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Lithium tracer-diffusion in an alkali-basaltic melt — An ion-microprobe determination
Earth and Planetary Science Letter, 53 (1981) 36-40 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
36
[5]
LITHIUM TRACER-DIFFUSION IN AN ALKALI-BASALTIC MELT - AN
ION-MICROPROBE DETERMINATION R.K. LOWRY
1, S.J.B.
REED 2, j . NOLAN l, p. HENDERSON 3 and J.V.P. LONG z
1 Department of Geology, Imperial College of Science and Technology, Prince Consort Road, London SW7 2BP (U.K.) Department o f Earth Sciences, University o f Cambrdige, Downing Street, Cambridge CB2 3EQ (U.K.) 3 Department of Mineralogy, BriHsh Museum (Natural History), Cromwell Road, London SW7 5BD (U.K.)
Received September 15, 1980 Revised version received December 11, 1980
An ion-microprobe-based technique has been used to measure lithium tracer-diffusion coefficients (DLi) in an alkali-basaltic melt at 1300, 1350 and 1400°C. The results can be expressed in the form: DLi = 7.5 X 10-2 exp(-27,600/RT) cm2 s-1 The results show significantly faster diffusion rates than those previously recorded for other monovalent, divalent and trivalent cations in a tholeiitic melt. Consequently, diffusive transport of ions acting over a given time in a basaltic melt can produce a wider range of transport distance values than hitherto supposed. Hence, it is concluded that great care should be exercised when applying diffusion data to petrological problems.
1. Introduction
TABLE 1 Analysis of experimental charge, alkali basalt 2266
Previously, tracer-diffusion coefficients in natural silicate liquids have usually been determined by using radioactive isotope as a tracer (radiotracer technique [1 ]); however, such a method is not applicable to all cations of geological interest, including Li. An alternative procedure is to use an artificially enriched stable isotope (e.g. 6Li) as the tracer, whose distribution can readily be measured with the ion microprobe. Indeed, two previous studies [2,3] have successfully used the ion microprobe for the determination of Li self-diffusion or tracer-diffusion coefficients in crystalline and glassy solids. This paper presents the results of a feasibility study on the extension of the technique to determinations in silicate melts.
si02 TiO2 A1203 Fe2Oa FeO MnO MgO CaO Na20 K20
P205
45.89 3.72 16.55 10.67 1.91 0.18 6.30 9.62 3.79 1.73 0.52
Total
100.88
2. Experimental procedure
Table 1) by a method which is similar to that described by Hofmann and Magaritz [ 1 ]. After annealing for 3 - 4 days at the run temperature, a thin deposit of LiC1 * was precipitated from solution onto one end of
Narrow platinum capillaries (1.5 mm nominal ID) were Filled with a natural alkaLi-basaltic melt (see
* 0.98 6Li; A.E.R.E., Harwell.
