ORIGINAL PAPER

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calciteaggregate at elevated temperatures and pressure

Wuu-Liang Huang & Teh-Ching Liu & Pouyan Shen &

Allen Hsu

Received: 9 March 2008 /Accepted: 12 November 2008 / Published online: 3 December 2008# Springer-Verlag 2008

Abstract This study measures the reaction rate of dolomiteand aragonite (calcite) into Mg-calcite at 800, 850, and900°C and 1.6 GPa. The dry synthetic dolomite-aragoniteaggregate transformed very rapidly into dolomite-calcitepolycrystalline aggregate while Mg-calcites formed at arelatively slow rate, becoming progressively richer in Mgwith run time. We modeled the reaction progress semi-empirically by the first-order rate law. The temperaturedependence of the overall transport rate of MgCO3 intocalcite can be described by the kinetic parameters (E=231.7 kJ/mol and Ao=22.69 h−1). Extrapolation using theArrhenius equation to the conditions during exhumation ofUHPM rocks indicates that the reaction of dolomite witharagonite into Mg-saturated calcite can be completed as theP-T path enters the Mg-calcite stability field in a geologicallyshort time period (<1 Ky). On the other hand, theextrapolation of the rate to prograde metamorphic conditionsreveals that the Mg-calcite formed from dolomitic marble in

the absence of metamorphic fluid may not reach Mg-saturation until temperatures corresponding to high-grademetamorphism (e.g., >340°C and >10 My). SEM-EDSanalysis of individual calcite grains shows compositionalgradients of Mg in the calcite grains. The Mg-Ca inter-diffusion coefficient at 850°C is around 1.68×10−14 m2/sec ifdiffusion is the major control of the reaction. The calculatedclosure temperatures for Ca-Mg inter-diffusion as a functionof cooling rate and grain size reveal that Ca/Mg resetting incalcite in a dry polycrystalline carbonate aggregate (withgrain size around 1 mm) may not occur at temperaturesbelow 480°C at a geological cooling rate around 10°C/My,unless other processes, such as short-circuit interdiffusionalong grain boundaries and dislocations, are involved.

Introduction

Carbonate rocks within the continental crust can besubducted to depths where ultrahigh-pressure metamor-phism (UHPM) prevails (Okay 1993; Wang and Liou 1993;Schertl and Okay 1994; Zhang and Liou 1996; Nishio et al.1998; Ray et al. 1999; Ogasawara et al. 2000; Imamura etal. 2002). Diamond-bearing dolomitic marble from Kumdy-Kol of the Kokchetav Massif (Sobolev and Shatsky 1990)is a prominent example of this process (Ogasawara et al.2000; Imamura et al. 2002). The marbles, which are closelyassociated with impure dolomite, contain micro-diamond,calcite, Mg-calcite, and dolomite as inclusions in garnet anddiopside and are believed to have been subjected to ultrahigh pressure metamorphism (UHPM). The mineralogicaltransformation of marbles and the compositional changes oftheir constituent minerals in response to chemical reactionsmay reflect changes in pressure and temperature duringmetamorphism.

Miner Petrol (2009) 95:327–340DOI 10.1007/s00710-008-0036-z

Editorial handling: D. Harlov

W.-L. Huang (*)Department of Geosciences, National Taiwan University,Taipei, Taiwane-mail: wlhuang@ntu.edu.tw

T.-C. LiuDepartment of Earth Sciences,National Taiwan Normal University,Taipei, Taiwan

P. ShenInstitute of Materials Science and Engineering,National Sun Yat-sen University,Kaohsiung, Taiwan

A. HsuDepartment of Geosciences, National Taiwan University,Taipei, Taiwan

Several important reactions in carbonate-bearing rockshave been recognized as associated with prograde andretrograde metamorphism. Mg-bearing carbonate rocksenter the aragonite stability field via a prograde metamor-phic P-T path to form an aragonite, Mg-calcite anddolomite assemblage (Fig. 1; Liu and Lin 1995; Zhu andOgasawara 2002; Lin and Huang 2004). With a furtherincrease in pressure, the Mg-calcite converts completelyinto aragonite and releases Mg to form dolomite. Dolomiteand aragonite may eventually convert into magnesite andaragonite at ultra-high pressures around 5–7 GPa duringprograde UHPM (Zhang et al. 2003). Conversely, thepresence of Mg-calcite inclusions in garnets from UHPMrocks has been interpreted as retrograde metamorphicproducts converted from aragonite and dolomite (Fig. 1;Ogasawara et al. 2000; Zhu and Ogasawara 2002). Sincethe rate of aragonite to calcite conversion in a displacivetransformation process is much faster than its reaction withdolomite (Liu and Yund 1993), the rate of formation of Mg-calcite may be limited by the reaction between calcite anddolomite. A quantitative interpretation of the formation andpreservation of Mg-calcite in metamorphic rocks requiresknowledge of the phase relationships and kinetics of thesolid-state reaction between aragonite/calcite and dolomiteand of the diffusion exchange and exsolution of Mg-calcite.

The phase relationships among minerals pertinent tometamorphic and UHPM rocks, which are mainly based onexperimental studies, has been previously reviewed byother workers such as Massonne (1995), Schreyer (2000),and Ernst (2000). While phase equilibria places a constraint

on mineral stability in subducted continental crust, thetransformation kinetics of minerals are crucial for estimat-ing the timing of tectonic events during metamorphism.However, kinetic information is less frequently reportedthan phase relations because of the complexity of nucleationand the growth processes involved in the transformation(e.g., Cahn 1956; Turnbull 1956; Carlson and Rosenfeld1981; Rubie and Thompson 1985; Joesten and Fisher1988; Rubie et al. 1990; Liu and Yund 1993; Hacker andPeacock 1994; Mosenfelder and Bohlen 1997; Putnis2002). In the case of carbonates, two important phaserelationships, the calcite-aragonite equilibrium curve andthe calcite-dolomite solvus, have been experimentallydetermined by previous studies, and the results arereasonably consistent (e.g., Boettcher and Wyllie 1968;Goldsmith and Heard 1961). The transformation kineticsbetween calcite and aragonite, although they have beenthoroughly experimentally and theoretically studied (e.g.,Carlson and Rosenfeld 1981; Carlson 1983a, b; Rubie andThompson 1985; McTigue and Wenk 1985; Gillet et al.1987; Snow and Yund 1987), are less applicable to naturalsystems. Recently, the rates of mineral reactions wereexperimentally measured as a function of time (t) over awide range of temperatures (T) and pressures (P) usingpolycrystalline aggregates so as to better simulatemetamorphic rocks (e.g., calcite into aragonite: Hackeret al. 1992; Lin and Huang 2004; and aragonite to calcite:Liu and Yund 1993; Huang 2003). The authors predictedthe amount of transformation along a given P-T-t path byextrapolating the experimentally determined growth rates

0

0.5

1

1.5

2

2.5

3

200 300 400 500 600 700 800 900 1000

Temperature (ºC)

Pre

ssu

re (

GP

a)

Aragonite + Dolomite

Mg-calcite

Calcite

Aragonite

Diamond

Coesite

KokchetavMassifChenpu,

Dabie

25 mol%20 %15 %10 %5 %

Sima,Dabie

Quartz

Graphite

Mg-calcite

a

baragonitcalcite

Fig. 1 Schematic diagram showing the pressure-temperature-compo-sition relations for dolomitic carbonate during retrograde metamor-phism. Arrows indicate the retrograde paths for the Sima-Dabie (Wangand Cong 2000), Chenpu-Dabie (Wang and Cong 2000), andKokchetave (Katayama et al. 2002) UHPM terrains. The dashed linesare mol % of MgCO3 Mg-calcite equilibrated at the indicated

temperatures (Goldsmith and Heard 1961). Solid lines are phaseboundaries; graphite = diamond (Kennedy and Kennedy (1976),quartz = coesite (Bohlen and Boettcher 1982), calcite = aragonite(Boettcher and Wyllie 1968), Mg-calcite = aragonite + dolomite (Linand Huang 2004)

328 W.-L. Huang et al.

of aragonite or calcite to natural conditions. Similarkinetic studies for polycrystalline samples have beenconducted for the olivine to spinel (Rubie et al. 1990;Kubo et al. 1998; Kubo 1999; Mosenfelder et al. 2000)and the coesite to quartz (Mosenfelder and Bohlen 1997)transformations.

