Chemical Geology 330-331 (2012) 188–196
Contents lists available at SciVerse ScienceDirect
Chemical Geology
journal homepage: www.elsevier.com/locate/chemgeo
Precise overgrowth composition during biomineral culture and inorganic precipitation
Alexander C. Gagnon a, b,⁎, Donald J. DePaolo a, Jess F. Adkins c
a
b
c
Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA
a r t i c l e
i n f o
Article history:
Received 2 May 2012
Received in revised form 22 August 2012
Accepted 22 August 2012
Available online 31 August 2012
Editor: U. Brand
Keywords:
Isotope geochemistry
Crystal growth
Biomineralization
Mass spectrometry
Metal/calcium
Trace metals
a b s t r a c t
We introduce a method to analyze element ratios and isotope ratios in mineral overgrowths. This general
technique can quantify environmental controls on proxy behavior for a range of cultured biominerals and
can also measure compositional effects during seeded mineral growth. Using a media enriched in multiple
stable isotopes, the method requires neither the mass nor the composition of the initial seed or skeleton to
be known and involves only bulk isotope measurements. By harnessing the stability and sensitivity of bulk
analysis the new approach promises high precision measurements for a range of elements and isotopes.
This list includes trace species and select non-traditional stable isotopes, systems where sensitivity and external reproducibility currently limit alternative approaches like secondary ion mass spectrometry (SIMS) and
laser ablation mass spectrometry. Since the method separates isotopically labeled growth from unlabeled
material, well-choreographed spikes can resolve the compositional effects of different events through time.
Among other applications, this feature could be used to separate the impact of day and night on biomineral
composition in organisms with photosymbionts.
Published by Elsevier B.V.
1. Introduction
Mineral composition is influenced by a host of environmental,
chemical, and biological factors during growth. To build accurate reconstructions of past environmental conditions we need to separate
the impact of each parameter on proxy behavior. These data can
then be used to build a chemical-scale understanding of mineral
growth. Biomineral culture and inorganic precipitation experiments,
where growth parameters are isolated and manipulated independently, are uniquely suited to address these questions.
Culture and precipitation experiments often involve overgrowth on
an initial material. For example, seed crystals are used to control mineralogy, avoid nucleation, and access low growth rates during
inorganic precipitation. Similarly, biomineral culture experiments typically start from wild specimens with preexisting and poorly
characterized skeletons. In both classes of experiments, new growth
corresponding to experimental conditions must be separated from initial material. This separation is typically achieved using microanalysis
(Holcomb et al., 2009; Houlbrèque et al., 2009), skeletal dissection
(Lea et al., 1999; Russell et al., 2004), or estimates of initial seed mass
and composition (Mucci and Morse, 1983; Kisakürek et al., 2008).
While these techniques have been crucial to our understanding of
co-precipitation, each approach imposes limits on the accuracy, precision, sensitivity, and the types of materials that can be analyzed. Slow
growth rates and complicated shapes make these techniques especially challenging when applied to biominerals.
Here we develop the theoretical basis for a new method of compositional analysis during mineral growth that overcomes many of these
challenges. The method relies on growth from a solution enriched in
multiple stable isotopes and is an adaptation of the isotope-dilution
technique, however in this case isotope dilution occurs within a
growing mineral. The new technique has several advantageous
characteristics: (1) it requires neither the amount nor the composition of the initial material to be known, (2) it harnesses the precision,
sensitivity, and accessibility typically associated with bulk analysis,
and (3) it works even when it is impossible to physically identify
and separate newly grown material. Furthermore, the method allows
new modalities. For example, it could be used to isolate different
events through time.
2. Mixed spike technique for element ratios of mineral overgrowths
2.1. Outline of the mixed spike method
⁎ Corresponding author at: Earth Science Division, 1 Cyclotron Road Mail Stop 67R3207,
Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA. Tel.: +1 510 486 7205.
E-mail addresses: [email protected] (A.C. Gagnon), [email protected]
(D.J. DePaolo), [email protected] (J.F. Adkins).
0009-2541/$ – see front matter. Published by Elsevier B.V.
http://dx.doi.org/10.1016/j.chemgeo.2012.08.022
Consider a solid mineral sample resulting from a biomineral culture experiment or from precipitation during seeded-growth. The
sample represents a mixture between two end-member components
(Fig. 1). The first component (o) corresponds to the seed crystal
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
Fig. 1. Schematic of an experimentally grown mineral sample comprised of two components mixed in unknown proportions: (o) the pre-experiment “seed” material,
and (x) new growth corresponding to experimental conditions. Using the
mixed-spike overgrowth method it is possible to determine the composition of the
newly grown material through bulk isotope analysis of the entire sample.
during inorganic precipitation or to the initial skeleton in a culture
experiment. This pre-experiment region is of unknown composition,
furthermore, composition may vary between different seeds or different skeletons. The second component (x) corresponds to growth
under controlled experimental conditions. The two regions exist in
unknown proportions and may be arranged in an arbitrary way. The
challenge is separating these components using only bulk analysis
of the mixed sample.