0012-821X/81/0000-0000/$ 02.50 © 1981 Elsevier Scientific Publishing Company
37 the charge. The tracer was incorporated into the glass for 5 - 1 0 minutes at 800°C and any excess removed with dilute HC1. The experiments were run for up to 6 hours at 1300, 1350 and 1400°C in a SiC tube resistance furnace to produce a diffusion profile 1 - 2 cm in length. The experiment durations were selected on the basis of two criteria. First, as Hofmann and Magaritz [ 1 ] have shown, diffusion experiments in basaltic melts for which Dt < 3 X 10 -2 cm 2 are prone to error caused b y transport processes other than volume diffusion. In this work the Dt values were always >7 × 10 -z cm 2. Secondly, it was deemed necessary to show that the diffusion coefficient was independent of experiment duration. Consequently, the durations of the experiments at each isotherm were varied by a factor of between 1.7 and 2.0. Unfortunately, the variation could not be increased as the durations were constrained at the lower bound by the minimum desirable Dt value and at the upper by the length of profile which can be accommodated by the ion microprobe. After quenching ( ~ 3 0
EXPERIMENT
D88
seconds) in compressed air, the charges were mounted in epoxy resin. The resultant block was then partially ground away to expose glass along a complete longitudinal section of each charge, and subsequently polished. The instrument used for profile determination was a modified version of the AEI IM-20 ion microprobe [4]. The primary beam consisted o f 160- ions accelerated to 30 kV and focused to a spot o f about 15 #m diameter. The Li isotope intensities were measured by ion counting at points along the centre-line of each sample, enabling 6 E l / T E l t o be plotted as a function of distance (Fig. 1). The measured 6Li/Tti ratios must be transformed into tracer concentrations before the tracer-diffusion coefficient can be obtained using the equation below, which is derived in Appendix 1 : B -RC tracer concentration (c) = R (1 - X) - X
(1)
where B = 6Li concentration in the matrix, R = measured 6Li/Tti ratio, C = 7Li concentration in the matrix, and X = 6 t i fraction in the tracer. The effect of the transform can be assessed from Fig. 1. The relevant solution o f Fick's second law for the diffusion from an instantaneous plane source into
12.00 5.00[
KEY
. . . .
,
. . . .
,
. . . .
eLifLiR a t i o
0 Tracer
10.00[
Concentration
4.00
E
2
~
.
~.oo~
6.00
2.00
E
o Z
D 88
s.oo
[3_ *_=-
ED
4-00
0
~- 1
.
0
0
~
2.00 m 0
8
0.0
, ]0
,
,
,
L
0.50
. . . .
J . . . . 1 -OO
Distance
0.00 J I .SO
,
, 2.00
(cm)
Fig. 1. Plot of the measured 6Li/TLi ratios and derived tracer concentrations against distance for experiment D88. The values in each data set have been divided by the largest value in it to facilitate comparison of the two prof'tles.
-I .OH 30 . . . .
I ~00 . . . . . 2.00 . . . . Distance
Squared
3.00
( c m 2)
Fig. 2. Log-square transform of the tracer-concentration profile shown in Fig. 1.
38 TABLE 2
a semi4nfinite medium [5] is:
Isothermal diffusion coefficients
C(x, t) - ~
.
exp 4 ~ -
1
(2)
where C(x, t) = concentration at a distance x (cm) from the plane source after a diffusion time t (s), M = mass o f tracer added per unit area, and D = diffusion coefficient (cm 2 s-l). If this is rewritten in the form: M in c = l n [ ~ ] -
[~Dt ]
(3)
it can be seen that a plot o f l n c against x 2 should be linear with a slope o f - ( 4 D t ) -] . The transformed data from Fig. 1 are shown in Fig. 2.
1
Experiment
Duration (hours)
Temperature (°C)
D (10 -s cm 2 s-1 )
1-
D85 D86 D87 D88 D121 D122
2.0 4.0 5.2 3.0 2.0 3.5
1296 1296 1346 1346 1390 1400
1.05 1.10 1.30 1.42 1.84 1.82
-0.998 -0.995 0.997 0.998 -0.990 -0.984
1 Pearson product moment correlation coefficient for transformed diffusion profiles.
mo1-1 and a pre-exponent (Do) of 7.5 × 10 -2 cm 2 S -1 "
3. Results The measured tracer-diffusion coefficients are given together with the relevant experimental data in Table 2, and are presented graphically in Fig. 3. A least-squares fit of the data to the Arrhenius equation:
D = Do e x p ( - Q / R T )
(4)
4. Discussion Two features of the data set obtained here are of particular interest and are discussed below.
4.1. Activation energy o f diffusion
gives an activation energy (Q) o f 27.6 + 2.5 kcal
TEMPERRTURE ~DEC, C) -4°00
I
. . . .
1386 I
. . . .
1356 I
1327 . . . .
I
. . . .
1300 =
. . . .
