Thermodynamic properties of chlorite CCa-2. Heat capacities, heat contents and entropies

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Geochimica et Cosmochimica Acta 73 (2009) 4738–4749 www.elsevier.com/locate/gca

Thermodynamic properties of chlorite CCa-2. Heat capacities, heat contents and entropies H. Gailhanou a,*, J. Rogez b, J.C. van Miltenburg c, A.C.G. van Genderen c, J.M. Grene`che d, C. Gilles a, D. Jalabert e, N. Michau f, E.C. Gaucher a, P. Blanc a b

a BRGM, 3 av. Claude Guillemin, BP 6009, 45060 Orle´ans Cedex 2, France IM2NP-CNRS, Faculte´ des Sciences et Techniques de Saint-Je´roˆme, Case 251, 13397 Marseille Cedex 20, France c Chemical Thermodynamics Group, State University of Utrecht, Padualaan 8, 3508 TB Utrecht, The Netherlands d LPEC, UMR CNRS 6087, Universite´ du Maine, 72085 Le Mans Cedex 9, France e Centre de Microscopie Electronique, Universite´ d’Orle´ans, 45071 Orle´ans Cedex 2, France f ANDRA, 1/7 rue Jean Monnet, 92298 Chaˆtenay-Malabry Cedex, France

Received 7 July 2008; accepted in revised form 29 April 2009; available online 28 May 2009

Abstract The heat capacities of the international reference clay mineral chlorite CCa-2 from Flagstaff Hill, California, were measured by low temperature adiabatic calorimetry and differential scanning calorimetry, from 5 to 520 K (at 1 bar). The studied chlorite is a Fe-bearing trioctahedral chlorite with an intermediary composition between ideal clinochlore (Si3Al)(Mg5Al)O10(OH)8 and chamosite (Si3Al)(Fe5Al)O10(OH)8. Only few TiO2 impurities were detected in the natural chlorite sample CCa-2. Its structural 2þ formula, obtained after subtracting the remaining TiO2 impurities, is (Si2.633Al1.367)(Al1.116Fe3þ 0:215 Mg2.952Fe1:712 Mn0.012Ca0.011)O10(OH)8. From the heat capacity results, the entropy, standard entropy of formation and heat content of the chlorite were deduced. At 298.15 K, the heat capacity of the chlorite is 547.02 (±0.27) J mol1 K1 and the molar entropy is 469.4 (±2.9) J mol1 K1. The standard molar entropy of formation of the clay mineral from the elements is 2169.4 (±4.0) J mol1 K1. Ó 2009 Elsevier Ltd. All rights reserved.

1. INTRODUCTION The need for a better understanding of chlorite equilibria in low temperature geochemical systems stems from their importance in various environments. Among them, it has been demonstrated that this type of clay may buffer CO2 fugacities in sedimentary rocks (Coudrain-Ribstein et al., 1998; Gaucher et al., 2006). The compositional variations of chlorites can also record significant changes in O2 fugacities related to circulation of geothermal fluids (Mas et al., 2006). In clay barriers of nuclear waste disposals, chlorite mineral may appear consequently to the degradation of illite and smectite minerals in contact with the steel overpack

*

Corresponding author. E-mail address: [email protected] (H. Gailhanou).

0016-7037/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2009.04.040

(Guillaume et al., 2003; De Combarieu et al., 2007). They can also be used as geothermometers in low to medium temperature systems (Cathelineau and Nieva, 1985; Teklemariam et al., 1996). More generally, chlorites are associated with metamorphic rocks with low to medium grade regional metamorphism. In soils and sedimentary rocks, they are largely inherited as primary minerals from metamorphic or igneous rocks, or they occur as alteration products from minerals such as hornblende, biotite and other ferromagnesian minerals (Barnhisel and Bertsch, 1989). Chlorite minerals are unstable in acidic environment. They are classically found as alteration products at the interface between cement and clay barriers (Gaucher and Blanc, 2006). In spite of this wide field of applications, thermodynamic data on chlorite are particularly scarce. There are few measured thermodynamic data available for chlorite minerals to our knowledge. They have been obtained from solubility

Thermodynamic properties of chlorite CCa-2

experiments (Kittrick, 1982; Aja and Small, 1999; Aja, 2002; Aja and Darby Dyar, 2002), or from regressions from hightemperature, high-pressure phase equilibrium experiments (Jenkins and Chernosky, 1986; Berman, 1988). Moreover, heat capacities of several chlorites have been measured using calorimetry by Henderson et al. (1983); Hemingway et al. (1984) and Bertoldi et al. (2001, 2007). Thus, a natural chromian clinochlore was studied by Henderson et al. (1983) using low temperature adiabatic calorimetry. Hemingway et al. (1984) measured the heat capacities of two chlorites with respectively high iron and low iron contents, by low temperature adiabatic calorimetry and DSC, between 5 and 500 K. Finally, Bertoldi et al. (2001, 2007) carried out heat capacity measurements on five natural chlorites, with chemical compositions distributed between end-members clinochlore and chamosite, using heat-pulse calorimetry, between 5 and 300 K. To conclude, it can be stated that no complete set of thermodynamic data (G, H, S, Cp) is available for a particular chlorite composition. This study aims to determine the first set of thermodynamic functions (G, H, S, Cp) by calorimetric method, in the range 0–520 K (at 1 bar) for a natural Fe-bearing chlorite. This is a trioctahedral chlorite, such as the majority of minerals belonging to the chlorite group (Bailey, 1975). It means that both octahedral sheets in the 2:1 layer and in the interlayer hydroxide sheet are trioctahedral. The chlorite composition is intermediary between the end-member clinochlore (ideal formula (Si3Al)(Mg5Al)O10(OH)8) and the end-member chamosite (ideal formula (Si3Al)(Fe5Al)O10 (OH)8). This paper deals with the heat capacity measurements and the derived entropy and heat content of the chlorite mineral, using the same calorimetric method as described in the thermodynamic study of anhydrous illite, smectite and interstratified illite–smectite minerals (Gailhanou et al., 2007). A further paper will be dedicated to the enthalpy of formation and the Gibbs free energy of formation of this first list of minerals.

