., 199 1). The SrO powder experiments can be modeled as diffusion into a semi-infinite medium from a source of constant concentration. The solution to the diffusion equation is then

I

800 C 20 h SrD powder

0.02

0.04 Depth

s

Y s

0.8

source

0.06

0.08

(microns)

-

0.6

o” c5

-7

5

0.4

-

C(.x,t)=(b(l-erf(s)). where C(x, t) is the concentration at depth x and time t, Co is the surface concentration, and D is the diffusion coefficient. Although the powder source is not in the strictest sense a uniform distribution, as its contact with the sample surface is a discrete point, other work with similar powder sources ( CHERNIAK and WATSON, 1992) has shown good agreement of diffusion data with this model. Theoretical arguments by TANNHAUSER ( 1956) also indicate that diffusion profiles will

FIG. 3. Diffusion profiles for Sr in apatite for three different annealing temperatures. Symbols represent data, lines are best fits to the data using the model described in the text.

0.00

0.01

0.02 Depth

0.03

0.04

0.05

(microns)

FIG. 4. (a) Depth profile from SrO powder source experiment. Symbols represent data, line is complementary error function (Eqn. 3) fit to the data. (b) linearization of data in (a) by inversion through the error function. Slope of line is equal to l/( 4Dt)“‘.

be unaffected by nonuniform surface distributions of diffusant, provided that one-dimensional, concentration independent diffusion is being measured. Diffusivities were obtained from Eqn. 3 by plotting the inverse of the error function of ((C, - C(x, t))/Co vs. the depth x, which results in a straight line of slope (4Dt)-‘j2. Co, the surface concentration, cannot be measured precisely because of limitations in the depth resolution of RBS. However, the fitting routine provides for an independent determination of Co by allowing this parameter to vary until the intercept of the line goes to zero. A typical Sr diffusion profile is shown in Fig. 4a, in Fig. 4b the profile is linearized as just outlined. Uncertainties in the RBS spectra, based on counting statistics, are proportional to the square root of the number of counts in each channel, taking into consideration the subtraction of the rare-earth background. Depth resolution is about 100 A.

4651

Diffusion of Sr in apatite

RESULTS

damage annealing. For example, UV absorption spectroscopy studies of annealing of natural radiation damage in Durango fluorapatite ( RITTER and MARK, 1984; 1986; GIRSTMAIR et al., 1983) suggest that annealing of defects (such as those induced by implantation) should occur on time scales on the order of fractions of seconds for the length scales and temperatures involved in the present study (CHERNIAK et al., 199 1). Although such first-order kinetic models describing fission-track annealing may not adequately describe the process over all temperatures (GREENet al., 1988), they provide

The results from the Sr diffusion experiments are presented in Table 1. Included are the Sr ion implantation experiments (all for transport perpendicular to c) and the SrO powder source experiments (both parallel and perpendicular to the c axis). The data are plotted in Fig. 5, from which we obtain the activation energy 65000 + 2200 cal mol-’ and pre-exponential factor 2.7 X low3 (+9.1 X 10e3/-2.1 X 10m3)cm’ set-’ for transport perpendicular to c. The results for the SrO powder source and ion implantation agree quite well. This finding is significant in that it suggests that any radiation damage of the apatite that results from the ion implantation is readily repaired and thus will not affect Sr transport. A similar conclusion was reached by CHERNIAK et al. ( 199 1) in their study of Pb diffusion in apatite, based primarily on evidence drawn from other studies of radiation

Table 1.

Sr

Sample ion

diffusion in

SrM-1 St-M-22 SrM-11 SrM-6 SrM-12 SrM-2 SAA-3 SrM-13 SrM-7 SrM-4 SAA-8 SrM-14 St-M-5 St-M-15 SrM-9 St-M-16 SAA-10

800 800 800 850 850 850 900 900 900 950 950 950 1000 1000 1000 1050 1050

SrOM-2 Transport

- log D

(+/-I

1.27x10-" 1.73x10-1? 3.14x10+7 4.11x10-17 5.09x10-'7 1.22x10-16 8.92x10-1' 9.75x10-16 4.84x10-'6 5.32x10-16 1.25x10-15 1.17x10-15 1.29x10-15 8.76x10-15 8.38x10-15 7.24x10-15 1.30x10-" 9.33x10-'5 1.51x10-'4 4.89x10-14 5.44x10-'4