] I
I
t O3 ZE
L~J (J
L~ O (J
-5,00
LL LL O
I -
. 6
bQ, 0
. . . . 92
, 6
. . . . 03
, 6
. . . . 14
, 6
. . . . 25
RECIPROCRL TEMPERRTURE •
,
.
6
30
10 4
[K
,
,
,
] 6
47
-~1
Fig. 3. Arrhenius diagram of the data presented in Table 2.
The significance o f the parameter Q in equation (4) is unclear. Magaritz and Hofmann [6] argue that the slope of the Arrhenius line obtained from diffusion determinations should not be considered as an activation energy, because the liquid does not have a fixed structure. Watson [7] postulates that Q is dependent upon melt microstructure (cation coordination polyhedra geometry) which is largely insensitive to temperature4nduced charges in the melt structure. Moreover, he successfully applied the concept to Ca 2+ diffusion data in a simple silicate melt. It, therefore, appears that whilst Q may not be an activation energy "sensu stricto" it is nevertheless a parameter which can be used to relate diffusion behaviour to certain aspects of silicate melt structure. Published data for tracer diffusion in a tholeiitic melt [1,6] show a range o f only 8 kcal mo1-1 in the activation energies of several divalent and trivalent cations, which is within the bounds of experimental error. However, the value obtained in the present study on a melt of alkali-basaltic composition is 8
39 kcal mo1-1 lower than the lowest value measured in the tholeiitic melt, suggesting that significant variation may be encountered if a wider range of cations is studied.
4.2. Isothermal diffusion coefficients The isothermal tracer diffusion coefficients exhibit two remarkable features. First, if the data of Jambon and Semet [3] for Li ÷ tracer diffusion in obsidian glass are extrapolated to 1350°C, they fall within a factor of two of our measured value for Li ÷ in an alkali-basaltic melt. However, such an extrapolation is fraught with sources of error resulting from changes in the diffusion matrix, and therefore it seems probable that the coincidence of values is fortuitous. Nevertheless, the possibility that the similarity is real provides impetus for further experiments. Secondly, the values in Table 2 are all significantly faster than the highest yet recorded for cations in a natural silicate liquid at 1300°C (D = 2.5 × 1 0 -6 cm 2 s -1 [8]) and therefore bring the range of observed diffusion coefficients in basaltic melts at this temperature to two and a half orders of magnitude. The value for Li ÷ is believed to represent the upper limit for diffusion of cations of geological relevance (with the possible exception of hydrogen)but the lower limit may not yet have been reached. It is tentatively proposed that such a limit may be represented by the diffusion of hexavalent uranium which may be as low as 10 -9 cm 2 s -1. This hypothesis is currently being tested experimentally. It is interesting to note the geological relevance of a four orders of magnitude variation in D for different cations in a single melt composition. Hofmann and Magaritz [I ] give the times taken for characteristic diffusional transport distances ((Dt) 1/2) of 5.6 cm, 56 cm and 1.8 km as i, 1 0 6 and 109 years respectively, assuming a diffusion coefficient of 1 0 -6 c m 2 s -1 . If the calculation is repeated for the data range suggested above, the results obtained are: 5.6 cm; 56 m; 1.8 kin;
t = 1 month to 103 years t = 10 s to 109 years t = I0 8 to 1012 years
From the above it can be clearly seen that the value for D used in mathematical models should be selected with some care. Hofmann and Magaritz [I ]
and Magaritz and Hofmann [6] have used tracerdiffusion coefficients for a variety of different concentration regimes. Whilst this is a valid first approximation (and indeed all that is possible with the data currently available), it should be realised that, strictly speaking, these coefficients should only be applied to regimes where the concentration gradient is extremely small. Otherwise, the effective diffusion coefficients are termed chemical diffusion coefficients or interdiffusion coefficients. Although these are linked mathematically to the tracer-diffusion coefficients (for the equations see Wei and Wuensch [ 10] ; Cooper [9]) they may deviate from them by several orders of magnitude. The application of tracer-diffusion coefficients to geological problems therefore requires careful consideration of the concentration regimes present in the system. As a general rule o f thumb, tracer-diffusion coefficients cannot be applied directly to geological problems which involve the transport of major or minor elements in silicate melts. However, the application of tracer-diffusion data to trace element transport is probably justified as the concentration differences (i.e. the difference in concentration between the two ends of a concentration gradient) are constrained, by definition, to tens or possibly hundreds of parts per million.
