Available online at www.sciencedirect.com
Geochimica et Cosmochimica Acta 73 (2009) 337–347
www.elsevier.com/locate/gca
The influence of temperature and seawater composition
on calcite crystal growth mechanisms and kinetics:
Implications for Mg incorporation in calcite lattice
Olivier Lopez a,b, Pierpaolo Zuddas a,c,*, Damien Faivre d,e
a
Institut de Physique du Globe de Paris, Paris, France
b
Numericalrocks AS, Trondheim, Norway
c
Département Sciences de la Terre, UMR 5125, Université Claude Bernard Lyon1, Villeurbanne, France
d
Max Planck Institut für marine Mikrobiologie, Celsisusstr. 1, Bremen, Germany
e
Max Planck Institut für Kolloid- und Grenzflächenforschung, Wissenschaftspark Golm, Potsdam, Germany
Received 14 June 2007; accepted in revised form 21 October 2008; available online 29 October 2008
Abstract
The composition of carbonate minerals formed in past and present oceans is assumed to be significantly controlled
by temperature and seawater composition. To determine if and how temperature is kinetically responsible for the
amount of Mg incorporated in calcite, we quantified the influence of temperature and specific dissolved components
on the complex mechanism of calcite precipitation in seawater. A kinetic study was carried out in artificial seawater
and NaCl–CaCl2 solutions, each having a total ionic strength of 0.7 M. The constant addition technique was used
to maintain [Ca2+] at 10.5 mmol kg!1 while [CO3 2! ] was varied to isolate the role of this variable on the precipitation
rate of calcite.
Our results show that the overall reaction of calcite precipitation in both seawater and NaCl–CaCl2 solutions is dominated
by the following reaction:
kb ;kf
Ca2þ þ CO3 2! $ CaCO3
where kf and kb are the forward and backward reaction rate constants, respectively, while the net precipitation rate R, can be
described at any temperature by
!
"n2
R ¼ kf ðaCa2þ Þn1 aCO3 2!
! kb
or in its logarithmic form
Log ðR þ kb Þ ¼ Log Kf þ n2 Log½CO3 2! '
where ni are the partial reaction orders with respect to the participating ions, a the ion activity, c the activity coefficients, and
Kf ¼ kf ðaCa2þ Þn1 ðcCO3 2! Þn2 is a constant at a given temperature.
*
Corresponding author. Address: Université Claude Bernard Lyon 1, UFR Sciences de la Terre, Bat. GEODE, 43, bld du 11 novemebre
1918, 69622 Villeurbanne cedex, France.
E-mail address: pierpaolo.zuddas@univ-lyon1.fr (P. Zuddas).
0016-7037/$ - see front matter ! 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.gca.2008.10.022
338
O. Lopez et al. / Geochimica et Cosmochimica Acta 73 (2009) 337–347
We find that, irrespective of the presence of Mg, SO4, and other specific seawater components known calcite reaction rate
inhibitors, the partial reaction order with respect to carbonate ion concentration changes from 2 to 5 while the rate constant
Kf, increases by 3–4 orders of magnitude when temperature varies from 5 to 70 "C. The observed variations of the kinetic
mechanism resulting from the temperature changes are correlated with the variable amount of Mg incorporated in the formed
calcites. Moreover, at a given temperature, the increase in the saturation state enhances the rate of calcite precipitation without influencing the reaction mechanism and without changing the amount of Mg incorporated in the growing lattice.
Thus, the results of this experimental study are consistent with present-day abiotic marine carbonates where low-Mg calcite
cements are mainly associated with cool water while high-Mg carbonates are dominantly found in warm-water environments.
This suggests that the apparent inverse relationship between the global average paleo-temperature and the Mg/Ca ratio in
past formed marine carbonate may correspond to major changes in seawater saturation state or (Mg/Ca) ratios that in turn
should reflect significant changes in the relative seawater geochemical cycles of these cations.
! 2008 Elsevier Ltd. All rights reserved.
1. INTRODUCTION
The chemical composition of abiotic carbonate mineral
(cements and ooids) in marine sediments has been extensively used as a tool to reveal historic changes in the
Earth’s marine and atmospheric chemistry given that the
distribution of carbonate minerals appears to be strongly
influenced by water temperature (Wilkinson et al., 1984;
Mackenzie and Morse, 1992; Dickson, 1995, 2004). In
the present-day oceans, magnesium is more abundant than
calcium. Today, high-Mg calcites (or aragonite) are dominantly associated with warm tropical to subtropical waters
while in the past, they were abundant under cooler climatic
conditions. Conversely today, low-Mg calcite levels are
generally found at higher latitudes or in cool deep waters
while in the past, they were mainly associated with warmer
global climatic periods (Lees and Butler, 1972; Wilkinson
and Algeo, 1989; Prasada and Jayawardane, 1994).
However, variations in carbonate-mineral composition
are not dependant solely on temperature but could also
be related to carbone dioxide partial pressure (PCO2) of
the paleo-atmosphere and to variations in the [Mg/Ca]
ratio in seawater. PCO2 may modify the saturation state
of near-surface seawater while variations in the [Mg/Ca]
ratio are also related to changes in the rate of oceanic ridge
production and alteration (Holland, 1984; Dickson, 2002).
Thus, it appears that temperature, as well as seawater composition (supersaturation state, [Ca2+]/[CO3 2! ] ratio and
parent solution composition) may play a significant role
in determining the composition of the carbonate minerals
formed in the present-day and past ocean (Dodd, 1965;
Lee and Morse, 1999; Boyle and Erez, 2004; Robert and
Chaussidon, 2006). These assumptions are of great importance in reconstructing paleo-temperatures of the ancient
oceans.
Experimental measurements of the kinetic rate of abiotic carbonate minerals precipitated from artificial seawater solutions indicate that calcium carbonate composition
is strongly influenced by solution composition (Zuddas
et al., 2003 and Nehrke et al., 2007) and by other factors
such as temperature (Mucci, 1987 and Morse et al.,
1997). Several previous investigations (Chave, 1954; Mucci,
1987; Morse et al., 1997; Elderfield and Ganssen, 2000;
Toyofuku et al., 2000; Katz, 1973; Burton and Walter,
1987; Arvidson and Mackenzie, 2000) have shown that
Mg content in modern abiotic and biogenic calcite samples
is positively correlated with the temperature, although they
offer no explanation of the active reaction mechanisms.
Recently, Nehrke et al. (2007) suggested that the extent
of foreign ion incorporation during calcite crystal growth
can be influenced by variations in the reaction mechanism
that is related to the non-stoichiometry of the parent
solution.