The present study experimentally determines theoverall rates of Ca-Mg carbonate reactions in syntheticpolycrystalline marbles, in particular the reaction ofdolomite and aragonite to form Mg-calcite as theretrograde P-T path enters the stability field of calcite.Additionally, this study aims to predict when the Mgcontent in neoformed calcite in marble reaches saturationand when Mg-saturated calcite may start to re-equilibrate(via exsolution) into dolomite and Mg-calcite with lessMg along the retrograde P-T-t path during the exhuma-tion of UHPM rocks.

Furthermore, the stability and composition of Mg-calcitemay shed light on the temperature histories of metamorphiccarbonates. Mg/Ca ratios in Mg-calcite equilibrated withdolomite have been widely used as a calcite-dolomitegeothermometer to estimate the temperatures of progrademetamorphism (Essene 1982; Anovitz and Essene 1987;Cook and Bowman 1994; Letargo et al. 1995; Roselle et al.1999). This geothermometry has been generally used withcaution because of the likelihood of a lack of equilibriumbetween coexisting calcite and dolomite, which mayunderestimate the temperature of formation of the dolomiticmarble during prograde metamorphism. The estimation oftemperature is further complicated by frequently observedheterogeneities in the Mg content in measured calcite frommetamorphic rocks (Müller et al. 2004, 2006). Theexperimentally determined reaction rates of dolomite andcalcite to form Mg-calcite may allow for the constraint ofthe time and temperature below which equilibrium cannotbe reached via an interdiffusion process. An additionaluncertainty in applying calcite-dolomite geothermometry isdue to the possible re-equilibration (or exsolution) of Mg-calcite during cooling, which can reset the correspondingtemperature from peak conditions during retrograde meta-morphism (Essene 1982; Letargo et al. 1995). In order toestimate the closure temperature, below which the diffusionrate of Mg in Mg-calcite would be too slow to besignificantly reset, information regarding Ca-Mg inter-diffusion rates is needed. The previous calculation usingthe self-diffusion coefficients of Ca in calcite indicatesabnormally high closure temperatures compared to thoseestimated from natural rocks (Farver and Yund 1996; Fislerand Cygan 1999). Accurate prediction of closure temper-atures may require knowledge of the Ca-Mg inter-diffusionrate in polycrystalline marble, which may be significantlydifferent from the intracrystalline self-diffusion rates(Farver and Yund 1996).

Experimental methods

Starting materials

The starting dolomite used is a natural sample fromNavarra, Spain. The starting calcite sample is ultrapureCaCO3 powder from Alfa Chemical Co. The naturaldolomite sample was ground and sieved to less than 400mesh. EDS analysis shows a negligible amount of Fe andother trace elements in the dolomite. The dolomite/calcitemix consisted of 30 wt.% dolomite mixed with 70 wt.%ultrapure CaCO3. This mix was used as the basis of thearagonite + dolomite aggregate.

Apparatus and procedures

Experiments were performed in a single stage piston-cylinder apparatus, similar to that described by Boyd andEngland (1960), using a half-inch diameter bore. Thetemperatures were measured using chromel-alumel thermo-couples and are precise to ±5°C. They are considered to beaccurate to +10°C, taking into account the geometry of thethermocouple in relation to the thermocouple as well aspressure effects on the thermocouple. The assembly wasconstructed from NaCl and MgO parts and utilizes agraphite furnace. The dolomite + calcite mix was com-pressed into a pellet 4.0 mm high and 3.4 mm in diameterwithin a graphite capsule, and dried at 110°C for 1 h justbefore the experiments. The distance between the top of thesample and the thermocouple tip was around 0.5 mmduring the experiment. All runs were brought to a finalpressure with the “piston-out” procedure as described inBoyd et al. (1967). Pressures reported are nominalpressures and incorporate no corrections for friction.Detailed pressure corrections have been reported in Linand Huang (2004).

In the experiments, a polycrystalline aggregate consist-ing of aragonite and dolomite was synthesized in situ in thefirst stage at 2.5 GPa and 700°C for 8 h (run H154). EDSanalysis of the synthetic aragonite-dolomite aggregateindicates trace amounts of Mg-calcite with about 10 mol% of MgCO3 (Table 1). Synthesis of the aragonite-dolomiteaggregate was immediately followed by a second stage at1.6 GPa for three temperatures, 800, 850 and 900°C, whichwere intended to convert dolomite and aragonite into Mg-calcite. In the second stage, the temperature was firstincreased to the desired temperature at a rate of 50°C/min,and then the pressure was decreased manually at a rate of12.5 MPa/sec to the desired pressure.

X-ray analysis was performed using a SCIENCE MXPIII diffractometer from MAC Co., Japan. The operatingvoltage and current were 35 kV and 15 mA, respectively,with a scanning rate of 2 degrees per minute from 20–40

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite 329

(2θ). The composition of the Mg-calcite was determinedfrom the shift of the 2θ value of the d104 x-ray peak, whichrepresents the average MgCO3 content in Mg-calcite in therun products. It is believed to be accurate to within ±2 mol%. Selected experimental runs were prepared for micro-structural analysis as well as polished and analyzed fortextural studies.

Microstructural analysis and EDS analysis was per-formed using the Hitachi S-2400 Scanning ElectronMicroscope (SEM). Grain textural relationships and com-positional contrasts between the carbonate phases wereobserved using back-scattered electron (BSE) images on aLEO-1530+PHORNIX EDS field emission electron micro-scope. Semi-quantitative analyses of the Mg and Ca contentof Mg-calcite and dolomite, with errors of around ±1.5 mol.%, were performed using the SEM-EDS technique. Thedolomite synthesized at 700°C and 2.5 GPa (H154) wasused as the standard for calibrating the Mg/Ca ratio in Mg-calcite using the Ca-saturated dolomite composition

(49 mol % MgCO3 at 700°C) reported in Goldsmith andHeard (1961).

Experimental results and discussion

Transformation rate of polycrystalline dolomite + aragonite(calcite) to Mg-calcite

The displacive aragonite-to-calcite transformation under thepresent experimental conditions (Liu and Yund 1993;Huang 2003) is very rapid relative to the Ca-Mg inter-diffusion rate. The transformation may be completed in lessthan 5 min at 800, 850, and 900°C when a constantpressure of 1.6 GPa is applied. Therefore, it is reasonable toassume that a negligible amount of Mg-calcite was formedbefore the complete transformation of aragonite into calcite.As a result, the overall rate of the aragonite + dolomite toMg-calcite reaction can be approximated by the reaction

Table 1 Experimental data

Run conditions Mg-calcite MgCO3 (mol%) inMg-calcite

Dolomite Dolomite/ Mg-calcite intensityratio

Run No. Timehours

a Initialdolomitewt %

X-ray-peakIntensity of(104)

FWHMb d(104) Å Based on(104)

Based onunit cellvolume

X-ray-peakintensity of(104)