5. Conclusion The ion microprobe provides an excellent method for the measurement of otherwise unobtainable lithium diffusion data in melts. The results for Li ÷ show an activation energy of 27.6 kcal mol-1 and a value for D1296 of 1.08 X l0 -5 cm 2 s -1 . These values are lower and faster respectively than any data previously reported for basaltic melts. For such a melt at 1300°C it is postulated that the tracer-diffusion coefficients for different cations may span a range as large as 10 -s to 10 -9 cm 2 s -1 and therefore the values used in numerical models of petrological processes need to be selected with care.
Acknowledgements One of us (R.K.L.) gratefully acknowledges the receipt of a N.E.R.C. research studentship at Chelsea
40 and Imperial Colleges, London. We are also indebted to N.E.R.C. for grants in support of the ion-microprobe unit, Department of Earth Sciences, University of Cambridge, where the diffusion-profile determinations were carried out. Critical comments by Dr. R. Freer, Dr. A. Hofmann and an anonymous referee greatly improved the final version of the manuscript. Mr. P. Watkins analysed the starting compositions.
Appendix 1. Derivation of equation (1) Let A be the number of moles of 6Li in the tracer, let B be the number of moles of 6Li in the matrix, let C be the number of moles of 7Li in the matrix, let D be the number of moles of 7Li in the tracer. At any point the measured 6Li/TLi ratio (R) will given by:
R --
A+B
(A-l)
C+D
If the fraction of 6Li in the tracer is X then: A = Xc
(A-2)
D = c(1 - X)
(A-3)
where c = number of moles of tracer (tracer concentration). Substituting A-2 and A-3 into A-1 gives: Xc +B
R
(1-X)
c+d
(A-4)
Rearranging for c: c =
B -RC
R(1 - X ) - X
(A-5)
References 1 A.W. Hofmann and M. Magaritz, Diffusion of Ca, Sr, Ba and Co in a basalt melt : implications for the geochemistry of the mantle, J. Geophys. Res. 82 (1977) 5432. 2 J.N. Coles and J.V.P. Long, An ion-microprobe study of the self diffusion of Li÷ in LiF, Philos. Mag. 29 (1974) 457. 3 A. Jambon and M.P. Semet, Lithium diffusion in silicate glasses of albite, orthoclase and obsidian composition: an ion-microprobe determination, Earth Planet. Sci. Lett. 37 (1978) 445. 4 A.E. Banner and B.P. Stimpson, A combined ion probe/ spark source analysis system, Vacuum 24 (1974) 511. 5 J. Crank, The Mathematics of Diffusion (Oxford University Press, Oxford, 1975) 2nd ed., 414 pp. 6 M. Magaritz and A.W. Hofmann, Diffusion of Eu and Gd in basalt and obsidian, Geochim. Cosmochim. Acta 42 (1978) 847. 7 E.B. Watson, Calcium diffusion in a simple silicate melt to 30 kbar, Geochim. Cosmochim. Acta 43 (1979) 313. 8 A.W. Hofmann and L. Brown, Diffusion measurements using fast deuterons for in-situ production of radioactive tracers, Carnegie Inst. Washington Yearb. 75 (1976) 259. 9 A.R. Cooper Jr., Model for multicomponent diffusion, Phys. Chem. Glasses 6 (1965) 55. i0 G.C.T. Wei and B.J. Wuensch, Tracer concentration gradients for diffusion coefficients exponentially dependent on concentration, J. Am. Ceram. Soc. 59 (1976) 295.