Thus, we investigated the effect of temperature and
chemical composition of parent solutions on the rate and
mechanisms of calcite crystal growth over a range of temperatures common to both the present-day and ancient seawaters in order to determine if and how temperature was
responsible for the amount of Mg incorporated in the calcite. We carried out experiments using both the presentday seawater and NaCl–CaCl2 (inhibitor-free) solutions at
the same ionic strength and calcium concentration, in order
to evaluate the independent role of temperature on both the
precipitation rate and the corresponding kinetic
expressions.
2. EXPERIMENTAL KINETIC RATE EXPRESSIONS
In natural seawater, precipitation of carbonate minerals
is commonly not easily predicted using straightforward
equilibrium thermodynamic assumptions, because seawater
is a highly complex solution (Morse, 1983; Morse and
Casey, 1988). However, in this complex solution, a similar
rate equation can be used to describe the kinetics of calcite
precipitation in both seawater and NaCl–CaCl2 (inhibitorfree) solutions having the same ionic strength and calcium
concentration, even when the presence of Mg2+ in the parent solution inhibits the rate by one order of magnitude at
25 "C (Zuddas and Mucci, 1994). Mineral precipitation and
dissolution rates have most often been expressed in terms of
a disequilibrium functional dependence. Since the net
growth rate of calcium carbonate is, a priori, a function
of both calcium and carbonate concentrations, rate data
has been commonly fitted to the following rate equation
(Nancollas and Reddy, 1971; Berner and Morse, 1974;
Morse, 1978; Arvidson and Mackenzie, 2000; Gledhill
and Morse, 2006):
R ¼ k ( ðXc ! 1Þn
or in the logarithmic form:
ð1Þ
Temperature influence in kinetics of seawater Mg–calcite
Log R ¼ Log k þ n LogðXc ! 1Þ
ð2Þ
where R is the precipitation rate normalized to the reacting
surface area (mol cm!2 s!1), k is the rate constant, n is the
order of the overall reaction (Nancollas and Reddy, 1971)
and Xc is the saturation state defined as
2þ
2!
Xc ¼
½CO3 ' ( ½Ca '
K)c
ð3Þ
where Ki ) is the calcite stoichiometric solubility constant at
a given temperature, [CO3 2! ] and [Ca2+] are the carbonate
and calcium ion concentrations, respectively.
This model is commonly adopted for precipitation from
aqueous solutions of minerals such as calcite and involves
alternating incorporation of cations and anions (Ca2+ and
CO3 2! ) into the lattice. In this case, the growth rate also depends on the relative abundance of the cations and anions
in solutions in addition to Xc.
Given the constancy of calcium ion concentration in the
ocean, Broecker and Peng (1982) suggested that variations
in seawater saturation states are better described by the variation of carbonate ion concentrations. Zhong and Mucci
(1993) showed that the kinetics of calcite precipitation in
seawater solutions can be described using [CO3 2! ] as the
sole or governing macroscopic operative variable because
[Ca2+] >> [CO3 2! ] and [Ca2+] is constant. Zuddas and
Mucci (1998) demonstrated that under these conditions,
the rate of calcite crystal growth is zero order with respect
to the [Ca2+]. Under these conditions, assuming that calcite
precipitation is controlled by the reaction:
Ca2þ þ CO3 2! $ CaCO3
ð4Þ
the net experimental rate, R, defined as the difference
between the precipitation rate (Rf) and the dissolution rate
(Rb), becomes:
R ¼ Rf ! Rb ¼ kf ðaCa2þ Þn1 ðaCO
3
2!
Þn2 ! kb ðaCaCO3 Þn3
ð5Þ
where, kf and kb are the forward and reverse reaction rate
constants, ai and ni are, the activity and partial reaction
order, respectively, for the species involved in the reaction
of precipitation. The activity of a relatively pure solid such
as calcite precipitated from seawater containing about 12%
(in mole) MgCO3 can be assumed equal to one on the scale
of this kind of kinetic experiment (Morse and Mackenzie,
1990; Zhong and Mucci, 1993). This assumption is in agreement with the low lattice volume change resulting from
MgCO3 incorporation (Marini, 2007). Given the constancy
of [Ca2+] throughout the growth experiments, Eq. (5) can
be reduced to (Zhong and Mucci, 1993):
n
R ¼ Kf ½CO3 2! ' 2 ! kb
ð6Þ
where:
Kf ¼ kf ðaCa2þ Þ
n1
!
cCO3 2!
"n2
ð7Þ
Kf is a constant for a given solution composition (i.e., temperature, PCO2, and ionic strength). Eq. (6) can also be written in the logarithmic form:
LogðR þ kb Þ ¼ Log Kf þ n2 Log½CO3 2! '
ð8Þ
339
when the rate of the forward reaction is much higher than
the reverse (when R >> kb), Eq. (8) can be reduced to
(Zhong and Mucci, 1993):
Log ðRÞ ¼ Log Kf þ n2 Log½CO3 2! '
ð9Þ
Eq. (9) represents a kinetic expression that takes into account the non-stoichiometry of the seawater composition
and is thus more suitable for obtaining mechanistic information on the calcite crystal growth reactions in this environment. This last expression has been fitted under
experimental conditions (Zhong and Mucci, 1993, 1995;
Zuddas and Mucci 1994, 1998; Zuddas et al., 2003) testing
a large range of salinity, PCO2 partial pressure and organic
matter concentrations of present-day seawater.
3. MATERIALS AND METHODS
The modified constant addition technique was used to
conduct the calcite crystal growth experiments (Zhong
and Mucci, 1993; Zuddas et al., 2003). This experimental
system, briefly described hereafter, provides a steady state
solution. It is suitable for both close and far from equilibrium investigations and maintains a constant reaction affinity over the range of oversaturation conditions investigated.
The reactor consisted of a double-walled glass 500 ml
separator funnel in which the temperature of the precipitating solution was maintained constant by circulating water
through the glass jacket from a constant temperature bath.
Different temperatures were investigated: 5, 25, 40, 55 and
70 "C. A supersaturated solution with respect to calcite
(i.e. 1.2 < Xc < 10) was delivered to the reactor at selected
constant rates by a peristaltic pump using Tygon# tubing.
A water-saturated CO2/N2 gas mixture (PCO2 = 2000 ±
20 ppm) was introduced in the reactor, at a controlled rate,
through a glass frit fitted at the bottom of the separator
funnel. Bubbling of the gas through the reacting solution
served to maintain the PCO2 at a desired and constant value
of 2000 ppm, as well as keeping the mineral seed in
suspension.
3.1. Initial materials
Baker# ‘Instra-analyzed flux reagent’ grade calcite, treated by the procedure described by Mucci (1986) was used as
seed material for the calcite precipitation experiments.