measured by adiabatic calorimetry, between 0 and 380 K, and by differential scanning calorimetry, between 380 and 520 K. As adiabatic conditions are difficult to maintain above 380 K with a low temperature calorimeter, DSC has been used as a complementary method for higher temperatures (Gailhanou et al., 2007). 2.1. Analysis and characterization of the sample The sample is the natural chlorite CCa-2 from Flagstaff Hill, California, USA (Post and Plummer, 1972) and belongs to the Source Clay Project of the Clay Minerals Society. X-ray diffraction (XRD) analyses were performed on a Siemens D5000 diffractometer equipped with variable slits, a Co anticathode and a diffracted beam monochromator to characterize and quantify impurities and clay phases. Firstly, in order to determine the abundances of clay and non-clay minerals, an X-ray pattern on powder was acquired from 4° to 84°2h with a rotation speed of 0.02°2h/s (Fig. 1). Powder sample was top-loaded into the sample holder cavity of 2.5 cm diameter without compaction to preserve random orientation (Hillier, 2000). The proportion of impurity was assessed by applying a least-squares fit method using XRD patterns of individual phases. Secondly, for clay minerals identification only, the sample was analysed by XRD, by making a glass slide deposit of the <2 lm fraction and saturating it with ethylene glycol for 12 h. X-ray patterns were acquired on oriented deposit from 2° to 36°2h with a rotation speed of 0.02°2h/s. The clay phases were quantified using the model of Blanc et al. (2007), which is based on a linear combination of simulated patterns of clay minerals. Afterwards, no mineral impurity was detected from XRD analyses. In particular, the modelling of the powder and glycolated patterns does not show any presence of phyllosilicates other than trioctahedral chlorite. The values of unit-cell parameters a, b and c were determined considering the powder pattern of chlorite (Table 1). Considering a monoclinic space group C2/m for chlorite structure, peak positions and b angle were refined using Powdercell 2.3 (Kraus and Nolze, 1996). Lattice parameters a and b were calculated from the (0 6 0) peak

2. MATERIALS AND METHODS

10

20

30

(06,33) – 1.547 Å

(005) - 2.83 Å

(004) - 3.54 Å

(003) - 4.72 Å

(002) - 7.07 Å

(001) - 14.15 Å

Intensity (arbitrary units)

Firstly, a precise mineralogical characterization was carried out on the chlorite sample. Then, heat capacities were

0

4739

40

50

60

70

80

Position (°2θ Co Kα) Fig. 1. Powder XRD pattern of chlorite CCa-2. The (00‘) and (06,33) reflections of chlorite are labelled.

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Table 1 Unit-cell parameters for the chlorite CCa-2. ˚) ˚) ˚) a (A b (A c (A

b (°)

˚ 3) V 0m (A

Chlorite CCa-2

97.33

211.82

5.35(7)

9.27(9)

14.26(6)

Table 2 Chemical composition (wt%) of the chlorite CCa-2 sample.

position, using the approximation a ¼ pbffiffi3 (Drits and Tchoubar, 1990). The c parameter was obtained from the (0 0 1) d0 0 1 peak position according to c ¼ sinðbÞ . Molar volume V 0m at ˚ 3, was calculated using relation (1): 298.15 K, expressed in A V 0m ¼

abc sinðbÞ N0 Z 1024

ð1Þ

where Z = 2 is the number of formula units per cell, N0 is the Avogadro number. Some High Resolution Transmission Electron Microscopy (HRTEM) images of the chlorite were taken using a CM20 PHILIPS with an acceleration voltage of 200 kV. The TEM samples were prepared by dispersing the powdered samples in alcohol by ultrasonic treatment, dropping them onto a porous carbon film supported on a copper grid, and then drying them in air. Many large size clay particles were observed, sometimes attaining a size of 6–8 lm (Fig. 2). Chlorite mineral was particularly well-crystallized. Moreover, some TiO2 impurities were detected; it was then assumed that the total amount of Ti was present as TiO2 impurities only (Table 2). The homogeneity of the sample with regard to the major elements Si, Al, Fe, Mg and Mn was checked by microprobe. Microprobe analyses were performed using a CAMEBAX SX50 electron microprobe with 15 kV accelerating voltage, 12 nA beam-current intensity and 1–2 lm beam width. Counting time was 10 s for major elements Si, Al, Fe, Mg, Mn and Ti. Standards used included both well-characterized natural minerals and synthetic oxides. Matrix corrections were performed using the PAP procedure (Pouchou and Pichouar, 1984). The chemical analyses were expressed in wt% oxides. After subtracting the contribution of 0.77 wt% TiO2 impurities, the chemical analyses were transformed into a

