Contrib Mineral Petrol (2011) 161:439–450 DOI 10.1007/s00410-010-0541-z

ORIGINAL PAPER

Ordering in double carbonates and implications for processes at subduction zones T. Hammouda • D. Andrault • K. Koga T. Katsura • A. M. Martin

•

Received: 18 January 2010 / Accepted: 28 May 2010 / Published online: 12 June 2010 Ó Springer-Verlag 2010

Abstract We have studied cation ordering in dolomite in situ as a function of pressure, temperature, and experimental time using the multi-anvil apparatus and synchrotron radiation. Starting with ordered dolomite, we observe the onset of disordering taking place at 950°C, while complete disordering is achieved at 1,070 (±20)°C, for pressures ranging between 3.37 and 4.05 GPa. Pressure does not appear to have significant effect on the order/ disorder transition over the investigated range. We find that dolomite can reach its equilibrium ordering state above 900°C within duration of laboratory experiment (few hours), both from disordered state and from ordered state. Communicated by J. Hoefs. T. Hammouda (&)  D. Andrault  K. Koga  A. M. Martin Laboratoire Magmas et Volcans, Clermont Universite´, Universite´ Blaise Pascal, BP 10448, 63000 Clermont-Ferrand, France e-mail: [email protected] T. Hammouda  D. Andrault  K. Koga  A. M. Martin CNRS, UMR 6524, LMV, 63038 Clermont-Ferrand, France T. Hammouda  D. Andrault  K. Koga  A. M. Martin IRD, R 163, LMV, 63038 Clermont-Ferrand, France

In addition, we have reversed the dolomite breakdown reaction [magnesite ? aragonite = dolomite] between 4.5 and 5.5 GPa, by monitoring diffraction peak intensity. We also have determined that dolomite is stable up to 7.4 GPa at 1,100°C. We confirm some earlier studies where a change in slope (dP/dT) has been observed, but we find a non-zero slope in the low pressure range. Combining the values of entropy obtained from dolomite degree of ordering with enthalpy values deduced from our bracketing of [magnesite ? aragonite = dolomite] equilibrium, we model the location of dolomite breakdown in the P–T space as a function of cation ordering. By comparing previous conflicting studies, we show that, although kinetics of order/disorder is fast, disequilibrium dolomite breakdown is possible. Our modeling shows that subducted disordered dolomite present in carbonated sediments could be decomposed to [magnesite ? aragonite] at lower pressure (3.5 GPa) than usually considered ([5 GPa). This 2-GPa (60 km) difference is valid on a fast subduction path and is possible if disorder inherited from sedimentation is preserved. On a slow subduction path, however, dolomite breakdown is encountered at about 250 km depth, which is 100 km deeper than currently considered.

T. Katsura Institute for the Study of the Earth Interior, Okayama University, Misasa, Japan

Keywords Carbonate  Dolomite  Aragonite  Magnesite  Synchrotron  Order/disorder  Kinetics  Subduction zone

Present Address: T. Katsura Bayerisches Geoinstitut, Universita¨t Bayreuth, 95447 Bayreuth, Deutschland

Introduction

Present Address: A. M. Martin NASA Johnson Space Center, Mailcode KT, 2101 NASA Parkway, Houston, TX 77058, USA

The identity of carbonate mineral species that are present on the solidus of carbonate-bearing lithologies is the critical information that determines the solidus phase relations and element partitioning (e.g., Hammouda 2003). Experimental

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Fig. 1 a Details on the 18/7 cell assembly used for synchrotron high-pressure hightemperature experiments. Sample and pressure marker are indicated by letters S and M, respectively. Scale bar is 2 mm. b X-ray radiography of the compressed cell assembly illustrating the relative position of sample, thermocouple, and pressure marker

determinations of pressure and temperature conditions of dolomite breakdown reaction, [aragonite ? magnesite = dolomite],1 carried out over the last several years (Martinez et al. 1996; Sato and Katsura 2001; Luth 2001; Shirasaka et al. 2002; Morlidge et al. 2006; Buob et al. 2006), show disparities that have been attributed to the disorder state in dolomite starting materials and subsequent equilibration during the experiments. Luth (2001) noted that if dolomite breakdown occurred at low pressure and high temperature, as suggested by Martinez et al. (1996), dolomite would not be stable at peridotite subsolidus conditions. Rather, aragonite would be the stable carbonate. Knowing the nature (calcite, dolomite, magnesite, aragonite) of carbonates introduced into the mantle at subduction zones is key in order to predict: (1) phase relationships (including melting curves) in carbonate–silicate systems at high pressure and high temperature and (2) partitioning behavior of key trace elements in mantle processes because trace element partitioning depends on the crystal chemistry of the host carbonate phases (Veizer 1983). It is therefore fundamental to elucidate the kinetics of ordering phase transitions in carbonates. In this study, we report the order parameter in natural dolomite as a function of pressure, temperature, and time duration of the reaction. We have conducted high-pressure, in situ synchrotron experiments at SPring8 (BL04B1) using multi-anvil apparatus and refined X-ray diffraction patterns in order to determine ordering state of dolomite. We also revisited the [aragonite ? magnesite = dolomite] boundary between 4.5 and 7.5 GPa in light of the concurrent measurement of ordering state.

