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Journal of Petrology | Volume 44 | Number 4 | Pages 773-788 | 2003
© Oxford University Press 2003
Kinetics of the Coesite–Quartz Transition: Application to the Exhumation of Ultrahigh-Pressure Rocks
LABORATOIRE DE SCIENCES DE LA TERRE, UMR 5570 CNRS–UCB LYON 1–ENS LYON, BAT. 402 GÈODE, 43 BD DU 11 NOVEMBRE 1918, 69622 VILLEURBANNE CEDEX, FRANCE
Telephone: +33 (0)4 72 44 84 90. Fax: +33 (0)4 72 44 85 93. E-mail: Jean-Philippe.Perrillat{at}univ-lyon1.fr
RECEIVED MARCH 22, 2002; ACCEPTED OCTOBER 29, 2002
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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The kinetics of the quartz–coesite phase transition has been studied in situ by X-ray diffraction in the 2·1–3·2 GPa, 500–1010°C pressure–temperature range. Analysis of the data within Cahn's model of nucleation and growth at grain boundaries reveals that the prograde and retrograde reactions have different kinetics. The quartz
coesite transformation is one order of magnitude faster than coesite quartz. Both reactions are characterized by high nucleation rates, so that the overall reaction kinetics is controlled by crystal growth processes. For the coesite quartz transformation, growth rates are extrapolated using Turnbull's equation with an activation energy for the transition of 163 ± 23 kJ/mol. This kinetic law is combined with an ‘inclusion in a host’ elastic model to study the contribution of kinetics in coesite preservation. This numerical modelling shows that above 400°C retrograde transformation of coesite to quartz is mainly controlled by the ‘pressure vessel’ effect of the host phase, whereas reaction kinetics is the controlling factor at lower temperatures. The influence of the shape of the P–T path and the exhumation rate upon the retrogression of coesite to quartz are investigated to use the percentage of unretrogressed coesite inclusions to constrain P–T–t paths. KEY WORDS: coesite; quartz; kinetics; ultrahigh-pressure metamorphism; P–T–t paths
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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The discovery of coesite (Chopin, 1984
; Smith, 1984) and micro-diamonds (Sobolev & Shatsky, 1990; Dobrzhinetskaya et al., 1995) in metamorphic rocks led to the definition of the ultrahigh-pressure (UHP) metamorphic facies. This facies has been now recognized world-wide in Phanerozoic orogenic domains (e.g. Coleman & Wang, 1995; Carswell, 2000), such that the burial of crustal rocks to mantle depths (>90 km) and their subsequent exhumation to the Earth's surface appears as a common process. The processes by which UHP metamorphic rocks are exhumed is still incompletely understood and several competing models exist (e.g. Ahnert, 1970; Cowan & Silling, 1978; Cloos, 1982; Platt, 1986, 1993; Andersen & Jamveit, 1990; England & Molnar, 1990; Chemenda et al., 1995; Guillot et al., 2000). Discriminating between these models requires comparison of pressure– temperature–time (P–T–t) paths calculated for the UHP units with those predicted by theoretical models (e.g. Duchêne et al., 1997). In particular, these P–T–t paths should allow the survival of high-pressure minerals such as coesite. The partial preservation of coesite is commonly explained by its inclusion in a host phase that acts as a ‘pressure vessel’. Purely elastic models based on the internal pressure in the inclusion (Gillet et al., 1984; Van der Molen & Van Roermund, 1986) allow degrees of retrogression, in agreement with those observed in natural samples, to be calculated. However, these models do not take into account the kinetics of the coesite–quartz transformation, which might be a controlling factor. Kinetic data for this transition are scarce; only four recent studies (Zinn et al., 1995, 1997a, 1997b; Mosenfelder & Bohlen, 1997) and an earlier one by Babich et al. (1989) are reported in the literature and display different kinetics.
The purpose of this contribution is first to present new kinetic data on the coesite–quartz transformation obtained by in situ X-ray diffraction using synchrotron radiation (Skelton et al., 1983; Will & Lauterjung, 1987). We analyse the kinetic data using the model of grain boundary nucleation and interface-controlled growth of Cahn (1956), which allows us to determine the kinetic law of the coesite to quartz transformation. This kinetic law is then combined with an ‘inclusion in a host’ elastic model to calculate the percentage of transformation of a coesite inclusion in a pyrope-rich garnet from the French Massif Central (Monts du Lyonnais UHP unit). The influence of the shape of the P–T paths and the exhumation rate upon the degree of retrogression of coesite to quartz is investigated to use the percentage of unretrogressed coesite as a new constraint for the construction of P–T–t paths.