16.896 16.762 16.503 16.386 16.293 15.914 16.050 15.011 15.315 15.274 14.903 14.932 14.889 14.057 14.077 14.140 13.886 14.030 13.821 13.311 13.264

0.117 0.080 0.021 0.085 0.092 0.086 0.114 0.120 0.029 0.025 0.106 0.109 0.120 0.017 0.018 0.118 0.105 0.089 0.166 0.174 0.122

6.70~105 7.20~10~

8.13x10-'* 1.13x10-'6

17.090 15.947

0.080 0.065

9.91x10-'7 4.00x10-'6 1.07x10-16 3.95x10-'6 5.93x10-'6 8.22x10-= 2.24x10-= 2.67x10-'4

16.004 15.398 15.973 15.403 15.227 14.085 14.649 13.574

0.056 0.032 0.041 0.108 0.047 0.111 0.064 0.129

6.12~104 1.35x105 1.66x105 3.24~105 3.56~105 2.16~104 2.88x104 3.60~104 7.20~10~ 1.08~104 1.35x104 1.80~103 2.40x103 4.5OxlO'J 9.00x102 1.20x103 1.80~103 6.00~102 1.80~10~

750 750

SrOAA-5

D (cm%ec-'1

2.16~10~ 3.46~105

SrM-20

experiments:

source

Transport I

data.

700 700

SE-M-21

to c: 700 804

II to

c:

SrOM-7

801

7.20~104

SrOM-12

850

5.76~10~

SrOM-14

850

2.55~10:

SrOM-8

900

2.25~104

SrOM-10

951

1.44x104

SrOM-15

950

1.08~103

SrOM-13

1001

4.20~103

SrOM-16

1000

2.70~10~

high temperature

here. In the present work, Sr diffusivities obtained using the implantation technique may be directly compared with those from experiments involving no radiation damage (i.e., the SrO powder experiments) run over a similar temperature range. In the Pb diffusion study of CHERNIAK et al. ( 199 1))

experiments:

implantation

St-0powder

over the relatively

range of interest

t (8.X)

T (%I

SAA-18 SAA-19

apatite

a good approximation

f). J. C’herniak and F. J. Kyerson

: CC) 1000

so0

800

700

FIG. 5. Arrhenius plot of Sr diffusion data, showing results from Sr ion implantation and SrO powder source for diffusion perpendicular to c, and those for diffusion parallel to C.

the data were compared with those from a study by WATSON et al. ( 1985), in which completely different techniques were used. However, WATSON et al. ( 1985) were limited to measurements at high temperatures, hence, there was little overlap in the investigated temperature ranges of the two studies. Measured diffusivities also appear to be independent of time at a given tem~ratu~. This is significant in a diffusion study as it indicates that the dominant transport mechanism being observed is diffusion, and other processes which may not be time-independent, such as chemical alteration of the sample or the species taking shortcut diffusion paths, have little influence on the measured profiles. This is illustrated in Fig. 6, in which time series data for runs at three different temperatures indicate no apparent time dependence of Sr diffusion. A fit to the data for diffusion parallel to c resulted in an activation energy of 62500 * 6500 cal mol-’ and a pre-exponential factor of 3.3 X 10e4 (+5.8 X 10-3/-3.1 X 10s4) cm* set-’ . While the Sr diffusivities parallel to c are generally smaller than those perpendicular to c (by up to 0.4 log units), it should be noted that the observed trend agrees within error with that for transport perpendicular to c, indicating that Sr diffusion in apatite is not strongly anisotropic. This finding is interesting in view of the crystal structure refinement studies of Sr-apatite by HtJGHES et al. ( 1991). They noted that the lattice sites available to Sr are not linked in the (00 1) plane, and interstitial sites are not large enough to accommodate the Sr+’ ion. Therefore, diffusion in (001) must involve vacancies or defects. In contrast, there are adjacent Ca2 sites in the [OOl] direction which can accommodate Sr ions, a circumstance that suggests that diffusion parallel to the c axis should be faster, rather than shghtly slower, than Sr diffusion perpendicular to c. There are a number of possible explanations for this apparent inconsistency. Because of the good agreement of the present data set with that of WATSON et al. ( 1985 ), it is unlikely that difficulties in the experimental procedure are responsible as both works employed completely different techniques and obtained