C mineral C total SiO2 Al2O3 FeO Fe2O3 CaO MgO MnO K2O Na2O TiO2 P2O5 H2O Total

Chlorite CCa-2

Analytical techniques

<0.02 <0.03 25.0 20.0 19.4 2.71 0.1 18.8 0.13 <0.05 <0.2 0.77 <0.05 11.9 98.8

(a) (a) (b) (b) (c) (c) (b) (b) (b) (b) (b) (b) (b) (d)

Notes: Analytical techniques: (a) elemental chemical analysis, (b) X-ray fluorescence, (c) volumetric titration and (d) weight loss while heating up to 1000 °C.

structural formula. A statistical analysis of the 172 chemical compositions was performed using the Principal Components Analysis method (XLSTATÓ, 2006). Graphic representation of the chemical compositions makes it possible to detect and to identify potential significant chemical dispersions, while the representation of the multiple correlations aims to understand the links between the chemical elements in the structure (Fig. 3). Hence, the strong anticorrelation (72%) between silica and aluminium is well described by the first eigenvector F1 and corresponds to the tetrahedral substitution of Si by Al. Moreover, the eigenvector F2 shows a weaker anti-correlation (39%) between Mg and Fe, equivalent to the anti-correlation (34%) between Mg and Al. This corresponds to the substitution of Mg by Fe and Al in the octahedral sites. The eigenvector F3 is only determined by Mn, which is statistically not correlated to any other element. The graphical representation of the analysis (black dots in Fig. 3) shows only one popu-

Fig. 2. HRTEM images of well-crystallized chlorite CCa-2. Typical crystallites with (a) small and (b) large sizes.

Thermodynamic properties of chlorite CCa-2

Mg

0.8

-- axis F2 -->

b

1

1

0.6 0.4

0.4

0.2 0 -0.2

Si

Al

Mn

-0.4

-1

Mg Fetot

0.2 0

Al

-0.2

Si

-0.4 -0.6

-0.6 -0.8

Mn

0.8 0.6

-- axis F3 -->

a

4741

Fetot

-0.8 -1

-1 -0.8 -0.6 -0.4 -0.2 0

0.2 0.4 0.6 0.8

-1 -0.8 -0.6 -0.4 -0.2

1

0

0.2 0.4 0.6 0.8

1

-- axis F1 -->

-- axis F1 -->

Fig. 3. Statistical treatment by PCA of the 172 microprobe analyses of the chlorite CCa-2. Biplot representation of individuals and variables onto plans defined by the eigenvectors (a) (F1, F2) and (b) (F1, F3).

associated with octahedral Fe3+ (Fig. 5). Recent Mo¨ssbauer investigation on chlorite group minerals indicates that the use of three discrete doublets for Fe2+ is justified by molecular orbital calculations (Lougear et al., 2000). This Mo¨ssbauer study provided considerable evidence that ordering effects of Fe2+ occur on the three octahedrally coordinated sites M(1), M(2), and M(3). The distribution -3

0

3

0

3

1.00

0.99

relative transmission

lation of particles. Moreover, standard deviations associated with the elements in the structural formula are low (Table 4). This result reveals that chlorite CCa-2 is chemically homogeneous, i.e., chlorite particles have very similar compositions. Chemical analyses for Si, Al, Ti, Fe (total), Mn, Ca, Mg, K, Na and P were performed using a PW2400 sequential X-ray fluorescence spectrometer (Philips). In order to determine the amount of Fe2+, the samples were dissolved in a non-oxidizing HF-H2SO4 solution and the released Fe2+ was titrated by a volumetric method in acidic K2CrO4 solution. The amount of total carbon was determined by infrared spectroscopy after burning the samples at 900 °C in an oxygen atmosphere. The measurement of carbonates was performed by dissolution in an HCl solution and titrating the CO2 produced by a volumetric method. The results of the analysis are presented in Table 2, expressed in weight percent of oxides; the relative uncertainties are estimated at ±2%. The proportions of ferric and ferrous iron were also determined by 57Fe Mo¨ssbauer spectrometry. The apparatus is a conventional constant acceleration Mo¨ssbauer spectrometer, in transmission geometry, using a 57Co(Rh) source. The isomer shift values were corrected according to the calibration of the velocity scale made from a-Fe at 300 K. For each spectrum, the amount of Fe in the sample was about 5 mg/cm2. Mo¨ssbauer spectra were obtained at 4.2, 10, 77 and 300 K. Because 300 and 77 K spectra exhibit an asymmetrical quadrupolar structure as is illustrated in Fig. 4a, further measurements were performed by a 54° (magic angle) rotation of the sample with respect to the c-beam (Greneche and Varret, 1982a,b): the disappearance of the symmetry as shown in Fig. 4b, allows the presence of preferential orientation to be concluded, probably originated from the chlorite flake shape. The spectral decompositions into quadrupolar doublets for Fe3+ are rather difficult, since a very small amount of Fe3+ is present in the sample and the spectra exhibit large bases. Mo¨ssbauer spectra at 77 and 300 K were fitted considering a combination of three doublets for Fe2+, associated with three different octahedral sites, and considering two doublets

0.98

b

1.00

300 K 0.98

0.96

a -3

V [mm/s] Fig. 4. Mo¨ssbauer spectrum recorded at 300 K (a) on the powdered sample and (b) after rotation of the sample by 54°. The decomposition makes it possible to compare Fe2+ (blue line) and Fe3+ (red line) contributions (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.).

