Contrib Mineral Petrol (2009) 158:675–681
DOI 10.1007/s00410-009-0403-8
ORIGINAL PAPER
Experimental boron isotope fractionation between tourmaline
and fluid: confirmation from in situ analyses by secondary ion
mass spectrometry and from Rayleigh fractionation modelling
Horst R. Marschall Æ Christian Meyer Æ
Bernd Wunder Æ Thomas Ludwig Æ Wilhelm Heinrich
Received: 27 January 2009 / Accepted: 3 April 2009 / Published online: 24 April 2009
Ó Springer-Verlag 2009
Abstract Tourmaline synthesised in an experiment with
low boron excess was analysed in situ by secondary ion
mass spectrometry. It revealed significant B isotope zonation with 11B/10B ratios increasing in the growth direction
of the crystals. Trend, magnitude and absolute values
strongly support results from high-B-excess isotope fractionation experiments. Furthermore, the closed system
B-isotopic evolution of the experimental fluid was modelled by Rayleigh fractionation. The model results are in
excellent agreement with the measured B-isotope composition of the run-product fluid. Consequently, low-elementexcess experiments are proposed as an ideal approach to
determine fluid-solid isotope fractionation factors for systems that are characterised by Rayleigh fractionation.
Keywords Tourmaline Experimental geochemistry Boron isotopes Fluid Ionprobe
Communicated by J. Hoefs.
H. R. Marschall (&)
Department of Earth Sciences, University of Bristol,
Wills Memorial Building, Queen’s Road, Bristol BS8 1RJ, UK
e-mail: [email protected]
C. Meyer B. Wunder W. Heinrich
Department 3, Section 3.3, GeoForschungsZentrum Potsdam,
Telegrafenberg, 14473 Potsdam, Germany
C. Meyer
Institut für Geologische Wissenschaften, Freie Universität
Berlin, Malteserstrasse 74-100, 12249 Berlin, Germany
T. Ludwig
Institut für Geowissenschaften, Universität Heidelberg,
Im Neuenheimer Feld 236, 69120 Heidelberg, Germany
Introduction
Stable isotope systems of light elements, such as Li and B
have been widely applied in Earth sciences to unravel
processes operating at the surface, as well as in the deeper
crust and the mantle (e.g., Leeman and Sisson 2002; Palmer and Swihart 2002; Tomascak 2004). The establishment
of these geochemical tools has progressed via two different
routes, namely the investigation of natural samples from
well-characterised settings and elaborate geochemical
modelling. However, both require profound knowledge on
equilibrium isotope fractionation among the various phases
of interest, such as rock-forming or accessory minerals,
fluids and melts. The sole method of acquisition of such
high-quality isotope fractionation data is to conduct wellcontrolled experiments, where the phases of interest are
equilibrated at a range of temperatures and pressures. Run
products recovered from such experiments are analysed
separately for their isotopic compositions, from which the
T–(P)-dependent isotope fractionation is derived. Recently,
a number of such experiments have been conducted using
hydrothermal apparatuses to determine equilibrium isotope
fractionation between minerals and hydrous fluids for Li
(e.g., Wunder et al. 2006, 2007) and B (e.g., Wunder et al.
2005; Meyer et al. 2008).
Generally, these experiments are conducted with an
ample excess of B (or Li), so that the minerals produced
during the experiment do not significantly deplete the fluid
in the element of interest. Hence, the synthesised mineral
grains grow in contact with a fluid of constant composition
and are isotopically unzoned. Fluids and solids recovered
from such an experiment, therefore, represent equilibrium
isotope fractionation at P and T. In practise, they are
independently analysed to obtain isotope fractionation
factors. Although this method has been successfully applied
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676
to a number of fluid-mineral systems, it has the disadvantage
of combining two different analytical procedures, i.e., the
analyses of solid and liquid run products, respectively. High
accuracy on both analytical protocols is, therefore, fundamental for the extraction of data, and limits the accuracy of
the resulting isotope fractionation factor.