starting material. Electron probe analysis of the sample yielded the following formula: Ca0.465Mg0.465Fe0.07(CO3). Diffraction pattern of the starting dolomite was obtained with a laboratory X-ray source using Cu Ka1 radiation. Rietveld refinement of the dolomite structure based on 16 reflections gave the following lattice parameter ˚ and c = 16.038(1) A ˚ , with coordinates a = 4.8143(4) A given in the hexagonal system. Those values are slightly ˚ and larger than reference values (a = 4.8069(2) A ˚ , Reeder 1983). We attribute the differc = 16.0034(6) A ence to the presence of small quantities of iron in our sample. In all following discussion, we have neglected the small amount of Fe in dolomite. All experiments used the SPEED-Mk II large volume press (Katsura et al. 2004) with the 18/7 assembly configuration (18-mm-edge length octahedra and 7-mm-truncation length WC cubes). Details on the assembly are shown in Fig. 1. We used Cr-doped MgO octahedra as pressure medium. A W–Re 3/25 thermocouple was positioned axially and was separated from the sample by a thin MgO spacer. No correction was made for the effect of pressure on the thermocouple e.m.f. The carbonate was loaded in capsules made of sintered MgO. Scanning electron microscope observations of samples from earlier experiments showed that no reaction occurred between sample and container at the P–T conditions chosen for the present investigation. The sample was in contact with the pressure marker, which consisted of mixture of MgO and Pt powders. Two holes were drilled in the octahedra and were subsequently filled with rods made of boron-epoxy, in order to limit X-ray absorption from the pressure medium. We used Mo sheets to bring power to the graphite furnace.

Experimental All experiments used ordered natural dolomite (DNY) from high-grade marbles in the area of Nyaoulou (Togo) as 1

Note that the equilibrium is written such as the product (right hand side of the equilibrium sign) has the highest entropy, following the convention of metamorphic petrology. This convention has been adopted throughout this paper.

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Data collection Data were collected for pressures ranging between 3 and 7.5 GPa, with temperatures ranging from 400 to 1,200°C. Details on the P–T paths are given in Fig. 2 together with earlier determinations of [aragonite ? magnesite = dolomite] equilibrium. We used the energy dispersive mode

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Structure refinement and determination of ordering parameter

Fig. 2 Pressure–Temperature trajectories of the present experiments. Symbols on the P–T paths represent conditions where data were acquired. Also shown are some earlier determinations of [aragonite ? magnesite = dolomite] equilibrium (L = Luth 2001; SK = Sato and Katsura 2001; S1 and S2 = Shirasaka et al. 2002). Lines from Shirasaka et al. (2002) are based on in situ determination: S1 was obtained from dolomite compression, while S2 results from aragonite ? magnesite heating. Both Luth (2001) and Sato and Katsura (2001) are based on quench experiments. The three studies have been selected in order to illustrate the discrepancy between earlier bracketing of dolomite breakdown equilibrium

Dolomite belongs to the group of rhombohedral carbonates. A thorough description of dolomite crystal chemistry is given by Reeder (1983). Ordered dolomite (space group R3) has layers filled by Ca only (type 1) alternating with layers filled by Mg only (type 2). In disordered dolomite, Ca and Mg are randomly distributed. The corresponding space group is R3c. Ordered dolomite X-ray diffraction pattern has three additional lines corresponding to (101), (015), and (021) planes. Figure 3 displays X-ray diffractograms for ordered and disordered dolomite structures obtained at high pressure and high temperature in the present study together with full profile refinements (see below). Our method to extract the degree of ordering from the experimental data differs from that of Schultz-Gu¨ttler (1986) who used the intensity ratio (006)/(015) as a measure of disorder. We modeled the experimental spectra by 1 1 fitting XCa and XMg corresponding to Ca and Mg fractions in 2 2 type 1 layers, and XCa and XMg corresponding to Ca and Mg fractions in type 2 layers. For mass balance reasons due to dolomite stoichiometry CaMg(CO3)2, we have the following relations:

with a Ge solid-state detector positioned at 4.95° (2 theta). The detector was calibrated using the following lines: PtKa2, ka1, Ta-Ka2, Ka1, Ag-Ka avg, Mo-Ka avg, Au-Ka2, Ka1, Pb-Ka2, Ka1, and Cu Ka avg. Pressure was determined using MgO equation of state of Jamieson et al. (1982) using the following diffraction lines: (111), (200), (220), (311), (222), (400), and (331). In order to reduce the effect of potential lattice preferred orientation in the sample, we applied oscillations of -3 to ?8 degrees about the press vertical axis. Acquisition time was 300 s for all spectra. After each temperature change, several spectra were acquired consecutively in order to obtain equilibrium ordering state at the studied temperature and to measure the time evolution of the sample toward equilibrium. Pressure was also determined after each temperature change. Temperature uncertainty arising from thermal gradient in the furnace is typically ±25 degrees, given the distance between the thermocouple junction and the sample. The error on pressure comes from two sources. The first one is the error on fitting the X-ray diffraction pattern of the calibrant. The second source is the uncertainty on the temperature that is used for calculating the pressure with the calibrant equation of state. The combination of the two errors yields an absolute error on pressure of ±0.2 GPa.