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relative transmission

1.00

Fe2+ 0.95

Fe3+

77 K

0.90

-3

0

3

V [mm/s] Fig. 5. Mo¨ssbauer spectrum recorded at 77 K and its decomposition as discussed in the text (insert shows decomposition into Fe2+ and Fe3+ quadrupolar components).

of Fe2+ among the three crystallographic positions follows Mð1Þ Mð2Þ Mð3Þ inequality xFe2þ < xFe2þ < xFe2þ . This relation was verified for several chlorite samples, including a ripidolite CCa-1 with a similar composition to CCa-2 (Lougear et al., 2001). However, the decomposition parameters for Fe2+ in chlorite CCa-2 are rather different from those of CCa1. These differences may be justified by cationic disorder as the environments of Fe2+ and Fe3+ cations are disturbed by the presence of other cations in octahedral sites. In chlorite CCa-2, only the M(1)-site has been identified from the spectral decomposition for Fe2+, as it is characterized by a significantly smaller quadrupole splitting compared to that of the M(2)- and M(3)-sites (De Grave et al., 1987). The spectral decomposition in two octahedrally coordinated doublets for Fe3+ may also be justified by cationic disorder. In particular, a broadening of the hyperfine structure associated with Fe3+ may result from this disturbance. The corresponding hyperfine parameters are listed in Table 3. The ratio Fe2+/(Fe2++Fe3+) is estimated at 0.90 (±0.02). This is in good agreement with the results of the preceding method based on X-ray fluorescence and volumetric titration of Fe2+, which led to a ratio of 0.89. This latter value was retained for the calculation of structural formula of the chlorite.

The 4.2 K spectrum reveals a partial splitting of the quadrupolar structure into a magnetic feature, indicating the occurrence of iron-rich domains or clusters giving rise to a magnetic ordered structure either blocked or with superparamagnetic fluctuations (Huffman and Dunmyre, 1975) (Fig. 6a). It also results from the fit of the total spectrum that the magnetic ordering would be associated with mainly Fe2+, and would concern about 28 mol.% of total Fe at 4.2 K. Contrary to the 4.2 K spectrum, the hyperfine structure at 10 K is unambiguously ascribed to a quadrupolar structure, the parameters of which are fairly consistent with those observed at 77 and 300 K (Fig. 6b). It has been thus deduced that a magnetic transition does occur between 4.2 and 10 K. This result is consistent with the 57Fe Mo¨ssbauer investigation by Townsend et al. (1986) about magnetic interaction at low temperature in chlorites of various Fe compositions. According to these authors, magnetic order in chlorites is established inhomogeneously in a range of temperatures below 7 K, as a result of a non-uniform distribution of iron atoms and further cationic species in octahedral sites of the hydroxide sheet and 2:1 layer. Finally, the resulting mean structural formula of chlorite CCa-2 (Table 4) was obtained by subtracting 0.77 wt% TiO2 impurity from the chemical composition of Table 2.

Table 3 Hyperfine parameters of the chlorite CCa-2 sample (IS, C, QS and d correspond to isomer shift, linewidth at half height, quadrupolar splitting and %Fe2+/(%Fe2+ + %Fe3+), respectively). Doublet 3+

300 K

Fe Fe3+ Fe2+ Fe2+ Fe2+ Fe3+ Fe3+ Fe2+ Fe2+ Fe2+

77 K

Notes:

(*)

(*)

(*)

IS (mm/s) ±0.02

C (mm/s) ±0.02

QS (mm/s) ±0.04

% ±1

d ±0.02

0.37 0.36 1.13 1.14 1.10

0.38 0.38 0.26 0.30 0.65

1.10 0.61 2.70 2.48 2.18

4 6 44 35 11

0.90

0.43 0.43 1.25 1.26 1.24

0.51 0.40 0.26 0.26 0.31

1.10 0.61 3.00 2.80 2.53

6 5 32 42 15

0.89

means that Fe2+ is located in crystallographic M(1)-site.

Thermodynamic properties of chlorite CCa-2 -10

-5

0

5

10

1.00

4743

of the chlorite sample (Table 2). The amount of TiO2 impurity in the dried sample is 0.78 wt%. 2.2. Adiabatic calorimetry

0.98

4.2 K

relative transmission

a

2+

3+

Fe

Fe

0.99

0.96

10 K 0.93

b -10

-5

0

5

10

V [mm/s] Fig. 6. Mo¨ssbauer spectra recorded (a) at 4.2 K with a decomposition showing Fe3+ contribution involving both magnetic and quadrupolar contributions, quadrupolar Fe2+ and magnetic ordered Fe2+ components, and (b) at 10 K with two quadrupolar doublets corresponding to Fe3+ and Fe2+ components.

This structural formula was then used for calorimetric measurements and calculations. It is in good agreement with the mean structural formula obtained from microprobe analysis also given in Table 4. The molar mass of the chlorite CCa-2 is 617.460 g mol1. In the following, ‘clay sample’ or ‘chlorite sample’ will mean ‘chlorite mineral with TiO2 impurities’, whereas ‘clay mineral’ will refer to ‘chlorite mineral’. Before carrying out calorimetric measurements, the chlorite sample was dried at 120 °C over 24 h, in order to remove pore and adsorbed water on external surfaces of the crystallites. The impurity content with respect to the dried sample was calculated by removing water (except mineral structural hydroxyl group) from the composition Table 4 Mean structural formula of the chlorite CCa-2 obtained (a) from overall chemical analyses and (b) from microprobe analysis, both calculated after subtracting TiO2 impurities. Numbers in parenthesis correspond to standard deviations.

