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Thermodynamic properties of anhydrous smectite MX-80, illite
IMt-2 and mixed-layer illite–smectite ISCz-1 as determined
by calorimetric methods. Part I: Heat capacities, heat contents
and entropies
H. Gailhanou
a,b,e,*
, J.C. van Miltenburg
c
, J. Rogez
d
, J. Olives
a
,
M. Amouric
a
, E.C. Gaucher
b
, P. Blanc
b
a
CRMCN-CNRS, Campus de Luminy, Case 913, 13288 Marseille Cedex 9, France
b
BRGM, 3 av. C. Guillemin, BP6009, 45060 Orle
´ans, France
c
Chemical Thermodynamics Group, State University of Utrecht, Padualaan 8, 3508 TB Utrecht, The Netherlands
d
TECSEN-CNRS, Faculte
´des Sciences et Techniques de Saint-Je
´ro
ˆme, Case 251, 13397 Marseille Cedex 20, France
e
ANDRA, 92298 Cha
ˆtenay-Malabry, France
Received 5 January 2007; accepted in revised form 12 September 2007; available onilne 29 September 2007
Abstract
The heat capacities of the anhydrous international reference clay minerals, smectite MX-80, illite IMt-2 and mixed-layer illite–
smectite ISCz-1, were measured by low temperature adiabatic calorimetryand differential scanning calorimetry, from 6 to 520 K (at
1 bar). The samples were chemically purified and Na-saturated. Dehydrated clay fractions <2 lmwere
studied. The structural formulae of the corresponding clay minerals, obtained after subtracting the remaining
impurities, are K0:026Na0:435Ca0:010 ðSi3:612Al0:388 Þ(Al1:593Fe3þ
0:184 Mg0:228 Fe2þ
0:038Ti0:011 )O10ðOHÞ2for smectite MX-80,
K0:762Na0:044ðSi3:387 Al0:613Þ(Al1:427 Fe3þ
0:292 Mg0:241Fe2þ
0:084ÞO10ðOHÞ2for illite IMt-2 and K0:530Na0:135ðSi3:565 Al0:435Þ(Al1:709
Fe3þ
0:051Mg0:218Fe2þ
0:017Ti0:005 )O10ðOHÞ2for mixed-layer ISCz-1. From theheat capacity values, we determined the molar entropies,
standard entropies of formation and heat contents of these minerals. The following values were obtained at 298.15 K and 1 bar:
2007 Elsevier Ltd. All rights reserved.
1. INTRODUCTION
Illite, smectite and mixed-layer illite–smectite are very
abundant clay minerals that are of great importance in geo-
logical cycles. They have been widely studied and present
many physical, chemical and mechanical properties that
are useful in various application fields, such as ceramics,
depollutants, waste storage, catalysis, cosmetics, medicine,
etc. (Montilla et al., 2002; Ferris et al., 2004; Vogels
et al., 2005). In particular, argillites containing various pro-
portions of illite, mixed-layer illite–smectite and smectite
are considered good candidates for waste confinement bar-
C0
p(J mol
1
K
1
)S
0
(J mol
1
K
1
)
Smectite MX-80 326.13 ± 0.10 280.56 ± 0.16
Illite IMt-2 328.21 ± 0.10 295.05 ± 0.17
Mixed-layer ISCz-1 320.79 ± 0.10 281.62 ± 0.15
0016-7037/$ - see front matter 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.gca.2007.09.020
*
Corresponding author.
E-mail address: h.gailhanou@brgm.fr (H. Gailhanou).
www.elsevier.com/locate/gca
Available online at www.sciencedirect.com
Geochimica et Cosmochimica Acta 71 (2007) 5463–5473
riers owing to their low permeability, high plasticity and
adsorption properties (Madsen, 1998; Thury, 2002; Landa-
is, 2006). Because chemical reactions with storage materials
may transform the clay (Gaucher and Blanc, 2006), it is
very important to know its degree of stability or instability
relative to the temperature, pressure and chemical poten-
tials of the surroundings, and then the geochemical and
thermodynamic behavior of the clay minerals over long
time periods. This is a key point for the safety analysis of
any future nuclear waste deep disposal. Until now, very
few thermodynamic data for these clay minerals were
available.