36
[5]
LITHIUM TRACER-DIFFUSION IN AN ALKALI-BASALTIC MELT - AN
ION-MICROPROBE DETERMINATION R.K. LOWRY
1, S.J.B.
REED 2, j . NOLAN l, p. HENDERSON 3 and J.V.P. LONG z
1 Department of Geology, Imperial College of Science and Technology, Prince Consort Road, London SW7 2BP (U.K.) Department o f Earth Sciences, University o f Cambrdige, Downing Street, Cambridge CB2 3EQ (U.K.) 3 Department of Mineralogy, BriHsh Museum (Natural History), Cromwell Road, London SW7 5BD (U.K.)
Received September 15, 1980 Revised version received December 11, 1980
An ion-microprobe-based technique has been used to measure lithium tracer-diffusion coefficients (DLi) in an alkali-basaltic melt at 1300, 1350 and 1400°C. The results can be expressed in the form: DLi = 7.5 X 10-2 exp(-27,600/RT) cm2 s-1 The results show significantly faster diffusion rates than those previously recorded for other monovalent, divalent and trivalent cations in a tholeiitic melt. Consequently, diffusive transport of ions acting over a given time in a basaltic melt can produce a wider range of transport distance values than hitherto supposed. Hence, it is concluded that great care should be exercised when applying diffusion data to petrological problems.
1. Introduction
TABLE 1 Analysis of experimental charge, alkali basalt 2266
Previously, tracer-diffusion coefficients in natural silicate liquids have usually been determined by using radioactive isotope as a tracer (radiotracer technique [1 ]); however, such a method is not applicable to all cations of geological interest, including Li. An alternative procedure is to use an artificially enriched stable isotope (e.g. 6Li) as the tracer, whose distribution can readily be measured with the ion microprobe. Indeed, two previous studies [2,3] have successfully used the ion microprobe for the determination of Li self-diffusion or tracer-diffusion coefficients in crystalline and glassy solids. This paper presents the results of a feasibility study on the extension of the technique to determinations in silicate melts.
si02 TiO2 A1203 Fe2Oa FeO MnO MgO CaO Na20 K20
P205
45.89 3.72 16.55 10.67 1.91 0.18 6.30 9.62 3.79 1.73 0.52
Total
100.88
2. Experimental procedure
Table 1) by a method which is similar to that described by Hofmann and Magaritz [ 1 ]. After annealing for 3 - 4 days at the run temperature, a thin deposit of LiC1 * was precipitated from solution onto one end of
Narrow platinum capillaries (1.5 mm nominal ID) were Filled with a natural alkaLi-basaltic melt (see
* 0.98 6Li; A.E.R.E., Harwell.
0012-821X/81/0000-0000/$ 02.50 © 1981 Elsevier Scientific Publishing Company
37 the charge. The tracer was incorporated into the glass for 5 - 1 0 minutes at 800°C and any excess removed with dilute HC1. The experiments were run for up to 6 hours at 1300, 1350 and 1400°C in a SiC tube resistance furnace to produce a diffusion profile 1 - 2 cm in length. The experiment durations were selected on the basis of two criteria. First, as Hofmann and Magaritz [ 1 ] have shown, diffusion experiments in basaltic melts for which Dt < 3 X 10 -2 cm 2 are prone to error caused b y transport processes other than volume diffusion. In this work the Dt values were always >7 × 10 -z cm 2. Secondly, it was deemed necessary to show that the diffusion coefficient was independent of experiment duration. Consequently, the durations of the experiments at each isotherm were varied by a factor of between 1.7 and 2.0. Unfortunately, the variation could not be increased as the durations were constrained at the lower bound by the minimum desirable Dt value and at the upper by the length of profile which can be accommodated by the ion microprobe. After quenching ( ~ 3 0
EXPERIMENT
D88
seconds) in compressed air, the charges were mounted in epoxy resin. The resultant block was then partially ground away to expose glass along a complete longitudinal section of each charge, and subsequently polished. The instrument used for profile determination was a modified version of the AEI IM-20 ion microprobe [4]. The primary beam consisted o f 160- ions accelerated to 30 kV and focused to a spot o f about 15 #m diameter. The Li isotope intensities were measured by ion counting at points along the centre-line of each sample, enabling 6 E l / T E l t o be plotted as a function of distance (Fig. 1). The measured 6Li/Tti ratios must be transformed into tracer concentrations before the tracer-diffusion coefficient can be obtained using the equation below, which is derived in Appendix 1 : B -RC tracer concentration (c) = R (1 - X) - X
(1)
where B = 6Li concentration in the matrix, R = measured 6Li/Tti ratio, C = 7Li concentration in the matrix, and X = 6 t i fraction in the tracer. The effect of the transform can be assessed from Fig. 1. The relevant solution o f Fick's second law for the diffusion from an instantaneous plane source into
12.00 5.00[
KEY
. . . .
