Empirical Calibration for Dolomite Stoichiometry Calculation: Application on Triassic Muschelkalk-Lettenkohle Carbonates (French Jura)

Résumé — Calibration empirique pour le calcul de la stœchiométrie de la dolomite : application aux carbonates triassiques du Muschelkalk-Lettenkohle (Jura français) — Cette étude propose une approche pour la quantification de la dolomite et le calcul de sa stœchiométrie grâce à l’utilisation de la diffraction des rayons X couplée aux affinements de maille et de Rietveld et complétée par de nombreuses données issues de la littérature. Elle permet d’obtenir une meilleure justesse et précision pour la quantification de la dolomite (et des autres phases minérales) ainsi que pour le calcul de sa stœchiométrie par rapport à l’équation de Lumsden et de méthodes antérieures. L’approche proposée est vérifiée grâce à l’analyse d’un échantillon référence de dolomite (Eugui) et appliquée à des roches carbonatées du Trias (Muschelkalk supérieur-Lettenkohle) du Jura français. Elle est combinée à une étude pétrographique Abstract — Empirical Calibration for Dolomite Stoichiometry Calculation: Application on Triassic Muschelkalk-Lettenkohle Carbonates (French Jura) — This study concerns an approach for dolomite quantification and stoichiometry calculation by using X-ray diffractometry coupled with cell and Rietveld refinements and equipped with a newly substantial database of dolomite composition. A greater accuracy and precision are obtained for quantifying dolomite as well as other mineral phases and calculating dolomite stoichiometry compared to the classical “Lumsden line” and previous methods. The applicability of this approach is verified on dolomite reference material (Eugui) and on Triassic (Upper Muschelkalk-Lettenkohle) carbonates from the French Jura. The approach


INTRODUCTION
Ideal dolomite has a crystal lattice consisting of alternating layers of Ca and Mg, separated by layers of CO 3 , and is typically represented by a stoichiometric chemical composition of CaMg(CO 3 ) 2 where calcium and magnesium are present in equal proportions (Reeder, 1990). Most of the properties of carbonate rocks (limestone and dolostone) are primarily defined during their deposition and subsequent early diagenesis. With reference to dolostones, rock properties tend to change with time and particularly so during mesogenesis (shallow marine to deep burial; Land, 1980). Commonly, these diagenetic stages represent an overprint of the previous depositional or early diagenetic events. Cation substitutions in the crystal lattice, in particular Ca and Mg, through dissolution-precipitation reactions, change the stoichiometry of the dolomite. As a result, dolomite exhibits variation in chemical composition and in atomic arrangements (Reeder, 1981;Hardie, 1987).
Very few sedimentary dolomites are truly stoichiometric (CaMg(CO 3 ) 2 ). They are better represented as: Ca (1+x) Mg (1-x) (CO 3 ) 2 typically with more Ca than Mg (Goldsmith and Graf, 1958;Lumsden, 1979;Searl, 1994;Budd, 1997). Therefore, the term "dolomite" describes a mineral series of carbonate that encompass a range of chemical variation and lattice structures. The stoichiometry, the texture and possible association with evaporates are generally used to identify different types of dolomite in sedimentary rocks (Morrow, 1978(Morrow, , 1982aLumsden and Chimahusky, 1980). This can also reveal diagenetic environmental settings that affected dolomite formation (Mattes and Mountjoy, 1980;Morrow, 1982;Machel and Mountjoy, 1986). Non-stoichiometric dolomite crystals are thermodynamically metastable under sedimentary conditions and therefore more reactive to diagenetic environments relative to "ideal" dolomites (Carpenter, 1980;Land, 1980;Lumsden and Chimahusky, 1980;Hardie, 1987;Vahrenkamp and Swart, 1994;Chai et al., 1995;Budd, 1997). For this reason, a burial trend towards stoichiometry exists (Sperber et al., 1984;Vahrenkamp and Swart, 1994) resulting in an overall reset of stable isotope ratios and trace elemental abundances through recrystallization (Land, 1980;Morse and Mackenzie, 1990). By knowing the "degree" of stability of dolomites (through stoichiometry) a more quantitative prediction whether the dolomite rock texture is prone for further changes -that may alter its reservoir properties such as porosity and permeability -is feasible.
X-Ray Diffractometry (XRD) is commonly used for measuring the crystallographic structure and the stoichiometry of dolomites. The Ca/Mg ratio of a dolomite is classically determined from the displacement of the d 104 main dolomite reflection. Lumsden (1979) established an equation linking molar content of CaCO 3 in dolomite to the d 104 spacing measured on XRD profiles. Several authors have shown that dolostones can diverge from the Lumsden line (Reeder and Sheppard, 1984;Kimbell, 1993;Jones et al., 2001).
This paper presents an empirical calibration for the assessment of stoichiometry and crystal lattice properties of dolomite based on XRD peaks. Dolomite crystals lattice parameters (a = b and c in Å in a rhombohedral crystal system) are determined by unit cell refinement, and by using a newly compiled database of dolomite composition. From these the related %Ca of the analyzed dolomites could be estimated. This approach yielded a better accuracy and precision than the previous methods. In addition, it is a rapid and inexpensive technique which only requires a small amount of sample. Hence, it allows for quantifying dolomite stoichiometry of bulk sediments as well as cements. This workflow also results in a mineralogical quantification of the coexisting phases in the samples based on the Rietveld refinement.