Seeds have a well-restricted size range between 3 and
7 lm as observed by Scanning Electron Microscopy and a
specific surface area respectively of 0.52 m2 ( g!1 as determined by the Kr-BET method (deKanel and Morse, 1979).
3.2. Experiments
The calcite crystal growth experiments were conducted
by first introducing 0.1 g of carbonate seed into the empty
reactor. The mineral growth was then initiated by pumping
the supersaturated solution into the reactor at a constant
rate. Typically, 5–10 ml of solution was sufficient to wet
the solid completely. During the experiments, 2 ml aliquots
of the reacting solution were sampled, filtered through a
Millipore# 0.45 lm filter, and stored in 15 mL Falcon#
340
O. Lopez et al. / Geochimica et Cosmochimica Acta 73 (2009) 337–347
plastic tubes for later analysis. The pH of the reacting solution was permanently monitored using a combination of
glass-reference electrodes. All experiments were performed
in NaCl–CaCl2 and seawater-like solutions at a total ionic
strength of 0.7 mol kg!1 and at a fixed calcium concentration of 0.01 mol kg!1 introduced as a chloride salt. Solution
of a desired initial saturation state was obtained by adding
appropriate amounts of Na2CO3 and NaHCO3 to both
inhibitor-free and seawater solutions (phosphate free),
which were previously equilibrated with a CO2–N2 gas mixture of known PCO2 (2000 ppm). The composition of the
precipitating solutions is detailed in Table 1.
3.3. Analysis
Calcium concentration was determined by potentiometric titration (Mucci, 1986) on aliquots sampled throughout
the experiments. Carbonate alkalinity was measured by a
combination of Gran titration (Gran, 1952) and Dickson’s
method for seawater samples (Dickson and Goyet, 1994)
using a Titrino Stat 718 (Metrohm#). Titrations were carried out in a thermo-regulated cell allowing an accuracy
of ±5 lmol kg!1. The electrode used for pH measurements
was calibrated against three NIST-traceable buffer solutions (pH = 4.01, 7.00, 9.00 at 25 "C). Reproducibility of
pH calibration carried out before and after measurements
of a single solution, was better than 0.005 pH units. However, because of problems inherent to the use of glass electrodes calibrated using NIST buffers in strong electrolyte
solutions (Dickson and Goyet, 1994), this measurement
was only used to verify that steady state conditions were
maintained throughout crystal growth. The carbonic acid
speciation in the reacting solution was calculated from the
PCO2 partial pressure and the carbonate alkalinity measured
at the end of the experiment. For seawater solutions, boric
acid apparent dissociation constants were used to calculate
the boric acid contribution to the titration alkalinity at the
different temperatures to (Millero, 1979). The MgCO3 content of Mg–calcite overgrowth was evaluated by atomic
absorption analysis done on aliquots of solids dissolved in
concentrated HCl (Mucci, 1987). The morphology of unreacted and reacted calcite was examined using a JEOL#
Scanning Electron Microscope at 5 KeV.
Table 1
Parent solution composition at 25 "C with an ionic strength of
0.7 M (S = 35).
Na+
Cl!
Ca2+
Mg2+
K+
BO3 3!
SO4 2!
Br
CO3 2!
Seawater (mol kg!1)
NaCl–CaCl2 (mol kg!1)
0.48
0.57
0.01
0.054
0.01
0.0009
0.03
0.002
25–250 ( 10!6
0.71
0.69
0.01
0
0
0
0
0
25–250 ( 10!6
3.4. Aqueous solution calculations
The saturation state of the precipitating solution with
respect to calcite (X), was calculated according to Eq.
(3). The total calcium concentration was measured directly; while the CO3 2! ion concentration was calculated
from PCO2, carbonate alkalinity and stoichiometric equilibrium constants of the carbonic acid system. The CO2 solubility, carbonic acid stoichiometric dissociation and
calcite and magnesium–calcite solubility constants were
calculated (and extrapolated for 55–70 "C) from constants
determined in artificial seawater ki ) (sw) at equivalent ionic
strengths (Roy et al., 1993; Millero et al., 2006 and Bertram et al., 1991). The total ion activity coefficient, ci, of
the carbonic acid species in the experimental solution
was estimated using the ion pairing model of Millero
and Scheiber (1982):
cHCO!3 ðSWÞ
ð10Þ
K)1ðNaClÞ ¼ K)1ðSWÞ (
cHCO!3 ðNaClÞ
K)2ðNaClÞ ¼ K)2ðSWÞ (
K)cðNaClÞ ¼ K)cðSWÞ (
cCO3 2! ðSWÞ ( cHCO!3 ðNaClÞ
cCO2! ðNaClÞ ( cHCO!3 ðSWÞ
3
cCa2þ ðSWÞ ( cCO3 2! ðSWÞ
cCO3 2! ðNaClÞ ( cCa2þ ðNaClÞ
ð11Þ
ð12Þ
where the subscripts NaCl and SW refer to the constants or
activity coefficient in NaCl–CaCl2 solutions and seawater
respectively. This method was shown to be the most accurate to determine dissociation and solubility constants
(Mucci et al., 1989). The estimated calcite stoichiometric
solubility constants and carbonic acid dissociation constants are reported in Table 2.
3.5. Rate estimation
The precipitation rate (R in lmol m!2 h!1) was calculated from the difference in carbonate alkalinity (meq kg!1)
solutions at steady state and J, the injection rate (kg h!1).
The rate was normalized to the initial surface area of the
calcite seeds:
R¼
J ( ðAlk0 ! Alkss Þ
( 1000
S ( Wseed
ð13Þ
where Wseed is the initial weight of the calcite seed and S is
the specific reactive surface area. Since less than 10% of the
initial seed weight was precipitated during any given experiment, surface area variations were neglected in the rate
calculations.
3.6. Estimation of errors in the carbonate concentration
The saturation state of the parent solutions as expressed
by Eq. (3) as well the kinetic seawater model of Eq. (9) are
function of the carbonate ion concentration ([CO3 2! ]). In
our work, this parameter was calculated using PCO2 at equilibrium with the solution (assumed to be constant through
all the experiments) and total carbonate alkalinity according to the following equation (Morse and MacKenzie,
1990; Zhong and Mucci, 1993; Zuddas and Mucci, 1994,
1998):
Temperature influence in kinetics of seawater Mg–calcite
)
k
½CO3 2! ' ¼
Alkf ( k2 ) þ a ( PCO2 *
1
341
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k
k
Alkf ( k2 ) ( ð2 ( a ( PCO2 ! 3 ( Alkf ( k2 ) Þ þ a ( ðPCO2 Þ
1
1
k
ð14Þ
)
8 ( k2 )
1
where k1 ) , k2 ) are the apparent dissociation constants of the
carbonic system and a is the Henry’s coefficient.