,
. . . .
,
. . . .
eLifLiR a t i o
0 Tracer
10.00[
Concentration
4.00
E
2
~
.
~.oo~
6.00
2.00
E
o Z
D 88
s.oo
[3_ *_=-
ED
4-00
0
~- 1
.
0
0
~
2.00 m 0
8
0.0
, ]0
,
,
,
L
0.50
. . . .
J . . . . 1 -OO
Distance
0.00 J I .SO
,
, 2.00
(cm)
Fig. 1. Plot of the measured 6Li/TLi ratios and derived tracer concentrations against distance for experiment D88. The values in each data set have been divided by the largest value in it to facilitate comparison of the two prof'tles.
-I .OH 30 . . . .
I ~00 . . . . . 2.00 . . . . Distance
Squared
3.00
( c m 2)
Fig. 2. Log-square transform of the tracer-concentration profile shown in Fig. 1.
38 TABLE 2
a semi4nfinite medium [5] is:
Isothermal diffusion coefficients
C(x, t) - ~
.
exp 4 ~ -
1
(2)
where C(x, t) = concentration at a distance x (cm) from the plane source after a diffusion time t (s), M = mass o f tracer added per unit area, and D = diffusion coefficient (cm 2 s-l). If this is rewritten in the form: M in c = l n [ ~ ] -
[~Dt ]
(3)
it can be seen that a plot o f l n c against x 2 should be linear with a slope o f - ( 4 D t ) -] . The transformed data from Fig. 1 are shown in Fig. 2.
1
Experiment
Duration (hours)
Temperature (°C)
D (10 -s cm 2 s-1 )
1-
D85 D86 D87 D88 D121 D122
2.0 4.0 5.2 3.0 2.0 3.5
1296 1296 1346 1346 1390 1400
1.05 1.10 1.30 1.42 1.84 1.82
-0.998 -0.995 0.997 0.998 -0.990 -0.984
1 Pearson product moment correlation coefficient for transformed diffusion profiles.
mo1-1 and a pre-exponent (Do) of 7.5 × 10 -2 cm 2 S -1 "
3. Results The measured tracer-diffusion coefficients are given together with the relevant experimental data in Table 2, and are presented graphically in Fig. 3. A least-squares fit of the data to the Arrhenius equation:
D = Do e x p ( - Q / R T )
(4)
4. Discussion Two features of the data set obtained here are of particular interest and are discussed below.
4.1. Activation energy o f diffusion
gives an activation energy (Q) o f 27.6 + 2.5 kcal
TEMPERRTURE ~DEC, C) -4°00
I
. . . .
1386 I
. . . .
1356 I
1327 . . . .
I
. . . .
1300 =
. . . .