STUDY LOCALITY AND MATERIAL
The direct applicability of the presented approach is demonstrated on Triassic carbonates (Upper Muschelkalk and Lettenkohle Formation) from the Chatelblanc 1 borehole located in the French Jura (Fig. 1). The Triassic is a period of transition associated with the beginning of the break-up of the Pangean supercontinent and the development of the Mesozoic basins. The Germanic facies province is characterized by a tripartite subdivision of the Triassic series (Ziegler, 1982) into the Scythian, the Anisian and Ladinian (including Muschelkalk carbonates and evaporates), and the Carnian to Norian (including Lettenkohle Formation). At the onset of the Late Ladinian, open-marine, clear water conditions induced the development of extensive carbonate platforms, Upper Muschelkalk dolomites were formed during burial dolomitization under fluids characterized by increased temperature and variable isotopic composition through burial. This is clear from their Ca content in dolomites which gradually approaches an ideal stoichiometry (from 53.16% to 51.19%) through increasing dolomitization. Lettenkohle dolostones consist of near-ideal stoichiometric (51.06%Ca) and well-ordered dolomites associated with anhydrite relicts. They originated through both sabkha and burial dolomitization. This contribution gives an improved method for the characterization of different dolomite types and their distinct traits in sedimentary rocks, which allows a better evaluation of their reservoir potential.
these grade westwards and northwards into dolomitic and evaporitic clays (Wolburg, 1969;Senkowiczowa and Szyperko-Silwczynska, 1975;Alten et al., 1980). The Jura Mountain range is a small, arcuate fold belt forming the frontal portion and the youngest deformation zone (from Middle Miocene onward) of the northwestern Alpine arc surrounded by Tertiary basins (Fig. 1). The Chatelblanc region is situated in the Haute Chaîne Jura of France (Fig. 1). The landscape of this area consists of folded mounts with a general NE-SW direction. The Chatelblanc 1 borehole is located on an anticlinal axis NE-SW corresponding to the front of the Haute Chaîne Jura which overlaps the Nozeroy Plateau (Fig. 1). The carbonate rock series of Upper Muschelkalk and Lettenkohle Formation are surrounded by two levels of decollement and are poorly or not affected by alpine compressive tectonic.
Forty carbonate samples from the Chatelblanc 1 borehole were collected from three core segments (No. 2, 3 and 4). Seventeen samples were taken from the Upper Muschelkalk (core segments 3 and 4 ranging from 2 289 m to 2 297 m depth), and twenty-three from the Lettenkohle Formation (core segment 2 ranging from 2 267 m to 2 277 m depth). The Upper Muschelkalk sedimentary rocks (limestones and dolostones) consist of mudstones, bioclastic wackestones and grainstones with rare evaporite nodules, while Lettenkohle sedimentary rocks are characterized by a succession of mudstones and evaporites (beds or displacive nodules of anhydrite) with some clay layers (see Fig. 3 in Sect. 4.1.1). Their facies are characteristic of a shallow lagoon environment.