Fig. 3 Selected energy region of the X-ray diffractograms for ordered (top) and disordered (bottom) dolomite structures obtained in the present investigation. Crosses represent actual data, while thin red line shows modeled patterns. The residual is shown as a thin blue line, offset below each pattern. Specific lines for ordered dolomite are (015) and (021). All indexed lines correspond to dolomite. MgO peaks, which are also present on the patterns, are not indexed

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1 1 XCa þ XMg ¼ 1; 2 2 þ XMg ¼ 1; and XCa 1 2 ¼ XMg ; XCa

2 1 XCa ¼ XMg :

All fractions can therefore be represented by a single 1 compositional parameter, x ¼ XCa : Diffractrograms were refined with the program GSAS (Larson and Von Dreele 2000) using the disordered dolomite structure refinement of Reeder and Wenk (1983) as an input. For each spectrum, we used the whole energy range (30–90 keV) except for the (104) peak (100% intensity), which we did not consider in order to allow for better fitting on the lower intensity lines. We used an adjustable isotropic thermal parameter, identical for all the atoms. This procedure was used as to introduce a correction to photon flux dependence upon X-ray energy. The refinement therefore used 14 lines for d-spacings ranging between those of (101) and (205) of dolomite, excluding line (104). Relative uncertainties of refined lattice parameters are 0.03, 0.05, and 0.05% for a, c, and V, respectively. The position of Ca and Mg is constrained by the lattice geometry. The position of the carbonate group can vary along the c axis. In addition, the carbonate group can rotate in the a–b plane. (All coordinates are given in the hexagonal system.) Both variations are functions of ordering (Reeder and Wenk 1983). In our treatment, C was allowed to move along the c axis, whereas O atoms were allowed to move in the a–b plane while keeping the same coordinate along c as C. Therefore, we considered that the carbonate molecule is planar and rigid, i.e., zO ¼ zC ¼ z; constant C–O bond length. Although not strictly true (Beran and Zemann 1977; Reeder 1983), this simplification does not affect X-ray spectrum simulations in the refinement procedure. Earlier structure refinements showed that z ranges between 0.2429 for complete order (Beran and Zemann 1977) and 0.25 for complete disorder. Previous studies showed that carbon atom position in ordered dolomite was neither affected by pressure (Ross and Reeder 1992) nor by temperature, as long as complete order persisted (Reeder and Markgraf 1986). Here, we have refined x (compositional parameter), / (carbonate molecule rotation), and z (carbonate molecule position) iteratively until best match was found between data and modeled spectra. In detail, it appears that the simultaneous fitting of all parameters yields the error bars too large for meaningful comparisons. This problem, already experienced before (Antao et al. 2004), is due to the fact that all three parameters (x, /, and z) affect the same diffraction lines. Therefore, we refined the data set in three steps. First, we used the whole energy range of the diffraction patterns,

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from 30 to 90 keV, to refine the unit cell parameters at all P–T conditions. Then, we concentrated on the order parameter by selecting an energy range between 50 and 75 keV where all relevant peaks are sufficiently intense. In the second step, we adjusted the compositional parameter x alone. Finally, we fixed the compositional parameter, and we adjusted the / and z parameters relevant to the carbonate molecule position. We verified that / and z converged close to value reported previously by Beran and Zemann (1977), although their values may not be considered as fully relevant since we did not adjust all parameters together. Still, the fact that we obtain a good agreement with previous study gives large confidence that the refined compositional parameter is relevant to the order parameter in dolomite. In conclusion, all fitted spectra yielded Ca and Mg fractions in each site, carbon atom position along the c axis, and carbonate group rotation angle about c axis. The order parameter s was subsequently calculated using s = 2x - 1. If the type 1 layers are filled by Ca only, s = 1 (complete ordering), whereas s = 0 for x = 0.5 (random distribution). Results Dolomite breakdown We have crossed the dolomite breakdown reaction at three points between 4 and 5.5 GPa and have determined that dolomite is stable at 1,100°C up to at least 7.4 GPa (Fig. 4). The three low pressure determinations have been reversed by monitoring dolomite and magnesite peak height variations while cycling temperature around the equilibrium value. Because the press was submitted to oscillations during data collection, we know that peak height variations are caused by reaction in the sample and not by selective grain growth or preferred orientation. Our results agree with quench studies of Luth (2001) and Buob et al. (2006) at 5 GPa and above. Our data confirm the slope change of the dolomite breakdown reaction in the 5–6 GPa range, as found by these authors. On the contrary, we disagree with Sato and Katsura (2001) and Morlidge et al. (2006) who reported constant value for the slope of the boundary. We also disagree with earlier in situ determination by Shirasaka et al. (2002). Our datapoint at 4.45 GPa does not fall on any extrapolated curve from any previous experimental investigation. Compared to Luth (2001), we rather suggest a non-zero dP/dT slope for the [aragonite ? magnesite = dolomite] equilibrium at low temperature. Indeed, the low pressure part of our experimental boundary has a slope consistent to that of Martinez et al. (1996), but the two curves are offset by about 1 GPa.

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Discussion Temperature effect on cation ordering in dolomite

Fig. 4 Location of [aragonite ? magnesite = dolomite] equilibrium determined in the present in situ investigation and comparison with earlier experimental determinations: M’96 = Martinez et al. 1996 (one in situ bracketing and extrapolation to high pressure and temperature) L’01 = Luth 2001 (quench); SK’01 = Sato and Katsura 2001 (quench); S’02 = Shirasaka et al. 2002 (in situ, dolomite compression); M’06 = Morlidge et al. 2006 (quench); B’06 = Buob et al. 2006 (quench). For the present determination, filled symbol represents dolomite stability field, and open symbol represents aragonite ? magnesite stability field. The arrow at ca. 7 GPa represents non-bracketed phase boundary (with question mark). Thick line is given as guide to the eye. Also shown is the location of the boundary calculated by Chatterjee et al. (1998) using the Bayesian approach