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EXPERIMENTAL AND ANALYTICAL METHODS |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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Starting material
To study the influence of grain size on kinetics, two types of samples were used. The first type was a micronic powder of
-quartz (grain diameter of 1–2 µm) intimately mixed with 5 wt % of NaCl + Au powder. This material has a OH content lower than 100 x 10-6 H/Si. This powder was pressed and heated simultaneously in the 500–1100°C, 2–3 GPa range, within the stability field of -quartz. During this annealing time, grain growth eliminated small grains, elastic strain was relaxed and high dislocation densities were reduced to obtain relaxed grains 2–10 µm in diameter (samples 1–3). The second type consisted of two cylinders of Suprasil® (synthetic dry type) silica glass (l = 1·45 mm, Ø = 1·5 mm) separated by a 50 µm layer of NaCl + Au powder. This glass has a low OH content of 10 x 10-6 H/Si. It was subjected to P–T conditions in the coesite stability field for grain growth, until the coesite diffraction lines were observed. This procedure led to a grain size of 50 µm (samples 4 and 5).
Experimental apparatus
Experiments were performed at the DW11 beamline of the Laboratoire pour l'Utilisation du Rayonnement Electromagnétique (LURE, Orsay, France) by energy dispersive X-ray (EDX) diffraction. The energy profile of the incident beam allowed diffraction patterns to be collected over the energy range 10–60 keV. The polychromatic beam was collimated to dimensions of 100 µm x 50 µm. Diffracted X-rays were recorded by a solid-state multichannel Ge detector at a fixed angle of 2
= 6·3°.
The use of a Paris–Edinburgh vessel (Besson et al., 1992) allows the application of hydrostatic pressures up to 7 GPa and temperatures up to 2000°C on an experimental volume of several cubic millimetres. As a consequence of this large experimental volume, combined with the high brilliance of the synchrotron radiation, diffraction patterns could be collected within 30–60 s. The cell assembly, placed between two anvils, was made of three main parts: the pressure-transmitting medium, the heating device, and the sample. The pressure transmitting medium consisted of a mixture of amorphous boron and epoxy resin. As its deformation is almost reversible (Le Godec, 1999), it is possible to work also along decompression paths. Consequently, measurements on several pressure cycles were made. The heating device was a cylindrical graphite furnace connected to a high-intensity power supply. Temperature was adjusted rapidly by varying the electrical power delivered to the furnace. The internal volume of the furnace was about 6 mm3 (l = 3 mm, Ø = 1·5 mm).
Temperature was measured by a K-type thermocouple in contact with the sample. The temperature gradient in the cell assembly was estimated by numerical modelling to be of the order of 10°C/mm at 700°C (Hammi, 1995). The temperature uncertainty was estimated to be ±20°C. To determine the pressure in situ, a powder of NaCl + Au was added to the sample as an internal pressure standard. Pressure was calculated from Vinet's equation of state (Vinet et al., 1987) for NaCl and Au using the estimated temperature and lattice parameters determined from X-ray diffraction patterns acquired periodically during each experiment. Unit-cell parameters and the volume of NaCl and Au were refined by a least-squares fitting technique using respectively the (111), (200), (220), (222) and the (111), (200), (220), (311) diffraction lines. The estimates using either NaCl or Au give nearly similar results (the difference between the two estimates being generally lower than the pressure uncertainty). The pressure uncertainty, related to discrepancies in the positioning of standard diffraction lines and propagation of temperature uncertainty, is considered to be ±0·1 GPa.