X-Ray Diffractometry and Refinements
Each dry sample was uniformly ground in an agate mortar for XRD measurements. Alumina standard material (NIST) was added to each powder sample as an internal standard (50 wt%) and the mixture was again ground for few minutes until homogeneous. The Alumina cell parameters were taken from the NIST information file (SRM 676a). XRD patterns were collected using Cu radiation, from 0°to 80°2θ with a 0.017°2θ step size and 91 s. 2θ -1 counting time with a position-sensitive detector on an X'pertPro Panalytical diffractometer. The identification of minerals was performed on the measured digitized diffractograms, using the ICDD database (PDF4+). XRD analyses in θ-2θ configuration were undertaken with a parallel beam focused by an elliptic W/Si crystal   mirror. The measurements were performed on the samples in holders (several g of powder) and also enclosed in a 1 mm glass capillary (0.1 g of powder).
Structure and cell refinements were performed on the resulting diagrams with HighScore Plus 2.2 software. The structure refinement method is based on a least-squares refinement procedure. This approach allows for a quantitative assessment of the agreement between observed and calculated integrated intensities by refining structural parameters (Rietveld, 1969). Based on all measured diffraction peaks, Rietveld refinement is used to quantify the relative proportions of coexisting phases in samples. Cell refinement was used to determine the unit cell parameters of the dolomite crystals. The peak positions of the NIST Alumina are used to correct the peak shift error (in two-theta) of the powder diagrams. The instrumental characteristics of the diffractometer, influencing peak shapes, have been taken into account for the refinement with Caglioti coefficients optimized (U = 0.07509, V = -0.05312 and W = 0.03425) on powder mineral standards (alumina, calcite, zinc oxide, quartz, molybdenite, muscovite). The relative error on quantification via Rietveld refinement was calculated for common minerals (Kohler et al., 2009). The uncertainty for non-clay phases is logically linked to the phase proportion in the sample. When the abundance is equal to 5%, the associated uncertainty is 60% while it decreases at 10% when the proportion is equal to 30%. Abundances higher than 40% are related to uncertainties less than 5%.

Petrography and Stable (C and O) Isotope Ratios
Samples were subjected to petrographic observations including conventional and cathodoluminescence (CL) microscopy (Cathodyne OPEA; operation conditions were 14 to 16 kV gun potential, 500 to 600 μA beam current, 0.05 torr vacuum).
The various carbonate (calcite and dolomite) phases (matrix and cements) were micro-sampled (using a dentist's micro-drill) for measuring their carbon and oxygen stable isotope composition. Analyses were carried out at the University of Erlangen, Germany. During this process, the carbonate powders were reacted with 100% phosphoric acid (density >1.9;Wachter and Hayes, 1985) at 75°C in an online carbonate preparation line (Carbo-Kiel -single sample acid bath) connected to a ThermoFinnigan 252 mass-spectrometer (Thermo Electron Corp., Waltham, MA, USA). All values are reported in per mill relative to Vienna Pee Dee Belemnite standard (V-PDB) by assigning a δ 13 C value of +1.95‰ and a δ 18 O value of -2.20‰ to National Bureau of Standards (NBS) 19. Oxygen isotopic compositions of dolomites were corrected using the fractionation factors given by Rosenbaum and Sheppard (1986). Reproducibility based on a replicate analysis of laboratory standards is better than ±0.02‰ for δ 13 C and ±0.03‰ for δ 18 O.