Recently, Meyer et al. (2008) have completed experiments on B isotope fractionation between tourmaline and
fluid. While the majority of the experiments were run
employing the established method of using a vast excess of
B (i.e., 900 mole%), some of the experiments were conducted with a limited B excess of only 10 mole%. Boron,
as a major component of tourmaline (Tur *3.3 wt%) is
largely removed from the fluid in the course of the
experiment. Solid state diffusion of B in Tur is negligible
for the experimental run time (Henry and Dutrow 2002),
thus no re-equilibration between fluid and early grown Tur
will occur. Under these conditions, any B isotopic fractionation between Tur and fluid should produce isotopically zoned crystals and a final fluid that is isotopically
different from the initial composition. Actually, Meyer
et al. (2008) found the B in the final fluid to be significantly
heavier than in the starting composition. They also recovered Tur separates of different grain sizes from the
experiment, which had a distinct variability in d11B values
[d11 B ¼ ð11 B=10 Bsample =11 B=10 BNBS951 1Þ1;000].
In this contribution, we present in situ analyses of Tur
crystals synthesised in a low-excess-B experiment, demonstrating that they are, indeed, isotopically zoned in
accordance with assumptions drawn from the bulk analyses
(Meyer et al. 2008). In addition, we employ a Rayleigh
fractionation model to predict the B isotopic composition
of the fluid produced by the experiment with limited excess
B. The in situ analyses and the model independently verify
the B isotopic fractionation between Tur and fluid as
quantified by Meyer et al. (2008) in both trend and
magnitude.
Experimental methods
Tourmaline CM2, analysed in this study was taken from a
series of experiments on B-isotope fractionation between
Tur and fluid, described in Meyer et al. (2008). Synthesis
CM2 produced dravitic Tur grown hydrothermally at
600°C and 200 MPa in the system Na2O–MgO–Al2O3–
SiO2– B2O3–H2O (NMASBH). Tourmaline was crystallised directly from the fluid, applying the method of
Wunder et al. (2005). The two-chamber Au-capsule
method was employed (von Goerne et al. 2001) with
starting materials added as oxide mixtures of 25 mg MgO,
SiO2, c–Al2O3, as well as solid boric acid (H3BO3) and
45 mg of a NaCl–H2O solution. Excess Si (20 mole%) and
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Contrib Mineral Petrol (2009) 158:675–681
Na (100 mole%) with respect to the ideal dravite composition were chosen to compensate for high fluid solubilities
of these components. Excess B was only 10 mole% in
order to monitor B-isotopic evolution of the fluid, as
expected from fractional crystallisation of Tur over the
course of the experiment. This translates to a mass ratio of
B between run-product fluid and Tur of only 0.1. The B
isotopic composition of the boric acid in the starting
material was d11B = -13.2 ± 0.4%. Applying the twochamber method, SiO2 was mechanically separated from
the other compounds within the Au-capsule. Cooling of the
hydrothermal cold-seal vessels below 200°C within 3 min
was achieved using compressed air. Chemistry and crystal
structure of the Tur run products have been determined by
X-ray powder diffraction, scanning electron microscopy
and electron probe micro analyser. Cell parameters and
chemical composition are given in Meyer et al. (2008). The
Tur’s chemical composition comprises a solid solution
between dravite (62%) and Mg-foitite (35%), and no evidence was found for tetrahedrally coordinated B in the
structure refinement. After a run time of 11 days, the fluid
extracted from the experiment by piercing and washing the
capsule with 80°C hot double-distilled water, had a
B-isotopic composition of d11B = -10.0 ± 0.3% (Meyer
et al. 2008). Solid by products of Tur synthesis were quartz
and traces of talc, which are both known to have very low
B partition coefficients towards hydrous fluid (*10-2 to
10-3; Marschall et al. 2006a) and can, hence, be neglected
for the B budget of the experiment.