essentially the same result (albeit over ditlerent tcmperaturc ranges). The findings of I-AKVEK and Gn I I I I ( it%!,) ;trc inconclusive on this matter. It may be the case that di~usi(~n occurs predominantly by a defect mechanism. If so, ditfusion could proceed at similar rates in both orientations (if‘ both have similar defect densities). Other evidence !?JI'such a process comes from the RBS spectra. If only direct Sr +? - (‘a ” exchange were taking place, a decrease in near-surface Ca co~espond~ng to the uptake ofSr would be observed, as was noted in a study of Sr diffusion in anorthitic feldspar ( CI%~KNlAK and WATSON. 1992 ). In the present cast. there is little evidence of this in the spectra. at least at levels corresponding to one-to-one Ca-Sr exchange. This does no! rule out Sr-Ca exchange completely. however. ‘The involvement of more than one mechanism for diffusion parallel to L’may contribute to the significant scatter observed for this orientation in both this study and that of F~KVEK and GII FTTI CI OX9j

We can compare our results with measurements of Sr diffusion in Durango fluorapat~te made by WATSON et al. ( 1985) and FARVERand GILETII ( 19X9 ). These data arc summarized in Fig. 7a and b. WATSON et al. ( 1985) used a Sr-enriched melt saturated in apatite as the source of diffusant and measured profiles with an electron microprobe. Over the temperature range I050-12SO*f. they obtained the Arrhenius relation 4.12 X 10’ exp (-.-.IOOO~/~~) cm* set-‘, which is an average between values for diffusion parallel and perpendicular to C. Transport parallel to c was observed to be somewhat slower than perpendicular to C. with differences averaging about 0.2 log units. a result similar to that found in our study. Their activation energy is significantly larger than that measured here ( 100 vs. 65 kcal mol ’ ). However. as can he seen in Fig. 7, the data from our study fall along a line that can be extrapolated up to the higher-temperature data of WA I-SON

..

r

? I

-,7L

--.--.-L-_-i---

103

.._^

104 time

105

--.-I

:Q6

(see)

FIG. 6. Diffusion coefficients as a function of annealing time for anneals using ion implanted source at 800°C (solid circles), 900°C (open circles). and 1000°C (squares).

4659

Diffusion of Sr in apatite

(4

et al. ( 1985). It should be noted, then, that the difference in

T(‘C) 1200

-11

1000 transport

activation energy is not the result of disagreement between these two data sets, but rather is a consequence of the errors inherent in determining activation energies from diffusion data encompassing a limited range of 1/ T.A least-squares fit of both data sets defines a single Arrhenius law:

700

800

perpendicular to c

-12

D = 2.4 X 10-3(+2.2 x 10-3/-1.2

-13 -i wf s 0 B

X exp i

-14

-15

-16

-17

0

This

n

Watson

study

0

Farver

I 6

-18

et al. and

(1985)

Giletti

(1989)

I

I

I

I

I

7

8

9

10

11

(~10~

K)

l/T

T(‘C)

7

\

s

"E

-14 -

iii

s D

$

-15 -

a 0

1

0

0

8

.

u

l

This study

n

Watson

0 -1%

.

ok. \

-16 -

-17 -

.O

Farver

I 6

0

et al. and

O *. 0.0

(1985)

Giletti

(1989)

I

I

I

I

I

7

8

9

10

11

(~10~

K)

l/T

FIG. 7. Arrhenius plots comparing data for Sr diffusion in apatite from this study with the results Of WATsoN et al. ( 1985) and FARVER and GILETTI(1989). In (a) and (b), the solid lines represent a fit to both our data and that of WATSONet al. ( 1985), and the dashed lines are the high and low temperature trends for Sr diffusion determined by FARVERand GILETTI ( 1989). (a) Results for diffusion perpendicular to c. Fitting parameters for the solid line, as cited in the text, are 65 kcal mol-’ and 2.4 X 10e3 cm’ set-‘. (b) Results for diffusion parallel to c. Fitting parameters for the solid line, as noted in the text, are 7 I kcal mol-’ and 1.2 X 10e2 cm2 se-‘.

x lo-3)