This paper presents the first heat capacity measurements
and derived thermodynamic properties of a smectite, an il-
lite and a mixed-layer illite–smectite, in anhydrous states,
from 0 to 520 K (at 1 bar). The heat capacities were ob-
tained by adiabatic calorimetry between 6 and 400 K (and
extrapolated between 0 and 6 K with a Debye type law)
and by differential scanning calorimetry (DSC) between
380 and 520 K. As adiabatic conditions are difficult to
maintain beyond 380 K with a low-temperature calorime-
ter, DSC was used as a complementary method for higher
temperatures. The three studied minerals are international
reference clays.
2. MATERIALS
The illite and mixed-layer illite–smectite studied belong
to the Source Clay Project of the Clay Minerals Society.
These are illite IMt-2 (Silver Hill, Montana, USA; Hower
and Mowatt, 1966; Vogt et al., 2002) and illite–smectite
ISCz-1 (Slovakia; Chipera and Bish, 2001; Vogt et al.,
2002). The smectite studied belongs to the bentonite MX-
80 (Wyoming, USA; Madsen, 1998; Guillaume et al., 2004).
2.1. Sample preparation
In order to remove organic matter and carbonates, the
samples were treated over 24 h with H
2
O
2
(30%) at 80 C
and pH 2, adjusted by the addition of an HNO
3
solution.
The solid phase was then separated by centrifugation,
and the treatment was repeated. After centrifugation,
the solid phase was saved and washed three times with
deionized water. To remove iron oxides, the solid was
suspended in an N
2
-saturated HCl 10
3
M solution, and
an HNO
3
solution was added to decrease the pH to 3.
The potential of the solution was then adjusted to be be-
tween 200 and 250 mV/ENH by addition of sodium
hydrosulphide. After centrifugation, the solid phase was
saved and washed in an HCl 10
4
M, NaCl 1 M solution
for 12 h.
Afterwards, the clays were Na-saturated in an NaCl 1 M
solution for 24 h. After washing in deionized water, the ab-
sence of chloride ions was checked by using the AgNO
3
test.
Finally, the <2 lm size-fraction was separated by
centrifugation.
These samples were maintained at ambient pressure,
temperature and relative humidity (RH) conditions of
1 bar, 25 C and 65% RH. In the following, ‘samples’ or
‘samples at 65% RH’ will mean ‘after the preceding treat-
ments’. They consist of the clay minerals and some
impurities.
2.2. Analysis and characterization of the samples
Chemical analyses for Si, AI, Ti, Fe (total), Mn, Ca, Mg,
K, Na and P were performed by X-ray fluorescence spec-
trometry. In order to determine the amount of Fe
2+
, the
samples were dissolved in a non-oxidizing HF–H
2
SO
4
solu-
tion, and the released Fe
2+
was titrated by a volumetric
method. The results of the analysis are presented in Table
1, expressed in weight percent of oxides; the relative uncer-
tainties are estimated at 2%. The amount of total carbon
was determined by infra-red spectroscopy after burning
the samples at 900 C in an oxygen atmosphere. The
measurement of carbonates was performed by dissolving
them in an HCl solution and titrating the CO
2
produced
by a volumetric method. The amount of total sulfur was
determined in the same way as the total carbon.
X-ray diffraction (XRD) analyses were performed on a
Siemens D5000 diffractometer equipped with variable slits,
a cobalt anticathode and a diffracted beam monochromator
to characterize and quantify impurities and clay phases.
Diagrams were acquired from 4to 842hwith a rotation
speed of 0.052h/s. First, in order to determine the abun-
dances of clay and nonclay minerals, a random powder
was top-loaded into the sample holder cavity (2.5 cm diam-
eter) without compaction to preserve random orientation
(Hillier, 2000). The proportions of impurities were obtained
by applying a least-squares fit method using XRD patterns
of individual phases. Second, to analyze clay phases only,
the sample was deposited on a glass slide and saturated with
ethylene glycol for 12 h. 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.