Our experimental curve is consistent with thermodynamic modeling of Chatterjee et al. (1998). Order/disorder in dolomite as a function of pressure and temperature For each time series, we report the dolomite final (equilibrium) degree of ordering (Table 1; Fig. 5). For comparison, we also give the (015)/(006) reflection intensity ratios used in the Schultz-Gu¨ttler method. We observed significant dolomite disordering starting at about 950°C. Degree of order remains high however, and at 1,000°C dolomite still is about 80% ordered. A sharp increase in the degree of disordering is noted at 1,030°C and order is completely loss within the next few tens of degrees. Complete disordering was found at 1,090, slightly higher than 1,050 (order parameter is very low but clearly non-zero), and 1,070°C at 3.37, 3.54, and 4.05 GPa, respectively. Given the experimental uncertainties, we consider that all these temperature values are equivalent. Overall, these values are consistent with most earlier reports as discussed in the next section. The behavior of ordering degree as a function of temperature appears to be consistent with second-order phase transition (Putnis 1992), with critical temperature Tc = 1,070 ± 20°C.

We found a value of 1,070 ± 20°C for the critical temperature of disordering (Tc), between 3.37 and 4.05 GPa. In their study at 1.1 GPa, Reeder and Wenk (1983) bracketed the critical temperature of disordering between 1,100 and 1,150°C, by using single crystal X-ray diffraction on quenched samples. Although precise determination of dolomite ordering state was made difficult because of back reaction during quenching, Reeder and Wenk (1983) observed twin domains only in samples quenched from 1,150°C and above. In their study, the observation of the domains served to identify the existence of disordering in dolomite at high pressure and temperature conditions. Given overall temperature uncertainties, ordering state of dolomite in our experiments is also consistent with that of Luth (2001) who found Tc C 1,100°C by using the method of Schultz-Gu¨ttler (1986) based on the intensity ratio of reflections (015)/(006). Morlidge et al. (2006) also found that complete disordering occurred between 950 and 1,100°C. Results presented by Antao et al. (2004) show a systematic offset (by more than 100°C), suggesting disagreement on pressure and/or temperature calibration. Note that their P and T determination is based on the method of the double isochor, which is less accurate than the use of a thermocouple for temperature measurement and subsequent pressure calculation. Figure 6 shows the degree of order as a function of temperature obtained in the present study. In addition, degree of order obtained by single crystal refinements of Reeder and Wenk (1983) is displayed together with results of Morlidge et al. (2006), Luth (2001), Schultz-Gu¨ttler (1986), which were all determined from powder X-ray diffraction. In the case of Morlidge et al. (2006), Luth (2001), and Schultz-Gu¨ttlerp(1986), weffi plotted the square ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi root of intensity ratios ( Ið015Þ =Ið006Þ ). We chose this representation because the ordering degree is proportional to the square root of the intensity of superlattice reflection (Redfern et al. 1989; Dove and Powell 1989), while the ratio is used to normalize the intensity of the (015) reflection (Schultz-Gu¨ttler 1986; Luth 2001). There is a general agreement between all data sets when in the vicinity of the critical temperature, Tc. Below 950°C, however, we note discrepancy between our data and results of quench studies (Luth 2001; Schultz-Gu¨ttler 1986). Since the latter were allowed to equilibrate for longer run durations (12–96 h vs. 1 h at most in our case), it is possible that our samples did not reach equilibrium ordering state at 800 and 900°C. It should be noted, however, that low temperature (850°C and less) samples of Luth (2001) and Morlidge et al. (2006) display lower degree of order

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Table 1 Summary of experiments where degree of order was measured Run#

T (°C)

Timea (hh:mm)

Order

I(015)/Ib(006)

˚ )c a (A

˚ )c c (A

˚ 3)c V (A

˚ 3) dV (A

M496

800

01:23

1

0.93

4.7806

15.893

314.57

0.169

3.5 GPad

900

01:01

0.98

0.89

4.7838

15.955

316.22

0.164

950

00:24

0.98

1.00

4.7846

15.986

316.93

0.166

1,000

00:23

0.79

0.74

4.7846

16.041

318.02

0.161

1,050

00:13

0.16

0.15

4.7841

16.112

319.36

0.158

1,000

00:39

0.57

0.56

4.7873

16.064

318.82

0.148

950

00:19

0.69

0.65

4.7892

16.038

318.57

0.101

850

00:15

0.70

0.63

4.7894

16.004

317.92

0.139

1,200

00:00

0

0

4.7836

16.208

321.19

0.165

M498 3.4 GPa

850

01:20

0.08

0.07

4.7894

16.053

318.89

0.117

1,000 800

00:08 01:00

0.11 1

0.04 0.99

4.7877 4.7878

16.096 15.977

319.52 317.18

0.123 0.147

950

00:07

0.97

0.83

4.7864

16.002

317.47

0.159

970

00:33

0.93

0.80

4.7871

16.027

318.07

0.149

990

00:12

0.86

0.71

4.787

16.04

318.32

0.149

1,010

01:04

0.76

0.60

4.7871

16.064

318.81

0.150

1,030

00:16

0.69

0.54

4.7869

16.083

319.16

0.153

1,050

00:13

0.54

0.43

4.7871

16.107

319.66

0.159

1,070

00:12

0.25

0.19

4.7861

16.134

320.05

0.162

1,090

00:05

0

0

4.7857

16.158

320.48

0.157

0.96

0.87

4.7744

15.842

312.73

0.157

00:11

0.98

0.88

4.7792

15.923

314.97

0.176

990

00:21

0.83

0.78

4.7791

15.966

315.8

0.183

1,030

00:22

0.28

0.37

4.7765

16.028

316.68

0.177

1,070

00:01

0

0

4.7746

16.067

317.2

0.162

M500

800

4.0 GPa

950

a

Time needed for sample equilibration or duration of step at given temperature

b

Ratio of reflection intensities characteristic of ordering (015) over (006) reference peak