64700 + 1900 cal/ mol

RT

cm* see-I,

i

describing diffusion perpendicular to c over a temperature range of 550°C and five orders of magnitude in D. For diffusion parallel to c, there is more scatter, but a fit to the two data sets results in an activation energy of 70600 cal mol-’ and pre-exponential factor of 1.2 X lo-* cm* set-’ . FARVERand GILETTI ( 1989 ) measured Sr diffusion under hydrothermal conditions using a %r-enriched fluid, with profiles measured by ion microprobe. They observed two distinct trends in the data for transport parallel to c. For temperatures 650-lOOO”C, diffusion could be described by the Arrhenius relation 2 X lo-” exp (-(25000 f 4OOO)/ RT) cm2 EC’. At higher temperatures ( 1 lOO-12OO”C), the relation 1 X lo5 exp (-( 120000 + 22000)/RT) cm* set-’ was established (Fig. 7 ) . No clear dependence of diffusion on orientation was observed. Our results, as just noted, display a single trend on an Arrhenius plot with no marked change in activation energy. It is possible that a change in activation energy might be observed if our measurements could be carried out to higher temperatures, but this seems unlikely in light of the agreement of the extrapolated line with the highertemperature data of WATSONet al. ( 1985). In addition, our lower temperature data (<8OO”C) plot below the measurements of FARVER and GILETTI (1989) and seem to suggest a larger activation energy than the value inferred from their data. There are a few possible explanations for these differing observed behaviors. The experiments of FARVERand GILETTI (1989) were run under hydrothermal conditions, while ours and those of WATSON et al. ( 1985) were run dry at one atmosphere. The presence of water has been shown to affect diffusion rates of oxygen in quartz ( ELPHICKand GRAHAM, 1988), anorthite ( ELPHICK~~al., 1988), diopside (RYERSON and MCKEEGAN, 1993), and CaA I-NaSi interdiffusion in plagioclase (YUND and SNOW, 1989) for example. However, no evidence exists for the occurrence of this effect for cation diffusion when charge-compensating exchanges (e.g., Na+’ + Si+4 + Ca+2 + Al+‘), which may be facilitated by proton activity, are not required. In addition, given that hydrolitic weakening of Si-0 bonds may play a significant role in enhancing diffusivities in some of the cases above, it cannot be assumed that nonsilicates (such as apatite) would display similar behavior. It is also not clear why, if Sr diffusion were influenced by the presence of water, that this effect is pronounced only at low temperatures, since the high-temperature results agree with those of WATSONet al. ( 1985). The experiments of FARVERand GILETTI( 1989) measured tracer diffusion, with no net chemical transport of Sr. Both our experiments and those of WATsoN et al. ( 1985) measured

4660

D. .I. Cherniak and F. J. Ryerson

1200

chemical diffusion. Differences between measured Sr tracer and chemical diffusivities in orthoclase (CHERNIAK and WATSON, 1392; GILETTI, 199 I ) have been noted. However,

the differences in these results may be related to the charge compensation required for Sr-K exchange (i.e.. Na ” + Sit4 + Ca+2 + A1”3) in the process of chemical diffusion. In the present case, no such mechanism should be necessary. There also exists the possibility that diffusion may be conce~tration-de~ndent, since the Sr concentrations in our experiments range from a several tenths to a few (atomic) percent, and those of FARVER and GILETT~ ( 1989) are about 600 ppm. However, the SrO powder and ion implantation experiments (as well as the work of WATSON et al. ( 1985 ) produce comparable diffusivities. despite the fact that Sr concentrations differ by nearly an order of magnitude between the data sets. In addition, both ht concentmtion-inde~ndent diffusion models quite well.

--

1100

Albite Apotite

-

1000

G

900

Y s3

800

Orthoclose

:i

kI 2E”

700

E 2 9 0

600

4 !

_i

500 t

400

GEOCHEMICAL IMPLICATIONS OF

THE

DATA

During heating, Sr is redistributed among coexisting minerals, changing the ch~acte~stic ?Sr/‘%r ratio ofeach. Apatite is especially important with respect to Sr dif-h.rsionkinetics, as the very low Rb /Sr ratio generally found in this mineral makes it quite sensitive to Sr remobilization as a result of thermal events subsequent to initial crystallization. Radiogenie Sr ( “Sr*), lost principally by biotite, can be taken up by apatite (BAADSGAARDand VAN BREEMEN,1970; WASSERBURG et al.. 1964). In view of the Sm& diffusion coefficients at subsolidus temperatures ( i X lo-l4 cm* set-’ and smaller), it appears that strontium is taken up by apatite grains primarily because it can be accepted into the lattice;

I

1200

/

/

-

i”c/uo

. . . .._

,

-

I

I

O°C/Ma

I

100°C/Mo

-.-

- -

I

-

f

1000°C/Mo

10-l

10-2 groin

radius

’

I

100

crystal

10-l radius

100

(cm)

FIG. 9. Comparison of closure temperatures for apatite with those for feldspars, with cooling rates of 1“C and 1000°C per million years. Feldspar closure temperatures were calculated with the diffision data of GILETTI(1991) for albite and CHERNIAK and WATSON( 1992) for anorthite and orthoeiase.

it generally remains concentrated in the outer portions of crystals without substantial inward diffusion. In order to assess the degree of Sr isotope homogeni~tion likely in whole-rock systems as a consequence of thermal events, closure temperatures can be calculated using diffusion parameters for apatite and other Sr-bearing mineral phases found in crustal rocks. Closure temperatures are determined using an equation from DODSON(~ 973):

f

’

,

/

10-3

/

I

10-2

.’