FWHMb

700 °C/2.5 GPa for 8 h (first stage)H154 8 30 5 0.26 2.9937 13.9 8.4 1,000 0.28700°C /2.5 GPa for 8 h, then 800°C /1.6 GPa for the desired timeH152 1.5 30 79 0.32 3.0214 4.2 4.6 35 0.28 0.44H128 3 30 1,000 0.32 3.0154 6.3 6.3 312 0.26 0.31H67 6 30 1,000 0.32 3.0055 9.7 9.6 175 0.28 0.18H66 12 30 1,000 0.30 2.9996 11.8 11.4 156 0.30 0.16H104 12 30 1,000 0.34 3.0035 10.4 11.0 131 0.28 0.13H63 24 30 1,000 0.30 2.9956 13.2 13.0 87 0.28 0.09H64 72 30 1,000 0.28 2.9937 13.9 13.7 60 0.28 0.06H65 133 30 1,000 0.28 2.9859 16.6 16.1 45 0.28 0.05700°C/2.5 GPa for 8 h, then 850°C/1.6 GPa for the desired timeH157 0.5 30 100 0.30 3.02 3.5 3.5 47 0.28 0.47H75 2 30 1,000 0.34 3.01 8.4 7.7 263 0.28 0.26H129 4 30 88.4 0.36 3.01 9.7 9.0 23 0.26 0.26H158 8 30 57.4 0.32 3.0055 9.7 9.2 14.6 0.26 0.25H74 12 30 1,000 0.26 2.9839 17.3 17.3 0.001 n.d. 0.00H173 12 30 100 3.0035 10.4 17.3 23 0.23H170 12 41.2 73.8 2.9820 18.0 20 0.27700°C /2.5 GPa for 8 h, then 900°C /1.6 GPa for the desired timeH171 0.3 41.2 36.4 3.0154 6.3 31 0.85H121 0.5 30 1,000 0.48 3.0055 9.7 10.9 239 0.26 0.24H127 1 30 1,000 0.34 3.0075 9.1 9.0 262 0.26 0.26H72 2 30 1,000 0.32 2.9937 13.9 13.5 54 0.26 0.05H172 4 41.2 49.3 2.9820 18.0 11.8 0.24H68 12 30 1,000 0.28 2.9839 17.3 17.4 0.001 n.d 0.00

a in starting calcite dolomite mixtureb half peak width at half peak maxima

330 W.-L. Huang et al.

rate of calcite and dolomite into Mg-calcite, which is therate limiting step in the overall reaction. Our results showthat at each temperature, the average Mg content in calciteincreases with increasing run duration, first quickly thenmore slowly as the supply of dolomite is exhausted (Fig. 2;Table 1). Residual compressive stress as the result ofaragonite-calcite transformation with accompanied volumeincrease, may facilitate composition change in the initialstage of reaction. Further study of defect microstructures,such as twinning and dislocations near the phase boundary,is required to prove this hypothesis. It should be noted thatthe data exhibit some scattering, indicating a largeexperimental uncertainty resulting from a combination ofexperimental errors from the first and second experimentalstages. Slight differences in the physical characteristicsbetween individual synthetic aggregates of dolomite andaragonite, such as variations in grain boundaries or contactareas between dolomite and calcite in different runs, mayresult in a significant difference in the overall diffusion rateof Mg into calcite. Other experimental uncertainties mayinclude the error in measuring the Mg content using XRD.The wide range of compositional variation of Mg in calcitegrains, particularly for the short duration experiments,could affect the measurement of the average d-spacing incalcite by XRD and thus hinder an accurate determinationof the average Mg-calcite composition.

Compositional variation within synthetic Mg-calcite

SEM-EDS analysis was conducted to study the micro-structures and composition of the synthetic aragonite-dolomite aggregate (in the first stage) and run products (inthe second stage). The BSE image shows that thepolycrystalline aragonite-dolomite aggregate appears as aninterlocking mosaic texture with considerable numbers ofintergranular pores. These can be attributed to volumeshrinkage associated with the calcite-aragonite transforma-

tion as well as to an incomplete sintering process. Thedolomite grain size ranges from 2–12 μm and appears assubhedral crystals. Whereas aragonite exhibits a similargrain size but is anhedral in shape (Fig. 3). EDS analysisconfirms the presence of Ca with negligible Mg in thearagonite and a nearly equimolar Mg/Ca ratio in thedolomite.

After reaction at 850°C at different run times (Table 1),the run products were analyzed. The run at 850°C/1.6 GPaand 0.5 h (H157) shows the presence of three differenttypes of carbonate grains (Fig. 3b) with significant differ-ences in grey level and corresponding Mg content. Thedark grey grains have a composition (47 mol % MgCO3)close to that of equilibrated dolomite (48.7 mol % MgCO3)at this run temperature (Goldsmith and Heard 1961),whereas for the same run, the Mg contents of the lightestgrey grains range from 1–8.4%, consistent with the averageMg-contents (3.5 mol % MgCO3) as determined by X-raydiffraction. The average composition indicates that the Mg-content in calcite from the 0.5 h run is far from the

0

5

10

15

20

25

0 20 40 60 80 100

Time (Hours)

Mo

l. %

Mg

CO

3

900oC

850oC800oC

Fig. 2 Experimental data showing the mol % of MgCO3 in Mg-calcite solid solutions as a function of run duration during aragonite +dolomite to Mg-calcite. Symbols: triangles = 900°C; solid squares =850°C, and circles = 800°C

Fig. 3 SEM images showing the backscattered electron images of runproducts. a synthetic aragonite + dolomite polycrystalline aggregate(Run H154), darker grains are dolomite. b Mg-calcite + dolomiteaggregate reacted from the synthetic polycrystalline aggregate at 850°C/1.6 GPa for 0.5 h (Run H157)

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite 331

calculated value (15.8 mol %) if the starting dolomite werecompletely incorporated into the calcite. The data also showthat the Mg contents of individual Mg-calcite grainsdecrease with distance from the Mg-calcite/dolomiteboundary (Fig. 4a and b). This implies that equilibrium,due to diffusion, has not been attained under the experi-mental conditions. Subsequently, this compositional profilewas then used to calculate effective diffusion coefficients.

The third type of carbonate grain, which was not commonlyfound, has a grey level similar to dolomite but exhibits asignificantly lower Mg-content (30–43 mol %; points 1 and5 in Fig. 4a; Table 2). This composition falls in themiscibility gap beneath the solvus of the calcite-dolomitesolid solution (Goldsmith and Heard 1961). No evidencewas found to show whether this third type of grain is asingle phase with the observed Mg/Ca ratio or a mixture of

01020

304050

-2 0 2

Distance (µm)

MgC

O3

(mol

e%)

1

23

5

010

20

3040

50

-2 0 6 10 12

Distance (µm)M

gCO

3 (m

ole%

)

1

2 3 4 5 6

0

20

40

60

-2 0 2 4 6 8 10 12 14

Distance (µm)

MgC

O3

(mol

e%)

1

2 3 4 5 6 7

0

20

40

60

-2 0 6 10 12

Distance (µm)

MgC

O3

(mol

e%)

1

23 4 5

0

10

20

pt.1 pt.2 pt.3 pt.4 pt.5 pt.6 pt.7 pt.8

MgC

O3

(mol

e%) 1 2

3 4

587

6

4

4 6 8

2 4 8

2 4 8

Fig. 4 SEM images showingthe backscattered electron im-age and the compositional vari-ation profile with errors ofaround ±1.5 mol. %. The dis-tances of the analytical pointswere measured from the dolo-mite/calcite boundary (dashedline) (for data see Table 2). aMg-calcite + dolomite aggregateat 850°C/1.6 GPa for 0.5 h (RunH157). Points 1 and 5 denotedolomite-like grains with Mgsignificantly less than dolomiteand others denote Mg-calcitegrains. b Same as (A) but ondifferent grains (H157-1). csimilar condition as (A) but with8 h (Run H158). Point 1 is on adolomite grain. d same as (C)but on different grains. e similarconditions as (A) but with 12 hrun time (Run H74). Data from(A), (B), (C) and (D) were usedto calculate diffusioncoefficients at 850°C

332 W.-L. Huang et al.

dolomite and Mg-calcite on the sub-micron scale, which isbeyond the resolution of EDS analysis.