The individual clay particles were chemically analyzed
with a high-resolution transmission electron microscopy
Table 1
Chemical compositions (wt%) of the samples at 65% RH
Smectite
MX-80
Illite
IMt-2
Mixed-layer
ISCz-1
Analytical
techniques
C mineral <0.05 <0.05 <0.05 (a)
C total 0.12 0.04 0.04 (b)
S total 1.10 0.01 0.06 (b)
SiO
2
60.20 53.00 52.60 (c)
Al
2
O
3
18.70 23.00 26.70 (c)
FeO 0.50 1.30 0.30 (d)
Fe
2
O
3
2.73 5.05 0.97 (c,d)
CaO 0.10 <0.10 <0.10 (c)
MgO 1.70 2.10 2.10 (c)
MnO <0.02 <0.02 <0.02 (c)
K
2
O 0.23 8.11 5.96 (c)
Na
2
O 2.50 0.30 1.00 (c)
TiO
2
0.16 0.87 0.09 (c)
P
2
O
5
0.09 0.20 0.13 (c)
H
2
O 12.80 5.90 10.00 (e)
Note. Analytical techniques: (a) volumetric method, (b) infra-red
spectroscopy, (c) X-ray fluorescence, (d) volumetric titration and
(e) weight loss while heating up to 1000 C.
5464 H. Gailhanou et al. / Geochimica et Cosmochimica Acta 71 (2007) 5463–5473
(HRTEM) study coupled with energy-dispersive X-ray
spectrometry (EDX). The electron microscope was a JEOL
2000 FX (200 kV accelerating voltage, 1.8 mm spherical
aberration coefficient, 50 lm objective aperture) equipped
with a low-light camera and a Tracor TN 5502 EDX spec-
trometer with an Si(Li) detector. A beam diameter of 5–
20 nm was used for EDX analyses, and collected data were
processed with a statistical method.
Spectroscopic analyses by FTIR were carried out with
an Equinox 55 Bruker spectrometer with 32 scans and a res-
olution of 4 cm
1
from 4000 to 400 cm
1
to quantify crys-
talline silica impurities. The mid-infrared spectra were
obtained by transmission mode using KBr pressed pellets,
containing 3 wt% clay sample. Crystalline silica impurities
were quantified using calibration curves with quartz stan-
dard QUIN 1 (Kauffer et al., 2002) and cristobalite NIST
Standard Reference Material (1879a). Standard deviations
are ±3 wt%.
The amounts of mineral impurities in IMt-2, as deter-
mined by XRD, were (in wt%) 7.5% quartz, 2% microcline,
0.3% kaolinite and traces of chlorite. The estimated stan-
dard deviations for XRD analyses are about ±2 wt% (Vogt
et al., 2002). In the IMt-2 sample, the HRTEM-EDX study
showed (i) the presence of a trioctahedral and magnesian
‘illite’ phase, of 25 mol % and (ii) the absence of Ti in illite
crystals, and the presence of rutile impurities.
XRD analyses of ISCz-1 led to impurity amounts of
0.5 wt% quartz and 1 wt% kaolinite. Because values ob-
tained for ISCz-1 by FTIR were slightly different (1 wt%
quartz and 2 wt% kaolinite), the following mean contents
deduced from both XRD and FTIR analyses were used:
0.75 wt% quartz and 1.5 wt% kaolinite. For IMt-2 and
ISCZ-1, results obtained by XRD and FTIR were in good
agreement.
For the MX-80 sample, silica impurities were underesti-
mated by XRD, compared with HRTEM-EDX and FTIR,
probably because of undetected amorphous silica. In this
sample, the HRTEM-EDX study showed a high content
of SiO
2
impurities (about 20 (±3) wt%) and a montmoril-
lonite–beidellite composition of the smectite. Moreover,
analyses by FTIR indicated 7.5 wt% quartz and 7.5 wt%
cristobalite impurities for the MX-80 sample. Finally, by
combining the results obtained from HRTEM-EDX and
FTIR, the values of 20 wt% SiO
2
impurities, split up into
7.5 wt% quartz, 7.5 wt% cristobalite and 5 wt% amorphous
silica, were used for MX-80. Table 2 summarizes the impu-
rity contents for these three samples.