Analytical methods
Boron isotope ratios of Tur were analysed using a Cameca
IMS 3f secondary ion mass spectrometer (SIMS) at the
Institut für Geowissenschaften, Universität Heidelberg.
The primary ion beam was 16O- accelerated to 10 keV
with a beam current of 1 nA, resulting in count rates for
11
B of *2 9 105s-1 and *5 9 104s-1 for 10B on Tur,
collected by a single electron multiplier. Diameter of the
1 nA spot was 5–10 lm. The energy window was set to
100 eV and no offset was applied. Fifty cycles were
measured on each analysis spot with counting times of
3.32 s and 1.66 s on 10B and 11B, respectively. For each
cycle, the 10B signal was integrated for 1.66 s before and
after collection of the 11B signal, thus minimising the
influence of increasing or decreasing count rates on
the measured isotope ratio. Count rates were corrected for
the counting system’s dead time of 16 ns. Presputtering
lasted for 5 min and settling time between two different
masses was 200 ms, resulting in total analysis time for one
spot of approximately 10 min. Internal precision of a single
analysis was B0.5% (1r). Boron isotopic compositions of
Contrib Mineral Petrol (2009) 158:675–681
samples are reported in delta notation (d11B in %) relative
to the SRM 951 accepted value (Catanzaro et al. 1970).
Instrumental mass fractionation was corrected by using
three samples of proposed reference tourmaline (98114:
elbaite, 108796: dravite, 112566: schorl; Leeman and
Tonarini 2001), yielding a correction factor of 1.0464.
Reproducibility of measured isotope ratios during an analytical session is typically ±0.5% (1r). For further details
on precision and accuracy of B isotope analysis of the
Heidelberg SIMS see e.g., Marschall et al. (2006b) and
Rosner et al. (2008).
Results
Tourmaline synthesised in experiment CM2 shows sheaflike aggregates of euhedral crystals, of *50 lm width and
300–800 lm in length (Figs. 1, 2). The sheaves consist of
anhedral, bulky roots with several large euhedral Tur
crystals diverging radially away from the central roots.
The B-isotope profile analysed by SIMS from root to tip
of one large representative crystal (Fig. 2a, b) reveals a
rather heterogeneous centre of the root with d11B values
scattering between -15.3 and -12.5% (Fig. 3; Table 1).
The free-standing crystal itself, however, displays a very
systematic increase of d11B values from -15.3% in the root
to -12.5% at the tip (Fig. 3; Table 1). In addition, several
analyses on tips of other large euhedral crystals (Fig. 2c–f)
were completed. These revealed consistently high d11B
values between -12.2 and -11.0% (Fig. 3; Table 1).
Analysis CM2-17 was probably conducted too close to the
edge of the crystal and overlapped the epoxy resin (Fig. 2d),
Fig. 1 Scanning electron microscope image of Tur sheaf synthesised
in experiment CM2 (T = 600°C; P = 200 MPa; t = 11 days). Note
the large euhedral Tur crystals diverging from the bulky root. Talc
was produced as a minor by product of experiment CM2.
677
resulting in lower count rates and an unreasonably high
d11B value of -6.2%, regarded as an artefact of the lowquality measurement and not further evaluated.
Discussion
In situ analyses by SIMS
We interpret the roots of the Tur sheaves as the nucleation
sites of the Tur, based on their petrographic appearance
(Figs. 1,2). The tips of the radially diverging Tur crystals
are interpreted to represent the last growth phase of Tur
before the experiment was quenched.
The increase in d11B from root to tip is consistent with
the predicted isotopic fractionation between fluid and Tur,
with the solid preferentially incorporating the light isotope,
and consequently leaving the remaining fluid enriched in
the heavy isotope. Subsequent growth zones of Tur, hence,
display higher and higher d11B values in temporary equilibrium with the evolving fluid. The magnitude of B-isotope fractionation can be estimated from the difference
between the lowest d11B values in the roots of the Tur
sheaves (-15.3 to -14.1%) and the initial fluid (-13.2%),
resulting in a value of D11 B ¼ d11 Bfluid d11 BTur ¼ 0:9 2:1& . This is in agreement with the value of D11 B ¼
1:29& derived from B-excess experiments (Meyer et al.