For longer runs (8 h; H158; Table 1) with an average of9 mol % of MgCO3 in Mg-calcite as determined by XRD,the compositional gradient in Mg-calcite is still present inthe product (Fig. 4c and d; Table 2). In this run, the thirdtype of Mg-calcite grain is rarely found. The graincompositions are consistent with the interpretation of theoverall reaction, which shows that equilibrium has not beenreached due to the short run time. The observed composi-tional gradients for these two runs are used to calculate theinter-diffusion coefficient in a later section. Compositionalvariations within or among the grains become lesspronounced as one of the reactants (dolomite) is nearlydepleted over the long run (12 h; H74, Fig. 4e; Table 2).The MgCO3 content determined by EDS is consistent withthe average composition (17.3±2%) measured using XRD,which is close to the calculated value (15.8%) if the startingdolomite is incorporated completely into the calcite. Thisindicates that the Mg-calcite is undersaturated relative tothe saturation content (21.6 mol %) of MgCO3 in calcite at850°C/1.6 GPa (Goldsmith and Newton 1969).

Kinetic modeling

Experimental data from this study is modeled using thekinetic model of nucleation and growth originally devel-oped by Avrami (1939) and later modified by Cahn (1956).This model has been applied to experimentally measuredkinetic data for several polycrystalline, and polymorphictransformations (Rubie et al. 1990; Hacker et al. 1992; Liuand Yund 1993; Mosenfelder and Bohlen 1997). However,lack of experimental data regarding Mg transport, which isnecessary for the nucleation and growth of Mg-calcite,

impedes detailed kinetic modeling using the nucleation andgrowth mechanism. Instead, we have attempted to fit theoverall rate using the simple empirical kinetic approach offirst-order kinetics for the reaction dolomite + calcite = Mg-calcite. In addition, analytical data from the compositionalgradient profile of Mg in single calcite grains have beenused to estimate the volume diffusion coefficient of Mg incalcite by assuming that the reaction is diffusion controlled.

Semi-empirical modeling

In order to model the rate of incorporation of the MgCO3

component into calcite using first order-reaction dissolutionkinetics, we assumed that both forward and reversereactions occur at fast enough rates that equilibrium orsteady state may be achieved (Lasaga 1998).

The first-order kinetic dissolution equation can bewritten as:

dCt=dt ¼ k Cs � Ctð Þ; ð1Þwhere Cs is the steady-state concentration of MgCO3 inMg-calcite, Ct is the concentration of MgCO3 in Mg-calciteat time (t), and k is the rate constant. Integrating equation(2) gives:

ln Cs � Ctð Þ= Cs � Coð Þ½ � ¼ kt; ð2Þwhere Co is the initial concentration of MgCO3 in calcite.Here, k can be obtained from the slope of linear equation(2) by plotting ln [(Cs−Ct)/(Cs−Co)] vs. t (Fig. 5). The Cs

used in equation (2) is 15.8 mol %, which is theconcentration of MgCO3 in solid solution if both the calciteand the dolomite in the starting mixture react completely.Regression of the experimental data (Table 1; Fig. 2) foreach temperature reveals that the data from runs with up toroughly 60–80% transformation can be fit nicely to the

Table 2 Mg contents as a function of distance showing the compositional gradient within carbonate grains

Sample Pt1ab Pt2 Pt3 Pt4 Pt5 Pt6 Pt7 Pt8

H157 Distancea μm −1.6 1.1 4.7 6.7 −1.5MgCO3 mol.% 43.2 10.9 2.4 4.4 36.2

H157-2 Distance μm −1.1 1.1 3.4 6.0 9.0 11.8MgCO3 mol.% 39.1 6.9 2.9 1.6 0.9 1.2

H158-1 Distance μm −0.6 1.4 2.7 5.3 7.4 9.6 12.6MgCO3 mol.% 51.6 19.7 16.1 12.3 5.2 5.9 4.9

H158-2 Distance μm −0.9 1.3 3.9 7.1 10.7MgCO3 mol.% 49 14.9 10.4 9.8 7.8

H74 Distance μm - - - - - - - -MgCO3 mol.% 14.9 15.5 12.0 12.0 16.5 16.4 15.2 15.0

H157 and H-157-2 were measured from different grains in the run products at 850°C and 1.6 GPa for 0.5 h whereas H-158-1 and 158-2 were atsame condition but with longer run duration (8 h)a Distance measured from grain boundary shown in Fig. 4. The negative distance indicates opposite direction of the boundary(dashed line in Fig. 4)ab Point numbers indicate positions on the SEM images (Fig. 4)

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite 333

model (linear in Fig. 5), whereas those from longer durationruns deviate significantly from the linear relationship. Thissuggests that reaction rates over long durations aresignificantly slower compared to the predicted values fromthe rate model, since the reactant (dolomite) is significantlyconsumed in the later stages of the reaction, probably dueto a significant decrease in the surface area of the contactbetween the dolomite and calcite. Eventually, the reactionceases as the dolomite is exhausted. As an approximation,the modeling in this study excludes the long duration runs.The rate constant and kinetic parameters derived from themodeling are therefore only applicable to the early andmedium stages of the reaction and inappropriate for the latestage when dolomite is nearly consumed. An apparentactivation energy (231.7 kJ/mol) and frequency factor(22.69 h−1) were determined from the rate constant k forthe three temperatures (800, 850, and 900°C) using theArrhenius equation.

Volume diffusion of Mg in calcite

The compositional profile of Mg-calcite grains as a functionof distance from the calcite/dolomite boundary can be usedto calculate the volume diffusion coefficient of a Mg atomthrough the calcite lattice using the solution of the diffusionequation for transport (Crank 1975; Farver and Yund 1996;Lasaga 1998). For approximation, we assumed a profilenormal to the surface of a semi-infinite volume. Theequation can be written as:

Cx;t � Cs

� ��Co � Csð Þ ¼ erf zð Þ; where z ¼ x

.2 Dtð Þ1=2h i

;

ð3Þwhere erf(z) represents the error function, Cx,t is theconcentration at some distance x for an annealing time t,Co is the initial Mg concentration in calcite (equal to zero inthis case), Cs is the concentration at the interface betweendolomite and calcite (in this case, Cs is assumed varying

with time), and D is the volume diffusion coefficient. Theinverse error function, therefore, is:

erf�1 Cx;t � Cs

� ��Co � Csð Þ� � ¼ x

.2 Dtð Þ1=2h i

: ð4Þ

The diffusion coefficient D can be computed from theslope (1/2(Dt)1/2) (Table 3) of the linear regression of theinverse error function of a concentration term vs. distanceusing the measured data from Cx,t (Farver and Yund 1996;Liermann and Ganguly 2002). In addition to experimentalerrors, sources of uncertainty in D from the diffusion modelinclude the assumptions of a fixed interface and Mg sourcefor diffusion (i.e., surface concentration of Mg on thecalcite/dolomite boundary). The reaction dolomite + calcite= Mg-calcite first occurs at the boundary between thedolomite and calcite. It is probable that after a thin layer ofMg-calcite forms, the reaction rate quickly decreases andeven ceases when the amount of Mg in the calcite layerapproaches saturation, because the thin layer may act as aprotecting layer unless there is another transport mediumsuch as a fluid or partial melt (cf. Putnis 2002). Furtherenrichment of Mg within the calcite grain may proceed viainter-diffusion of Ca-Mg from the interface into the calcitevolume. This may lower the Mg concentration of the Mg-calcite layer below the saturation level, which is the drivingforce to continue the reaction between dolomite and Mg-calcite at the grain boundary. The thin Mg-calcite layer, incontact with the dolomite, may remain near Mg saturationif the rate of the dolomite-calcite reaction is faster than thediffusion of Mg into calcite, but may be under saturation ifthe opposite is true. As the reaction proceeds, the positionof the interface may move towards the center of thedolomite grain as dolomite is consumed. This maycomplicate the modeling of the diffusion process and thuscreate additional uncertainty in the calculated D.