Stoichiometry Calculation
A pioneering technique for the calculation of the dolomite crystal stoichiometry (%mol CaCO 3 ) was established by Lumsden (1979), who used the relationship between the calcium content and the measured d 104 spacing on X-ray profiles. Calcium in excess of stoichiometry (Ca 50 Mg 50 ) increases the d 104 distance of dolomite as a linear function of the excess Ca amount (Goldsmith and Graf, 1958;Runnells, 1970;Lumsden, 1979). Lumsden (1979) used two d 104 data points (Ca 50 Mg 50 and Ca 55 Mg 45 ) determined by Goldsmith and Graf (1958) Reeder and Sheppard (1984), Kimbell (1993) and Jones et al. (2001) reporting on the d 104 value and the average %Ca (measured by electron microprobe) documented that Ca-rich dolostones differ significantly from the "Lumsden line" and could commonly deviate in the order of 4-5%Ca (Jones et al., 2001). These authors assign such discrepancies to a significant difference between the percentage of Ca atoms per formula unit determined by electron microprobe analysis and by XRD. Hence, Jones et al. (2001) have proposed a means of determining stoichiometries and abundances of dolomite phase based on a XRD peak fit method focusing on the d 104 peak. The study presented here develops an empirical calibration for calculating the dolostones stoichiometry based on the determination of the unit cell parameters of the dolomite crystals. It is based on the Rietveld technique, not solely on the dolomite main diffraction peak (d 104 ), as the classical Lumsden equation or as the peak fit method of Jones et al. (2001), but on several dolomite diffraction peaks. According to a unit cell refinement (crystal lattice deformation), this approach gives access to the lattice parameters of dolomite crystals (a = b and c in Å). Using a new database of dolomite compositions as a function of lattice parameters allows calculating the %Ca in dolomites. This database is based on a comprehensive literature review. It is compiled from the crystallographic characteristics (cell parameters related to the lattice Ca percentage) of ninety-eight natural dolomites (Tab. 1). Dolomites solely composed of Ca and Mg (no Fe and Mn, except for the well studied Eugui reference) have been considered in order to test the method in a simpler case study. Depending on the authors, stoichiometry of these natural dolomites has been determined by four distinct methods (X-ray refinement, electron microprobe analysis, X-ray fluorescence spectroscopy analysis, Lumsden equation; Tab. 1) associated with an own   Barber et al. (1981), Reeder and Wenk (1983) and Jones et al. (2001) using other Eugui samples obtained a mean value of 50.4%Ca (Peakfit-XRD and EMP). Eugui sample analysis demonstrates that the uncertainty on the stoichiometry calculation using the approach presented in this study is related to the empirical calibration. The determination of lattice parameters values via the cell refinement is very accurate. It provides stoichiometry with a standard deviation estimated to be within ±0.05% and ±0.04% from a (= b) and c linear regressions respectively, and ±0.01% for the mean stoichiometry value from both linear regressions. The uncertainty related to the empirical calibration results in %Ca values deviating on average of ±1.90% and ±1.56% using a (= b) and c linear regressions respectively, at the 95% confidence level (Fig. 2). Hence, the %Ca difference for Eugui sample between values determined by this procedure (50.70%) and by EMP (51.30%) in this study is thus within the uncertainty interval.  standard deviation on the %Ca calculation. Some of these studies include dolomites with a small %Ca range (Spötl and Burns;1991;McCarty et al., 2006). However, they have been considered in order to propose an extensive database. From the collected data, two linear regressions can be calculated. A first one links the a (= b) crystallographic parameter to the %mol CaCO 3 in dolomite and a second one the c crystallographic parameter to the %mol CaCO 3 in dolomite (Fig. 2). A natural and nearly stoichiometric dolomite from the metamorphic carbonate complex of Eugui in Spain, extensively characterized (Barber et al., 1981;Reeder and Nakajima, 1982;Reeder and Wenk, 1983;Reeder and Markgraf, 1986;Navrotsky and Capobianco, 1987), was used as a comparative standard. This material is considered as ideally ordered with very few dislocations. The Eugui sample was used to test the reproducibility and the accuracy of the method proposed in this study for both lattice parameters refinement and stoichiometry calculation. The cell refinement analysis on the Eugui dolomite reference sample gives mean lattice parameters values of a (= b) = 4.8074(7) Å and c = 16.013(1) Å. The Eugui sample stoichiometry calculation based on the linear regressions from the database of dolomite compositions (Fig. 2) has a mean value of 50.69%Ca (50.70% on average based on Jones et al. (2001) have developed a dolomite stoichiometry calculation based on a X-ray peak fit method on multi-phases dolomites. Lettenkohle and Upper Muschelkalk dolomites used here for application correspond to the matrix of dolostones. They are related to uniform and symmetrical diffraction peaks and do not show composite peak-forms (produced by the superposition of two peaks; see Jones et al., 2001 andDrits et al., 2005). If stoichiometric differences exist within samples (due to various populations of dolomite crystals), the difference is too small to be observed on the measured diffraction peaks of dolomite. Dolomites analyzed from Lettenkohle and Upper Muschelkalk are thus considered as mono-phase dolomites. It is feasible to determine the lattice parameters of multi-phases dolomites by cell refinement, however it couldn't be tested on the French Jura Triassic mono-phase dolomites. It is then difficult to compare accuracies on stoichiometry results from the Jones et al. (2001) method with the approach of the present study. However, Jones et al. (2001) looked only at the position and profile of d 104 while the Rietveld and unit cell refinements used here are considering several dolomite diffraction peaks, providing a better accuracy and precision on results.