Adsorption of water is a well-known and important
property of clay minerals. The samples characterized above
(chemical compositions and impurity contents of Tables 1
and 2) correspond to ambient conditions of 1 bar, 25 C
and 65% RH. In order to study the clay minerals: (i) in their
anhydrous state and (ii) in highly hydrated states with the
aim of obtaining the thermodynamic functions of the
hydration reactions, the preceding samples were, respec-
tively, (i) dehydrated and (ii) highly hydrated. For the pur-
pose of the present paper, which concerns only the study of
the anhydrous clay minerals, the samples were dehydrated
at 150 C under 10
5
bar vacuum for 5 h, in order to re-
move (i) pore water, (ii) adsorbed water on the external sur-
faces of the crystallites, and (iii) interlayer water. These
dehydration conditions were adopted because they were ex-
pected to not damage clay structure; they are not drastic en-
ough to lead to solid state transformation of clays. The
modification which might appear, if any, would be the loss
of expandability of clay layers, but this phenomenon would
be very limited. Whitney and Northrop (1988) studied the
changes in expandability of clay layers for a smectite after
heat treatments at 250 C for 220 days, by first K-saturating
it before the heat treatment and then Na-saturating it be-
fore expandability measurements by XRD. After 7 days
at 250 C, only 8% of the smectite layers were no longer
expandable.
The impurity contents with respect to the dehydrated
samples were calculated from the values of Table 2 by
removing water (except mineral structural hydroxyl groups)
from the compositions of the samples at 65% RH (Table 3).
The present study concerns these anhydrous samples. The
structural formulae of the corresponding clay minerals are
given in Table 4.
Table 2
Impurities (wt%) in the samples at 65% RH
Quartz Cristobalite Amorphous silica Microcline Rutile Kaolinite Chlorite
MX-80 7.5% 7.5% 5% n.d. n.d. n.d. n.d.
IMt-2 7.5% n.d. n.d. 2% 0.87% 0.3% traces
ISCz-1 0.75% n.d. n.d. n.d. n.d. 1.5% n.d.
Note. Standard deviations ±1–2 wt% for each impurity.
n.d., not detected.
Table 3
Impurity contents (wt%) in the anhydrous samples
Quartz Cristobalite Amorphous silica Microcline Rutile Kaolinite Chlorite
MX-80 8.29% 8.29% 5.53% n.d. n.d. n.d. n.d.
IMt-2 7.65% n.d. n.d. 2.04% 0.89% 0.31% Traces
ISCz-1 0.79% n.d. n.d. n.d. n.d. 1.59% n.d.
Note. Standard deviations ±1–2 wt% for each impurity.
n.d., not detected.
Thermodynamic properties of anhydrous smectite, illite and illite–smectite 5465
3. MEASUREMENT METHODS
Heat capacities are usually measured by two main meth-
ods. (i) The adiabatic calorimetry method consists in mea-
suring the increase in temperature of the sample
associated with a heat supply. Under ideal adiabatic condi-
tions, the heat capacity of the sample is simply the ratio of
the supplied power to the rate of temperature variation. (ii)
In DSC, the heat adsorbed by the sample is measured vs
temperature variation, and the heat capacity is obtained
from the ratio of the heat adsorbed to the associated tem-
perature increment.
3.1. Adiabatic calorimetry
The heat capacities at constant pressure C0
pwere mea-
sured between 6 and 400 K with the CAL V adiabatic cal-
orimeter (built in the State University of Utrecht and
described by van Miltenburg et al., 1987, 1998). The vessel
is made of gold-plated copper and has a volume of 11 cm
3
.