] I
I
t O3 ZE
L~J (J
L~ O (J
-5,00
LL LL O
I -
. 6
bQ, 0
. . . . 92
, 6
. . . . 03
, 6
. . . . 14
, 6
. . . . 25
RECIPROCRL TEMPERRTURE •
,
.
6
30
10 4
[K
,
,
,
] 6
47
-~1
Fig. 3. Arrhenius diagram of the data presented in Table 2.
The significance o f the parameter Q in equation (4) is unclear. Magaritz and Hofmann [6] argue that the slope of the Arrhenius line obtained from diffusion determinations should not be considered as an activation energy, because the liquid does not have a fixed structure. Watson [7] postulates that Q is dependent upon melt microstructure (cation coordination polyhedra geometry) which is largely insensitive to temperature4nduced charges in the melt structure. Moreover, he successfully applied the concept to Ca 2+ diffusion data in a simple silicate melt. It, therefore, appears that whilst Q may not be an activation energy "sensu stricto" it is nevertheless a parameter which can be used to relate diffusion behaviour to certain aspects of silicate melt structure. Published data for tracer diffusion in a tholeiitic melt [1,6] show a range o f only 8 kcal mo1-1 in the activation energies of several divalent and trivalent cations, which is within the bounds of experimental error. However, the value obtained in the present study on a melt of alkali-basaltic composition is 8
39 kcal mo1-1 lower than the lowest value measured in the tholeiitic melt, suggesting that significant variation may be encountered if a wider range of cations is studied.
4.2. Isothermal diffusion coefficients The isothermal tracer diffusion coefficients exhibit two remarkable features. First, if the data of Jambon and Semet [3] for Li ÷ tracer diffusion in obsidian glass are extrapolated to 1350°C, they fall within a factor of two of our measured value for Li ÷ in an alkali-basaltic melt. However, such an extrapolation is fraught with sources of error resulting from changes in the diffusion matrix, and therefore it seems probable that the coincidence of values is fortuitous. Nevertheless, the possibility that the similarity is real provides impetus for further experiments. Secondly, the values in Table 2 are all significantly faster than the highest yet recorded for cations in a natural silicate liquid at 1300°C (D = 2.5 × 1 0 -6 cm 2 s -1 [8]) and therefore bring the range of observed diffusion coefficients in basaltic melts at this temperature to two and a half orders of magnitude. The value for Li ÷ is believed to represent the upper limit for diffusion of cations of geological relevance (with the possible exception of hydrogen)but the lower limit may not yet have been reached. It is tentatively proposed that such a limit may be represented by the diffusion of hexavalent uranium which may be as low as 10 -9 cm 2 s -1. This hypothesis is currently being tested experimentally. It is interesting to note the geological relevance of a four orders of magnitude variation in D for different cations in a single melt composition. Hofmann and Magaritz [I ] give the times taken for characteristic diffusional transport distances ((Dt) 1/2) of 5.6 cm, 56 cm and 1.8 km as i, 1 0 6 and 109 years respectively, assuming a diffusion coefficient of 1 0 -6 c m 2 s -1 . If the calculation is repeated for the data range suggested above, the results obtained are: 5.6 cm; 56 m; 1.8 kin;
t = 1 month to 103 years t = 10 s to 109 years t = I0 8 to 1012 years
From the above it can be clearly seen that the value for D used in mathematical models should be selected with some care. Hofmann and Magaritz [I ]
and Magaritz and Hofmann [6] have used tracerdiffusion coefficients for a variety of different concentration regimes. Whilst this is a valid first approximation (and indeed all that is possible with the data currently available), it should be realised that, strictly speaking, these coefficients should only be applied to regimes where the concentration gradient is extremely small. Otherwise, the effective diffusion coefficients are termed chemical diffusion coefficients or interdiffusion coefficients. Although these are linked mathematically to the tracer-diffusion coefficients (for the equations see Wei and Wuensch [ 10] ; Cooper [9]) they may deviate from them by several orders of magnitude. The application of tracer-diffusion coefficients to geological problems therefore requires careful consideration of the concentration regimes present in the system. As a general rule o f thumb, tracer-diffusion coefficients cannot be applied directly to geological problems which involve the transport of major or minor elements in silicate melts. However, the application of tracer-diffusion data to trace element transport is probably justified as the concentration differences (i.e. the difference in concentration between the two ends of a concentration gradient) are constrained, by definition, to tens or possibly hundreds of parts per million.