Si Al Fe2+ Fe3+ Mg Mn Ca

Mean structural formula (a)

Mean structural formula (b)

2.633 2.483 1.712 0.215 2.952 0.012 0.011

2.66 (0.04) 2.55 (0.07) 1.66 (0.05) 0.21 (0.01) 2.89 (0.07) 0.007 (0.005) –

The heat capacities were measured between 5 and 380 K, with the CAL V adiabatic calorimeter, built in the State University of Utrecht and described by van Miltenburg et al. (1987, 1998). The vessel in gold-plated copper has a volume of 11 cm3. It was filled with 8–10 g of anhydrous clay sample under a nitrogen atmosphere. In an airtight chamber, the atmosphere inside the vessel was removed and replaced by helium gas at 1 kPa to improve heat exchanges. The vessel was hermetically sealed in the helium chamber by means of a screwed cap compressing a thin gold plate seal. The temperature of the vessel was measured by means of a 30 ohms Rh/Fe thermometer, calibrated by Oxford Instruments to 0.001 K, from the ITS-90 temperature scale (Preston-Thomas, 1990). The calorimeter was checked with n-heptane and synthetic sapphire, showing a deviation less than ±0.2% from the recommended values of these materials (van Miltenburg et al., 1987). Measurements were performed in the intermittent mode, by alternating heating and stabilization periods of about 500 s. Between 5 and 30 K, heating and stabilization periods of about 100 to 150 s were used. The repeatability of the measurements was good, with maximum deviations of ±1% between 5 and 30 K, ±0.05–0.1% between 30 and 100 K, and ±0.03% above 100 K. Each heat capacity measurement corresponds to an increase in temperature of 2–3 K during the heating period. For a given sample, various measurement series were performed, so that each interval of temperature was covered at least twice.

2.3. Differential scanning calorimetry The heat capacities were measured between 300 and 520 K using a Calvet DSC111 differential scanning calorimeter from Setaram, in the TECSEN laboratory. The vessel made of stainless steel, with a volume of 0.18 cm3, was filled with about 140 mg of anhydrous clay sample and sealed with a nickel ring, under a nitrogen atmosphere. DSC calibration consisted of a commonly used procedure for temperature and enthalpy calibration and a heat capacity calibration. Standard elements indium (Goodfellow, purity 99.999%), zinc (Goodfellow, purity 99.999%) and aluminium (Goodfellow, purity 99.999%) were used for temperature and enthalpy calibration (Stølen and Grønvold, 1999), and synthetic sapphire (National Bureau of Standards, Ditmars et al., 1982) for the heat capacity calibration, in the same conditions of nitrogen flow rate and heating rate as for Cp measurements on chlorite sample. The Cp measurements on chlorite CCa-2 were performed at a 2 K/min heating rate. The intermittent method was implemented with an increase in temperature of 2.5 K for the measurement period, alternated with a temperature stabilization period of 800 s, in which the heat flow recovered the baseline value. At least two DSC runs were carried out for each material (blank, standard and sample runs).

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3. RESULTS 3.1. Heat capacity measurements 3.1.1. Heat capacity of the sample All of the heat capacity values measured respectively by adiabatic calorimetry between 7 and 380 K and by DSC between 380 and 520 K are given in Table EA-1 of Electronic Annex EA-1. The values obtained by adiabatic calorimetry and by DSC are in good agreement (Fig. 7). Below 7.26 K, the heat capacities are very low and too close to the values corresponding to the empty cell to get reliable results. Thus, between 0 and 7.26 K, the Debye approximation Cp  Cv = a. T3 at very low temperatures was used. The a coefficient was evaluated taking into account the first measurement at 7.26 K (T in K, Cp in J mol1 K1) : C p = 5.7507  106T3 between 0 and 7.26 K. Between 12 and 15 K, the heat-capacity curve shows an abnormal increase, the origin of which is discussed hereafter. It could be either associated with a magnetic transition or it could result from an experimental artifact, due to the adsorption of He gas in the vessel at temperatures below 15 K. Between 365 and 383 K, the heat-capacity curve exhibits a small peak. This anomaly is neither associated with a phase transition of TiO2 impurities nor with a magnetic transition which occurs at much lower temperatures. Above 386 K, the heat capacities measured by DSC were modelled by a function of the type C p = a0 + a1T + a2T2 + a3T0.5 using the least-squares method. By applying a suitable multiplying factor k (k  0.99) due to calibration problems (Chen et al., 1996; Gailhanou et al., 2007), this function was then fitted to the measurement point of highest temperature obtained by adiabatic calorimetry. The final modelled function is (T in K, Cp in J g1 K1): C p = 1.87917 + 8.24023  10 5 T  9.92147  10 3 T 2  15.7746T0.5 between 385 and 520 K. The scattering of the measurements was estimated by comparing the measured values with interpolated values, when several series of measurements were carried out for

1.050

1.025

1.5

1.000 380

-1

Cp° (J.g .K )