Experimental procedure
After synthesis, the samples were subjected to the P–T conditions required for the kinetic experiment. The high-pressure cell was carefully aligned with respect to the X-ray set-up and kept at constant position. The P–T path followed during an experiment is schematically shown in Fig. 1. In the case of the quartz coesite transformation, once the sample was under high pressure and temperature, close to the coesite–quartz equilibrium, the temperature was allowed to fall slightly until the first coesite diffraction lines were observed. The P–T conditions were then held constant as long as the transition proceeded. After complete phase transformation (i.e. when quartz diffraction lines disappear), pressure was increased and temperature raised to achieve the completion of the reaction throughout the sample volume. A similar procedure was used to study the coesite quartz transition. As a consequence of the purely elastic behaviour of the pressure-transmitting medium, several prograde and retrograde transformations could be studied within the same sample. During transition, X-ray diffraction patterns were collected every 1–3 min with a counting time for each pattern of 30–60 s. Even for the shortest counting times, the diffraction patterns showed a good resolution and a high signal-to-noise ratio. At the end of each experiment, the temperature was allowed to fall quickly (25°C/min) to quench the sample texture. Pressure was decreased progressively (50 MPa/min) to prevent crack formation in the sample. The recovered samples were then prepared for SEM study to estimate grain size.
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Data processing
Seven coesite
quartz and five quartz coesite transitions were achieved in the pressure range 2·1–3·2 GPa and the temperature range 500–1010°C (Table 1). The degree of transformation X can be estimated from the relative intensity of the quartz and coesite diffraction peaks. For each peak, the position (i.e. the energy in keV) and the intensity at peak maximum (i.e. peak height, in number of photons/m2/s) were evaluated by fitting the diffraction spectra with Gaussian curves, after background subtraction. As the conditions of spectrum acquisition (i.e. counting time, intensity of incident X-rays) varied with time, intensities were normalized to the intensity of the ß4LIMII fluorescence X-ray of Au. The degree of transformation X(t) is thus calculated as
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Figure 2a and b illustrates the transformation–time data obtained in the experiments. These data show a good time resolution, of the order of a minute, and a low uncertainty in the degree of transformation, as low as 0·05–0·1 for experiments up to 900°C. The uncertainty is mainly linked to the error propagation on the intensity of the diffraction peaks.
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ANALYSIS OF THE KINETIC DATA |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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Relative influence of nucleation and growth
The formation of a new phase in the sample results from a combination of nucleation and growth processes whose relative influence on kinetics must be determined. The kinetics of polymorphic phase transitions is usually described using the Avrami equation (Avrami, 1939
) which expresses the degree of transformation X as a function of time t:
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:
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is the time at which a nucleus forms, and t' is the necessary time for a nucleus to grow to radius y. This model relies on a steady-state transformation scheme with both nucleation and growth rates constant. Two limiting cases have been discussed by Cahn (1956). Before site saturation (i.e. before the nucleation sites on the grain surface are exhausted), the kinetic equation (3) can be expressed as
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/3)Nx'3] and [-2Sx'] for the two limiting cases. Similarly, n varies between one and four for instantaneous and slow nucleation, respectively.
The values of n for our experimental data have been determined from the slope of plots of ln{ln[1/(1 - X)]} against ln(t) (Fig. 3a and b). Linear least-square fits to these data give values of n in the 0·44–0·58 range for prograde transitions, and in the 0·42–1·09 range for retrograde transitions. The n values can be alternatively deduced by adjusting the k and n parameters of the Avrami equation to the X(t) data (Table 2). Both methods led to similar results, and to n values always close to or lower than one, indicating a high nucleation rate for both prograde and retrograde transformations. Values for n below the theoretically lowest value of one have already been reported by Rubie et al. (1990) in their study of the Ni2SiO4 olivine–spinel transformation and can be related to the weakness of the simple model of Cahn to describe data with accuracy. This very fast nucleation is confirmed by the strong slope of the X(t) curves during the first stages of transformation (Fig. 2). The addition of a NaCl + Au powder to the sample does not seem to affect the nucleation rate, as there are no significant differences in the n values and the shape of X(t) curves between experiments where the NaCl + Au powder is mixed with the -quartz and those where it is placed as a layer between cylinders of Suprasil glass. The overall kinetics of transformation is thus controlled by growth processes. As a consequence, our study focuses on the determination of growth rates at various P–T conditions.
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Determination of growth rates
Growth rates (x') at isobaric and isothermal conditions are calculated by fitting the X(t) data to equation (5) with a linear regression algorithm minimizing a
2 function. The grain boundary surface area S is taken as S = 3·35/d, where d is the mean grain size of each sample, estimated from SEM observations (Table 1). Although established for tetrakaidecahedral grains, this relation leads to reasonable values of S for most shapes (Liu & Yund, 1993). The best fits, together with the optimized value for x' and the 2 value, are displayed in Fig. 4a and b. Interestingly, the transformation–time data do not show a random scatter around the fitted Cahn curve, but often lie below this curve in the last stages of transformation. This indicates a decrease in growth rates that is not considered in the Cahn model based on the assumption of constant growth. This decrease in growth rates may be caused by grain impingement or the development of transformation stress.