2008). In addition, the difference in d11B values between
the tips of the Tur crystals (-12.7 to -11.0%) and the runproduct fluid (-10.0%) results in a value of
D11 B ¼ 1:0 2:7&. Again, this is in agreement with the
previously established fractionation. It is a technical challenge to find and analyse the very initial Tur that crystallised in the experiment, as well as it is difficult to analyse
growth zones that are very close to the edge. This may
explain the rather large spread in fractionation data (D11B),
and limits the potential of this method in quantification of
the B isotope fractionation between the two phases. However, most important, the differences in d11B between roots
and tips and the increase along the analysed crystal clearly
proves that B isotope fractionation between Tur and
hydrous fluid is indeed significant at 600°C, with Tur
preferentially incorporating the light isotope 10B.
Also, cutting effects may be expected from sections
oblique to the crystallographic c axis of the Tur crystals
and from sections not cutting the centre of the trigonal
prisms. In such cases, one would still observe a systematic
increase in B isotopes, but may not expose the earliest
grown Tur, and/or may have cut off the tip of the crystals
and lose the youngest and isotopically most evolved portions. Note, that SIMS (in contrast to Laser ablation) has
the advantage of very high depth resolution. The progress
of sputtering into the crystals is at the order of 0.5–1 nm/s,
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Contrib Mineral Petrol (2009) 158:675–681
Fig. 2 Transmitted (a, c, e) and
reflected (b, d, f) light
microscope images of Tur
sheaves synthesised in
experiment CM2 (T = 600°C;
P = 200 MPa; t = 11 days).
SIMS spots for B isotope
analyses (*10 lm diameter)
are marked with black circles in
transmitted-light images and are
visible as black spots in
reflected light. Number labels
refer to d11B values.
resulting in a total depth of the sputter crater of \0.5 lm
after completion of a 10 min analysis. Consequently, SIMS
analyses of Tur represent the portions of the crystals as
they are exposed in reflected-light or back-scattered electron images, and effects of zonation in the third dimension
can be neglected.
The B isotopic heterogeneity of the root (Fig. 3) may be
explained by initially large pore space in the roots at the
start of the experiment that would be filled by Tur grown at
a later stage during the run. Hence, the connection between
geometry and growth history in the roots may be obscured,
while the euhedral Tur crystals clearly show a steady
increase in d11B from root to tip.
zones. The fluid is, thus, expected to be progressively
enriched in the heavier isotope 11B. The B isotopic fractionation between Tur and fluid in a closed system, such as
our experimental capsule, can generally be modelled using
a Rayleigh formulation:
Rayleigh model
where d11 Bi and d11B are the initial and the final d11B
values, respectively. In the case of experiment CM2, the
initial d11B value was -13.2 ± 0.4%, and the excess
amount of B was 10 mole%, translating to a ratio of B in
The growing Tur crystals incorporate significant portions
of B without subsequent re-equilibration of earlier growth
123
R=Ri ¼ F a1
ð1Þ
where R is the final 11B/10B ratio, Ri is the initial 11B/10B
ratio, F is the fraction of B remaining in the fluid, and a is
the temperature-dependent B-isotope fractionation factor.
Replacing isotope ratios by delta values, Eq. 1 can be
rewritten as:
d11 B ¼ ð1;000 þ d11 Bi ÞF a1 1;000
ð2Þ
Contrib Mineral Petrol (2009) 158:675–681
Fig. 3 Boron isotope profile of
CM2 Tur analysed by SIMS.