c

All parameters were determined by Rietveld refinement using GSAS (see text for details on the procedure)

d

Pressure given is indicative of investigated range. Detailed P–T paths are illustrated in Fig. 2

compared to higher temperature, which is unexpected and could be attributed to the normalization procedure of diffraction peak intensity. It may also be possible that scatter in the previous data is caused by grain preferred orientation or dolomite breakdown, as suggested by Luth (2001). In an attempt to model the evolution of ordering as a function of temperature, we have considered a Landau-type expansion of the free energy (for a tricritical transition, ½ðTc  TÞ=Tc 1=4 ¼ s; Landau and Lifchitz 1967), and the Bragg–Williams model (tan h½sTc =T  ¼ s; Bragg and Williams 1934) for temperature vs. order relation. In both cases, temperature was calculated using Tc = 1,070°C. Both models satisfactorily reproduce the trend near Tc, but discrepancy is observed within less than 100 degrees below Tc (Fig. 6). Although agreement is found again at 800°C and below (data of Luth 2001), the sharp increase in ordering observed below Tc is reproduced neither by the Landau tricritical model, nor by the Bragg–Williams model. Antao et al. (2004) proposed a modified Bragg–Williams model

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wherein the ‘mixing enthalpy’ (i.e., corresponding to mixing of ordered and disordered forms of dolomite) is augmented by a term proportional to (s4 - 1), s being the order parameter. The additional term was attributed to a contribution coming from carbonate group rotation (lattice strain) to the energy budget. We have applied their model (using a = -1/3, the lowest value allowed) and found improved agreement between model and experimental data although the observed sharp increase of degree of ordering is still poorly reproduced (Fig. 6). Strictly speaking, the Bragg– Williams model should be irrelevant to the case of dolomite because of the sign change of the dolomite formation enthalpy from fully ordered to fully disordered (Putnis 1992). The interaction parameter (Vo of Bragg and Williams (1934), w of Antao et al. (2004)) should therefore depend on site filling, i.e., on the degree of ordering. In their study of CdMg-dolomite, Capobianco et al. (1987) concluded that none of the models they tested (Bragg–Williams, generalized point approximation, cluster variation method) could

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rotation about the c axis) could give the transition a cooperative character that would reduce the temperature interval over which order is lost. Volume associated with dolomite disordering, and compressibility of disordered dolomite

Fig. 5 Ordering state of dolomite as a function of temperature at 3.38, 3.54, and 4.05 GPa. Lines connecting datapoints are guides to the eye and are used to identify each individual series of measurements. Note that within error, the temperature of complete disordering does not depend on pressure

Fig. 6 Summary of degree of cation ordering in dolomite obtained in the present investigation (in situ X-ray diffraction) and comparison with previous experimental determinations. References used are M’06, Morlidge et al. (2006); L’01, Luth (2001); S-G’86, SchultzGu¨ttler 1986; R-W’83, Reeder and Wenk 1983. Vertical size of boxes of L’01 corresponds to several determinations at one given temperature, while open squares represent a single determination. Lines represent order parameter modeling using Landau expansion (tricritical transition, Landau and Lifchitz 1967), Bragg–Williams model (B–W, Bragg and Williams 1934), and modified Bragg–Williams model (mod. B–W) of Antao et al. (2004). Discrepancy among experimental data and between experiments and models is discussed in the text

reproduce the sharpness of the order/disorder transition they observed. They suggested that involvement of carbonate groups in the transition (change in shape and bond length,

Figure 7 illustrates the increase of dolomite cell parameters as disordering proceeds, upon an isothermal time series. In agreement with Reeder and Wenk (1983), we found a linear relationship between order parameter and both cell volume and lattice parameter c, while a remains unchanged. The datapoints were linearly fitted, and the line fit was extrapolated to 0 and 1 in order to estimate volume of disordering, assuming the linear relationship is valid throughout. The obtained volume changes (DV) for disordering range ˚ 3, depending on P and T conditions between 0.79 and 2.24 A (Table 2). In all cases, these values represent less than 1% of the dolomite unit cell volume. Although this difference is close to the uncertainty associated with the refinement pro˚3 cedure, our results are in good agreement with the 1.46 A estimate by Reeder and Wenk (1983) at 1.1 GPa.

Fig. 7 Isothermal time evolution of dolomite cell volume (top) and lattice parameters c (bottom), as a function of cation ordering. Datapoints were fitted linearly (see text for discussion). Fit line is extended across the diagram in order to retrieve the difference between fully ordered and fully disordered dolomites for each parameter

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Table 2 Volume variations associated with disordering Run

P (GPa)

T (°C)

Vordered ˚ 3)a (A

Vdisordered ˚ 3)a (A

DV ˚ 3) (A

DV rel. (%)b

M498

3.38

1,050

320.88

322.98

2.10

0.65

M498

3.38

1,070

320.68

322.92

2.24

0.70

M498

3.37

1,090

320.43

321.75

1.32

0.41

M496

3.54

1,050

319.53

320.83

1.30

0.41

M500

4.24

990

317.06

318.58

1.52

0.48

M500

4.05

1,030

316.9

317.69

0.79

0.25

Our experimental results are thus consistent with there being similar PVT equation of state for ordered and disordered dolomite forms, except for the room pressure volume. We find that disordered dolomite is about 0.55% larger than the ordered form, in agreement with our determination based on isothermal time series. Disordered dolomite having a larger cell volume should be more compressible than the ordered form. This effect, however, must be small and not detectable in the investigated pressure range, particularly at high temperature.