As an approximation, we attempted to model the datausing a simple diffusion model by assuming a fixedinterface. The Mg concentration on the surface of thecalcite may vary significantly along the dolomite-calciteboundary and are difficult, if not impossible, to determineby SEM-EDX analysis because of the obliqueness of thecontact due to irregular grain boundaries. We have tried topredict the interface concentration projected from the datawithin the calcite grain using a linear regression betweenthe Mg % and the logarithm of the distance for extrapola-tion. However, preliminary results, using the extrapolationof compositional profiles to zero distance (i.e., on thesurface), show that the surface concentrations are in therange of 7–23 mol % (Table 3) which are generally lowerthan the saturation of Mg in Mg-calcite (21.6 mol %). Byassuming a fixed interface and varied surface concentrationon calcite, we obtained inverse error functions for the datafrom runs at 850°C/0.5 h and 850°C/8 h using equation (4)

-1

-0.8

-0.6

-0.4

-0.2

0

0 8 10 12 14

Time (hours)

ln[(

Cs-

Ct)

/Cs-

Co

)]

900oC

850oC

800oC

2 4 6

Fig. 5 Modeling of experimental data using first-order kinetics (seetext for model details)

334 W.-L. Huang et al.

(cf. Fig. 6). We observed linearity in the data, predictedfrom the diffusion model, for each single grain from the 8 hruns (Fig. 6b) but non-linearity for the 0.5 h runs (Fig. 6a).The deviation of the compositional gradient, from thatpredicted by the diffusion model (Fig. 6a) and the scatteringof the data around the predicted lines, may be attributed to

additional complexity contributed by the polycrystallineaggregate and its irregular grain geometries. The composi-tional profile for specific directions in each individual graincan be influenced by different initial compositions on thegrain surface in different directions. Therefore, the uncer-tainty in the apparent diffusion coefficients determinedfrom different grains in the same run product may beattributed to variations in the grain geometry and the effectof grain boundary diffusion (Florence and Spear 1995).

It is interesting to note that the apparent diffusioncoefficients at the same temperature appear to decreasewith increasing run time (Figs. 6; Table 3). This discrep-ancy may be attributed to the incorrect assumptions that thedolomite and Mg-calcite interface is fixed and thatnegligible Mg-calcite forms during the aragonite-calcitetransformation before diffusion starts. The calculatedeffective diffusion coefficients (D) from different grainsranges from 3.3×10−15 to 4.8×10−14, with an average ofaround 1.68×10−14 m2/sec at 850°C and 1.6 GPa (Table 3).Alternatively, by assuming that the Mg concentration at thecalcite-dolomite interface maintains a level close to satura-tion with Mg-calcite and is invariable with time, thediffusion coefficients (D) ranges from 3.3×10−15 to 3.5×10−14 with an average of around 3.16×10−14 m2/sec at 850°C and 1.6 GPa, which does not differ significantly from theprevious calculation (Table 3).

The diffusion of Mg ions in calcite, in the presence of achemical gradient, is considered as “chemical diffusion” incontrast to “self-diffusion,” which occurs without a chem-ical gradient (Kent et al. 2001). Since the diffusion of Mginto calcite requires simultaneous diffusion of Ca ions outof calcite, the coefficient, although measured based on Mgin the present study, may actually represent Ca-Mg inter-diffusion in calcite. The measured chemical inter-diffusioncoefficient of Ca-Mg in calcite at 850°C and 1.6 GPa isabout two to three orders of magnitude faster than that(3.4×10−17 m2/sec) at the same temperature extrapolatedfrom the lower temperature data for self-diffusion reported

0

0.3

0.6

0.9

1.2

1.5

0 8 10 12Distance (µm)

erf

-1 [

(Cx,

t –

Cs)

/(C

o –

Cs)

]

H157 H157-2

0

0.3

0.6

0.9

1.2

1.5

0 2 4 6 8 10 12 14Distance (µm)

erf

-1 [

(Cx,

t –

Cs)

/(C

o –

Cs)

]

H158-1

H158-2

2 4 6

a

b

Fig. 6 Compositional gradient of Mg-calcite fitted to the inverse errorfunction for MgCO3 concentration with distance into the grain fromthe surface of the Mg-calcite grains. a Two grains, H157 and H157-2from run H157 at 850°C/0.5 h and b two grains, H158-1 and H158-2from run H158 at 850°C/8 h

Table 3 Diffusion coefficients calculated using inverse error function

Sample I. Assume variable Cs with time II. Assume invariable Cs with time

Cs (mol % MgCO3) D (m2/sec.) Log D Cs (mol % MgCO3) D (m2/sec.) Log D

H157 11.4 2.01×10−14 −13.7 21.6 6.85×10−14 −13.2H157-2 7.9 3.52×10−14 −13.5 21.6 4.82×10−14 −13.3H158-1 22.8 3.32×10−15 −14.5 21.6 3.30×10−15 −14.5H158-2 15.4 8.60×10−15 −14.1 21.6 6.37×10−15 −14.2

Average 1.68×10−14 −13.8 Average 3.16×10−14 −13.5

Cs is the Mg concentration on interface of calcite-dolomite, and D is the Ca-Mg inter-diffusion coefficient. 1/[2(Dt)1/2 ] is the slope of lines fittedto the inverse error function (see Fig. 6 and text). Two Scenarios were calculated: I. the Cs is variable with time and was calculated byextrapolation of compositional profile, II. Cs is invariable with time and is the saturated Mg in calcite at the temperature

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite 335

by Fisler and Cygan (1999). The presence of a chemicalgradient during inter-diffusion in the current experiments,in contrast to the absence of a chemical gradient for self-diffusion, may contribute to this large discrepancy (Farverand Yund 1996; Fisler and Cygan 1999). This discrepancymay also be attributed to the effects of pressure, which werenot evaluated in this study because of insufficient data.Other uncertainties, due to differences in experimentalconfiguration, may also contribute. These include the useof polycrystals with irregular grain contacts, in contrast tothe single regular grain contacts in previous studies, andpossible short-circuit interdiffusion along grain boundariesand dislocations.

The Ca-Mg inter-diffusion coefficients (1.18×10−24,6.69×10−23, 2.24×10−21, 4.9×10−20 m2/sec) at 400, 450,500 and 550°C, respectively, obtained from extrapolatingour measured D at 850°C using the average activationenergy (326.5 kJ/mol) of Fisler and Cygan (1999) andFarver and Yund (1996) are roughly consistent, withinexperimental uncertainty, with the Ca-Mg inter-diffusioncoefficients (1.78×10−22, 3.09×10−22, 9.77×10−22, 1.20×10−21 m2/sec) determined at the same temperatures by Kentet al. (2001). Since Ca-Mg inter-diffusion may be limitedby the slow diffusion rate of Ca, which has a larger ionicsize than Mg (Fisler and Cygan 1999), the Ca-Mg inter-diffusion coefficients in calcite may be represented by theself-diffusion coefficients for Ca in calcite, if the effect ofthe chemical gradient is negligible. However, the Ca-Mginter-diffusion coefficient (1.68×10−14 m2/sec) at 850°C isabout four orders of magnitude higher than the self-diffusion coefficients for Ca (6×10−19 and 1.24×10−18

m2/sec), extrapolated from data below 800°C by Farver andYund (1996) and Fisler and Cygan (1999), respectively.This suggests that chemical gradient plays an important rolein accelerating cation diffusion. In order to more accuratelydetermine the Ca-Mg inter-diffusion coefficients in calciteand their associated activation energies, future experimentsare required with configurations similar to those of Kent etal. (2001) or Liermann and Ganguly (2002). Nevertheless,the use of polycrystalline aggregates in the current experi-ments, although complicated and leading to a largeruncertainty, may better simulate actual geological condi-tions as opposed to simple diffusion experiments.