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The study of growth rates results in two major conclusions. First, prograde and retrograde reactions have different kinetics. The quartz
coesite transformation is more or less one order of magnitude faster than the coesite quartz transformation. For example, at 700°C the growth rate is 7·9 x 10-10 m/s for the quartz coesite transition and 4·1 x 10-10 m/s for the coesite quartz transition. Second, crystal growth appears to be a thermally activated process. Indeed, growth rates range from 4·1 x 10-11 m/s at 600°C to 6·4 x 10-8 m/s at 1010°C for the coesite quartz transformation. Plotted in an Arrhenius diagram of ln(x') vs 1000/T (Fig. 5), growth rates plot along a straight line, showing an exponential dependence of growth rates on temperature.
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Extrapolation of growth rates
The application of the above experimental results to natural cases requires the extrapolation of measured growth rates at any P–T conditions, assuming the transformation mechanism is unchanged. This assumption is valid in the temperature range investigated in the experiments but is questionable at lower temperatures. An expression of the growth rate for the product phase in an interface-controlled polymorphic phase transformation has been proposed by Turnbull (1956)
:
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Gr is the free energy change of reaction at given P–T. The Gr values are calculated from the thermodynamic data of Robie et al. (1978) and Saxena et al. (1993). The k0 and Q values are estimated from the slope and the intercept of a least-squares linear fit to the growth rate data on an ln{x'/T [1 - exp(-Gr/RT)]} vs 1000/T plot. For the coesite quartz transition (Fig. 5) a slope of 19·6 is calculated with a correlation coefficient R = 0·94, giving a value for Q of 163 ± 23 kJ/mol. The intercept gives a value for k0 of 2 (±1) x 10-3. Equation (6) is then used to extrapolate the growth rate of coesite over a wide range of P–T conditions (Fig. 6). These growth rates are equivalent to speeds of reaction if nucleation can be considered instantaneous, as in our experiments. The shape of iso-growth rate curves clearly shows the exponential dependence on temperature. The pressure dependence is weaker and mainly acts close to the coesite–quartz equilibrium.
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Comparison with previous studies
The kinetics of the coesite–quartz transition has already been investigated by Babich et al. (1989)
using thermal destabilization of coesite, Zinn et al. (1995, 1997a, 1997b) using in situ X-ray diffraction, and Mosenfelder & Bohlen (1997) using the quench technique. As in our study, these previous works stressed the importance of a very fast nucleation stage and a thermally activated transformation. Babich et al. (1989) reported rates of transformation from coesite to quartz several orders of magnitude slower than ours, and much more dependent on pressure. For example, a rate of transformation of 1 mm/Myr was calculated for a temperature of 850°C, at 1·5 GPa. However, these results were obtained by extrapolation of thermally activated transformation of coesite at ambient pressure and hence are subject to caution. Mosenfelder & Bohlen (1997), analysing their data within Cahn's model, calculated growth rates for the coesite quartz transition one order of magnitude slower than ours. To explain this difference, we first question data analysis. Mosenfelder & Bohlen (1997) adjusted their X(t) data to equation (3) with N and x' used as fitting parameters; whereas we fit our data to equation (5) so that only the x' value is determined. We have reanalysed the original data of Mosenfelder & Bohlen (1997) using the procedure described above. Growth rates calculated (Table 3) are similar to those obtained by Mosenfelder & Bohlen, indicative of a real difference in reaction kinetics. This result emphasizes the non-influence of nucleation, as taking it into account or not yields similar results for growth rates. Second, we checked if this difference in growth rate can be linked with the different grain sizes characteristic of each experiment. No notable effect of grain size is revealed in our experiments between runs using the 2–10 mm or the 50 mm samples. Grain-size reduction results theoretically in an increase in surface energy favourable to the nucleation process (e.g. Lasaga, 1998). However, as the kinetics of the coesite–quartz transition is controlled by grain growth, grain size has little influence. In conclusion, we consider that the experimental procedure seems to be the source of the difference. In our experiments the sample was subjected to several prograde and retrograde transitions. This polyphase treatment could lead to the accumulation of defects, which might speed up the transformation (Rubie et al., 1990). The activation energy for growth (Q) was estimated by Mosenfelder & Bohlen to be 269 ± 26 kJ/mol; more than 100 kJ/mol higher than our value of 163 kJ/mol. The accumulation of defects in the sample would also reduce the activation energy.