It was filled with 8–10 g of anhydrous clay sample under a
nitrogen atmosphere. In an airtight chamber, the atmo-
sphere inside the vessel was removed and replaced with he-
lium gas at 1 kPa to improve heat exchange. The vessel was
hermetically sealed in the helium chamber by means of a
screwed cap compressing a thin gold plate seal. The temper-
ature of the vessel was measured with a 30 XRh/Fe ther-
mometer, 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; it showed less than a 0.2% deviation
from the recommended values for these materials (van Milt-
enburg et al., 1987).
Measurements were performed in the intermittent mode,
by alternating heating and stabilization periods of about
500 s. Between 6 and 30 K, heating and stabilization peri-
ods of about 100–150 s were used. The repeatability of
the measurements was good. The maximum deviations ex-
pected in the measurements of the clays, derived from mea-
surements of the standard materials n-heptane and
synthetic sapphire, are: 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. Various
measurement series were performed on each sample. Suc-
cessive measured values, separated by about 0.5–2 K, were
interpolated at every Kelvin degree.
3.2. Differential scanning calorimetry
The heat capacities were measured between 380 and
520 K using a Calvet DSC111 differential scanning calo-
rimeter (from Setaram) in the TECSEN laboratory. The
vessel is made of stainless steel and has a volume of
0.18 cm
3
. It was filled with about 140 mg of anhydrous
clay sample and sealed with a nickel ring under a nitro-
gen atmosphere. The calorimeter was calibrated with
synthetic sapphire supplied by the National Bureau of
Standards (Ditmars et al., 1982). However, the calibra-
tion may be subject to discussion, as the thermal resis-
tances of sapphire-vessel and sample-vessel interfaces are
slightly different from each other. The measurements were
performed at a 1.5-K/min heating rate. The 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, during which time the heat
flow recovered the baseline value.
From the preceding measurements of the heat capacities
of the anhydrous clay sample by adiabatic calorimetry and
DSC, the heat capacities of the corresponding anhydrous
clay minerals were obtained by subtracting the contribu-
tions of the impurities. The heat contents H
0
(T)
H
0
(298.15) and the entropies S
0
(T) of the clay minerals
were then calculated by numerical integration versus Tof
the respective functions C0
pðTÞand C0
pðTÞ=T.
4. RESULTS
4.1. Heat capacity measurements
4.1.1. Heat capacities of the samples
Tables EA 1–3, in the respective Electronic annexes
EA 1–3, present (i) the whole adiabatic calorimetry val-
ues (eight runs for each sample) and (ii) the DSC values
for higher temperatures. The values obtained by adiabatic
calorimetry and DSC are in agreement (Fig. 1); the slight
difference observed for the illite and smectite curves is
probably due to a DSC calibration defect.
Between 0 K and the lowest temperature measurement
(7.32, 6.64 and 8.81 K, respectively, for MX-80, IMt-2
and ISCz-1), a power law C
p
=aT
n
was used by analogy
with the Debye approximation C
p
C
v
=aT
3
at very low
temperatures, where C
v
is the heat capacity at constant
volume (Debye, 1912). The best fit with the experimental
data led to n= 3 for MX-80 and ISCz-1, and n= 2.5 for
Table 4
Structural formulae and molar masses of the anhydrous clay minerals
Smectite MX-80 K0:026Na0:435 Ca0:010ðSi3:612Al0:388 Þ(Al1:593Fe3þ0:184 Mg0:228Fe2þ0:038 Ti0:011 )O10ðOHÞ2M= 378.787 g mol
1
Illite IMt-2 K0:762Na0:044 ðSi3:387Al0:613Þ(Al1:427 Fe3þ0:292Mg0:241Fe2þ0:084 )O10ðOHÞ2M= 401.836 g mol
1
Mixed-layer ISCz-1 K0:530Na0:135 ðSi3:565Al0:435Þ(Al1:709 Fe3þ0:051 Mg0:218Fe2þ0:017Ti0:005 )O10ðOHÞ2M= 385.143 g mol
1
Note. Structural formulae are obtained after subtracting the impurities in Table 2 and H
2
O (except mineral OH groups) from the compositions
in Table 1.