To demonstrate the method, consider an experiment designed to
measure the Sr/Ca of CaCO3 precipitated during overgrowth on a
seed crystal. The number of moles of newly precipitated calcium is
equal to the mole fraction of total calcium that is found in the new
growth region times the total amount of calcium in the combined
solid,
spectrometry. As a first step, an easy to measure reference isotope is
chosen for both strontium and calcium. These reference isotopes
must be different than the isotopes used to enrich the spiked precipitation solution, with reference isotope enrichments affected only by
minor spike impurities. Reference isotopes are often but not always
the most abundant isotope of a particular element. In this example
we use the reference isotopes 88Sr and 43Ca. The isotopic abundances
of these isotopes in the new growth component are defined as 88Ax =
88
nx/Srx and 48Ax = 48nx/Cax, where inx is the number of moles of isotope i in component x. Since Srx = 88nx/ 88Ax and Cax = 48nx/ 48Ax,
Sr
Ca
Sr
Ca
x
¼
Srx
Sro þSrx
Cax
Cao þCax
ðSro þ Srx Þ
:
ðCao þ Cax Þ
Sr
Ca
x
Sr
¼ Ca
χ x Sr
:
χ x Ca T
88
Ax n x
:
Ax 48 nx
48
ð4Þ
!
nx
48
48
no þ nx ; …
48
48
no þ nx
48
nx ¼
ð1Þ
88
88
nx
¼
48
nx
88
no þ88 nx
48
48
!
nx
nx
88
! 48
no þ 88 nx
:
no þ 48 nx
no þ48 nx
Finally, substituting this expression into Eq. (4),
ð2Þ
88
The second term on the right-hand side of Eq. (2) is just the total
Sr/Ca of the combined solid, (Sr/Ca)T, while the numerator and
denominator of the first term on the right hand side of Eq. (2) are
the mole fraction of strontium in the new solid ( Srχx) and the mole
fraction of calcium in the new solid ( Caχx), respectively. Using these
substitutions,
x
48
¼ 88
Taking the appropriate quotient,
Here Cao and Cax refer to the number of moles of a calcium found
in component o or component x. Much like Eq. (1), there is a similar
expression for the number of moles of newly precipitated strontium.
The Sr/Ca of the new growth end-member is simply the quotient of
these two expressions,
Following a similar strategy as Eqs. (1)–(3), we put the second
term on the right hand side of Eq. (4), 88nx/ 48nx, in terms of mole fractions and total solid composition. The number of moles of each reference isotope precipitated during new growth is:
Cax ¼
Cax
ðCao þ Cax Þ:
Cao þ Cax
189
ð3Þ
From Eq. (3), it is clear that we can calculate the Sr/Ca of new
growth from the total Sr/Ca if we know how both calcium and strontium are distributed between the initial and new growth components. In the mixed spike method this distribution is followed by
isotopically labeling new growth, un-mixing this new growth from
the natural abundance initial component, and then solving for the
crucial quantities Caχx and Srχx.
To label new growth, CaCO3 is precipitated from a solution
enriched in stable isotopes of both calcium and strontium. In this
example we use 43Ca and 87Sr. Although the isotopes used in this
example are arbitrary, the choice of isotopes and the amount of enrichment control methodological precision (see Section 3).
Before developing the equations necessary to calculate χx values,
we first transform Eq. (3) to put the Sr/Ca of newly grown material
in terms of reference isotopes rather than elements. This transformation allows all unknowns to be expressed as isotope ratios, quantities
that can be directly measured at high precision through mass
nx
88
88
no þ nx
48
Sr
A
¼ 88 x
Ca x
Ax
48
¼ 88
48
nx
48
48
no þ nx
!
88
! 48
no þ 88 nx
no þ 48 nx
ð5Þ
88
Ax χ x
T:
Ax 48 χ x
Here iχx is the mole fraction governing the distribution of isotope i
in the new growth component and T = 88nT/ 48nT. T is proportional to
the Sr/Ca of the entire solid sample and is determined directly
through isotope-dilution mass spectrometry, as will be described
below.
For most experiments where the mixed spike method is used to
measure elemental ratios, we assume that isotopic fractionation between solution and solid is small compared to overall isotopic enrichment. Thus, the isotopic composition of the new growth end-member
is approximately the same as the enriched solution and abundances
can be measured from solution samples (this assumption and minor
corrections for this assumption are treated in Section 3). Provided
the amount of mineral growth is small compared to the amount of
each element in solution, then solution composition will remain constant during a single or even multiple growth experiments. Under
these conditions, only one set of solution measurements may be necessary for many precipitation experiments. Alternatively, the precipitation solution can be analyzed at different time points during the
growth experiment to ensure constant isotopic composition.
190
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
The remaining mole fraction terms in Eq. (7) are now converted
into ratios. Using 48χx as an example,
and rearranging to solve for
48
F,
!
!
43
Ca
Ca
48
48
43
43
n
−
n
¼
n
−
no
x
x
o
48
48
Ca m
Ca m
"
!
! #
!
! #
43
43
43
43
Ca
Ca
Ca
Ca
48
¼ no 48
− 48
− 48
48
Ca m
Ca x
Ca o
Ca m
3
!
!
43
43
Ca
Ca
7 48
− 48
48
Ca m
Ca x 7
n
48
!