Comparison with Previous Studies
The study of McCarty et al. (2006) concerns dolomite stoichiometry and quantification of mono and two-phases samples using refinements on dolomite diffraction peaks. It also provides two linear equations relating a or c parameter to Ca content based on a combined X-ray, ICP-AES and XRF study. Based on the cell parameters values and the d 104 peak position determined in the present study, stoichiometry of Eugui dolomite has been calculated with the Lumsden (1979) and the McCarthy et al. (2006) linear equations for comparison (Tab. 2). As mentioned above, the stoichiometry of the Eugui sample of this study determined by microprobe is equal to 51.3%Ca. Stoichiometry calculated from the different linear equations show that the result from this study appears to be the closest value compared to the EMP value (Tab. 2). It also emphasizes that stoichiometry is underestimated with the three different equations. Calculation of stoichiometry with the Lumsden equation exhibits the largest standard deviation (0.42%) while the lowest one is associated to the present study (0.1%). The stoichiometry value determined using either a (= b) or c equations is much more consistent in this study (absolute difference of 0.01% with a standard deviation of 0.02%) than using McCarthy et al. equations (absolute difference of 0.41% with a standard deviation of 0.18%). The calculations made in this study show that stoichiometry is always under-estimated based on the a (= b) equation compared to the c equation of McCarthy et al. (2006) while no rule is underlined using both equations from the present work. Uncertainty on stoichiometry calculation given in McCarthy et al. (2006) is lower than in the present study. However, calculation on Eugui shows that results from this work are more accurate and precise comparing to results based on McCarthy et al. (2006) equations (Tab. 2).
The empirical calibration proposed in this study (Fig. 2) uses dolomites with negligible Fe and Mn while the Eugui dolomite reference sample and the Lettenkohle and Upper Muschelkalk dolomites do contain traces of Fe and Mn in their lattices. However, the %Ca calculated on Eugui dolomite by the approach presented here is consistent with the microprobe analysis and the previous studies (Barber et al., 1981;Reeder and Wenk, 1983;Jones et al., 2001). Therefore, this method can be equally applied to dolomites having few percent of Fe and Mn in their lattice. Care must be taken, however, when dolomites display higher Fe and Mn contents and tend toward the ankerite pole.

APPLICATION ON TRIASSIC CARBONATES
OF THE FRENCH JURA

Mineral Quantification
The main components of Upper Muschelkalk sedimentary rocks are both dolomite and calcite (Fig. 3). Quartz, feldspars, anhydrite, felsdpathoids and others minerals occur in minor or trace proportions. The main constituents of Lettenkohle sedimentary rocks are anhydrite and dolomite (Fig. 3). These

Figure 3
Detailed lithological log of the Upper Muschelkalk (core segments 3 and 4) and Lettenkohle Formation (core segment 2) of the Chatelblanc mineralogies alternate with intervals composed of quartz, feldspars, micas, chlorite group minerals and pyrite.