As previously stated in this study, alkalinity titration
precision was ± 5 lmol kg!1 and PCO2 was maintained constant at 2000 ± 20 ppm and adopted apparent thermodynamic constants (k1;2 ) ) had an accuracy of 2–5% (Roy
et al., 1993).
The errors in estimated carbonate ion concentration
were evaluated by a Monte Carlo method (Anderson,
1976). The choice of this stochastic method was preferred
to the classical regression or propagation methods which
are more tedious and complex and also extremely difficult
to adapt to [CO3 2! ] calculations (Nelson and Ellenberger,
1972). Under our experimental conditions, carbonate ion
speciation had an uncertainty ranging from 12 to 17%
which corresponds to between 6 and 10% respectively on
the logarithmic scale. Precision for the parameterization
of the following equations (Eqs. (2), (9), (13), slope and
intercept) was obtained after propagation of errors
according to Minster et al. (1979) and Provost (1990)
procedures.
4. RESULTS AND DISCUSSION
4.1. Disequilibrium functional dependence of the calcite
crystal growth kinetics
For any given temperature investigated in this study,
data was used to parameterise the empirical parabolic rate
law expressed by Eq. (2) for the investigated range of calcite
supersaturation (1.2 < Xc < 10). Our data does not fit on
the same line (Fig. 1a and b), and yields distinct kinetic
parameters (Table 3). The order of the overall reaction
(n) enhances from 1.3 to 2.9 in both artificial seawater
and NaCl–CaCl2 solutions when temperature increases
from 5 to 70 "C. The rate constant (k), in logarithmic form,
increases with the temperature from 0.20 to 0.66 and 1.15 to
3.59 in seawater and inhibitor-free solutions, respectively.
Numerous studies have indicated that disequilibrium
functionality is higher than one (i.e. n = 2) in complex solutions such as seawater at 25 "C, suggesting that the reaction
of calcite growth in seawater solution is not an elementary
reaction (Burton and Walter, 1987; Zhong and Mucci,
Fig. 1. Growth rate (Log R) in lmol m2 h!1 versus Log(X ! 1) in NaCl–CaCl2 (a) and seawater (b) solutions at ionic strength of 0.7 M and
PCO2 of 2000 ppm at different temperatures.
Table 2
Stoichiometric dissociation constants of carbonic system K*i(SW) (Roy et al., 1993 converted in mol kg-soln!1) and K*i(NaCl) and calcite
solubity constants K*c(SW) and K*c(NaCl) in, respectively, seawater and NaCl–CaCl2 solutions at different investigated temperatures.
Temperature
*
K 1(SW)
K*2(SW)
K*c(SW)
K*1(NaCl)
K*2(NaCl)
K*c(NaCl)
5 "C
25 "C
!7
8.8 ( 10
5.2 ( 10!10
4.3 ( 10!7
8.6 ( 10!7
3.1 ( 10!10
2.2 ( 10!7
40 "C
!6
1.4 ( 10
1.2 ( 10!9
4.3 ( 10!7
1.4 ( 10!6
7.1 ( 10!10
2.2 ( 10!7
55 "C
!6
1.9 ( 10
2.1 ( 10!9
4.1 ( 10!7
1.8 ( 10!6
1.2 ( 10!9
2.1 ( 10!7
70 "C
!6
2.5 ( 10
3.4 ( 10!9
3.8 ( 10!7
2.4 ( 10!6
2.0 ( 10!9
2.0 ( 10!7
3.2 ( 10!6
4.7 ( 10!9
3.7 ( 10!7
2.9 ( 10!6
2.6 ( 10!9
1.8 ( 10!7
342
O. Lopez et al. / Geochimica et Cosmochimica Acta 73 (2009) 337–347
Table 3
Least-square fit parameters evaluated from rate measurements, Eq. (2), in NaCl–CaCl2 (NaCl) and seawater (sw) solutions.
Temperature
5 "C
25 "C
40 "C
55 "C
70 "C
n(NaCl)
Log k(NaCl)
r2(NaCl)
1.28 ± 0.19
1.15 ± 0.14
95%
1.90 ± 0.22
1.50 ± 0.17
96%
2.26 ± 0.27
2.17 ± 0.31
96%
2.57 ± 0.26
2.78 ± 0.31
96%
2.88 ± 0.31
3.59 ± 0.39
96%
n(sw)
Log k(sw)
r2(sw)
1.55 ± 0.17
0.20 ± 0.04
95%
1.84 ± 0.20
0.33 ± 0.05
94%
2.30 ± 0.28
0.40 ± 0.04
96%
2.55 ± 0.29
0.51 ± 0.05
96%
2.72 ± 0.30
0.66 ± 0.07
96%
1993; Zuddas and Mucci, 1994). The kinetic order of the
overall reaction obtained in this study is, for both types
of solution, close to 2 at the standard temperature in agreement with previous studies (Kazmierczak and Tomron,
1982; Zhong and Mucci, 1993; Zuddas et al., 2003). In
the range of investigated temperatures and within the limits
of accuracy for the order of the overall reaction (n), temperature slightly affects the value of kinetic parameters expressed by the model of Eq. (2). This would suggest that
temperature should not significantly influence the kinetic
mechanism of calcite growth.
However, irrespective of the solution saturation state,
we found that the amount of magnesium incorporated by
calcite grown from seawater solutions increased from 6 to
18 (in mol%) as the temperature increased from 5 to
70 "C (Fig. 2). Previous investigations have shown that
Mg contents in modern abiotic and biogenic calcite samples
are positively correlated with temperature (Burton and
Walter, 1991; Gross-Mesilaty et al., 1997; Elderfield and
Ganssen, 2000). However, Lea (2003) suggested that pH,
salinity and the seawater [Mg/Ca] ratio might influence
the Mg-thermometer thereby preventing its robust calibration. Our molar scale rate evaluation and microscopic
observations of the surface state do not allow us to verify
whether or not mineral-solution boundary steps control
the Mg distribution as observed by Wasylenki et al.
(2005) in calcite growth from solution of stoichiometric
composition (i.e. Ca/CO3 = 1). Examining the morphological status of the surface during growth at the different
investigated temperatures, we simply observed that while
Fig. 2. Evolution of the MgCO3 content (in mol% of MgCO3) for
the calcite overgrowths as a function of temperature.
unreacted crystals were well formed with sharp-edged
rhombohedra bounded by {10!