5. Conclusion The ion microprobe provides an excellent method for the measurement of otherwise unobtainable lithium diffusion data in melts. The results for Li ÷ show an activation energy of 27.6 kcal mol-1 and a value for D1296 of 1.08 X l0 -5 cm 2 s -1 . These values are lower and faster respectively than any data previously reported for basaltic melts. For such a melt at 1300°C it is postulated that the tracer-diffusion coefficients for different cations may span a range as large as 10 -s to 10 -9 cm 2 s -1 and therefore the values used in numerical models of petrological processes need to be selected with care.
Acknowledgements One of us (R.K.L.) gratefully acknowledges the receipt of a N.E.R.C. research studentship at Chelsea
40 and Imperial Colleges, London. We are also indebted to N.E.R.C. for grants in support of the ion-microprobe unit, Department of Earth Sciences, University of Cambridge, where the diffusion-profile determinations were carried out. Critical comments by Dr. R. Freer, Dr. A. Hofmann and an anonymous referee greatly improved the final version of the manuscript. Mr. P. Watkins analysed the starting compositions.
Appendix 1. Derivation of equation (1) Let A be the number of moles of 6Li in the tracer, let B be the number of moles of 6Li in the matrix, let C be the number of moles of 7Li in the matrix, let D be the number of moles of 7Li in the tracer. At any point the measured 6Li/TLi ratio (R) will given by:
R --
A+B
(A-l)
C+D
If the fraction of 6Li in the tracer is X then: A = Xc
(A-2)
D = c(1 - X)
(A-3)
where c = number of moles of tracer (tracer concentration). Substituting A-2 and A-3 into A-1 gives: Xc +B
R
(1-X)
c+d
(A-4)
Rearranging for c: c =
B -RC
R(1 - X ) - X
(A-5)
References 1 A.W. Hofmann and M. Magaritz, Diffusion of Ca, Sr, Ba and Co in a basalt melt : implications for the geochemistry of the mantle, J. Geophys. Res. 82 (1977) 5432. 2 J.N. Coles and J.V.P. Long, An ion-microprobe study of the self diffusion of Li÷ in LiF, Philos. Mag. 29 (1974) 457. 3 A. Jambon and M.P. Semet, Lithium diffusion in silicate glasses of albite, orthoclase and obsidian composition: an ion-microprobe determination, Earth Planet. Sci. Lett. 37 (1978) 445. 4 A.E. Banner and B.P. Stimpson, A combined ion probe/ spark source analysis system, Vacuum 24 (1974) 511. 5 J. Crank, The Mathematics of Diffusion (Oxford University Press, Oxford, 1975) 2nd ed., 414 pp. 6 M. Magaritz and A.W. Hofmann, Diffusion of Eu and Gd in basalt and obsidian, Geochim. Cosmochim. Acta 42 (1978) 847. 7 E.B. Watson, Calcium diffusion in a simple silicate melt to 30 kbar, Geochim. Cosmochim. Acta 43 (1979) 313. 8 A.W. Hofmann and L. Brown, Diffusion measurements using fast deuterons for in-situ production of radioactive tracers, Carnegie Inst. Washington Yearb. 75 (1976) 259. 9 A.R. Cooper Jr., Model for multicomponent diffusion, Phys. Chem. Glasses 6 (1965) 55. i0 G.C.T. Wei and B.J. Wuensch, Tracer concentration gradients for diffusion coefficients exponentially dependent on concentration, J. Am. Ceram. Soc. 59 (1976) 295.