Petrological implications

Calcite/dolomite geothermometry

The Mg content in calcite has been used for geothermom-etry, via the partitioning of Mg between coexisting calciteand dolomite as a function of temperature along the calcite-dolomite solvus (Anovitz and Essene 1987). The accuracy

of calcite/dolomite thermometry depends strongly onwhether coexisting Mg-calcite and dolomite reach equilib-rium during prograde metamorphism. Experimentally mea-sured kinetic information may provide some clues toevaluate the extent of equilibrium using empirical ratesthat describe the incorporation of Mg into Mg-calciteduring prograde metamorphism. The extrapolation of theseexperimental rates to geological conditions (Fig. 7) revealsthat, on a geological time scale (1–10 My), the temperaturesrequired to attain the saturation of Mg in calcite range from340–380°C. These temperatures would have to be higher innature since the grain size of natural marble (about 0.1–5 mm) is much larger than that (about 0.01 mm) used in theexperiments. These results suggest that the equilibration ofMg-calcite in the absence of a metamorphic fluid can beattained under the high temperatures found only during high-grade metamorphism. Equilibrium temperatures, however,will probably be lower in the presence of fluids such as wateror NaCl/KCl/CaCl2 brines, during which Mg-calcite couldform through the process of dissolution-reprecipitation(Buick and Cartwright 1996; Buick et al. 1997; Farver andYund 1996; Putnis 2002).

On the other hand, temperature estimation may becomplicated by the re-equilibration of Mg-calcite throughCa-Mg exchange or diffusion during retrograde metamor-phism. For proper application of the geothermometer, it isimportant to perform the necessary temperature correctionby reintegrating dolomite exsolution lamellae back into thecalcite host (Letargo et al. 1995). Alternatively, the closuretemperature (Tc), below which the extent of Ca-Mg inter-diffusion in the calcite solid solution is negligible, can becalculated based on the diffusion model to evaluate thevalidity of calcite/dolomite thermometry (Essene 1982).

5

7

9

11

13

15

1 1.2 1.4 1.6 1.8

1000/T ºK

log

t (

sec)

10 My

10 y

1 Ky

0.1 My

300 º400 ºC500 ºC600 ºC

Mg-Saturation

Half-saturation

3/4 - saturation

Fig. 7 Temperature-time exposure required to react calcite withdolomite to form Mg-calcite in a polycrystalline aggregate with agrain size similar to that in the experiments (around 10 µm). Differentextents of Mg saturation in calcite solid solution were calculated usingexperimentally determined kinetic parameters

336 W.-L. Huang et al.

Dodson (1973) has developed a diffusion model tocalculate Tc during cooling of geological and petrologicalsystems using kinetic parameters, an activation energy (Ea),and diffusion coefficients at an infinite temperature (Do),for a specific geological cooling rate and grain parameter(a) (eqn (23) in Dodson 1973). The measured effectivediffusion coefficient at 850°C and 1.6 GPa in this study canbe used to tentatively estimate Tc. For the first approxima-tion, the activation energy of the inter-diffusion of Ca-Mg wasassumed to be close to 326.5 kJ/mole, which is the mean of thetwo Ca self-diffusion activation energies (382 and 271 kJ/mole) measured by Farver and Yund (1996) and Fisler andCygan (1999), respectively. A sphere grain geometry (A=55), with an effective diffusion radius (a=1/2 d), wasassumed (Dodson 1973). The calculated Tc shows thatresetting of the thermometer by diffusion exchange mayeffectively cease below temperatures of 350–650°C, depend-ing on the cooling rates (1–1,000°C /My) and graindiameters (0.01–10 mm) (Fig. 8). The closure temperaturesare most likely around 480°C in marbles with 1 mmdiameter grain sizes at a geological cooling rate of 10°C/My.

The closure temperatures inferred from natural observa-tions vary significantly. Essene (1982) noted that theestimated temperatures for high-grade marbles, based oncalcite-dolomite geothermometry, are mostly around 300–400°C, rarely higher than 600°C, with closure temperatureslikely around 500°C (Essene 1983; Bestmann et al. 2000).The abnormally low reset temperatures (e.g., <400°C)observed in nature may be attributed to the presence ofmetamorphic fluids (Letargo et al. 1995; Farver and Yund1996; Buick et al. 1997; Putnis 2002) or dynamic recrystal-lization (Matthews et al. 1999; Bestmann et al. 2000).Rathmell et al. (1999) reported temperatures of 530–540°Cestimated using calcite-dolomite geothermometry for high-

grade graphitic marbles in the Grenville Orogen in southernOntario, Canada. Compared with those from garnet-biotiteand calcite-graphite thermometry, the temperatures werefound to have been reset by approximately 50–100°C. Letargoet al. (1995) reported higher metamorphic temperatures(475–600°C) based on the composition of calcite coexistingwith dolomite in 63 marbles from the Llano uplift of centralTexas. The good agreement between calcite-dolomite tem-peratures and those inferred from silicate-carbonate equilibriain the marbles indicates that the temperatures generallyreflect peak metamorphic conditions (Letargo et al. 1995).However, the closure temperatures for these marbles may belower than the peak temperatures since some exsolutiontextures have been observed. Subsequently, the Mg-calcitecomposition and reported calcite-dolomite temperatures werecorrected for these marbles.

Application of calcite-dolomite geothermometry to sili-ceous carbonates, associated with contact metamorphism,yields temperatures of 410–575°C for metamorphic aur-eoles surrounding the Alta stock (Cook and Bowman1994), suggesting that closure temperatures may be closeto or higher than this temperature range. For the UbehebePeak contact aureole in California, calcite-dolomite ther-mometry yields temperatures of 410–440°C in the tremolitezone, 475–610°C in the forsterite zone, and as high as 620–665°C at the periclase-in isograd (Rosselle et al. 1999).Similarly, a petrological profile radial to the pluton in theAllt Guibhsachain area of the Ballachulish aureole exhibitsabnormally high calcite-dolomite temperatures (650–750°C)(Ferry 1996). The preservation of high Mg contents andcorresponding high calcite-dolomite temperatures in contactmetamorphic rocks suggests unusually high closure temper-atures, probably due to very high cooling rates and muchcoarser grains (Fig. 8). In addition, the presence ofhydrodynamic systems in contact aureoles may causereaction overstepping and incomplete consumption ofreactants (Nabelek 2007). Estimates of closure temperaturesbased on calcite-dolomite geothermometry in siliceouscarbonates associated with contact metamorphism shouldtherefore be approached with caution.

A comparison of our experimentally determined closuretemperatures of 350–650°C with those estimated frommetamorphic terrains shows reasonable consistency, butour temperatures are considerably lower than those (600–800°C and 350–750°C) calculated using the self-diffusioncoefficient of Ca in calcite by Farver and Yund (1996) andFisler and Cygan (1999), respectively.