14} faces (Fig. 3a), crystals
that grew at lower temperatures (5 "C) exhibited smooth
planes of growth with steps of relatively uniform thickness
irrespective of the solution composition (Fig. 3b and c). In
contrast, the morphology of the crystals produced at elevated temperatures (70 "C) exhibited thicker and rougher
planes of growth for both kinds of precipitating solutions
(Fig. 3d and e). Thus, precipitations at elevated temperatures generated a different and more ‘‘disordered” crystal
growth reflecting a possible variation of the kinetic mechanism. We found that crystal morphologies were not affected
by the solution’s degree of saturation either in seawater or
in inhibitor-free parent solutions and that, at the SEM scale
of observation, a similar morphology was found in calcites
formed from both seawater and inhibitor-free parent solutions at the same temperature and saturation state.
4.2. Carbonate ion concentration functional dependence of
the calcite crystal growth kinetics
The kinetic rates obtained during our study for each
temperature investigated were used to the parameterise
Eq. (9) (Fig. 4a and b). The resulting least squares fit
parameters, corresponding to the partial reaction order of
the carbonate ion (n2: slope) and the apparent forward rate
constant (Kf: intercept), are reported in Table 4 for each
temperature in both artificial seawater and NaCl–CaCl2
solutions. Fig. 4a and b indicate distinct trends for precipitation rate variations as a function of temperature.
In NaCl–CaCl2 solutions (Fig. 4a) the partial reaction
order with respect to [CO3 2! ] increases from 2.1 to 5.1 while
the apparent kinetic constants enhance from 4.0 to 9.4 (on
the logarithmic scale) when the temperature increases from
5 to 70 "C. The significant increase of the partial reaction order with respect to the carbonate ion suggests a change in
the calcite precipitation reaction mechanism, whereas the increase in the rate constant can be attributed to the catalytic
effect of temperature. In artificial seawater (Fig. 4b), the partial reaction order with respect to the carbonate ion concentration increases, similarly to NaCl–CaCl2 conditions, from
2.1 to 5.0 as the temperature increases from 5 to 70 "C while
the apparent kinetic constant increases from 2.6 to 6.0.
Our results indicate that the calcite precipitation rates
from an inhibitor-free (NaCl–CaCl2) supersaturated solution with carbonate ion concentrations of 25 and
250 lmol kg!1 would increase respectively by 1 and 3 orders of magnitude when temperature varies from 5 to
70 "C. The presence of inhibitors in artificial seawater pro-
Temperature influence in kinetics of seawater Mg–calcite
343
Fig. 3. Scanning electron micrograph of a typical unreacted calcite crystal used as seed material (a) with a well-restricted size range between 3
and 7 lm. Calcite seeds with smooth planes of overgrowth collected at the end of the experiments at 5 "C in NaCl–CaCl2 (b) and (c) seawater
solutions respectively. Calcite seeds with thick and rough planes of overgrowth collected at the end of the experiments at 70 "C in NaCl–CaCl2
(d) and artificial seawater (e) solutions, respectively.
vokes a diminution of approximately one order of magnitude of the reported values for NaCl–CaCl2 solution over
the range of investigated carbonate ion concentration.
The results of this study, showing that temperature variations produced a change in the partial reaction order with
respect to the carbonate ions independently from the presence of inhibitors in the parent solutions, indicate that temperature should be responsible for the observed change in
the reaction kinetic mechanism.
By substituting temperature functionality for both
kinetic parameters n2 and Log Kf into Eq. (9) and using a
multidimensional least square minimization based on the
inversion of experimental rate data (Tarantola, 2004), the
influence of temperature on the kinetic rate in the typical
range of carbonate ion concentration of present-day seawater can be estimated.
In NaCl–CaCl2 solution, the rate of pure calcite crystal
growth can be expressed by:
Log R ¼ 3:79ð*0:30Þþ0:08ð*0:008Þ(T
þð2:14ð*0:05Þþ0:04ð*0:005Þ(TÞLog½CO3 2! ' ð15Þ
while in artificial seawater, the rate of Magnesium–Calcite
growth is:
344
O. Lopez et al. / Geochimica et Cosmochimica Acta 73 (2009) 337–347
Fig. 4. Growth rate (Log R) in lmol m2 h!1 versus Log [CO3 2! ] in mmol.kg!1 in NaCl–CaCl2 (a) and seawater (b) solutions at ionic strength
of 0.7 M and PCO2 of 2000 ppm Pa at different temperatures.
Table 4
Least-square fit parameters evaluated from rate measurements, Eq. (9), in NaCl–CaCl2 (NaCl) and seawater (sw) solutions and activity
coefficients of carbonate ion (cCO3 2! ) evaluated for all the investigated temperature.
Temperature
5 "C
25 "C
40 "C
55 "C
70 "C
n2(NaCl)
Log Kf(NaCl)
cCO3 2! (NaCl)
r2(NaCl)
2.08 ± 0.21
3.97 ± 0.22
0.093
95%
3.29 ± 0.28
5.95 ± 0.26
0.086
95%
4.08 ± 0.29
7.56 ± 0.31
0.074
98%
4.42 ± 0.30
8.74 ± 0.31
0,066
97%
5.10 ± 0.31
9.39 ± 0.31
0.056
96%
n2(sw)
Log Kf(sw)
cCO3 2! (sw)
r2(sw)
2.11 ± 0.21
2.56 ± 0.22
0.050
97%
3.09 ± 0.20
3.69 ± 0.26
0.043
98%
3.97 ± 0.28
4.79 ± 0.31
0.038
96%
4.48 ± 0.25
5.46 ± 0.36
0.032
98%
4.99 ± 0.29
5.99 ± 0.39
0.026
95%
Log R ¼ 2:92ð*0:28Þ þ 0:03ð*0:002Þ ( T
2!
þ ð2:57ð*0:05Þ þ 0:02ð*0:003Þ ( TÞLog½CO3 ' ð16Þ
In NaCl–CaCl2 solutions, the net rate corresponds to
the growth of pure calcite crystals while in artificial seawater solutions this same rate is related to the growth of Magnesium–Calcite. It is thus possible to quantify the inhibiting
effect on the kinetic rate (R) generated by the specific seawater constituents by comparing the kinetic expressions in
the two experimental conditions:
DR ¼ Eq15 ! Eq16
¼ 1:23ð*0:06Þ þ 0:036ð*0:003Þ ( T þ e
the rate of calcite precipitation without influencing the reaction mechanism and without changing the amount of Mg
incorporated in the growing lattice.