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APPLICATION OF THE KINETIC RESULTS TO NATURAL EXAMPLES |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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The coesite–quartz kinetic law is used to numerically model the role of kinetics in the preservation of coesite in UHP metamorphic rocks. The influence of the P–T path's shape and exhumation rate upon retrogression is also investigated.
Numerical model
Both the kinetics of the coesite quartz transformation and the elastic model for a coesite inclusion in a host mineral are taken into account. As pointed out by Gillet et al. (1984) and Van der Molen & Van Roermund (1986), the host mineral acts as a ‘pressure vessel’ that maintains a high internal pressure on the coesite inclusion and thus prevents its retrogression. The model assumes that the host mineral remains unfractured until it reaches the surface. Consequently, the internal pressure (Pin) on the inclusion and the speed of the coesite–quartz transition are calculated for each P–T–t step of the exhumation path.
The internal pressure is computed using the analytical method proposed by Zhang (1998). This approach is based on the following hypotheses: (1) the host phase and the coesite inclusion are of spherical shape; (2) the inclusion is centred in the host mineral; (3) the host-inclusion temperature is homogeneous; (4) inclusion and host have a purely elastic behaviour; (5) when the inclusion-host system formed (i.e. at P0, T0) the internal pressure was uniform. The pressure on the inclusion (Pin) is given by the relation
where 
(Ri and Ri0 are the inclusion radius at T, P and T0, P0, respectively; Rh and Rh0 are the host radius at T, P and T0, P0, respectively), Ki and Kh are the inclusion and host bulk modulus, i and h are their thermal expansion, and µh is the host shear modulus. Within the P–T range considered, the elastic constants can be written
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, K, µ, and their first P and T derivatives taken as constant. Equation (7) is solved by iteration, starting with the inclusion elastic parameters at external pressure. Elastic parameters and internal pressure are refined in this way until convergence is achieved.
In a second stage, the model calculates the free energy change (Gr) of the coesite quartz reaction at Pin, T, using the available thermodynamic data for quartz and coesite (Robie et al., 1978; Saxena et al., 1993). Depending on the sign of Gr, the transition proceeds or not. If Gr is negative a growth rate (x') is calculated using equation (6) with the Q and k0 values determined above. The use of equation (6) relies on two hypotheses: (1) the nucleation is instantaneous on geological time scale; (2) quartz growth is confined to grain boundaries. Both hypotheses are justified by the retrogression textures of coesite inclusions (Fig. 7). Indeed, coesite inclusions are always surrounded by an inversion rim of polycrystalline quartz. This ‘palisade’ texture indicates the nucleation and growth of quartz at the coesite–host mineral interface and suggests a high nucleation rate.
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The radial thickness of palisade quartz is then computed by multiplying the growth rate by the iteration time step. To account for the overpressure created by the volume increase at the coesite
quartz transition (V/V = 7·4% at 50°C, 2 GPa; 13% at 800°C, 3 GPa) , an additional term is inserted in equation (7):
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Vmol the molar volume variation between the two phases. Equation (7) becomes
The evolution in size of a coesite inclusion can be followed throughout the entire exhumation path.
Modelling the rate of retrogression of a coesite inclusion to quartz
The numerical model has been applied to a coesite inclusion in pyrope garnet host from the Monts du Lyonnais eclogitic unit, French Massif Central (Ledru et al., 1989; Mercier et al., 1991). This UHP unit belongs to the western part of the Variscan chain (Matte, 1991). Coesite occurs as inclusions in garnet within eclogite lenses (Lardeaux et al., 2001) and exhibits a typical retrogressive texture. The single crystal of coesite is surrounded by an inversion rim of polycrystalline quartz showing a radiating texture (i.e. palisade texture) and diffuse quartz develops inside the coesite grain (Fig. 7). In thin sections, the degree of retrogression can be estimated at 60% when considering only the palisade-textured quartz (i.e. quartz formed before the fracturing stage of garnet) and 98% when considering both palisade and diffuse quartz. The P–T–t path determined for this unit (Lardeaux et al., 2001) is shown in Fig. 8. It is characterized by an initial nearly isothermal decompression at high temperature. The decompression is very fast: pressure drops from 2·8 to 0·8 GPa in less than 20 Myr, involving a high exhumation rate >1·5 mm/yr. The last part of this path is characterized by a decrease in both temperature and pressure and thereby lower exhumation rates (<0·3 mm/yr). Assuming the inclusion–host system has followed this exhumation path, the internal pressure on the inclusion and the degree of transformation from coesite to quartz are computed. The elastic parameters used in the model for pyrope and coesite, and the initial size of inclusion and host pyrope are listed in Table 4.