Petrographic Description and Paragenesis
The Upper Muschelkalk carbonate facies include two types of matrix (low-magnesium calcite and dolomite), three types of dolomite cements and three types of low-magnesium calcite cements (Fig. 4, 5). The original lime-micritic matrix (CM) is completely or partially preserved in samples.
Original calcite crystals form the foliated and prismatic structures of brachiopod shells whereas Calcite Cement 1 (CC1) is a mimetic replacement of precursor aragonite in bivalve shells (Fig. 4b). Calcite Cement 2 (CC2) fills biomoldic pores (Fig. 4e) and also occurs in rare vugs. Calcite Cement 3 (CC3) fills fractures and occasionally veins (Fig. 4d). The Dolomite Matrix (DM) is characterized by rhombs with an average size less than 20 μm, floating in the micritic limestone matrix (Fig. 4). According to the classification proposed by Sibley and Gregg (1987), this dolomite is defined by a unimodal texture and euhedral (planar-e type) to subhedral (planar-s type) rhombs. Dolomite Cement 1 (DC1) consists of a unimodal planar-e texture with crystals size ranging from 15 to 75 μm (Fig. 4c). Dolomite Cement 2 (DC2) occurs in biomolds and in rare vugs, is associated with CC2 (Fig. 4e) and defined by a polymodal texture and euhedral (planar-e type) crystals. Dolomite Cement 3 (DC3) is a blocky cement which fills fractures and rarely veins. It shows a polymodal planar-s texture composed by non-luminescent crystals with a size ranging from 50 to 1 500 μm. Fractures are filled either with CC3 or DC3 but never with both mineralogies. All dolomites have a mottled-red luminescence in CL except DC3. A relatively uniform Dolomite Matrix and two types of dolomite cements are distinguished in Lettenkohle sediments (Fig. 5, 6). The Dolomite Matrix (DM) is defined by a unimodal texture and subhedral (planar-s type) rhombs, whose size is less than 20 μm. The matrix dolomite rhombs have a bright orange CL-pattern with a diffuse zonation (cloudy centres surrounded by clear rims ; Fig. 5a). The Dolomite Cement 1 (DC1) occurs in rare vugs and has a polymodal planar-s texture composed by non-luminescent crystals with a size ranging from 15 to 150 μm (Fig. 5b). The Dolomite Cement 2 (DC2) is characterized by a blocky cement type (Fig. 5c, d). Dolomite crystals of this fracturefilling cement are defined by a polymodal planar-s texture, are non-luminescent under CL viewing and have sizes ranging from 50 to 1 500 μm. The petrographic relationships between these various calcite and dolomite phases shed light on the relative timing of their formation (Fig. 5). In the Upper Muschelkalk sedimentary rocks, the paragenesis proposed is based on the following arguments: -the crosscutting of CC1 by DC1 suggests an early precipitation of CC1; -the crosscutting of DC1 by CC2 indicates the previous occurrence of DC1; -the corrosion of DC2 by CC2 favours an earlier precipitation of DC2; -the crosscutting of all structures by fractures and veins, filled with CC3 or DC3, implies that they represent the latest carbonate precipitation. Evidence for a chronology between CC3 and DC3 is lacking. In the Lettenkohle sedimentary rocks: -the alternation of Dolomite Matrix (DM) and anhydrite (laminated macro-and microscopically) suggests their concomitant precipitation; -the DM corrosion by anhydrite (irregular nodules macroand microscopically) indicates a previous formation of the matrix; -the crosscutting of all structures by the fractures and veins (except anhydrite with a regular nodule form macro-and microscopically), filled with DC2, suggests that DC2 represents the latest dolomite precipitation.

Description of Carbon and Oxygen Stable Isotopic Compositions
The isotopic ratios from well-preserved Middle Triassic brachiopods (low-magnesium calcite) represent the seawater composition (Korte et al., 2005; Fig. 7). Marine dolomite δ 18 O must not be directly compared with marine calcite δ 18 O as the equilibrium fractionation between dolomite and water at low temperature is debatable (Land, 1980). A common method to avoid this problem is to calculate the equilibrium isotopic composition of calcite for a particular fluid and temperature, and then to assume a geologically reasonable value for Δ 18 O dol-cal (= δ 18 O dolomite -δ 18 O calcite V-PDB), in order to derive an estimate of the equilibrium isotope composition of dolomite from that fluid at that temperature. A mean value of Δ 18 O dol-cal widely accepted to determine the marine dolomite signature, and applied here, is 3‰ (Budd, 1997;Fig. 7