5466 H. Gailhanou et al. / Geochimica et Cosmochimica Acta 71 (2007) 5463–5473
IMt-2. Continuity with the first measurement, at the low-
est temperature, was obtained by using the functions in
Table 5.
Above the highest temperature measurement acquired
by adiabatic calorimetry (380.64, 400.95 and 380.89 K,
respectively, for MX-80, IMt-2 and ISCz-1), the heat capac-
ities measured by DSC were modeled by the function
C0
p=a
0
+a
1
T+a
2
T
2
+a
3
T
0.5
using the least-squares
method. By comparing with DSC measurements, adiabatic
calorimetry usually leads to more confident absolute values
of heat capacities. Therefore, by applying a suitable multi-
plying factor k(k= 0.993, 0.973 and 0.999, respectively, for
MX-80, IMt-2 and ISCz-1), the above function was fitted to
the measurement point of highest temperature obtained by
adiabatic calorimetry. The final modeled functions are
given in Table 5. Standard deviations for the least-squares
fit method are about 0.5%. The scattering of the low-tem-
perature measurements from adiabatic calorimetry de-
creases progressively from about 20% to 1% between 6
and 50 K, from 1% to 0.3% between 50 and 150 K and be-
low 0.3% beyond 150 K.
4.1.2. Heat capacities of the clay minerals
The heat capacity values for the anhydrous samples were
interpolated at every degree before applying the impurity
corrections. The heat capacities of the clay minerals
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
1
1.2
T
(K)
C
p
°
(J.g-1.K-1 )
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
1
1.2
T
(K)
C
p
°
(J.g
-1
.K
-1
)
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
1
1.2
T
(K)
C
p
°
(J.g
-1
.K
-1
)
a
c
b
Fig. 1. Heat capacities of the clay samples, not corrected for impurities (thick dark curve: adiabatic calorimetry; m: DSC; modeled
DSC values). (a) Smectite MX-80; (b) illite IMt-2; (c) mixed-layer ISCz-1.
Table 5
Heat capacities of the samples as functions of temperature (in K) at very low temperatures (Debye type extrapolation) and high temperatures
(modeled DSC values)
Sample C0
p(J g
1
K
1
) Temperature range (K)
Low-temperature range
MX-80 C0
p= 2.546 ·10
6
T
3
0–7.32
IMt-2 C0
p= 9.334 ·10
6
T
2.5
0–6.64
ISCz-1 C0
p= 9.059 ·10
7
T
3
0–8.81
High-temperature range
MX-80 C0
p= 4.05716–1.11329 ·10
3
T+ 3.05618 ·10
4
T
2
56.0134T
0.5
380.64–520.20
IMt-2 C0
p= 4.02952–1.27969 ·10
3
T+ 2.99437 10
4
T
2
–54.8771T
0.5
400.95–507.07
ISCz-1 C0
p= 1.69878 + 1.75040 ·10
4
T1.15064 ·10
4
T
2
14.0150T
0.5
380.89–520.28
Thermodynamic properties of anhydrous smectite, illite and illite–smectite 5467
C0
p;miner (in J g
1
K
1
) were then determined by subtracting
the contribution of impurities to the heat capacities of the
samples, according to:
C0
p;miner ¼
C0
p;sample P
i
xiC0
p;i
xminer
;
where x
miner
is the mass fraction of the mineral, C0
p;sample is
the heat capacity of the sample, obtained in the preceding
section, x
i
is the mass fraction of the impurity i(Table
3) and C0
p;iis the heat capacity of the impurity i(in
Jg
1
K
1
). The heat capacities of the clay minerals
can then be calculated at any temperature. Molar heat
capacity values at selected temperatures are given in
Tables 6–8. Heat capacity data for the silica impurities
were provided by Richet et al. (1982) (quartz, cristobalite
and amorphous silica, from 50 to 520 K). Silica impurity
contributions to the measured heat capacities vary be-
tween 20% and 27% for MX-80 and 7% and 8% for
IMt-2 and are about 0.8% for ISCz-1. For microcline, heat
capacity data were taken from Openshaw et al. (1976) be-
tween 5 and 298 K and from Robie and Hemingway
(1995) between 298.15 and 520 K. For kaolinite, data were
taken from Robie and Hemingway (1991) between 7 and
298 K and from Robie and Hemingway (1995) between
298.15 and 520 K. For rutile, data were provided by Sho-
mate (1947) between 52 and 298 K and by Robie and
Hemingway (1995) between 298.15 and 520 K. For these
latter impurities, data were extracted from two different
referenced works, which cover, respectively, temperature
ranges lower and higher than 298.15 K. For a given impu-
rity (except silica), some differences were observed between
heat capacities at 298.15 K. Nevertheless, the resulting er-
rors in the heat capacity of the minerals at 298.15 K are
lower than 0.03% for mixed-layer and 0.003% for illite.