a

Values were obtained by extrapolating unit cell volume between state of complete order and that of complete disorder as illustrated on Fig. 7

b

DV relative is calculated relative to the volume of ordered dolomite

We also used the measured cell parameters recorded during dolomite compression at 1,100°C in order to calculate disordered dolomite bulk modulus at this temperature. The experimental data were refined using an isothermal second-order Birch–Murnaghan equation of state (using dK/dP = 4). Figure 8 shows experimental disordered dolomite compression curve (our data) together with calculated ordered dolomite compression curve, using the EoS of Martinez et al. (1996), both at 1,100°C. We note that compressibility is almost identical (Kdisordered = 62(1) vs. Kordered = 63.1(11) GPa), whereas V(1,100°C, 1 bar) of disordered dolomite is slightly, but significantly, larger ˚ 3). than that of the ordered phase (336.6(5) vs. 334.75 A

Order/disorder in dolomite and dolomite breakdown The slope of the [dolomite = magnesite ? aragonite] DSr dP equilibrium in the P–T space is given by dT ¼ DV where r ordered od DSr ¼ Sdol  Smgst  Sarag ¼ Sdol þ Sdol  Smgst  Sarag : Using thermodynamic and compressibility data on magnesite, aragonite, and ordered dolomite compiled by Martinez et al. (1996) together with the volume associated with disordering, we have calculated the slope involving partially or completely disordered dolomite. Considering that the entropy difference between the disordered and the ordered dolomite, Sod dol ; corresponds to configurational entropy, its value can be estimated (Putnis 1992) using Ca and Mg site filling obtained from X-ray diffraction data refinement: Sod dol ¼ 2R½x lnðxÞ þ ð1  xÞ lnð1  xÞ with 1 x ¼ XCa : Resulting values are given in Table 3. The agreement between the calculated slopes and the experimental bracketing of the dolomite breakdown equilibrium is good. Our calculated values differ slightly from those of Luth (2001) although the discrepancy can be accounted for by experimental uncertainties. Overall, our data confirm the curvature of the dolomite breakdown reaction as found by Luth (2001) and Buob et al. (2006) in the 5–7 GPa range. Finally, we estimated the enthalpy variation across the [aragonite ? magnesite = dolomite] equilibrium by using the computed entropy deduced from our experimentally determined order parameter values together with volume changes calculated using appropriate equations of state (Table 3). The low temperature value is in good agreement Table 3 Experimental bracketing of the [aragonite ? magnesite = dolomite] equilibrium, and calculated slopes and DHr P (GPa)

Fig. 8 Comparison of isothermal compressibility curves at 1,100°C between our data on disordered dolomite (circles ? solid line) and prediction using Martinez et al. (1996) equation of state for ordered dolomite (dashed line). Both lines were calculated or fitted using second-order Birch–Murnaghan EoS (dK/dP = 4)

123

T (°C)

dP/dT (bar/deg)a

DHr (kJ/mol)a

4.45

500

10.5

-7.30

5.1

800

15.2

-5.75

5.5

905

20

-4.83

7.4

\1,100

86

6.79

a

Values are obtained using experimentally measured ordering state and corresponding DSr, while DVr is computed from appropriate equations of state (see text)

Contrib Mineral Petrol (2011) 161:439–450

447

with modeling at room temperature and pressure using calorimetric data (-7.30 vs. -8.40 kJ/mol, respectively). The difference between the high and low temperature values can be taken as representing the enthalpy of dolomite disordering (e.g., Luth 2001). Note that, in the case of fully ordered phases, computed high pressure—high temperature and low pressure—low temperature values for DHr differ by 0.02 kJ/mol only. The data compiled in Table 3 yield a disordering enthalpy value of 15.19 kJ/mol when taking into account volume variation due to disordering. If volume difference due to disordering is neglected, the resulting disordering enthalpy is 17.40 kJ/mol. Our value is comparable to earlier determinations of 13.94 ± 0.44 kJ/mol by Navrotsky and Capobianco (1987) and 13.96 kJ/mol by Antao et al. (2004). It is lower than more recent determinations by Navrotsky et al. (1999) who give 32 ± 5 kJ/mol for poorly crystallized disordered dolomite prepared by low temperature precipitation, and by Luth (2001) who found 26 kJ/mol using the slope of his experimentally bracketed dolomite breakdown equilibrium. Kinetic of order/disorder transformation Within an isothermal time series of X-ray diffraction spectra, order parameter s first decreases with respect to time then reaches a steady state, suggesting attainment of near equilibrium state (Fig. 9a). Typically, this time transient behavior takes less than 40 min to complete above 950°C (Table 1). The exchange of Ca and Mg is expressed as, 1 2 1 2 XCa þ XMg ¼ XMg þ XCa :

Following the kinetic model based on the second-order reaction rate law, above reaction is expressed as,  2   1 h 2 i  2 h 1 i d XCa XMg  kb XCa XMg ; ¼ kf XCa ð1Þ dt where kf and kb are forward and backward reaction rate constants. The Eq. 1 can be derived for the variable s, 