Formation rate of Mg-calcite during retrogrademetamorphism of UHPM rocks

The experimentally determined reaction rates andcorresponding kinetic parameters can be used to estimate

300

350

400

450

500

550

600

650

Log (dT/dt)

Clo

sure

Tem

p.(

ºC

)

1 100010010

d = 0.1 mm

d = 10 mm

d = 1 mm

d = 0.01 mm

0 321

Cooling Rate ( ºC/my)

Fig. 8 Closure temperatures for Ca-Mg inter-diffusion in Mg-calciteover a range of cooling rates (dT/dt) and diameters (d) of sphericalgrains calculated using Eq. 23 of Dodson (1973). See text for details

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite 337

the temperature and time at which a specific composition ofMg-calcite is formed when the dolomite- and aragonite-bearing rock enters the stability field of calcite (Fig. 1)during retrograde metamorphism. For instance, Fig. 7shows the time required to raise Mg-contents in calcitewith different degrees of saturation (one-half, three-quartersand full) as a function of temperature. According to thepreviously reported P-T paths for the exhumation of mostUHP rocks (e.g., Carswell and Zhang 2000; Wang andCong 2000), the extrapolation of experimental results totemperatures where the interpreted P-T path entered thecalcite stability field (around 500–900°C) during exhuma-tion (Fig. 1) indicates that the formation of saturated Mg-calcite can be completed in a geologically short time period(<1 Ky). In the case of UHP rock from the KokchetavMassif, the complete saturation of calcite with Mg in thepresence of dolomite can occur within a period of years attemperatures of around 900°C, according to the interpretedP-T path of Ogasawara et al. (2000). The observedcompositional variations of Mg-calcite in UHP rocks afterexhumation (Ogasawara et al. 2000) are, therefore, morelikely due to variations in the Mg content in the originalrocks or in included minerals than to an incomplete solidsolution between Mg-calcite and calcite in contact withdolomite. However, extrapolation of the measured rates totemperatures, pressures and grain sizes beyond the exper-imental conditions in this study should be approached withcaution due to a lack of understanding regarding reactionmechanisms, which involve {hkl}-specific interfaces, Kir-kendall pores, capillary effects and/or defect microstruc-tures due to retrograde zoning.

Acknowledgments The back-scattered electron (BSE) images wereacquired using the field emission electron microscope of the Instituteof Material Sciences at National Taiwan University. The authorsacknowledge Drs. Ralf Milke, Frei Universität, Berlin, Germany andThomas Müller, Ruhr-Universität Bochum, Germany for their criticaland thorough reviews which resulted in improvement of themanuscript. The careful and thorough editorial handling of the paperby Dr. Daniel Harlov is also acknowledged. The research wassupported by the Earth Sciences Section, National Science Councilof ROC (Wuu-Liang Huang and Teh-Ching Liu).

References

Anovitz LM, Essene EJ (1987) Phase equilibria in the system CaCO3-MgCO3-FeCO3. J Petrol 28:389–414

Avrami M (1939) Kinetics of phase change. I: general theory. J ChemPhys 7:1103–1112

Bestmann M, Kunze K, Matthews A (2000) Evolution of a calcitemarble shear zone complex on Thassos Island, Greece: micro-structural and textural fabrics and their kinematic significance. JStruct Geol 22:1789–1807

Boettcher AL, Wyllie PJ (1968) Jadeite stability measured in thepresence of silicate liquids in the system NaAlSiO4-SiO2-H2O.Geochim Cosmochim Acta 32:999–1012

Bohlen SR, Boettcher AL (1982) The quartz ⇆ coesite transformation:a precise determination and the effects of other components. JGeophys Res 87:7073–7078

Boyd FR, England JL (1960) The quartz-coesite transition. J GeophysRes 65:749–756

Boyd FR, Bell PM, England JL, Gilbert MC (1967) Pressuremeasurements in single-stage apparatus. Year Book CarnegieInst. Washington 65:410–414

Buick IS, Cartwright I (1996) Fluid/rock interaction during low-pressure polymetamorphism of the Reynolds Range Group,central Australia. J Petrol 37:1097–1124

Buick IS, Cartwright I, Williams IS (1997) High-temperatureretrogression of granulite-facies marbles from the ReynoldsRange Group, central Australia; phase equilibria, isotopicresetting and fluid fluxes. J Petrol 38:877–910

Cahn JW (1956) The kinetics of grain boundary nucleated reactions.Acta Metallurgica 4:449–459

Carlson WD (1983a) The polymorphs of CaCO3 and the aragonite-calcite transformation. In: Reeder RJ (ed) Carbonates: mineral-ogy and chemistry. Mineral Soc of Am, Washington DC, pp 191–225

Carlson WD (1983b) Aragonite-calcite nucleation kinetics: anapplication and extension of Avrami transformation theory. JGeol 91:57–71

Carlson WD, Rosenfeld JL (1981) Optical determination of topotacticaragonite growth kinetics: metamorphic implications. J Geol89:615–638

Carswell DA, Zhang RY (2000) Petrographic characteristics andmetamorphic evolution of ultrahigh-pressure eclogites in plate-collision belts. In: Ernst WG, Liou JG (eds) Ultra-high pressuremetamorphism and geodynamics in collision-type orogenic belts.Bellwether, Columbia, pp 39–56

Cook SJ, Bowman JR (1994) Contact-metamorphism surrounding theAlta stock: thermal constrains and evidence of advective heat-transport from calcite + dolomite geothermometry. Am Mineral79:513–525

Crank J (1975) The Mathematics of diffusion, 2nd edn. Oxford Univ.Press, London

Dodson MH (1973) Closure temperature in cooling geochronologicaland petrological systems. Contrib Mineral Petrol 40:259–274

Ernst WG (2000) H2O and ultrahigh-pressure subsolidus phase relationsfor mafic and ultramafic systems. In: Ernst WG, Liou JG (eds)Ultrahigh-pressure metamorphism and geodynamics in collision-type orogenic belts: final report of the task group III-6 of theinternational lithosphere project. Bellwether, Columbia, pp 121–129

Essene EJ (1982) Geologic thermometry and barometry. In: Ferry JM(ed) Characterization of metamorphism through mineral equilibria.Mineralogical Society of AmericaWashington DCpp 153–206

Essene EJ (1983) Solid solution and solvi among metamorphiccarbonates with application to geologic thermometry. In: ReederRJ (ed) Carbonates: mineralogy and chemistry. Mineral Soc ofAm, Washington DC, pp 77–96

Farver JR, Yund RA (1996) Volume and grain boundary diffusion ofcalcium in natural and hot-presses calcite aggregates. ContribMineral Petrol 123:77–91

Ferry JM (1996) 3 novel isograds in metamorphosed siliceousdolomites from the Ballachulish aureole, Scotland. Am Mineral81:485–494

Fisler DK, Cygan RT (1999) Diffusion of Ca and Mg in calcite. AmMineral 84:1392–1399

Florence FP, Spear FS (1995) Intergranular diffusion kinetics of Feand Mg during retrograde metamorphism of a pelitic gneiss fromthe Adirondack Mountains. Earth Planet Sc Lett 134:329–340

Gillet P, Gerard Y, Willaime C (1987) The calcite-aragonite transition:mechanism and microstructures induced by the transformationstress and strain. Bulletin de Mineralogie 110:481–496

338 W.-L. Huang et al.

Goldsmith JR, Heard HC (1961) Subsolidus phase relations in thesystem CaCO3-MgCO3. J Geol 69:45–74

Goldsmith JR, Newton RC (1969) P-T-X relations in the systemCaCO3-MgCO3 at high temperatures and pressures. Am J Sci267-A:160–190

Hacker BR, Kirby SH, Bohlen SR (1992) Time and metamorphicpetrology calcite to aragonite experiments. Science 258:110–113

Hacker BR, Peacock SM (1994) Creation, preservation, and exhuma-tion of ultrahigh pressure metamorphic rocks. In: Coleman RG,& Wang X (Eds) Ultrahigh Pressure Metamorphism: CambridgeUniversity Press, pp 159–181

Huang WL (2003) Synthetic polycrystalline aragonite to calcitetransformation kinetics: experiments at pressures close toequilibrium boundary. Mineral Petrol 79:243–258

Imamura K, Yoshioka N, Ogasawara Y (2002) Morphology anddistribution of microdiamonds in dolomite marble from Kumdy-Kol. In: Parkinson CD, Katayama I, Liou JG, Maruyama S (eds)The diamond-bearing Kokchetav Massif, Kazakhstan. UniversalAcademy Press, Tokyo, pp 93–102

Joesten R, Fisher G (1988) Kinetics of diffusion-controlled mineralgrowth in the Christmas Mountains (Texas) contact aureole. GeolSoc Am Bull 100:714–732