370

-1

1.0

a given temperature range. The relative errors obtained from measurements in adiabatic calorimetry were decreasing progressively from 50% to 0.5% between 7 and 50 K, from 0.5% to 0.1% between 50 and 200 K and were lower than 0.05% beyond 250 K. By DSC, standard deviations for the least-squares fit method were lower than 1%. 3.1.2. Heat capacities of the clay mineral First, the heat capacity values for the sample were interpolated at every degree, before applying the impurity corrections. The heat capacities of the clay mineral C p;miner (in J g1 K1) were then determined using the additivity law of heat capacities: C p;sample ¼ xminer: C p;miner þ xTiO2  C pTiO2 ; where xminer. = 0.9922 is the mass fraction of the mineral, C p;sample the heat capacity of the sample obtained in the preceding section, xTiO2 = 0.0078 the mass fraction of rutile, and C p;TiO2 the heat capacity of TiO2 (in J g1 K1). The heat capacities of the clay mineral can then be calculated at any temperature. For rutile, data were provided by Shomate (1947) between 52 and 298 K, and by Robie and Hemingway (1995) between 298.15 and 520 K. These data were extracted from two different referenced works, which cover, respectively, temperature ranges lower and higher than 298.15 K. A slight difference of 0.45% of Cp value was observed between heat capacities at 298.15 K. Nevertheless, the resulting error on the heat capacity of the mineral at 298.15 K, which is ±0.003%, can be neglected compared to the uncertainties on measurements of the heat capacities of the mineral. Molar heat capacity values of the chlorite C op;m are given at selected temperatures in Table 5. Expected maximum absolute errors are 1% between 5 and 30 K; 0.05–0.1% between 30 and 100 K; 0.03% from 100 to 380 K (adiabatic calorimetry measurements) and 0.1% in the 380–520 K range (DSC measurements). Relative uncertainties are given in Section 3.1.1. Some analytical expressions of C p;m are proposed in Table 6 with the associated temperature ranges. They were obtained using several spline functions between 15 and 520 K. The thermal anomaly observed below 15 K was not fitted, as well as the Cp anomaly between 363 and 381 K. The relative deviations between the fitted values and the molar heat capacities corrected for impurities are globally lower than uncertainties on the measurements, but may reach sometimes four or five times the uncertainties, in particular, between 120 and 160 K and between 380 and 480 K.

0.05

3.2. Heat contents H  ðTÞH  ð0Þ 0.00 10 1

0.5

15

0.0 0

200

400

600

Heat contents of minerals H  ðT Þ–H  ð0Þ can be calculated at any temperature, by numerical integration of the C p;m ðT Þ values. Values at selected temperatures are given in Table 5. Maximum deviations are obtained from the deviations on C p values, given in Section 3.1.2.

T (K)

Fig. 7. Heat capacities of chlorite CCa-2 (—, adiabatic calorimetry; s, DSC; – –, modelled DSC values). Insets correspond to anomalies observed respectively between 12 and 15 K, and between 365 and 383 K.

3.3. Entropies S  ðTÞ Entropy S  ðT Þ can be calculated at any temperature, by numerical integration of the C p;m ðT Þ=T values with the

Thermodynamic properties of chlorite CCa-2 Table 5 Molar heat capacities and derived thermodynamic properties of the chlorite CCa-2, at selected temperatures. T (K)

C p;m (J mol1 K1)

S  ðT Þ (J mol1 K1)

H  ðT Þ–H  (298.15) (kJ mol1)

0 5 10 11 12 13 14 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300 310 320 330 340 350 360 370 371 372 373 374 375 376 377 378 379 380 381 382

0.00 0.45 2.03 2.37 2.62 3.15 10.41 11.42 14.29 17.18 20.03 27.07 32.04 39.98 48.79 67.75 88.74 112.00 136.79 162.09 186.75 211.64 236.23 260.66 283.96 307.08 329.52 350.46 371.24 391.27 410.10 428.24 446.19 463.26 479.76 493.12 508.09 523.65 537.28 547.02 550.03 563.60 575.92 588.35 599.49 610.66 621.47 633.02 634.59 636.55 638.64 641.73 644.42 644.09 643.50 641.15 639.09 639.38 639.73 640.66

0.0 0.2 1.0 1.2 1.4 1.6 2.1 2.9 6.5 10.0 13.4 17.0 20.9 25.1 29.8 40.3 52.3 65.7 80.3 96.0 112.6 129.9 147.8 166.2 185.0 204.1 223.4 242.8 262.3 281.9 301.4 320.9 340.4 359.7 379.0 398.0 416.9 435.7 454.3 469.4 472.8 491.0 509.1 527.0 544.7 562.3 579.6 596.8 598.5 600.2 602.0 603.7 605.4 607.1 608.8 610.5 612.2 613.9 615.6 617.2

80.78 80.78 80.77 80.77 80.77 80.76 80.76 80.75 80.68 80.60 80.51 80.39 80.25 80.07 79.85 79.27 78.49 77.48 76.24 74.75 73.00 71.01 68.77 66.29 63.56 60.61 57.42 54.03 50.42 46.60 42.59 38.40 34.03 29.48 24.76 19.90 14.89 9.73 4.42 0.00 1.01 6.58 12.28 18.10 24.04 30.09 36.26 42.52 43.16 43.79 44.43 45.07 45.72 46.36 47.00 47.65 48.29 48.92 49.56 50.20

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Table 5 (continued) T (K)

C p;m (J mol1 K1)

S  ðT Þ (J mol1 K1)

H  ðT Þ–H  (298.15) (kJ mol1)

383 384 385 390 400 410 420 430 440 450 460 470 480 490 500 510 520

641.59 642.51 643.43 647.94 656.68 665.04 673.06 680.76 688.16 695.27 702.13 708.75 715.13 721.30 727.27 733.05 738.65

618.9 620.6 622.3 630.6 647.1 663.4 679.6 695.5 711.2 726.8 742.1 757.3 772.3 787.1 801.7 816.2 830.5