(4)

10’

(cm)

FOG.8. Closure temperatures for Sr in apatite as a function of diffusion radius for a series of cooling rates, calculated using the diffusion parameters obtained in this study.

where R is the gas constant, EA is the activation energy for diffusion, Do is the pre-ex~n~ntial factor, dT/dt is the cooling rate, “a” is the effective diffusion radius, and “A ” is a geometric factor ( 55 for a sphere). The spherical geometric factor is used in this case because Sr diffusion does not appear to be strongly anisotropic in apatite. Using Dodson’s equation and the diffusion parameters measured in this study, we obtain closure temperatures of 613 and 803°C for “a” equal to 0.1 cm and cooling rates of 1“C and 1000DC per million years, respectively (Fig. 8 ) . Based on information from other diffusion studies ( CHERNIAKand WATSON, 1992; GILETTI, 199 1), the primary Sr reservoirs in granitoid rock systems, the feldspars, close to Sr exchange at higher temperatures than either biotite (which closes around 300 C, CLARK and J#GER, 1969 ) or apatite (Fig. 9 ) . Or&o&se closes at slightly higher temperatures than apatite (differing by lo-15°C for

4661

Diffusion of Sr in apatite similar grain radii), while closure temperatures for anorthite are over 100°C higher (CHERNIAK and WATSON, 1992). Given that feldspar grain radii are often considerably larger than those of apatite (and provided that one may make the assumption that effective diffusion radii and crystal radii are comparable), differences in closure temperatures may be even more pronounced. However, this is not necessarily so in all cases. GILETTI ( 199 1) found Sr closure temperatures to be significantly lower ( 125 to 16O“C less, depending on cooling rate) in albite than in apatite (Fig. 9). In addition, exsolved or twinned feldspars, with small effective diffusion domains, may have significantly depressed closure temperatures. Therefore, the order of closure in a particular system depends not only on the mineral constituents of that system but also on their respective effective diffusion radii. In multicomponent natural systems, closure temperatures are likely to be affected by the relative differences between diffusivities in constituent minerals and their modal abundances ( EILER et al., 1992). The Sr diffusion data can be used to assess the degree of equilibration of the Sr isotope composition of an apatite grain with its external environment. It can then be determined whether apatites entrained in granitoid melts are likely to retain the trace-element and isotopic character of their source rock. This is modeled by considering the apatite crystals to be spheres of radius a with concentration C’,, exposed to an external source with concentration C,. When the dimensionless parameter Dt/a’ is less than 0.03, the center of the spherical crystal will be unaffected by the externally imposed concentration (CRANK, 1975). When this parameter is greater than 0.03, the concentration at the crystal core will be influenced by the external source and may no longer be equal to its initial value. A time vs. temperature plot of the curve satisfying the equality Dtja’ = 0.03 is shown in Fig. 10. Also included are curves for Pb and Sm, using the diffusion data ofCHERNIAKetal.(l99l)forPb(55kcalmol-’, 1.3X 10m4 cm2 set-‘) and CHERNIAKand RYERSON( 1991) for Sm (55 kcal mol-‘, 5.1 X 10m6cm2 set-I). The results of these calculations indicate that apatite is more likely to retain information about a source rock’s Sr composition than its Pb composition. Rare-earth isotope ratios are even less likely to be affected than Sr. For typical durations of crustal melting events ( 50,000 to several million years), apatites should retain Sr source information at temperatures up to 630°C for longer events and up to 760°C for those of shorter duration (assuming 0.05 cm radius grains). This temperature range is also significant in that entrained apatite is most likely at temperatures below about 76O”C, since apatite solubility decreases at lower temperatures (GREEN and WATSON, 1982). Hence, the isotopic composition of the cores of larger apatite crystals should reveal valuable information about the source rock unless they have been subjected to extreme heating or have undergone recrystallization. The most appropriate candidates for this type of study are large-grained apatites found in granitic rocks that contain more P205 than required for apatite saturation at super-solidus temperatures (WATSONet al., 1985). Granitoids having such compositions are likely to contain entrained residual apatite (WATSONand CAPOBIANCO,198 1; GREEN and WATSON, 1982; HARRISONand WATSON, 1984).