Katayama I, Maruyama S, Parkinson CD, Terada K, Sano Y (2002)Pressure-temperature-time path of the Kokchetav UHP metamor-phism deduced from mineral inclusions and SHRIMP geochro-nology of zircons. In: Parkinson CD, Katayama I, Liou JG,Maruyama S (eds) The diamond-bearing Kokchetav Massif,Kazakhstan. Universal Academy Press, Tokyo, pp 381–395

Kennedy CS, Kennedy GC (1976) The equilibrium boundary betweengraphite and diamond. J Geophys Res 81:2467–2470

Kent AJR, Hutcheon ID, Ryerson FJ, Phinney DL (2001) Thetemperature of formation of carbonate in Martian meteoriteALH84001: constraints from cation diffusion. Geochim Cosmo-chim Acta 65:311–321

Kubo T (1999) Transformation kinetics in the earth’s interior. RevHigh Press Sci Technol 9:26–33

Kubo T, Ohtani E, Kato T, Morishima H, Yamazaki D, Suzuki A,Mibe K, Kikegawa T, Shimomura O (1998) An in situ X-raydiffraction study of the—transformation kinetics of Mg2SiO4.Geophys Res Lett 25:695–698

Lasaga AC (1998) Kinetic Theory in the Earth Sciences. PrincetonUniversity Press, Princeton, NJ

Letargo CMR, Lamb WM, Park J-S (1995) Comparison of calcite +dolomite thermometry and carbonate + silicate equilibria:constraints on the conditions of metamorphism of the Llanouplift, central Texas, U.S.A. Am Mineral 80:131–143

Liermann HP, Ganguly J (2002) Diffusion kinetics of Fe2 and Mg inaluminous spinel: Experimental determination and applications.Geochim Cosmochim Acta 66:2903–2913

Lin SJ, Huang WL (2004) Polycrystalline calcite to aragonitetransformation kinetics: experiments in synthetic system. ContribMineral Petrol 147:604–614

Liu M, Yund RA (1993) Transformation kinetics of polycrystallinearagonite to calcite: new experimental data, modeling, andimplications. Contrib Mineral Petrol 114:465–478

Liu L, Lin CC (1995) High-pressure phase transfromations ofcarbonates in the system CaO-MgO-SiO2-CO2. Earth Planet SciLett 134:297–305

McTigue JW Jr, Wenk H-R (1985) Microstructures and orientationrelationships in the dry-state aragonite-calcite and calcite-limephase transformations. Am Mineral 70:1253–1261

Massonne HJ (1995) Experimental and petrogenetic study of UHPM.In: Coleman RG, Wang X (eds) Ultrahigh-pressure metamor-phism. Cambridge University Press, pp 33–95

Matthews A, Lieberman J, Avigad D, Garfunkel Z (1999) Fluid-rockinteraction and thermal evolution during thrusting of an

Alpine metamorphic complex. Contrib Mineral Petrol 135:212–224

Mosenfelder JL, Bohlen SR (1997) Kinetics of the coesite to quartztransformation. Earth Planet Sci Lett 153:133–147

Mosenfelder JL, Connolly JAD, Rubie DC, Liu M (2000) Strength of(Mg, Fe)2SiO4 wadsleyite determined by relaxation of transforma-tion stress. Phy Earth and Planet Interiors 120:63–78

Müller T, Baumgartner LP, Foster CT, Vennemann TW (2004)Metastable mineral growth in contact aureoles. Geology32:821–824

Müller T, Baumgartner LP, Foster CT, Roselle GT (2006) Quantitativeforward modeling on the effect of growth, diffusion andexsolution on calcite—dolomite thermometry data. EOS trans.AGU fall meeting supplement 87:v42a–04

Nabelek PI (2007) Fluid evolution and kinetics of metamorphicreactions in calc-silicate contact aureoles From H2O to CO2 andback. Geology 35:927–930

Nishio Y, Sasaki S, Gamo T, Hiyagon H, Sano Y (1998) Carbon andhelieum isotope systematics of North Fiji Basin basalt glasses:carbon geochemical cycle in the subduction zone. Earth PlanetSci Lett 154:127–138

Ogasawara Y, Ohta M, Fukasawa K, Katayama I, Maruyama S (2000)Diamond-bearing and diamond-free metacarbonate rocks fromKumdy-Kolin the Kokchetav Massif, northern Kazakhstan. TheIsland Arc 9:400–416

Okay AI (1993) Petrology of a diamond and coesite-bearing metamor-phic terrain: Dabie Shan, China. Eur J Mineral 5:659–673

Putnis A (2002) Mineral replacement reactions: from macroscopicobservations to microscopic mechanisms. Mineral Mag 66:689–708

Ray JS, Ramesh R, Pande K (1999) Carbon isotopes in Kerguelenplume-derived carbonatites: evidence for recycled inorganiccarbon. Earth Planet Sci Lett 170:205–214

Rathmell MA, Streepey MM, Essene EJ, van der Pluijm BA (1999)Comparison of garnet-biotite, calcite-graphite, and calcite-dolo-mite thermometry in the Grenville Orogen; Ontario, Canada.Contrib Mineral Petrol 134:217–231

Roselle GT, Baumgartner LP, Valley JW (1999) Stable isotopeevidence of heterogeneous fluid infiltration at the Ubehebe PeakContact Aureole, Death Valley National Park, California. Am JSci 299:93–138

Rubie DC, Thompson AB (1985) Kinetics of metamorphic reactionsat elevated temperatures and pressures: an appraisal of experi-mental data. In: Thompson AB, Rubie DC (eds) MetamorphicReactions: Kinetics, Textures, and Deformation. Spring, NewYork, pp 27–79

Rubie DC, Tsuchida Y, Yagi T, Utsumi W, Kikegawa T (1990) An insitu X-ray diffraction study of the kinetics of the Ni2SiO4 olivine-spinel transformation. J Geophy Res 95:15829–15844

Schertl HP, Okay AI (1994) A coesite inclusion in dolomite in Dabieshan, china: petrolgical and reological significance. Eur J Mineral6:995–1000

Schreyer W (2000) Experimental aspect of UHP metamorphism:granitic systems. In: Ernst WG, Liou JG (eds) Ultrahigh-pressuremetamorphism and geodynamics in collision-type orogenic belts:final report of the task group III-6 of the international lithosphereproject. Bellwether, Columbia, pp 95–104

Snow E, Yund RA (1987) The effect of ductile deformation on thekinetics and mechanisms of the aragonite-calcite transformation.J Metamorph Geol 5:141–153

Sobolev NV, Shatsky VS (1990) Diamond inclusions in garnets frommetamorphic rocks: a new environment for diamond formation.Nature 343:742–746

Turnbull D (1956) Phase change. Solid State Phys 3:225–306Wang X, Liou JG (1993) Ultrahigh pressure metamorphism of

carbonate from Dabie Mountainous, Central China. J MetamorphGeol 11:575–588

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite 339

Wang Q, Cong BL (2000) Exhumation of UHP terranes: a case studyfrom Dabie Mountains, eastern China. In: Ernst WG, Liou JG(eds) Ultra-high pressure metamorphism and geodynamics incollision-type orogenic belts. Bellwether, Columbia, pp 170–180

Zhang RY, Liou JG (1996) Coesite inclusions in dolomite fromeclogite in the Southern Dabie Mountains, China: the signifi-cance of carbonate minerals in UHPM rocks. Am Mineral81:181–186

Zhang L, Ellis DJ, Arculus RJ, Jiang W, Wei C (2003) ‘Forbiddenzone’ subduction of sediments to 150 km depth—the reactionof dolomite to magnesite + aragonite in the UHPM meta-pelites from western Tianshan, China. J Metamorph Geol21:523–529

Zhu Y, Ogasawara Y (2002) Carbon recycled into deep earth:evidence from dolomite dissociation in subduction-zone rocks.Geology 30:947–950

340 W.-L. Huang et al.