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The calculated degree of retrogression of 64·5% (Fig. 8) agrees well with the palisade-texture percentage of 60% measured in the sample. As the P–T path modelled for the inclusion (Pin, T) shows a two-stage evolution, we attempted to discriminate the contribution of the elastic model and the kinetic law on the rate of retrogression. At temperatures higher that 400°C, the kinetics are fast enough such that the pressure is kept on the coesite–quartz equilibrium, whereas at temperatures below 400°C, the Pin,T curve moves away from the coesite–quartz equilibrium, to lower pressures. This indicates that the transformation is not efficient in maintaining sufficiently high pressures on the inclusion. Consequently, above 400°C the retrogression is mainly controlled by the elastic model, whereas the kinetics of the coesite–quartz transition is the controlling factor at lower temperature. Using the kinetic parameters of Mosenfelder & Bohlen (1997)
in our model would shift this temperature limit of 400°C only 50–100°C higher. For P–T paths showing decompression at high temperature (as in the Monts du Lyonnais UHP unit) the assumption of instantaneous transformation (Gillet et al., 1984; Van der Molen & Van Roermund, 1986) is valid. On the other hand, for P–T paths characterized by decompression at low temperature (near or below 400°C) this assumption could lead to an overestimation of the degree of retrogression.
Consequently, the recognition of coesite in metamorphic rocks cannot be systematically considered as evidence for a ‘cold’ retromorphic path (i.e. with significant cooling during decompression); as demonstrated by the occurrence of relict coesite in the Monts du Lyonnais. This is consistent with the discovery of coesite in granulite retrogressed from eclogite in Weihai, eastern China (Wang et al., 1993).
Factors acting upon the preservation of coesite
This model provides the opportunity to investigate the influence of several factors that could contribute to the survival of coesite during exhumation. In this section, the effects of the type of host mineral, the P–T conditions at which the inclusion–host system formed, and the rupture of the host mineral are discussed qualitatively.
In nature, coesite inclusions occur in various host minerals: garnet, pyroxene, kyanite, titanite, zircon, rutile and diamond (e.g. Liou et al., 1998), which differ in their structures and elastic properties. In particular, the bulk modulus (K0) ranges from 129 GPa for omphacite to 150 GPa for pyrope, 227 GPa for zircon and 444 GPa for diamond (e.g. Knittle, 1995). Increasing the bulk modulus of the host phase increases the ‘pressure vessel’ effect, and following our model, the coesite inclusion will consequently reach the coesite–quartz equilibrium at lower temperatures. The amount of quartz retrogressed will thus be reduced. This is in agreement with the measurements by Parkinson & Katayama (1999) of present-day ultrahigh-pressure conditions (19–23 kbar) in coesite inclusions in zircon. The P–T conditions at which the inclusion–host system was formed influence also the preservation of coesite. Because, for a given temperature, the estimated pressure of trapping of the inclusion is a minimum value, higher pressures cannot be excluded. A higher pressure of formation for the inclusion–host system would delay the transformation of coesite to quartz to lower temperatures. Consequently, the higher the pressure of trapping of the inclusion, the more coesite will be preserved. Nevertheless, the survival of coesite is also strongly dependent on the rupture of the host mineral. Our model does not take into account this effect, which would cause a strong decompression of the coesite inclusion, leading to the nucleation and growth of diffuse quartz. As a result of the exponential decrease in retrogression kinetics with temperature, the lower the temperature of fracture, the more coesite will be preserved. The conditions at which fracture takes place are difficult to evaluate as they depend on numerous factors, including the P–T conditions and the exact chemical composition of the host mineral. Van der Molen & Van Roermund (1986) estimated that the internal pressure has to exceed three times the external pressure before fracture can occur. Nishiyama (1998) used this failure criterion to calculate the temperature at which rupture would happen for various exhumation P–T paths. Modelling of the internal pressure (Fig. 8) suggests that slow kinetics would reduce the pressure differential between the inclusion and the host, and thus delay fracture to lower temperatures, where the transformation is sluggish.