One large crystal was analysed
from root to tip (Fig. 2a, b). In
addition, one root and several
tips from other Tur sheaves
were analysed and are plotted to
the left and right of the profile,
respectively. The growth
direction of Tur is indicated by
the arrow. The starting material
(d11B = -13.2 ± 0.4%;
TIMS = thermal ionisation
mass spectrometry) should
produce Tur with
d11B = -14.5% (fractionation
indicated by arrow No. 1), while
the final fluid
(d11B = -10.0 ± 0.3%)
should produce Tur with
d11B = -11.3% (fractionation
indicated by arrow No. 2)
according to Meyer et al.
(2008).
Table 1 Boron isotope
analyses of CM2 Tur
determined by SIMS
679
-9
CM2 tourmaline δ11B analyses by SIMS (all errors 1σ)
final fluid
(TIMS)
-10
2
-11
δ11B (‰)
-12
-13
starting material
(TIMS)
1
-14
-16
other root
-15
growth direction
root
tip
other tips
-17
0
100
200
300
400
Distance (µm)
Analysis ID
Total count rate
B ? 10B (kHz)
d11B (%)
1RSDmean
(%)
Type
11
Distance from centre
of root (lm)
Profile crystal 1 (Fig. 2a, b)
CM2-1
227
-14.54
0.48
root
CM2-2
271
-12.69
0.42
tip
0
CM2-3
272
-12.55
0.43
tip
CM2-4
CM2-5
274
285
-12.73
-12.45
0.47
0.38
424
402
CM2-6
284
-13.46
0.42
379
CM2-7
292
-13.89
0.38
345
CM2-8
271
-13.59
0.44
303
CM2-9
263
-14.23
0.35
263
CM2-10
247
-13.84
0.40
221
CM2-11
266
-13.73
0.44
CM2-12
252
-14.42
0.46
root
118
CM2-13
242
-12.52
0.46
root
66
CM2-14
256
-13.41
0.44
root
28
CM2-15
245
-15.31
0.41
root
93
464
445
170
Other crystals (Fig. 2c–f)
1RSDmean 1 9 relative standard
deviation of the mean
a
Analysis of CM2-17 was
probably overlapping the
crystal’s edge (Fig. 2d), hence,
this isotope ratio is regarded
erroneous
CM2-16
279
-12.15
0.41
tip
CM2-17a
234
(-6.17a)
0.42
tip
CM2-18
272
-11.71
0.37
tip
CM2-19
CM2-20
278
265
-12.00
-14.06
0.43
0.46
tip
root
CM2-21
291
-11.75
0.44
tip
CM2-22
295
-12.21
0.38
tip
CM2-23
288
-11.01
0.41
tip
the remaining fluid to B in Tur of 1:10, which can be
expressed as F = 1/11 & 0.091. Hence, 9.1% of the initial
B remained in the fluid at the end of the experiment.
The equilibrium B-isotope fractionation factor
a = 1.00129 for T = 600°C derived from B-excess experiments (Meyer et al. 2008), can be tested independently by
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Contrib Mineral Petrol (2009) 158:675–681
10 mole% boron excess
-4
∆11B = -4.20 (1000/T (K)) + 3.52
-6
T = 600 °C (= 873.25 K)
δ11B = (1000 + δ11B i ) F
α-1
- 1000
δ11B (‰)
-8
-10
first Tur
M’08
(900%)
-12
tou
0.9
0.8
rmaline
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
F (fraction of B remaining in the fluid)
Fig. 4 Experiment CM2 with 10 mole% excess B modelled by
Rayleigh fractionation. The B isotopic composition of the initial and
final fluid and its evolution with progressive Tur growth (stippled
curve) are displayed. In addition, the B isotopic composition of the
growing Tur is displayed (dashed curve). Note, that the theoretical
d11B value of -10.14% calculated from the temperature-dependent
fractionation value of Meyer et al. (2008) is in very good agreement
with the value of d11B = -10.0 ± 0.3% measured after the experiment. Experiments for the determination of the fractionation factor a
completed by Meyer et al. (2008) had 900 mole% B in excess, which
is marked by the broken line labeled ‘‘M’08’’
123
a
δ a X = (1000 + δ X i ) F
α-1
12.1 ‰
- 1000
10
5.0
‰
05
1.0
0‰
3.