! 7
7 ¼ 48 o ¼ F :
43
43
7
nx
Ca
Ca
5
− 48
48
Ca o
Ca m
43
48
48
χ x ¼ 48
nx
1
¼
¼
no þ 48 nx 48 no =48 nx þ 1
"48
#−1
h
i−1
no
48
þ
1
¼
F þ1
: ð6Þ
48
nx
"
48
nx
2
Here 48F = 48no/ 48nx; 48F represents the relative distribution of the
unenriched reference isotope 43Ca between the initial and new
growth components. Combining Eqs. (5), (6), and a similar equation
for 88χx,
ð7Þ
6
6
6
6
6
4
This expression is analogous to an isotope-dilution equation
(Webster, 1960); however, in this case isotope dilution occurs within
a mineral sample as it grows. Following a similar approach for strontium,
2
Using this expression overgrowth composition can be calculated
from 48F, 88F, and T. Each of these quantities can be determined
though bulk isotope ratio analysis of a dissolved solid sample, measurements we now describe in detail and which are also outlined in
Fig. 2.
2.2. Measurement strategy
Referenced to 43Ca, the bulk calcium isotope ratio of the total
mixed sample is simply the number of moles of each isotope from
both components,
!
43
Ca
no þ 43 nx
¼
:
48
Ca mixed 48 no þ 48 nx
43
ð8Þ
With some algebra we can solve Eq. (8) for 48F while also putting
the expression in terms of isotope ratios that are directly measurable
by mass spectrometry: the natural abundance ratio of the initial inorganic seed, ( 43Ca/ 48Ca)o; the isotope ratio of the enriched culture solution, ( 43Ca/ 48Ca)x; and the measured bulk (mixed) isotope ratio of
the total dissolved mineral sample, ( 43Ca/ 48Ca)m. Expanding Eq. (8),
!
Ca 48
no þ
48
Ca m
43
!
Ca 48
43
43
nx ¼ no þ nx ;
48
Ca m
43
ð9Þ
6
6
6
6
6
4
87
88
87
88
!
Sr
87
! 3
Sr
7
7 88 n
88
! x7
7 ¼ 88 o ¼ F :
87
n
x
Sr 7
5
− 88 Sr
−
Sr
88
Sr
!m
Sr
Sr
o
ð10Þ
m
Eqs. (9) and (10) give the relative distribution of calcium and strontium between the two components. The third quantity T is measured
through a true isotope-dilution experiment. In this true isotopedilution experiment a mixed element spike that is more enriched
than the growth solution is added to an aliquot of the dissolved solid
sample (for example, this measurement could be conducted using an
adaptation of Fernandez et al. (2010) when measuring Sr/Ca),
88
T ¼ 48
nT
¼
nT
" 87 # "43
43 #
88
Sr
Axx 87
88 ID − 88 xx
48 ID − 48 xx
:
=
87
43
43
Ca xx 48 Axx 87
88 m − 88 ID
48 m − 48 ID
ð11Þ
Here (87/88)m and (43/48)m are the ratios that were already measured
to solve Eqs. (9) and (10); (87/88)xx and (43/48)xx are the ratios of the calibrated isotope dilution spike; and (87/88)ID and (43/48)ID are the ratios of
the dissolved solid sample measured during this step after equilibration
with the isotope dilution spike. The quantity (Sr/Ca)xx 88Axx/48Axx is determined during a one time calibration of the isotope-dilution spike.
Since Eqs. (9)–(11) involve ratios of ratios, calibrated absolute isotope ratio measurements are unnecessary. Instead, for ease of analysis,
isotope ratios can be referenced to uncalibrated standards. This is
equivalent to dividing the numerator and denominator of each fraction
in Eqs. (9)–(11) by the same reference ratio. In summary, when
Fig. 2. Schematic of the mixed spike overgrowth method for the analysis of elemental ratios.
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
minerals are grown in an isotopically enriched solution, then isotope
ratio measurements of bulk dissolved samples followed by an
isotope-dilution experiment on the same dissolved sample can be
used to calculate the elemental composition of new growth.
191
Using Eq. (14) and substituting a shorthand form of Eqs. (9) and
(10), F = (m − x)/(o − m), we quantify the relative error in (F + 1):
2
rel err ðFþ1Þ ¼ rel err m
2
m2
:
ðm−oÞ2
ð15Þ
3. Experimental design and error analysis
3.1. General error analysis of the mixed spike overgrowth method
Methodological precision is controlled by a number of experimental
parameters, primarily the level of isotopic enrichment in the growth
solution, the relative amount of new growth, and instrumental uncertainty during isotope ratio analysis. Given a particular level of instrumental error, an ideal experiment minimizes uncertainty in the
measured Me/Ca. We derive expressions for methodological precision
and develop design guidelines for experiments that minimize this
uncertainty.
Assuming that the isotopic abundances of the growth solution and
the natural seed are known, that errors are uncorrelated, and continuing the Sr/Ca example, precision depends on the relative error
in T and of each F term:
2
2
2
2
rel err SrCa ¼ rel err T þ rel err ð48 F þ1Þ þ rel err ð88 F þ1Þ :
ð12Þ
Terms for uncertainty in 48Ax and 88Ax are excluded from this
expression as different precipitation experiments are all assumed to
occur from a single and well characterized master solution. Under
these conditions the abundances in Eqs. (7) and (11) affect accuracy
but not precision. Considering this accuracy error briefly, in both
Eqs. (7) and (11) relative analytical uncertainty in abundance measurements propagates as expected for a typical multiplicative factor.