Interpretation of Diagenetic Environments
The  were available for incorporation into calcite), or were reducing but lacked a source of sufficient Mn 2+ to generate a luminescent phase, and alternatively the fluids contained so much Fe 2+ relative to Mn 2+ that any luminescence generated is completely quenched. The δ 18 O signature of some of these calcites (CM, CC1 and CC2) is close to reconstructed Triassic marine calcite compositions (Fig. 7). This suggests that the fluid responsible for those precipitations most likely was seawater, at least for the calcite phases associated to the less depleted isotope values. Based on the paragenesis (Fig. 5), the fracture fill cement (CC3) represents the latest precipitation in sediments. CC3 is associated to the lowest δ 18 O value indicating formation from warm (hot?) waters during burial. The decrease in δ 18 O (Fig. 7) could thus be associated to an increase of temperatures of precipitation during burial. The positive δ 13 C values, close to the predicted paleo-seawater composition (Fig. 7), suggest a local carbon source represented by the dissolution of marine carbonates. The decrease in δ 13 C could be related to the increasing inputs of 12 C associated with organic matter alteration during burial. All of this results in a linear covariance in δ 18 O-δ 13 C through burial. The mottled red luminescence of Upper Muschelkalk Dolomite Matrix and Cements (DC1 and DC2) indicates considerable amounts of Mn had to be present relative to Fe, pore waters had thus to be reducing. As dolomitization requires an ample Mg source, seawater could be the dolomitizing fluid. However, the dolomites are more depleted in δ 18 O compared to the calcites and they differ substantially from the oxygen signature of predicted Triassic marine dolomites. If the dolomites are originated from seawater they should display a more enriched stable isotopic composition compared to the calcitic cements, which they do not (Fig. 7). Consequently, the Upper Muschelkalk dolomites must be the result of the circulation of burial fluids. As with the calcites, the linear trend in dolomite δ 18 O values is interpreted to reflect increasing temperature with increasing burial as dolomitization proceeded. In Lettenkohle rocks, the co-occurrence of dolomite and anhydrite suggests a dolomite formation in an evaporative environment. In such environments, 16 O is selectively removed by evaporation from the water body, so that the residual evaporated water is enriched in 18 O (Epstein and Mayeda, 1953;Lloyd, 1966). As a result, 18 O enriched values could indicate a dolomitization from higher salinity waters (Land, 1980). There is no simple relationship between isotopic composition and salinity, as interaction with the atmosphere and groundwater can decrease the degree of isotope enrichment (Major et al., 1992;Meyers et al., 1993) Finegrained Lettenkohle dolomites (DM) do indeed have more positive δ 18 O compositions and more variable δ 13 C compositions compared to those of the Upper Muschelkalk matrix dolomites. Lettenkohle dolomite isotope values are more negative than what would even be expected for a dolomite from a Triassic seawater (Fig. 7). This discrepancy can be explained by a diagenetic overprint. The Lettenkohle matrix dolomites exhibit a cloudy-centre-clear-rim texture. The cloudy centre often represents synsedimentary or early postdepositional dolomite precipitation, while the clear rims are the evidence of a continuing dolomite formation during burial (Machel, 2004;Choquette and Hiatt, 2008). Such overprinting during burial diagenesis would have also generated a decrease in the stable isotope signature of the Lettenkohle matrix dolomites relative to a purely evaporated seawater signal. In both Upper Muschelkalk and Lettenkohle sedimentary rocks, diagenetic conditions generate coarser dolomite crystals, as cements in fractures (DC3 in Upper Muschelkalk and DC2 in Lettenkohle) originated from a non original seawater fluid, characterized by an elevated temperature.

Dolomite Stoichiometry
Several types of Dolomite Matrix and Cements, associated to different crystal sizes, have been underlined by petrography (Fig. 4-6). However, some carbonate phases couldn't be micro-sampled as a single phase explaining the distinction between mono-and multi-phase samples (Fig. 7). For this reason, the stoichiometry calculated here is only associated to the Dolomite Matrix of samples. Only the DC2 in Lettenkohle have been micro-sampled as a single phase due to a sufficient amount of cement occurring in a large fracture (sample 2-3e).
The resulting stoichiometric calculations from empirical calibration (Fig. 2) show a distinction between dolomites of Upper Muschelkalk and Lettenkohle (Tab. 3). Although Carbon and oxygen isotope compositions of the various carbonate phases (dolomite/calcite, matrix/cement) of Upper Muschelkalk and Lettenkohle sedimentary rocks (present study). Grey dashed line square represents the isotopic values of well-preserved brachiopods (in low-magnesium calcite) precipitated from Middle Triassic seawater (Korte et al., 2005). Dark dashed line square symbolizes the predicted stable isotope record for dolomites precipitated with respect to the Triassic seawater (Δ 18 O dol-cal = +3‰; Budd, 1997  sedimentary rocks, the abundance of dolomite in samples is correlated to the stoichiometry (Fig. 8). When the dolomite amount increases in sediments dolomite is related to a lower %CaCO 3 . However, such a trend is not as clear in the Lettenkohle samples (Fig. 8). The stoichiometry calculation for Upper Muschelkalk and Lettenkohle dolostones is robust for a wide range of dolomite abundances (Fig. 9) as the difference between the stoichiometries calculated with the a (= b) and c linear regressions is in general smaller than 0.6%. This difference tends to get larger only when the dolomite abundance in sample is smaller than 6% (Fig. 9). Upper Muschelkalk dolomites show higher and scattered lattice parameters (a = b and c) values than Lettenkohle dolomites, displaying lower and less variable lattice parameters (Fig. 10).
The deficiency of larger Ca ions in the unit cell of Lettenhkohle dolomites compared to Upper Muschelkalk dolomites is potentially a cause for the contraction in the a direction (see Rosen et al., 1988). The expansion of the c parameter has been previously related to a cation disordering (Reeder and Wenk, 1983) or other lattice defects (Miser et al., 1987). This is an explanation for the c variability of Upper Muschelkalk dolomites and could be caused by a faster crystallization (Rosen et al., 1988) compared to Lettenkohle dolomites.