Our experimental data are consistent with and confirm
the latitude observations of the distribution of marine ooid
and cement mineralogy (Opdyke and Wilkinson, 1990) of
ð17Þ
where DR represents the difference between the pure calcite
crystal growth and Magnesium–calcite crystal growth. e is a
low value that can be neglected (<2% of DR). We assume
then that DR does not depend on carbonate ion concentration but only on temperature. The simple effect of the temperature reported in Fig. 5 shows that the rate of calcite
precipitation linearly increased by about two orders of
magnitude only (from 1.4 to 3.6) as a result of an increase
in temperature from 5 to 70 "C. The observed variations of
the kinetic mechanism resulting from the temperature
changes are correlated with the variable amount of Mg
incorporated in the formed calcites. Moreover, at a given
temperature, the increase in the saturation state enhances
Fig. 5. Inhibiting effect on the kinetic rate generated by the
present-day seawater solution composition: DR (in lmol m2 h!1) as
a function of temperature.
Temperature influence in kinetics of seawater Mg–calcite
present-day abiotic marine carbonate where low-Mg calcite
cements are mainly associated with cool water while highMg carbonates are dominantly found in warm-water environments and are in contrast to the interpretations of the
past climate record. This apparent inverse relationship
between the global average paleo-temperature and the
[Mg/Ca] ratio in calcite may correspond to either an unintentional bias on latitudinal matter (leading coincidentally
to the inverse expected relationship) or to major changes
in seawater saturation states or [Mg/Ca] ratios (capable
of overriding the past kinetic influence of temperature). If
the first hypothesis seems unlikely, because the majority
of the studied samples have been low paleo-latitudes,
several studies (Opdyke and Wilkinson, 1990; Morse
et al., 1997) concluded that carbonate accumulation could
be related to the relative abundance of available continental
and tropical shelf areas.
PCO2 is the parameter generally considered as responsible for changing the seawater saturation state with respect
to carbonate minerals and thus to [CO3 2! ] (Tyrrell and
Zeebe, 2004). The results of our study show that the saturation state does not significantly influence the amount of Mg
incorporated in calcite (<2%) while previous experimental
data (Zuddas and Mucci, 1998) indicated that variations
in PCO2 did not change the partial reaction order with respect to the carbonate ions. We propose that PCO2 cannot
be the primary factor in the control of calcite precipitation
mechanisms and thus should not control the amount of Mg
in calcite precipitate from seawaters. Large differences in
the [Mg/Ca] ratio in seawater should be invoked for controlling the variation in sedimentary abiotic calcite over
time associated with significant changes in the relative seawater geochemical cycles of these cations. Variations in the
seawater floor rate of expansion and associated cycling of
seawater with hydrothermal brines may eventually be
invoked as responsible for such variations.
5. CONCLUSION
A molar scale kinetic model, defined by macroscopic
operative variables, enables us to describe the rate of precipitation in both NaCl–CaCl2 (inhibitor-free) and artificial
seawater solutions at different temperatures as a function of
the [CO3 2! ] over the range of common values observed in
present-day oceans. This expression indicates that changes
in temperature affect the order of kinetic rate law (n2)
reflecting some changes in the mechanism of calcite formation at the PCO2 of 2000 ppm.
Despite the inhibiting effect of magnesium, we estimated
that the calcite precipitation rate could increase by 3–4 orders of magnitude as the temperature increases from 5 to
70 "C. The amount of magnesium incorporated in the calcite overgrowths at any given temperature is independent
of the precipitation rate over a wide range of saturation
states but is positively correlated to the rise of temperature.
The changes in reaction mechanisms identified during this
study for the different investigated temperatures are potentially responsible for the variations in the amount of magnesium incorporated in the calcite lattice.
345
ACKNOWLEDGMENTS
We thank Dr. Marwan Charara (Schlumberger, Russia) for his
helpful collaboration during the data inversion and modelling, Dr.
Hajatollah Valli (Mac Gill University, Canada) for all the SEM
micrographs and Pr. Franck Millero for giving gracefully access
to the co2brine program. This research was partially supported
by Bonus Qualité Recherche (Université Claude Bernard), the
IPGP-TOTAL-SCHLUMBERGER research centre on CO2
geological storage and the ADEME. Damien Faivre acknowledges
support from Marie Curie fellowship from the European Union
(BACMAG, EIF-2005-9637) and from the Max Planck Society.
We thank also the three anonymous reviewers and the Dr Lyons
(associate editor) for their important contribution that significantly
improved the quality of the manuscript and Robin Silver for her
assistance in English-language editing.
APPENDIX A. DATA FOR PRECIPITATION RATES
IN ARTIFICIAL SEAWATER SOLUTIONS AT
2000 PPM
T "C
R in
lmol m2 h!1
X
[CO3 2! ] in
lmol kg!1
5
5
5
5
5
5
5
5
5
5
5
5
5
5
25
25
25
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
40
40
55
55
55
55
0.00
0.23
0.48
0.50
0.69
0.69
0.70
0.91
1.00
1.11
1.13
1.47
1.64
1.81
0.08
0.27
0.52
0.54
0.66
0.75
0.91
1.13
1.15
1.28
1.29
1.62
0.28
0.55
0.68
0.91
1.29
1.40
1.56
1.83
2.15
0.10
0.41
1.16
1.75
2.1
2.3
2.5
2.7
2.8
3.3
3.8
4.0
4.5
5.0
6.1
7.7
8.9
9.1
1.8
1.9
2.1
2.3
2.6
2.8
3.1
3.4
3.7
4.1
4.5
6.0
1.9
2.2
2.4
2.5
3.2
3.8
4.2
4.6
7.8
2.0
2.3
1.7
3.0
79
86
95
102
111
113
137
155
165
185
204
251
303
317
72
75
87
95
105
115
126
138
151
166
182
200
72
87
94
99
125
148
165
180
223
63
71
115
155
(continued on
[Ca2+] in
mol kg!1
0.011
0.009
0.010
0.009
0.010
0.009
0.011
0.009
0.011
0.010
0.010
0.010
0.010
0.010
0.011
0.009
0.011
0.010
0.011
0.009
0.010
0.010
0.011
0.009
0.011
0.010
0.011
0.009
0.011
0.009
0.011
0.009
0.010
0.010
0.010
0.010
0.011
0.010
0.011
next page)
346
O. Lopez et al. / Geochimica et Cosmochimica Acta 73 (2009) 337–347
Appendix A. (continued)
Appendix B. (continued)
T "C
R in
lmol m2 h!1
X
[CO3 ] in
lmol kg!1
[Ca ] in
mol kg!1
T "C
R in
lmol m2 h!1
X
[CO3 2! ] in
lmol kg!1
[Ca2+] in
mol kg!1
55
55
55
55
70
70
70
70
70
70
70
2.32
2.59
2.73
3.37
0.14
0.75
1.25
1.96
2.56
2.86
3.76
4.9
7.7
9.8
17.8
2.1
1.7
2.6
3.9
5.9
7.2
14.2
219
240
251
355
65
83
115
145
200
231
331
0.009
0.011
0.010
0.010
0.010
0.010
0.009
0.011
0.009
0.011
0.010
70
70
70
70
70
70
70
2.0
2.7
3.1
3.9
3.9
4.5
5.1
1.4
1.8
2.1
2.9
3.1
5.0
6.5
34
41
59
72
78
102
126
0.010
0.010
0.011
0.009
0.010
0.009
0.011
2!