.

Crystal radius = 0.05

cm

I

I

I 3

4

5

6

7

log years

FIG. 10. Diagram illustrating the time and temperature conditions under which the original Sr, Sm, and Pb isotopic concentration information at the cores of 0.05 cm apatite crystals is lost or retained. The curves correspond to values of 0.03 for the dimensionless parameter Dt/a2. For time-temperature conditions to the left of each curve, the apatite core will retain original information for that species; conditions to the right will result in modification of the original isotopic and trace-element character even at the crystal core. The curves for Pb and Sm were generated using the diffusion parameters from CHERNIAKet al. ( 199 1) and CHERNIAK and RYERSON ( 1991 ), respectively.

As an example, VONBLANCKENBURG ( 1992 ) has analyzed Rb-Sr, Sm-Nd, and U-Th-Pb systematics of the accessory minerals from the Central-Alpine Bergell intrusion. The grandioritic phase of the intrusion contains 0.26 w-t%PzO~, indicating that for reasonable estimates of the melting temperature and Si02 content, the grandiorite contains restitic apatite. The Sr isotopic composition of the apatite is identical to that of the whole rock within analytical error. If it is assumed that the whole rock composition is the composition of the melt in which the apatite crystal was entrained, then the similar isotopic compositions indicate that diffusive exchange has gone to completion. Based on our diffusion parameters and the observed grain size of apatite, VON BLANCKENBURG( 1992) constrained the duration of an isothermal melting event to ca. 0.1 Ma at 800°C and 0.4 to 2.1 Ma at 700°C (again, assuming that there has not been recrystallization of the apatite). Along with the core isotopic compositions of restitic grains, diffusion gradients present in these crystals could be investigated in ion microprobe studies. With use of the diffusion parameters presented here, these profiles could reveal substantial information about the time-temperature histories of partial melting events. Acknowledgments-We thank E. B. Watson and W. A. Ianford for helpful discussion throughout the course of this work. Bob Lentile’s assistance with ion implantation is also greatly appreciated. This work was supported by the Geosciences Research Program of the Depart-

4662

I). _I. C’herniak and F. J. Ryerson

ment of Energy’s Office of Basic Energy Science and by grant EARScience Foundation.

GRELN T H. and

Editorrul handling: R. A. Schmitt

lr’ol 79, 96-105. GREEN P. F., DLJ[>D~I. R.. and LASLI;I I G. M. ( I9XXI Can t&on track annealing in apatite be described by first order kinetics? Eurth Plunet. Sci I.rtt. 87 2 16-?4. _ I Gvut Al J. ( 1988) Exberimental annealing and activation. In I~,I Impkantatiw .Scienw und 7i?~hnolog>~ (ed. J. F. Z~rc;r FR) ~pp. 93- 163. Acad. Press. HARRISONT. M. and WATSONE. B. ( 1984) The behavior ofapatite during crustal anatexis: Equilibrium and kinetic considerations. Geochim. Cosmochim. .4cta 48, 1467-1477. HUGHESJ. M.. CAMERONM.. and CROWLEYK. D. ( I99 I ) Ordering of divalent cations in the apatite structure: Crystal structure rcfinements of natural Mn- and Sr-bearing apatite. Amer. Mineral. 76, 1857-1862. MOREHEAII F. F. and CROWL)LR B. L. ( 197I ) A model for the formation of amorphous Si by ion bombardment. In Ion Implantation (ed. F. H. EISFN and L. 7‘. CtIAZDDFRTON). .DD. . 25-30. Gordon and Breach. NESMA\.ANOV.A. N. ( 1963 ) I ‘u~~or Pressure O/ the (‘hams& E/Cmen/.~ Elsevier. PRESSW. H., FLANNERYB. P., T~LIKOLSKY S. A., and VFI IEKL~N<; W. T. ( I987 ) numerical Rcc,ipa\The Art qfScicntifk C’omputing. Cambridge Univ. Press. RITTER W. and MARK T. D. ( 1984) Optical studies of radiation damage and its annealing in natural fluorapatite. Nzu/. Instr Me/h.

920.5793 from the National

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