50.85 51.49 52.13 55.36 61.88 68.49 75.18 81.95 88.80 95.71 102.70 109.76 116.88 124.06 131.30 138.60 145.96

Notes: Molecular weight of the chlorite CCa-2 is 617.460 g mol1.

trapezoid method. Values at selected temperatures are given in Table 5. Maximum deviations are obtained from the deviations on C p values (see Section 3.1.2). 3.4. Entropies of formation at 298.15 K The standard entropy of formation of the chlorite was calculated by considering the reaction of formation from the elements in their stable thermodynamic form in standard conditions. Entropy of the chlorite at 298.15 K is given in the preceding section and the entropies of the elements are tabulated in Table EA-2 of Electronic Annex EA-2. The standard molar entropy of formation of chlorite from elements is 2169.4 (± 4.0) J mol1 K1. 4. DISCUSSION 4.1. Cp anomaly at low-temperature One assumption concerning the Cp anomaly at low temperature was that it could be assigned to magnetic ordering in chlorite. Octahedral sites are occupied both by paramagnetic ions (Fe3+, Fe2+ and Mn2+) and diamagnetic ions (Al3+, Mg2+ and Ca2+). The chlorite probably exhibits some iron-rich clusters with interactions between magnetic moments at low-temperature (Townsend et al., 1986). Between these iron-rich domains, diamagnetic ions act as dilutor and thus prevent formation of a well-ordered 3D magnetic system. Schottky anomalies, associated with magnetic ordering at low temperature, have already been observed by Hemingway et al. (1984) on a natural low-iron content chlorite, and by Bertoldi et al. (2007) on several chlorites with various iron contents. According to these authors, Schottky anomalies were observed at temperatures lower than 7 K (Bertoldi et al., 2007) or centred at about 8 K (Hemingway et al., 1984). These ranges of temperature

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Table 6 Analytical expressions of the molar heat capacities of the chlorite CCa-2. Expression of molar heat capacity of chlorite 7 2

T range 3 0.5

4

2

= 242.147 + 3.03153T  5.62565  10 T + 1.01826  10 T  1.25789  10 T = 533.426 + 1.60403T  1.34808  103T2  6.10606  103T0.5 + 9.23461  105T2

4.2. Excess heat capacities According to Ulbrich and Waldbaum (1976), the heat capacity curve of a crystalline phase with transition metal ions is usually different from that of a diamagnetic compound. The difference consists of two additional thermal effects, which superpose the contributions due to structure vibrations. The first occurs at low temperature and is observed as a marked k-type discontinuity. It is associated with magnetic ordering of paramagnetic transition metal ions. The second effect consists of a continuous background in the heat capacity curve. It is commonly estimated using a method based on the comparison between the heat capacity of the phase and the heat capacity of a diamagnetic phase, having a very similar structure (Stout and Catalano, 1955; Robie et al., 1982; Bertoldi et al., 2007). Excess heat capacities were estimated for chlorite CCa-2. Clinochlore was used in this study as the reference diamagnetic phase and its heat capacity data were provided by Bertoldi et al. (2007). The method described by Robie et al. (1982) consists in plotting the ratio T/T* versus T*, where T* is the temperature at which Cp of chlorite CCa-2 is equal to Cp of clinochlore at T. The ratio T/T* versus temperature shows a linear trend at high-temperatures, beyond 200 K (Fig. 8). It is then assumed that no magnetic contribution affects the heat capacities of the chlorite in this high-temperature domain, i.e., the magnetic entropy is constant at high-temperature. The ratio T/T* was then extrapolated to 0 K. Finally, the excess heat capacities DCp,ex were estimated from the ratio values and from the Cp data of chlorite CCa-2 and clinochlore (Fig. 9). Excess heat capacity reaches a maximum value between 50 and 60 K. This result is in agreement with maximum values obtained by Bertoldi

15–100 K 100–520 K

1.08

1.06

T/T*

for magnetic ordering were consistent with the 57Fe Mo¨ssbauer study of chlorites at low temperature carried out by Townsend et al. (1986). In this study, the range of temperature is slightly higher, between 12 and 15 K. However, the assumption of magnetic ordering between 12 and 15 K in chlorite CCa-2 turns out to be erroneous, considering the 10 K Mo¨ssbauer spectrum. No magnetic order was detected at this temperature, which is lower than the temperature range of the anomaly, whereas the 4.2 K spectrum revealed the occurrence of some magnetic Fe2+. This result shows that magnetic ordering occurred below 10 K. Consequently, the Cp anomaly observed between 12 and 15 K is not associated with a Schottky anomaly but is certainly an experimental artefact, caused by the adsorption of He gas in the calorimetric vessel down to 15 K. The lack of He gas prevents efficient heat exchange inside the vessel and consequently the measured heat capacity is almost zero.