Dolomites and Reservoir Properties
The Ideal dol. (Rosen et al., 1989) Ideal dol. (Reeder, 1990) Rosen et al., 1989;Reeder, 1990) are situated below this line due to the unit cell contraction when dolomite is well ordered. Eugui sample from this study is also indicated. The three Lettenkohle samples associated to inaccurate stoichiometry values are not considered (see Tab. 2). (Fig. 10), associated with anhydrite, is in agreement with Warren (2000) proposing that dolomites formed in evaporite settings tends toward ideal stoichiometry and to a generally better ordered crystal lattice. Although Lettenkohle dolomites have undergone an early diagenetic overprint, they show a lower %CaCO 3 than Upper Muschelkalk dolomites probably due to their original evaporative environment of formation.
Upper Muschelkalk dolomites have been associated with a dolomitization during burial, marked by the %Ca of dolomites tending to ideal stoichiometry through dolomitization (Fig. 8).
In contrast, a sabkha model combined to a burial dolomitization are favoured for explaining Lettenkohle dolomite formation. Arguments that support the sabkha-related dolomitization are based on their near-perfect stoichiometry, their well-ordered lattice parameters and the occurrence of evaporite relicts, evidenced by nodular and displacive anhydrite (Fig. 3, 10, Tab. 3). Shallow-water evaporative environments are associated with strong microbial activity, promoting dolomite precipitation and early dolomitization of other carbonates at low temperatures (Schreiber and El Tabakh, 2000). As a result of elevated salinity in these environments, calcite cementation of the associated deposits may not be prominent, as it is in normal marine settings and dolomite forms. This relation might explain the pervasive matrix dolomitization in Lettenkohle sediments which differs from Upper Muschelkalk sediments.
The dolomite recrystallization leads to the transformation of a non stoichiometric dolomite to a pure stoichiometric dolomite mineral in equilibrium with its pore fluids, including intermediate stages consisting of more disordered crystals (i.e. Ostwald ripening; Sibley et al., 1994). This process commonly generates large crystals which grow at the expense of smaller ones (Morse and Casey, 1988;Nader et al., 2004). Dolostone reservoir properties are related to their crystal size distributions, with more permeable dolostones being those consisting of overall larger crystals (Lucia, 1995). Therefore, in stable nearly stoichiometric sabkha-type dolomites, as Lettenkohle finely-crystalline dolostones, no further reservoir-enhancement is expected with burial and recrystallization. In contrast, reservoir properties of metastable poorly stoichiometric dolostones, originally composed of high Ca content dolomites, have the potential to improve with burial/ recrystallization. However, on a larger scale, non stoichiometric dolomites could dissolve in one area and reprecipitate in another causing either porosity enhancement or porosity occlusion.

CONCLUSION
This paper documents an approach for the stoichiometry calculation of dolomites based on using linear regressions linking the %Ca and the unit cell parameters values (a = b or c) obtained from a cell refinement on XRD profiles, also used for mineralogical quantification. Because mineral abundance and unit cell parameters determinations are not solely based on the d 104 main dolomite diffraction peak, this approach allows quantification and stoichiometry calculation of dolomite with a better accuracy and precision relative to previous methods. The value and applicability of this method is directly demonstrated on Triassic reservoir rocks. The dolomite types from Upper Muschelkalk and Lettenkohle could be well distinguished by means of the stoichiometry calculation approach proposed in this contribution. Based on the stoichiometry level, the Upper Muschelkalk dolomites were prone to recrystallization during burial diagenesis, leading to increasing crystal sizes which potentially can enhance their reservoir quality. The originally nearstoichiometric, very finely crystalline, sabkha dolomites of Lettenkohle were less affected by recrystallization and remained with a lower reservoir quality, although they were