2.0
initial
fluid
4.8 ‰
‰
2.4 ‰
1.0 ‰
1.2 ‰
0.5 ‰
0
1.0
7.2 ‰
4.
0
α
5
9.6 ‰
‰
∆aX
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
F (fraction of element X remaining in the fluid)
Fig. 5 General Rayleigh fractionation model of the isotopic composition of an element X in a fluid with an initial isotopic composition
daX = 0%, evolving with different isotopic fractionation factors a,
ranging from 1.0005 to 1.0050 (corresponding to fluid-solid fractionations Da X of 0.5 to 5.0%). Isotopic compositions of the runproduct fluids of experiments with 10 mole% excess of element X are
given on the right hand side
accuracy of the method is limited by the uncertainty on F,
which can be estimated from the initial composition (such
as Al2O3/B2O3 ratio in the case of Tur synthesis), but can
also be determined more accurately from the concentration
of the element in the run-product fluid.
The method may be applied to any liquid–solid system
that satisfies the requirement of Rayleigh fractionation, i.e.
where the element of interest is denied any re-equilibration
with the liquid in as small increments as possible. Solids
with very slow solid-state diffusion coefficients, such as
Tur, will fulfil this requirement.
Conclusions
fluid
-14
1.0
10 mole%
excess of X
final fluid (theoretical): δ 11B = -10.14 ‰
last Tur (theoretical): δ 11B = -11.43 ‰
initial
fluid
15
δaX (‰)
applying Eq. 2 to experiment CM2 and comparing the d11B
value calculated for the final fluid with the one actually
measured after the experiment. The B-isotope evolution
modelled for the parameters of experiment CM2 predicts an
increase of d11B of both Tur and fluid by *3%, and a
d11B value of the final fluid of -10.14% (Fig. 4). This is in
excellent agreement with the measured value of
d11B = -10.0 ± 0.3%, thus supporting the accuracy of the
fractionation factor established by Meyer et al. (2008).
In general, this provides a new method of determining
isotope fractionation factors between solids and fluids or
melts, without analysing the solids. It only requires the
determination of F, i.e. the level of excess of the element of
interest. The fluid curve in Fig. 4 can be established from
Eq. 2, and the isotope fractionation factor a can be derived,
as it is the only unknown parameter (Fig. 5). The advantages of this method are (1) only the fluid phase has to
be analysed, which reduces uncertainties introduced by
limited accuracies, and (2) the isotope fractionation is
amplified at low F values, thus reducing the error on the
determination of a. This effect is displayed in Fig. 5: at 5%
fractionation between solid and fluid (a = 1.005), the final
fluid containing 10 mole% of the initial budget of the
element will have a d value increased by 12.1%. The
SIMS analyses of Tur synthesised with limited excess B
(10 mole%) revealed a significant d11B zonation from relatively light B in the early grown roots to heavy B in the tips.
The trend, magnitude and the absolute d11B values measured
by SIMS verify the B-isotopic fractionation derived from
high-B-excess experiments published recently by Meyer
et al. (2008).
Modelling the B-isotope fractionation in the experimental run by Rayleigh fractionation, reproduces the
measured d11B value of the run-product fluid well within
the margins of analytical uncertainty. This encourages the
completion of Rayleigh-fractionation experiments for the
determination of mineral-fluid isotope fractionation factors
with better precision and accuracy compared to conventional equilibrium experiments.
Contrib Mineral Petrol (2009) 158:675–681
Acknowledgments We are grateful to R. L. Romer for fruitful
discussions. Comments from two anonymous reviewers are appreciated. This study was financially supported by a European Union
Marie-Curie Fellowship awarded to HRM (ID 025844: ‘‘Isotopes in
subduction zones—the metamorphic perspective’’), which is greatly
acknowledged.
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