2+
APPENDIX B. DATA FOR PRECIPITATION RATES
IN NACL–CACL2 SOLUTIONS AT 2000 PPM
T "C
R in
lmol m2 h!1
X
[CO3 2! ] in
lmol kg!1
[Ca2+] in
mol kg!1
5
5
5
5
5
5
25
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
40
40
40
40
55
55
55
55
55
55
55
55
55
55
55
70
70
1.4
0.8
1.1
1.1
2.1
1.4
1.5
2.1
2.4
1.7
2.1
2.9
2.0
1.0
0.8
0.5
4.0
4.0
3.6
3.3
3.3
3.0
2.5
1.1
1.6
1.9
0.8
0.6
1.1
1.7
2.0
2.2
2.5
2.8
3.5
3.6
4.2
4.8
1.1
1.5
4.8
1.5
1.6
1.9
7.2
3.1
2.1
3.7
4.2
2.0
2.9
6.7
3.7
1.6
1.4
1.3
7.4
7.1
5.6
4.9
4.7
3.2
2.8
1.4
1.5
1.9
1.2
1.2
1.3
1.4
1.5
1.8
2.0
2.5
3.3
3.9
5.4
9.6
1.2
1.3
67
31
35
42
102
56
45
78
78
43
50
142
61
33
29
28
151
145
115
100
95
66
58
28
30
40
25
22
27
33
39
48
54
68
83
89
117
145
26
29
0.012
0.010
0.010
0.010
0.011
0.009
0.012
0.009
0.012
0.010
0.011
0.009
0.012
0.009
0.012
0.009
0.010
0.009
0.011
0.010
0.011
0.009
0.012
0.009
0.010
0.009
0.012
0.009
0.011
0.009
0.012
0.009
0.012
0.009
0.011
0.010
0.011
0.010
0.010
0.009
REFERENCES
Anderson G. M. (1976) Error propagation by the Monte Carlo
method in geochemical calculations. Geochim. Cosmochim. Acta
40(12), 1533–1538.
Arvidson R. S. and Mackenzie F. T. (2000) Temperature dependence of mineral precipitation rates along the CaCO3–MgCO3
join. Aquat. Geochem. 6, 249–256.
Berner R. A. and Morse J. W. (1974) Dissolution kinetics of
calcium carbonate in sea water; IV, Theory of calcite dissolution. Am. J. Sci. 274(2), 108–134.
Bertram M. A., MacKenzie F. T., Bishop F. C. and Bischoff W. D.
(1991) Influence of temperature on the stability of magnesian
calcite. Am. Mineral. 76(11-12), 1889–1896.
Boyle E.A., Erez J. (2004). Does carbonate ion influence foraminiferal Mg/Ca? EOS Trans. AGU 84, OS21G-01.
Broecker W. S. and Peng T. H. (1982). Tracers in the sea. , 690pp.
Burton E. A. and Walter L. M. (1987) Relative precipitation rates
of aragonite and Mg calcite from seawater; temperature or
carbonate ion control? Geology 15(2), 111–114.
Burton E. A. and Walter L. M. (1991) The effects of PCO2 and
temperature on magnesium incorporation in calcite in seawater
and MgCl2–CaCl2 solutions. Geochim. Cosmochim. Acta 55(3),
777–785.
Chave K. E. (1954) Aspects of the biogeochemistry of magnesium:
1 calcareous marine organisms. J. Geol. 62, 266–283.
deKanel J. and Morse J. W. (1979) A simple technique for surface
area determinations. J. Phys. E. Sci. Inst. 12, 272–273.
Dickson A.G., Goyet C. (1994). Handbook of methods for the
analysis of various parameters of the carbon dioxide system in
seawater. DOE Version 2. ORNL-CDIAC-74.
Dickson J. A. D. (1995) Paleozoic Mg calcite preserved: implications for the Carboniferous ocean. Geology 23(6), 535–538.
Dickson J. A. D. (2002) Fossil echinoderms as monitor of the
Mg/Ca ratio of Phanerozoic Oceans. Science 298(5596),
1222–1224.
Dickson J. A. D. (2004) Echinoderm skeletal preservation: calcitearagonite seas and the Mg/Ca ratio of Phanerozoic Oceans. J.
Sedim. Res. 74(3), 355–365.
Dodd J. R. (1965) Environmental control of strontium and
magnesium in Mytilus. Geochim. Cosmochim. Acta 29(5), 385–
398.
Elderfield H. and Ganssen G. (2000) Past temperature and d18 O of
surface ocean waters inferred from foraminiferal Mg/Ca ratios.
Nature 405(6785), 442–445.
Gledhill D. K. and Morse J. W. (2006) Calcite dissolution kinetics
in Na–Ca–Mg–Cl brines. Geochim. Cosmochim. Acta 70(23),
5802–5813.
Gran G. (1952) Determination of the equivalence point in
potentiometric titrations. The Analyst 77, 661–671.
Temperature influence in kinetics of seawater Mg–calcite
Gross-Mesilaty S., Hargrove J. L., Ciechanover A., Rosenthal Y.,
Boyle E. A. and Slowey N. (1997) Temperature control on the
incorporation of magnesium, strontium, fluorine, and cadmium
into benthic foraminiferal shells from Little Bahama Bank:
Prospects for thermocline paleoceanography. Geochim. Cosmochim. Acta 61, 3633–3643.
Holland H. D. (1984) The chemical evolution of the atmosphere
and oceans. Princeton University Press, p. 587.
Katz A. (1973) The interaction of magnesium with calcite during
crystal growth at 25–90 "C and one atmosphere. Geochim.
Cosmochim. Acta 37(6), 1563–1578.
Kazmierczak T. F., Nancollas G. H. and Tomron M. B. (1982)
Crystal growth of calcium carbonate: a controlled composition
kinetic study. J. Phys. Chem. 86, 103–107.
Lea D. (2003). Trance elements in foraminiferal calcite. In Modern
Foraminifera, pp. 259–277.
Lees A. and Butler A. T. (1972) Modern temperate water and
warm water shelf carbonate sediments contrasted. Mar. Geol.
13, 67–73.
Lee Y. J. and Morse J. W. (1999) Calcite precipitation in synthetic
veins: implications for the time and fluid volume necessary for
vein filling. Chem. Geo. 156, 151–170.