Since this uncertainty does not depend strongly on spike enrichment
or growth amount, it is not a key factor determining experimental design. Thus, while it can make a minor contribution to the overall error
budget of the method, uncertainty in abundance measurements will
not be considered further.
Since T is measured through a conventional isotope-dilution (ID)
experiment, relative error is controlled by well-known parameters.
Relative error in T can be minimized to values near instrumental
uncertainty by (1) using high enrichments in the ID spike, and
(2) by spiking the sample to yield a final isotope ratio near the geometric mean between the enriched mineral and the more enriched ID spike
(Webster, 1960). This optimization is largely independent of the
mineral growth solution and puts few constraints on experimental
design.
In contrast, the (F + 1) error terms are the largest source of methodological uncertainty and are sensitive to experimental design. The
general error propagation expression for the variance in (F + 1) as a
function of instrumental uncertainty in the measured isotope ratio
of the mixed solid (m) is simply the variance in m scaled by the sensitivity of F + 1 to m (Bevington and Robinson, 2003):
2
2
σ ðFþ1Þ ¼ σ m
∂ðF þ 1Þ 2
:
∂m
ð13Þ
Dividing both sides of Eq. (13) by (F + 1) 2 and m 2 puts the expression in terms of relative uncertainty,
This equation is derived in detail in the Supplemental Data. Proceeding forward, Eq. (15) can be put in terms of the two major experimental parameters: isotope enrichment of the growth solution (S =
x/o), and the mole fraction new growth (χx) using Eqs. (6) and (9),
again details are provided in the Supplemental Data. The magnitude
of the relative error in (F + 1) as a function of instrumental uncertainty then simplifies to:
rel err ðFþ1Þ ¼ jrel err m j 1 þ
1
:
ðS−1Þχ x
ð16Þ
3.2. Optimizing the mixed spike method
Eq. (16) can be used to understand and minimize uncertainty. In a
mixed spike overgrowth experiment, Me/Ca precision improves
monotonically with the amount of labeled growth (Fig. 3). This
trend makes it impossible to “overspike” through too much growth.
However, χx values below 5% can lead to high errors, an important
consideration during experimental design.
In samples with small relative growth rates, it may be possible to
boost the proportion of new growth and improve precision by physically scraping the mineral surface. The potential of this approach was
demonstrated with coral cultured during a six day experiment in
isotopically enriched seawater. Scraping the cleaned skeletal surface
yielded samples with mole fractions of new growth up to 30%. While
the details of this experiment will be presented elsewhere, these preliminary results exhibit new growth fractions far higher than those
seen during bulk analysis of the whole skeleton, while also demonstrating the challenge of isolating a pure new growth end-member exclusively through physical micro-sampling methods. By combing
physical sampling with the mixed spike technique it may be possible
to completely isolate and characterize small amounts of experimentally
grown material in slow growing systems like coral.
The other major parameter affecting precision is isotopic enrichment. Higher enrichments improve precision and reduce the need
for high growth fractions (Fig. 3). Spike enrichments greater than
five-fold provide diminishing improvements, although higher enrichments result in more flexibility should unexpectedly low portions of
new growth occur. Assuming a conservative instrumental uncertainty, specifically that isotope ratios can be measured to a precision of
1‰, and also assuming isotope enrichments of twofold to tenfold
with 10–20% new growth, it should be possible to measure Me/Ca
to sub-percent precision (Table 1). This error is comparable or
better than SIMS based micro-analysis where the precision of minor
element Me/Ca analysis is about 1%, with worse precision for trace
elements (Allison, 1996; Hart and Cohen, 1996; Sano et al., 2005). Furthermore, the high sensitivity of solution based mass spectrometry
makes precise trace element measurements possible. The only factors
limiting the application of the mixed spike method are (1) an element
must have two or more stable isotopes, (2) an enriched spike for one
isotope must be available, and (3) a method for bulk isotope analysis
must be feasible.
3.3. The impact of natural isotope fractionation
2
rel err ðFþ1Þ ¼ rel err m
2
2
m
ðF þ 1Þ2
∂ðF þ 1Þ 2
:
∂m
ð14Þ
In the mixed spike method the isotope ratio of the new growth
end-member (x) is estimated from solution measurements. Natural
192
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
Fig. 3. Left: Increasing proportions of new growth (χx) decrease relative uncertainty in (F + 1), the major source of error in Me/Ca determinations using the mixed spike overgrowth
method. Precision also improves with higher isotope enrichment in the growth solution as indicated by the different curves (S = x/o, the relative enrichment of the growth solution
over natural abundance). Sub-percent precision is possible with 20% new growth even at moderate enrichments. Right: Relative error in (F+ 1) as a function of isotope enrichment
in the spike solution (S). Each curve represents a different amount of new growth. Three-fold enrichment yields sub-percent relative uncertainty at new growth levels nearly as low
as 5%. For both plots, error curves were calculated assuming a conservative relative instrumental error of 1‰ for each measured isotope ratio.
isotope fractionation between the growing mineral and solution
biases this ratio by a fractionation factor a = xmineral/xsolution (approximated in permil units by Δ ≅ (a − 1) × 1000). While the magnitude of
this fractionation is small compared to overall enrichment, it is important to identify when fractionation may be large enough to affect
Me/Ca calculations.