2ds ¼ kf ð1 þ sÞ2  kb ð1  sÞ2 : dt

ð2Þ

Fitting the experimental data to Eq. 1 (Fig. 9a), with initial condition s = s0 at t0 and the boundary condition s = seq at tinf, one can solve for kf and kb (Table 4). Because the reaction rate law only states the mass balance of a chemical reaction, these reaction rate constants are macroscopic representation of physical processes taking place within dolomite. At equilibrium, d[X]/dt = 0; therefore, KD ¼

kf ð1  sÞ2 ¼ ; kb ð1 þ sÞ2

ð3Þ

Fig. 9 a A typical reaction model fit. The circles are the values obtained for cation ordering (s) at conditions 3.38 GPa and 1,050°C. The line is the model fit using Eq. 1. b A model showing transient evolution of s with respect to time. Using Eq. 2 and calculated kf and kb corresponding to 1,050°C, the evolution of s is shown. Two initial conditions are illustrated, both offset by the same absolute value relative to equilibrium s value (s = 0.55): so = 0.95, i.e., close to fully ordered dolomite, and so = 0.15, i.e., poorly ordered dolomite. The slope originating from dolomite having higher degree of order is milder than the other indicating slower reaction rate when starting from highly ordered structure

where KD is the exchange constant. The reaction rate constants determined from Eq. 2 are shown in Table 4. As expected from Eq. 3, the ratio, kf/kb, shows an agreement with the measured KD values (Table 1). Here, when s = 1, the backward reaction dominates the progress, inversely at s = 0, the forward reaction is at the same rate as the backward reaction. The application of the rate law implies that the rate of the order–disorder reaction is controlled by the probability of atom jumps between the type 1 and type 2 sites, rather than the transport of atoms farther than the neighbors by random walks (i.e., diffusion). We consider that the reaction rate law is a realistic description of the order–disorder phenomena. First of all, the values of kf are somewhat comparable to those determined for orthopyroxene (Skogby 1992; Ganguly 1982). It should be noted that chemical potential energies of type 1 and type 2 sites

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Contrib Mineral Petrol (2011) 161:439–450

Table 4 Kinetic parameters determined for second-order reaction rate law Kf (s-1)

T

Kb (s-1)

s0 chosen

of magnitude (Table 4). Our current data are inadequate to assess the rate of ordering at temperature conditions lower than 950°C. Clearly, further investigations are needed.

M496 950

1.81 9 10-6

1.07 9 10-2

1.000

3.65

1,000

-5

1.55 9 10

9.10 9 10-4

0.976

3.54

1,050

3.47 9 10-4

6.83 9 10-4

0.789

1,000

-5

3.17 9 10

4.36 9 10-4

0.177

3.83

3.56 M498 3.47 3.42

970 990

5.53 9 10-6 1.50 9 10-5

3.92 9 10-3 2.78 9 10-3

0.968 0.929

3.38

1,010

2.04 9 10-5

1.18 9 10-3

0.860

3.38

1,030

-5

4.58 9 10

1.32 9 10-3

0.771

3.38

1,050

5.18 9 10-5

5.86 9 10-4

0.686

3.34

1,070

-4

1.37 9 10

-4

3.56 9 10

0.549

3.37

1,090

2.69 9 10-4

2.63 9 10-4

0.256

990

1.49 9 10-5

1.51 9 10-3

0.983

1,030

-4

3.08 9 10-4

0.829

M500 4.24 4.05

1.09 9 10

change with respect to s. However, the formulation of the second-order reaction rate law does not account for such change. We consider such change in site chemical potential energy plays a minor role compared to the activation process needed to create a jump across the sites. For example, the maximum DHr (Table 3), which is analogous to the difference in the chemical potential energies between the sites, is 9.26 kJ/mol. On a contrary, the activation enthalpy of Ca–Mg exchange is on the order of 250 kJ/mol, inferred from Ca–Mg exchange reaction in dolomite aggregate (Huang et al. 2009), and from diffusion creep of dolomite (Davis et al. 2008). The time-dependent evolution of dolomite ordering is calculated from the reaction rate constants and Eq. 2 (Fig. 9b). Examining the slope near t = 0, the rate of reaction is faster for the disorder ? order (backward) reaction than the order ? disorder (forward) reaction. This is an expected conclusion given that kb C kf because 0 B s B 1 in Eq. 3. Given that dolomite can reach its equilibrium ordering state within the duration of laboratory experiment, either from disordered state or from ordered state, we conclude that disequilibrium dolomite is unlikely to persist in typical laboratory experiments conducted above 950°C. We did not observe a clear temperature dependence of the ordering (or disordering) rate. Assuming activation enthalpy of 250 kJ/mol, approximately six times more atomic jump is expected at 1,050°C than 950°C. However, through out the experiments, the near steady-state s values are attained after 10–30 min, suggesting similar overall reaction rates. While Kf increases about 2 orders of magnitude from 950 to 1,090°C, Kb decreases by about 2 orders

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Implications for dolomite breakdown and for carbonate stability during subduction Figure 10 summarizes the effect of dolomite ordering on the location of [aragonite ? magnesite = dolomite] equilibrium. The calculated boundary curves (labeled with s values) are based on dolomite entropy and enthalpy variations associated with disordering determined in the present study. Starting from totally disordered dolomite, increasing the degree of order (s) results in shifting the equilibrium boundary toward higher pressure at fixed temperature. Note that the higher the value of s, the larger its effect on the boundary location. The results of Morlidge et al. (2006) are compatible with degree of order close to 1 up to 900°C and s [ 0.75 at 1,100°C. Data of Luth (2001) as well as our data correspond to s [ 0.9 at low temperature and s close to zero at high temperature. We conclude that our boundary curve represents the true equilibrium curve that takes into account dolomite ordering state. It may seem paradoxical that although kinetics of ordering/disordering is fast compared to