Mackenzie F. T. and Morse J. W. (1992) Sedimentary carbonates
through Phanerozoic time. Geochim. Cosmochim. Acta 56(8),
3281–3295.
Marini L. (2007). Geological sequestration of carbon dioxide,
thermodynamics, kinetics, and reaction path modeling. In
Developments in geochemistry 11, p. 453.
Millero F. J. (1979) The thermodynamics of the carbonate system
in seawater. Geochim. Cosmochim. Acta 43(10), 1651–1661.
Millero F. J. and Scheiber D. R. (1982) Use of the ion pairing
model to estimate activity coefficients of the ionic components
of natural water. Am. J. Sci. 282, 1508–1540.
Millero F. J., Graham T. B., Huang F., Bustos-Serrano H. and
Pierrot D. (2006) Dissociation constants of carbonic acid in
seawater as a function of salinity and temperature. Mar. Chem.
100(1-2), 80–94.
Minster J.-F., Ricard L.-P. and Allegre C. J. (1979) 87Rb-87Sr
chronology of enstatite meteorites. Earth Planet Sci. Let. 44(3),
420–440.
Morse J. W. (1978) Dissolution kinetics of calcium carbonate in sea
water; VI, The near-equilibrium dissolution kinetics of calcium
carbonate-rich deep sea sediments. Am. J. Sci. 278(3), 344–353.
Morse J. W. (1983) The kinetics of calcium carbonate dissolution
and precipitation. Rev. Mineral Geochem. 11(1), 227–264.
Morse J. W. and Mackenzie F. T. (1990). Geochemistry of
Sedimentary Carbonates, Developments in Sedimentology, vol.
48. Elsevier.
Morse J. W. and Casey W. H. (1988) Ostwald processes and
mineral paragenesis in sediments. Am. J. Sci. 288(6), 537–560.
Morse J. W., Wang Q. and Tsio M. Y. (1997) Influences of
temperature and Mg:Ca ratio on CaCO3 precipitates from
seawater. Geology 25(1), 85–87.
Mucci A. (1986) Growth kinetics and composition of magnesian
calcite overgrowths precipitated from seawater: quantitative
influence of orthophosphate ions. Geochim. Cosmochim. Acta
50(10), 2255–2265.
Mucci A. (1987) Influence of temperature on the composition of
magnesian calcite overgrowths precipitated from seawater.
Geochim. Cosmochim. Acta 51(7), 1977–1984.
Mucci A., Canuel R. and Zhong S. (1989) The solubility of calcite
and aragonite in sulfate-free seawater and the seeded growth
kinetics and composition of the precipitates at 25 "C. Chem.
Geol. 74(3-4), 309–320.
347
Nancollas G. H. and Reddy M. M. (1971) The crystallisation of
calcium carbonate II. Calcite growth mechanism. J. Col. Interf.
Sci. 37, 824–830.
Nelson R. D. and Ellenberger M. R. (1972) Numerical error
propagation with computer assistance. J. Chem. Educ. 49, 678.
Nehrke G., Reichart G. J., Van Cappellen P., Meile C. and Bijma J.
(2007) Dependence of calcite growth rate and Sr partitioning on
solution stoichiometry: non-kossel crystal growth. Geochim.
Cosmochim. Acta 71(9), 2240–2249.
Opdyke B. N. and Wilkinson B. H. (1990) Paleolatitude distribution of Phanerozoic marine ooids and cements. Palaeogeogr.
Palaeoclimat. Palaeoecol. 78(1-2), 135–148.
Prasada Rao C. and Jayawardane M. P. J. (1994) Major minerals,
elemental and isotopic composition in modern temperate shelf
carbonates, Eastern Tasmania, Australia: implications for the
occurrence of extensive ancient non-tropical carbonates. Palaeogeogr. Palaeoclimatol. Palaeoecol. 107(1-2), 49–63.
Provost A. (1990) An improved diagram for isochron data. Chem.
Geol. 80, 85–99.
Robert F. and Chaussidon M. (2006) A palaeotemperature curve
for the Precambrian oceans based on silicon isotopes in cherts.
Nature 443(7114), 969–972.
Roy R. N., Roy L. N., Vogel K. M., Porter-Moore C., Pearson T.,
Good C. E., Millero F. J. and ampbell D. M. (1993) The
dissociation constants of carbonic acid in seawater at salinities
5–45 and temperatures 0–45 "C. Mar. Chem. 44(2-4), 249–267.
Tarantola A. (2004) Inverse Problem Theory and Methods for
Model Parameter Estimation. S.I.A.M., p. 342.
Toyofuku T., Kitazato H., Kawahata H., Tsuchiya M. and Nohara
M. (2000) Evaluation of Mg/Ca thermometry in foraminifera:
comparison of experimental results and measurements in
nature. Paleoceanography 15, 456–464.
Tyrrell T. and Zeebe R. E. (2004) History of carbonate ion
concentration over the last 100 million years. Geochim.
Cosmochim. Acta 68(17), 3521–3530.
Wilkinson B. H. and Algeo T. J. (1989) Sedimentary carbonate
record of calcium–magnesium cycling. Am. J. Sci. 289(10),
1158–1194.
Wasylenki L. E., Dove P. M. and De Yoreo J. J. (2005) Effects of
temperature and transport conditions on calcite growth in the
presence of Mg2+: implications for paleothermometry. Geochim. Cosmochim. Acta 69(17), 4227–4236.
Wilkinson B. H., Buczynski C. and Owen R. M. (1984) Chemical
control of carbonate phases; implications from Upper Pennsylvanian calcite–aragonite ooids of southeastern Kansas. J.
Sed. Res. 54(3), 932–947.
Zhong J. and Mucci A. (1995) Partitioning of rare-earth elements
(REE) between calcite and seawater solutions at 25"C, 1 atm
and high dissolved REE concentrations. Geochim. Cosmochim.
Acta 59, 443–453.
Zhong S. and Mucci A. (1993) Calcite precipitation in seawater
using a constant addition technique: a new overall reaction
kinetic expression. Geochim. Cosmochim. Acta 57(7), 1409–
1417.
Zuddas P., Pachana K. and Faivre D. (2003) The influence of
dissolved humic acids on the kinetics of calcite precipitation
from seawater solutions. Chem. Geol. 201(1–2), 91–101.
Zuddas P. and Mucci A. (1994) Kinetics of calcite precipitation
from seawater: I. A classical chemical kinetics description for
strong electrolyte solutions. Geochim. Cosmochim. Acta 58(20),
4353–4362.
Zuddas P. and Mucci A. (1998) Kinetics of calcite precipitation
from seawater: II. The influence of the ionic strength. Geochim.
Cosmochim. Acta 62(5), 757–766.
Associate editor: Timothy W. Lyons