For carbonates, solid-solution fractionation is typically 2‰ or lower
(Table 2). Important exceptions are low mass elements like Li, and systems like B where the mineral growth mechanism selects a specific and
Table 1
Example recipe for enriched isotopes designed for sub-percent precision Me/Ca analysis during CaCO3 biomineralization experiments. For each element of interest the
amount of dissolved isotope that should be added to 500 ml of natural seawater is
listed. The amount of spike and choice of isotopes is designed to achieve high enrichment, and thus low Me/Ca error, while simultaneously minimizing any perturbation
to the Me/Ca of the final growth solution. Alternatively, a recipe mixing isotopically
enriched artificial seawater and natural seawater in a 40%–60% ratio should still support many marine organism while also maintaining natural Me/Ca. The amount of
each spike is calculated using commercially available isotopes from Oak Ridge National
Lab. Total cost is a few thousand dollars depending on the spike vendor. The estimated
precision of overgrowth Me/Ca measurements is based on a conservative estimate of
1‰ for the analytical uncertainty in isotope ratio measurements and a new growth
fraction of 20%. At least one isotope of calcium is required to measure Me/Ca, other isotopes are chosen based on the system or systems of interest. The use of 43Ca–48Ca double enrichment to measure calcium isotope fractionation is discussed in Section 3.
Proxy
Li/Ca
B/Ca
Mg/Ca
Sr/Ca
Ba/Ca
Cd/Ca
U/Ca
δ44Ca
Enriched Level of
Predicted Change in elemental Amount of
isotope
enrichment relative
concentration
enriched
(S)
error
compared to
element required
seawater
6
Li
B
25
Mg
84
Sr
135
Ba
111
Cd
235
U
48
Ca
43
Ca
10
2
2
1.8
8
2
2
5
10
10
0.6%
0.6%
0.7%
0.3%
0.3%
0.6%
0.3%
100 ppm
16%
38%
19%
5%
17%
27%
4%
2%
2%
12 μg
0.8 mg
123 mg
0.2 mg
50 μg
15 ng
60 μg
5.2 mg
3.4 mg
fractionated species during co-precipitation. Propagating the impact of
isotopic fractionation on (F + 1) in a manner similar to Eq. (16),
δðFþ1Þ
ðF þ 1Þ
¼
S
δx
S
Δsolidsolution
≅
:
1000
ðS−1Þ x
ðS−1Þ
ð17Þ
Here the difference in overgrowth isotope composition due to isotopic fractionation is approximated as δx = ax − x.
The fractionation effect on Me/Ca decreases at high enrichments
(increasing S), eventually converging to Δ/1000. Table 2 lists the impact of uncorrected isotopic fractionation on Me/Ca for typical CaCO3
precipitation experiments assuming three-fold isotopic enrichment
in the growth solution. The ratio B/Ca shows the largest effect with
a 3% accuracy error. In contrast, calculated Sr/Ca changes by less
than 0.05% due to isotopic fractionation. Even in cases where the
magnitude of the fractionation effect is several percent, this effect
can be reduced by applying an estimated value of a to correct solution
measurements. Final Me/Ca is then influenced only by the smaller
variance between true and estimated isotopic fractionation. This correction should make B/Ca and other low mass Me/Ca measurements
precise to better than 1% (Table 2).
4. Isotopic composition of mineral overgrowths
4.1. Overgrowth fractionation method
For many geochemical questions isotope fractionation during
mineral growth is a key parameter together with elemental composition. In the previous section we minimized the effect of fractionation
on compositional measurements. Using a different approach we can
instead accurately measure this isotopic fractionation for elements
with at least four isotopes (some elements require six isotopes to correct for instrumental mass fractionation).
Much as the mixed spike overgrowth technique is inspired by
isotope-dilution, our approach to fractionation builds upon the
double-spike concept. The conventional double-spike technique was
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
193
Table 2
Literature values for the magnitude of natural isotope fractionation between CaCO3 and solution during inorganic precipitation and biomineral growth. Percent level fractionation
only occurs for low mass elements (Li) and for systems where mineral growth selects a specific and fractionated species from solution (B). In most cases the impact of this fractionation on the mixed-spike method is small, as calculated assuming three-fold isotopic enrichment in the growth solution. The effect can be reduced using a constant factor to
approximate the fractionation between measured solution isotope ratios and the estimated isotope ratios of the new-growth end-member. Literature fractionation factors and
notes.
Δcalcite-solution
Δ114/110Cd
Δ88/86Sr
Δ44/40Ca
Δ26/24Mg
Δ10/11B
Δ7/6Li
a
b
c
d
e
f
g
h
i
j
k
l
Δskeleton-seawater
−0.45‰a
−1‰c
−2.5‰f
−15 to −20‰i
−9‰k
−0.1‰b
−1.2‰d, −1‰e
−4‰g, −1.1‰h
−14 to −22‰j
−11‰l
Impact of uncorrected fractionation
on Me/Ca
Precision using a constant fractionation
correction term
0.05%
0.02%
0.2%
0.3%
3.3%
1.6%
b0.05%
b0.02%
0.05%
0.1%
0.6%
0.2%
Horner et al. (2011).
Coral (Fietzke and Eisenhauer, 2006).
Fractionation varies with precipitation rate (Tang et al., 2008). Δaragonitesolution ¼ −1:5 (Gussone et al., 2003).
Cultured planktic foraminifera (Kisakürek et al., 2010).
Cultured coral (Böehm et al., 2006).