1.04

1.02

1 0

50

100

150

200

250

300

T* (K)

Fig. 8. Method of Robie et al. (1982) used for estimating excess heat capacities of the chlorite CCa-2. Ratio T/T* was approximated at T > 200 K by a linear function T/T* = 8.0591  105T* + 1.0249.

et al. (2007) for Fe-rich chlorites. Moreover, the calculated excess entropy for chlorite CCa-2 is 25 J mol1 K1. However, the approximations made for fitting the ratio T/T* at high temperatures may lead to important uncertainties of about 20% on the excess entropy value. For comparison, the theoretical magnetic entropy was calculated assuming that the crystalline field surrounding each paramagnetic ion led to a splitting of spin states in a high spin configuration, and that the orbital angular momentum of the ground state of the paramagnetic ions was zero. Thus, the theoretical magnetic entropy was obtained using a spin quantum number s = 2 for Fe2+ and s = 5/2 for Fe3+ and for Mn2+, according to the

15

ΔCp,ex (J.mol -1.K-1)

C p;m C p;m

10

5

0

-5

0

50

100

150

200

250

300

T (K)

Fig. 9. Excess heat capacities DCp,ex of chlorite CCa-2, obtained by the method of Robie et al. (1982) assuming a linear variation of T/T* versus temperature.

4.3. Comparison to previous work on clinochlore and chamosite For the chlorite CCa-2, our entropy value at 298.15 K, 469.4 (±2.9) J mol1 K1, is consistent with entropy values for chamosite and clinochlore. It lies between Hemingway et al. (1984) values, who obtained respectively 431.7 (±5.0) J mol1 K1 for a high-magnesium chlorite and 495.7 (±10) J mol1 K1 for a high-iron chlorite. Moreover, Bertoldi et al. (2007) estimated at respectively 425.6 (±0.4) J mol1 K1 and 572.0 (±0.2) J mol1 K1 the entropy values for ideal clinochlore and chamosite. All these values do not contain configurational entropy contributions. Among the different chlorites studied by Hemingway et al. (1984) and Bertoldi et al. (2007), one sample, the chlorite from Maltatal (Ka¨rnten, Austria), has a chemical composition close to that of chlorite CCa-2, particularly on the iron content. For comparison, its mean structural 2þ formula is (Si2.67Al1.33)(Al1.29Fe3þ 0:23 Fe1:90 Mg2.38Mn0.069Ti0.003Li0.028)O10(OH)8. Fig. 10 shows the heat capacities measured for both chlorites between 5 and 320 K. Both curves are very similar, except at the lowest temperatures below 15 K, due to the artifact of measurement for chlorite CCa-2. The average relative deviations between the two curves are about 7% between 15 and 50 K and about 1% between 50 and 300 K. 5. CONCLUSIONS Chlorite CCa-2 is found to be very pure and homogeneous, propitious to this calorimetric study. 57Fe Mo¨ssbauer spectrometry provides relevant information on Fe network, which make it possible to interpret the low temperature Cp anomaly. It has been shown that magnetic ordering inside iron-rich domains occurs below 10 K. Comparison of the data obtained in this work with the results of

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600

10000

500

1000

400

100

300

10

200

1

100

0.1

0

0

50

100

150

200

250

300

Deviation (%)

P relation DS tr;th ¼ R i xi lnð2si þ 1Þ where R = 8.314 J mol1 1 K is the molar gas constant, xi is the quantity of paramagnetic ion i per mole of clay and si, its spin quantum number (Hemingway et al., 1984). Its maximum value was estimated at 26.28 J mol1 K1. Therefore, the magnetic entropy obtained by the preceding method is rather close to the theoretical value, despite the occurrence of the artefact on Cp values below 15 K. These results are different from the interpretation of the 4.2 K Mo¨ssbauer spectrum, which reveals that only 28% of total iron is magnetic at 4.2 K. However, as shown by Townsend et al. (1986) for Fe-chlorites, the magnetic transition occurs progressively in a range of temperature below 7 K, due to the presence of defects or heterogeneous distribution of paramagnetic ions in the octahedral sites of the hydroxide sheet and 2:1 layer. For chlorite CCa-2, it probably already occurred for some iron ions with low magnetic coupling interactions, at temperature lower than 4.2 K. A more advanced study by Mo¨ssbauer spectrometry at different temperatures should be carried out to know more about the magnetic ordering at low temperature. In conclusion, the magnetic entropy is probably lower than the theoretical value, as the magnetic ordering should rather be partial.

Cp,m ° (J.mol -1.K-1)

Thermodynamic properties of chlorite CCa-2

0.01 350

T (K)

Fig. 10. Comparison between the heat capacities of chlorite CCa-2 (solid line) and a natural trioctahedral chlorite from Maltatal (Bertoldi et al., 2007) (black circles), between 5 and 320 K. Deviations (in %) between the two curves are also represented (dashed line).

Bertoldi et al. (2007) and Hemingway et al. (1984) shows a general coherence on Cp and entropy. This is an interesting result in the prospect of the use of these data in numerical modelling of the evolution of geochemical systems. The heat capacity data, entropies and heat contents of chlorite CCa-2 will be used in a further study, dedicated to determining all the thermodynamic properties of the chlorite, between 0 and 520 K. In particular, standard enthalpy of formation of the chlorite will be obtained from isothermal dissolution calorimetry and Gibbs free energy of formation will be determined from the preceding results. The procedure followed to study the chlorite mineral CCa-2 is the same as for the smectite, illite and mixed-layer illite– smectite (Gailhanou et al., 2007). These results are necessary to complete the thermodynamic databases on clay minerals and will be used for the calibration of models for predicting the thermodynamic properties of phyllosilicates (e.g., Vieillard, 2000, 2002). ACKNOWLEDGMENTS This study, part of the THERMOCHIMIE project, was financially supported by the French Radioactive Waste Management Agency (ANDRA) and by the French Geological Survey (BRGM), which are both gratefully acknowledged. We thank Christian Bertoldi and anonymous reviewers for their detailed reviews with many useful comments for improving the manuscript.

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