Hence, the survival of coesite results from a process combining the ‘pressure vessel’ effect of the host mineral, the kinetics of the reaction and the conditions of subsequent fracturing. Our model provides information about the coupling between the two first parameters. The conditions under which the host mineral fractures need further investigation for a better understanding of the coesite preservation.
Influence of P–T path shape and exhumation rate upon retrograde reaction
In a further development of the above model, we investigated the influence of P–T path shape and exhumation rate upon transformation of coesite to quartz. P–T–t paths are usually obtained by linear interpolation between thermobarometric and geochronological data points. This interpolation is arbitrary and cooler or hotter, slower or faster paths passing through the data points are also possible. The degree of retrogression of natural coesite samples might help to improve this interpolation.
To test this hypothesis, we have computed the size of a 150 µm coesite inclusion in pyrope along several exhumation paths (Fig. 9) passing through lower or higher temperatures than the path resulting from linear interpolation. The calculated retrogression rates do not show significant variations. In all cases the inclusion radius at 0·8 GPa, 550°C is close to 124 µm. This can be explained by the fact that, at such temperatures, retrogression is mainly controlled by the elastic role played by the host mineral (see previous section). Consequently, as elastic deformation is a reversible process, the amount of quartz produced is independent of the P–T path followed and depends only on the initial and final P–T conditions. For the same reason, varying exhumation rates along these paths would have no influence on the degree of retrogression.
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The coesite–quartz transition appears to be too fast to use the percentage of retrogression of coesite inclusions to constrain P–T–t paths more precisely. However, the model developed in this study could be used with success for polymorphic phase transitions characterized by slower kinetics, i.e. with a higher temperature below which kinetics is the controlling factor. Reaction kinetics might thus be a useful tool for studying exhumation, as it provides a continuous record from the HP–LP phase equilibrium to the surface. As the conversion from the HP to the LP polymorph depends on both P–T path shapes and exhumation rates, reaction rate data must be used in parallel with thermobarometric and geochronological data. Consequently, one of these two sets of variables must be known (or fixed) to provide information on the other. Moreover, the solution obtained would not be unique, as a range of exhumation rates or P–T paths can account for a given degree of retrogression. Hence, reaction kinetics will define a ‘trend’ or family of P–T–t paths, which will be of great interest when compared with the exhumation models.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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The analysis of transformation–time data based on simple models of nucleation and growth at grain boundaries proves that the kinetics of the coesite–quartz transition is controlled by thermally activated growth processes. The coesite
quartz kinetic law, deduced from these laboratory experiments, can be used to study the preservation of coesite in UHP rocks, as the texture of coesite inclusions in host minerals such as garnet suggests high nucleation rates at geological time scales. Coupling this kinetic law with an ‘inclusion in a host’ elastic model allows us to calculate the degree of retrogression of a coesite inclusion during its ascent to the Earth's surface. Application to the Monts du Lyonnais UHP units shows that retrogression is mainly controlled by the elastic behaviour of the host mineral above 400°C; whereas reaction kinetics is the controlling factor below this temperature. Ultimately, such a model can be used to constrain exhumation P–T–t paths from the percentage of retrogression of inclusions even if the coesite–quartz transition appears too fast for this purpose, although this approach might be successful for more sluggish transitions. Reaction kinetics would thus be an additional approach for studying exhumation mechanisms of UHP metamorphic rocks.
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ACKNOWLEDGEMENTS |
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This study benefited from the support of J. P. Itié and Y. Le Godec (Lab. Physique Milieux Condensés, Paris VI) during X-ray diffraction experiments at LURE. J. Matas helped in thermodynamic calculations. Careful and constructive reviews by C. Chopin, H. P. Liermann and P. J. O'Brien are also gratefully acknowledged.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...ANALYSIS OF THE KINETIC...APPLICATION OF THE KINETIC...CONCLUSIONREFERENCES |
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