Kisakürek et al. (2009).
Planktic foraminifera (Pogge von Strandmann, 2008; Wombacher et al., 2011).
Coral (Wombacher et al., 2011).
Fractionation varies with pH (Sanyal et al., 2000).
Fractionation varies with pH. Planktic foraminifera (Sanyal et al., 1996) and coral (Hönisch et al., 2004).
Marriot et al. (2004).
Coral (Marriot et al., 2004).
developed to accurately measure the isotopic composition of a single
isolated component (Dodson, 1963; Eugster et al., 1969; Rudge et al.,
2009) and is conducted by adding a spike enriched in two isotopes of
the same element to a dissolved sample. In contrast we doubly enrich
the growth solution to conduct a modified double-spike experiment
within growing minerals. This enrichment is used to resolve isotope
fractionation during new growth, to determine the isotopic composition of the initial material, and to quantify the portion of new growth.
If an internal correction for instrumental mass fractionation is necessary, a second double-spike enriched in two different isotopes is
added after bulk dissolution. Measurements by mass-spectrometry of
the two to four enriched isotopes plus two additional non-enriched isotopes are used to solve for all the unknown parameters in the system.
This process is detailed below and in Fig. 4.
For a particular pair of stable isotopes i and j, the isotope ratio of
the new growth end-member is xi = in/ jn. This ratio is related to the
known isotope ratio of the doubly enriched growth solution (si)
through an exponential fractionation law (Russell et al., 1978), the
law followed by most terrestrial mass-dependent processes (Young
et al., 2002):
Isotope ratios of the final mineral sample (mi) depend on the elemental mixing fraction χx between the two components x and o:
i
mi ¼ j
xi ¼ si
MW i
MW j
:
ð18Þ
Here, MWi is the molecular weight of isotope i and the general
fractionation term α applies to all isotope ratios of the same element
(α is related to the ratio specific fractionation factor ai considered in
α
Section 3 by ai ¼ MW i =MW j ). We wish to measure α between
the overgrowth and solution using only bulk isotope analysis of the
final mineral sample, a sample that contains an unspecified proportion of initial material with unknown isotopic composition.
Like most natural samples, the initial material (oi) is assumed to be
isotopically fractionated from a known reference (ni), but by an unknown amount (γ). Following a similar exponential fractionation law
γ
as Eq. (18), oi ¼ ni MW i =MW j . The so-called “normal” reference ni
is typically set to match the composition of the mean earth. Alternatively, a well characterized reservoir from which most natural samples
are derived can be used.
ð19Þ
For use in Eq. (19), the abundance ( iA) of a particular isotope i in
component x or o is calculated from the set of all the unique isotope
ratios of a particular element in that component using either equation
i
Ax ¼ xi =ð1 þ Σxk Þ or i Ao ¼ oi =ð1 þ Σok Þ. In these equations xi and oi
are the ratios of isotope i to an arbitrary reference isotope of the
same element, as described earlier in the text. Furthermore, Σxk and
Σok represent the sum, for a given element and component, of all isotope ratios with the same reference isotope. For example, calcium has
six stable isotopes: 40Ca, 42Ca, 43Ca, 44Ca, 46Ca, and 48Ca. To calculate
the abundance of 40Ca in component x, we could arbitrarily choose
44
Ca as a reference isotope and then use every isotope ratio with respect to 44Ca:
40 40
!α
i
Ax χ x þ Ao ð1−χ x Þ
Ax χ x þ j Ao ð1−χ x Þ:
Ax ¼
1þ
40 44
Ca
Ca x
þ
42 44
Ca
Ca x
44
þ
Ca
Ca
43 x
44
Ca
Ca x
þ
46 44
Ca
Ca x
þ
48 :
44
Ca
Ca x
ð20Þ
In their treatment of the conventional double-spike method
Rudge et al. (2009) use an alternative linearized mixing relationship,
an elegant but unnecessary step for numerical solutions to the overgrowth problem.
Combining the mixing relationship described by Eq. (19) with the
two fractionation equations defined above yields one equation for
each isotope ratio in the sample. Thus there is one equation for each
mi. Since the reference and solution isotope ratios are known (ni
and xi), the equations for each ratio in the solid sample share the
same three unknowns, α, γ, and χx. Measuring three isotope ratios
yields a tractable system of three nonlinear equations that can be
solved numerically for unique values of the three unknowns.
The importance of isotope enrichment now becomes clear. By
enriching two isotopes in the growth solution we separate the effect
of mixing and the effects of each fractionation factor on the measured
ratios. Enrichment ensures that the resulting set of equations are independent. This effect is analogous to the role of enrichment in a
194
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
si
ni
enriched
growth
solution
normal
reference
x
xi
oi
new
growth
mi
Mineral Growth
Experiment
second
double
spike
ri
initial
material
yi
ratio from
mass spec
mineral
sample
y
qi
quadruple
spiked
sample
IMF
IMF Correction
(Optional)
Fig. 4. Schematic of the overgrowth fractionation method. During mineral growth, isotope ratios are fractionated between the doubly-enriched solution (si) and new growth
(xi) by an unknown amount (α). To solve for this fractionation three different isotope
ratios must be measured in the mixed sample (mi). These measurements are used to
solve a system of equations for three unknowns: α, the mole fraction of new growth
(χx), and the isotopic fractionation (γ) between a well characterized reference (ni)
and the initial material. For some elements mi can be measured directly using external
standardization to correct for instrumental mass fractionation (IMF). For other elements an internal correction for IMF is necessary. In these cases, a calibrated
double-spike (yi) is added to the dissolved mineral sample before analysis. The
double-spike must be enriched in different isotopes than the growth solution. Measuring five isotope ratios (r1 to r5) results in a system of equations that can be solved for all
unknown parameters (α,γ, β, χx, χy). In practice this method only requires one set of
isotope ratio measurements per sample once the growth solution is characterized and
the double-spike is calibrated.
conventional double-spike calculation (Johnson and Beard, 1999;
Rudge et al., 2009).