Fig. 10 The effect of cation ordering (s) on dolomite stability relative to [magnesite ? aragonite]. Equilibrium boundaries were calculated as a function of degree of ordering (s) using thermodynamic and compressibility data on magnesite, aragonite, and ordered dolomite (s = 1) compiled by Martinez et al. (1996), combined with our data on disordered dolomite (s = 0). They are plotted as thin lines indexed with corresponding values of s. For intermediate values 0 \ s \ 1, we used a linear combination of fraction of s ordered dolomite and (1 - s) disordered dolomite. Comparison with our experimental boundary and with those of Morlidge et al. (2006, M’06), Luth (2001, L’01), and Buob et al. (2006, B’06) is discussed in the text. Also shown are pressure–temperature paths for two end-member subduction regimes (slow and fast subduction) taken from van Keken et al. (2002). Note that pressure of dolomite breakdown depends both of cation ordering and of subduction regime. See text for further discussion

Contrib Mineral Petrol (2011) 161:439–450

laboratory timescales as stated in the above section, disequilibrium boundaries are nevertheless observed in some studies. It may be that kinetics of dolomite breakdown could be even faster, depending on the nature of starting material (including grain size, mechanical treatment, and presence of small amounts of impurities). Can ordering state control dolomite stability during subduction? Sedimentary natural dolomite is usually disordered and although cation ordering might take place upon heating, the kinetics is sluggish for diagenetic conditions. For example, Malone et al. (1996) used Ca-rich disordered dolomite simulating non-ideal dolomite found in nature. They observed significant (but incomplete) ordering only at 200°C in saline solution at low pressure. At present, we have no information about the kinetics of cation ordering in dolomite at low temperature and in fluidpoor environment, but we cannot exclude persistence of disordered dolomite up to blueschist to low temperature eclogite facies. Figure 10 also shows Pressure–Temperature paths for subducting slab according to van Keken et al. (2002) modeling that takes into account stress- and temperaturedependent viscosity. On a fast subduction path, the equilibrium [magnesite ? aragonite = dolomite] boundary is encountered at ca. 5.5 GPa. Were sedimentary disordered dolomite to persist, however, its breakdown would occur at 3.5 GPa. A minimum 2-GPa difference can therefore be expected due to non-equilibrium ordering state of dolomite. Indeed, the P–T path crosses the stability field of [dolomite ? magnesite] at low temperature, and sedimentary dolomite breakdown could occur there as well. In consequence, magnesite presence in high-grade metamorphic terranes (Zhang et al. 2002) could be a deceptive indicator of ultrahigh pressure metamorphism. Turning now to the slow subduction path, higher temperatures involved result in crossing dolomite breakdown boundary at ca. 8.5 GPa, which corresponds to depth of about 250 km. In such condition, there is moderate influence on ordering state upon dolomite stability, but the pressure of dolomite breakdown is now increased by 3 GPa compared to the usually accepted value.

449

We also revisited the dolomite breakdown reaction and confirmed earlier determination by quench experiments of Luth (2001) and Buob et al. (2006) and disagree with Sato and Katsura (2001) and Morlidge et al. (2006) as well with in situ determination by Shirasaka et al. (2002). Our results suggest, however, a non-zero slope below 5 GPa, which is opposite to results of Luth (2001) and Buob et al. (2006). Our experimental boundary of the [magnesite ? aragonite = dolomite] equilibrium is fully compatible with thermodynamic modeling that takes into account the effect of cation ordering on the value of dolomite entropy. We are therefore confident that our determination represents the true equilibrium boundary. Discrepancy between earlier quench experiments is best explained by non-equilibrium ordering in dolomite, and we suggest that the disparities between published determinations are related to the competition between the kinetics of cation ordering and that of dolomite breakdown. Modeling of dolomite stability during subduction shows that magnesite occurrence might be a deceiving pressure indicator. For instance, persistence of metastable disordered sedimentary dolomite can contract dolomite stability field by about 2 GPa on a fast subduction path. Only equilibrated dolomite is stable up to about 5 GPa (150 km) along this path. Conversely, the slow subduction path does not encounter dolomite breakdown boundary before [8 GPa ([250 km) whatever the ordering state. We may consider that, in general, cation ordering affects mineral stability. In the present case of dolomite, however, we note extreme variations that can result in incorrect interpretation of metamorphic assemblage equilibration conditions. Acknowledgments The dolomite used in this investigation was kindly provided by C. Renac (Universite´ Jean Monnet, Saint-Etienne). We thank J.-L. Devidal for X-ray characterization of starting materials at Laboratoire Magmas et Volcans and K.-I. Funakoshi and Y. Tange for their help during the experiments at SPring8. We thank RW Luth and an anonymous reviewer for their helpful comments. We thank JASRI for supporting the experimental work (Spring8 Proposal number 2007A1570). Part of traveling expenses was covered by the Japan-France Integrated Action Program (Sakura), project 12295XL (2006-2007). Preliminary experiments used the multianvil press of Laboratoire Magmas et Volcans, which is financially supported by the Centre National de la Recherche Scientifique (Instrument National de l’INSU).

Conclusions References We have measured cation ordering in natural dolomite at high pressure (4–7 GPa) and high temperature by in situ X-ray diffraction apparatus using synchrotron radiation in the multianvil. The onset of disordering occurs at 950°C, and complete disordering is achieved at 1,070 ± 20°C. Although the volume of the disordered phase is larger than that of the ordered phase, the volume difference is so small that pressure has virtually no effect on the transition.

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