4.2. Internal standardization to correct instrumental mass fractionation
Isotope ratios reported by a mass spectrometer differ from the
actual ratios in a sample due to the physics of the measurement process (Albarède and Beard, 2004). Thus analysis introduces an additional
and unknown instrumental mass fractionation (IMF). For instruments
with stable ion sources like multicollector-inductively coupled plasma
mass spectrometry (MC-ICP-MS), this IMF is often corrected with
external standards or by standard-sample bracketing. Several elements
with four or more isotopes can be measured using this approach,
including Sr (Ramos et al., 2004; Fietzke and Eisenhauer, 2006), Fe
(John and Adkins, 2010), and Zn (Maréchal et al., 1999). The overgrowth method described thus far has the potential to quantify isotopic
fractionation during mineral growth for these elements when used
together with externally standardized MC-ICP-MS.
In other instruments, like thermal ionization mass spectrometry
(TIMS), IMF varies and must be corrected through the use of internal
standards. To correct for an unknown and drifting IMF, we use a second double-spike enriched in isotopes different than the growth
solution. After equilibrating the dissolved sample with this calibrated
spike (yi), each isotope ratio of the now quadruple-spiked sample (qi)
will follow a mixing function similar to Eq. (19) such that qi = f(mi,
yi,χy), where χy is the elemental mole fraction of spike y.
During mass-spectrometry the instrument then fractionates qi by
an unknown magnitude (β) to yield the measured ratio ri. For TIMS
instruments we assume this fractionation follows an exponential
β
law (Russell et al., 1978), and thus r i ¼ qi MW i =MW j . Fractionation
laws may differ between TIMS, ICP-MS, and other instruments
(Albarède and Beard, 2004), changing the form of this equation but
not the mechanics of the method. Combining the new mixing equation, the new IMF fractionation equation, and the equations in
Section 4.1 yields a system with five unknowns (α, β, γ, χx, and χy)
that can be solved through analysis of five isotope ratios. Although
conceptually complicated, in practice the method only requires one
set of isotope measurements per sample once the growth solution
has been isotopically characterized and following a one-time calibration of the second double-spike. Elements that have six or more isotopes and where mineral-solution fractionation could be measured
by the IMF corrected overgrowth method include Ca, Cd, Mo, Se and
many rare earth elements.
4.3. Calcium isotope fractionation during mineral overgrowth
To illustrate this method consider calcium isotope fractionation
during seeded CaCO3 precipitation from enriched seawater. Calcium
isotope fractionation varies with calcite growth rate (Tang et al.,
2008) and this promising system is an important tool for answering
geological questions (DePaolo, 2004; Griffith et al., 2008; Fantle,
2010) and for solving fundamental problems in mineral growth
(DePaolo, 2010).
To test our method and assess precision we built synthetic calcium
isotope experiments using a set of reasonable growth parameters and
fractionation factors. In these hypothetical experiments the culture solution is first enriched tenfold in 43Ca and 48Ca. To calculate the composition of the mineral sample at the end of experimental growth we
prescribe an initial end-member isotope composition of δ44Cao =−0.5‰
referenced to the mean earth (Russell et al., 1978; Simon et al., 2009); a
solution-solid fractionation factor typical for calcite of Δ44Ca =−1.2‰
(Tang et al., 2008); and a new growth fraction of χx =20%. The dissolved
mineral sample is then mixed with a double-spike made of 67% 46Ca
spike (low purity) and 33% 42Ca from Oak Ridge National Lab, the typical
source for such spikes. For this second double-spike we follow the recipe
of Rudge et al. (2009) using a spike proportion of χy =15%. Under these
conditions and an IMF of −15‰, the five isotope ratios that would be
measured on a mass-spectrometer before inverting for fractionation
are: 40Ca/44Ca=38.2; 42Ca/44Ca=2.27; 43Ca/44Ca=0.141; 46Ca/44Ca=
1.32; 48Ca/44Ca=0.673. For a 10 V 40Ca signal, the synthetic sample
would still yield a 36 mV beam on 43Ca, the least abundant isotope.
Following a similar procedure as used for the above synthetic
sample, thousands of computer generated samples were used to
test the method with parameters chosen to span likely experimental conditions (− 3‰ ≤ δ 44Cao ≤ 1‰, − 3‰ ≤ Δ44 Casolidsolution ≤ 1‰,
− 30‰ ≤ IMF ≤ 10‰, 0.1 ≤ χx ≤ 0.9, and 0.1 ≤ χy ≤ 0.9). Using only
the final isotope ratios together with the normal and spike compositions, we solved the overgrowth fractionation problem for α, β, γ,
χx, and χy. Over the entire range of conditions numeric solutions
converge uniquely to the correct values.
We also used numerical methods to evaluate the theoretical external precision of the method. Provided instrumental uncertainty is
controlled by counting error and amplifier noise (Wieser and
Schwieters, 2005; John and Adkins, 2010), routine calcium isotope
measurements by TIMS should yield relative internal errors between
10 and 40 ppm depending upon the particular isotope ratio (these
analytical errors are calculated for a 10 V 40Ca beam, 10 11 Ω resistors,
and a measurement time of 1 h with a 40% duty cycle to
A.C. Gagnon et al. / Chemical Geology 330-331 (2012) 188–196
200
Predicted External Error (ppm)
180
160
140
120
100
80
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
Internal (Instrumental) Error (ppm)
Fig. 5. External error of the calcium isotope fractionation method as a function of analytical internal error for numerically simulated experiments. These data suggest the
precision of the overgrowth method is not limited by structural constraints but rather
by instrumental error. In practice, calcium isotope measurements by the conventional
double-spike technique rarely beat 100 ppm reproducibility. We expect a similar limit
will apply to the overgrowth method. Despite this practical limit, assessing the theoretical capabilities of the technique is an important test of the method. Each data
point represents 700 simulated experiments where “measured” ratios varied randomly
around the same synthetic “true” mean following Poisson distributed internal error
consistent with a 10 V 40Ca beam. In this hypothetical experiment the seawater culture
media were enriched 10-fold in 43Ca and 48Ca with a 42Ca–46Ca double-spike added to
the final dissolved solid sample to correct for IMF.
accommodate a two-step magnet hopping method). This internal
error is propagated through the overgrowth technique using numerical simulations (Fig. 5) to yield an estimated external error of
40 ppm (2σ), much smaller than the 1000 ppm (equivalent to 1‰)
signal typical of natural fractionation.
Our error analysis suggests that the overgrowth method is capable
of high-precision measurements, however, we expect worse precision
in practice. Despite similarly low calculated external errors, the
reproducibility of conventional calcium isotope measurements by the
analogous double-spike technique is rarely better than 100 ppm
(Heuser et al., 2002; Fantle and Bullen, 2009). This limit is attributed
variously to mixing between distinct reservoirs on the TIMS filament,
ion-optics effects, divergence from mass fractionation laws, nonlinear cup gains, or differences in cup efficiencies (Fantle and Bullen,
2009; Simon et al., 2009). As the same effects will limit calcium isotope
ratio measurements by the multi-spike overgrowth method, we expect
a similar and useful level of precision (100 to 200 ppm).
5. Conclusion
Using a calibrated mixture of stable isotopes we outline a procedure
to measure select elemental ratios and isotope fractionation factors for
inorganic and biological overgrowths. As the method is general and applies to many systems with two components it can be tailored to a
range of applications from minerals to metalloproteins.
For inorganic mineral growth the technique promises high sensitivity
and precision when using seed crystals. This should enable experiments
to explore low supersaturations and low growth rates while still controlling mineralogy. Provided different materials can be distinguished, the
method could even be used to grow several minerals or mineral polymorphs simultaneously from the same growth solution to measure effective mineral–mineral partitioning. Furthermore, the method is
compatible with flow-cell techniques and could be combined with atomic force microscopy towards an understanding of mineral growth that
unifies compositional effects and chemical-scale processes.
One aspect of the method makes the technique especially promising. Only the material grown in an enriched spike solution is labeled,
195
thus the compositional impact of periodic environmental signals can
be isolated through the choreographed use of spike. Amongst other
applications, this feature could be used to answer an important question in paleoceanography, the effect of light and photosymbionts on
biomineral composition. Microanalytical approaches have demonstrated more than twofold changes to Mg/Ca between day and night
in planktic foraminifera (Eggins et al., 2004; Sadekov et al., 2005), a
widely used paleothermometer, even in samples cultured at constant
temperature. Understanding the mechanism of this effect and the diurnal behavior of other proxies has been limited in part by analytical
constraints. Despite important progress (for example, Hathorne et al.
(2009) and Allen et al. (2011)), it is difficult to measure useful trace
elements like boron to sufficient precision while also resolving micron scale daily features. The overgrowth method represents an alternative to microanalysis that promises high precision and time
resolved analysis of proxies like B/Ca, Li/Ca, U/Ca and δ 44Ca.
To isolate the impact of light on these proxies, cultured forams
would be exposed to spike exclusively during daylight hours. Bulk analysis would then be used to recover the composition of just the skeletal
material grown during the day. Conversely, night composition could be
measured by labeling a separate experiment only at night. This and
other unique capabilities make the overgrowth spike method a promising tool to quantify compositional effects during mineral growth towards a more accurate interpretation of the geologic record.
Acknowledgements
This work was supported in part by the Director, Office of Science,
Office of Basic Energy Sciences, Chemical Sciences Geosciences and
Bioscience Program of the U.S. Department of Energy under Contract
No. DEAC02-05CH11231. ACG would like to thank Jonathan Erez for
his encouragement and for thoughtful discussions; conversations
that helped motivate this research. This manuscript benefited from
constructive suggestions by two anonymous reviewers.
Appendix A. Supplementary data
Supplementary data to this article can be found online at http://
dx.doi.org/10.1016/j.chemgeo.2012.08.022.
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