They are small compared to the expected maximum abso-
lute errors on measurements of the heat capacities of the
minerals, which are: 1% between 5 and 30 K; 0.05–0.1%
between 30 and 100 K; 0.03% from 100 to 380 K for
MX-80 and ISCz-1 and from 100 to 400 K for IMt-2 (adi-
abatic calorimetry measurements); and 0.1% in the range
380–520 K for MX-80 and ISCz-1 and in the 400–510 K
range for IMt-2 (DSC measurements). In Fig. 2, the
C0
p;mðTÞcurves of the three minerals appear similar in
outline but actually present differences, owing to the differ-
ent cation distributions in the octahedral, tetrahedral and
interlayer sites of these minerals. Some analytical expres-
sions of the molar heat capacity values C0
p;mare proposed
in Table 9 to match the heat capacity values. Between 0
and 520 K, some spline functions have been used for dif-
ferent temperature ranges. The relative deviations between
the fitted values and the molar heat capacities corrected
for impurities are within the scattering margins of the
measurements given in Section 4.1.1.
4.2. Heat contents: H
0
(T)H
0
(298.15)
Heat contents of minerals, H
0
(T)H
0
(298.15), can be
calculated at any temperature from the heat capacity data,
according to: H0ðTÞH0ð298:15Þ¼ZT
298:15
C0
p;mdT
Table 6
Molar heat capacities and derived thermodynamic functions of the
anhydrous smectite MX-80 (corrected for impurities) at selected
temperatures
T(K) C0
p;m
J mol
1
K
1
S
0
(T)
(J mol
1
K
1
)
H
0
(T)H
0
(298.15)
(kJ mol
1
)
0 0.00 0.00 48.508
10 0.88 0.30 48.505
20 4.48 1.84 48.481
30 10.62 4.75 48.407
40 19.24 9.00 48.257
50 29.76 14.40 48.014
60 42.48 20.93 47.654
70 56.77 28.53 47.158
80 70.95 37.01 46.522
90 85.67 46.21 45.740
100 101.12 56.02 44.807
110 115.82 66.32 43.724
120 129.43 77.01 42.496
130 144.69 87.99 41.123
140 158.67 99.23 39.605
150 172.29 110.64 37.950
160 185.42 122.18 36.162
170 198.18 133.80 34.244
180 210.51 145.48 32.200
190 222.41 157.18 30.036
200 233.77 168.88 27.755
210 244.87 180.55 25.361
220 255.56 192.19 22.858
230 265.88 203.78 20.251
240 275.88 215.31 17.542
250 285.39 226.76 14.736
260 293.82 238.12 11.841
270 302.88 249.38 8.857
280 311.38 260.54 5.786
290 319.64 271.61 2.632
298.15 326.13 280.56 0
300 327.39 282.58 0.604
310 334.85 293.43 3.912
320 341.88 304.16 7.294
330 349.07 314.79 10.748
340 355.78 325.31 14.272
350 362.18 335.72 17.862
360 368.36 346.01 21.514
370 374.49 356.18 25.229
380 380.32 366.25 29.003
390 386.31 376.21 32.836
400 392.10 386.06 36.728
410 397.64 395.81 40.677
420 402.93 405.46 44.680
430 407.97 415.00 48.735
440 412.77 424.43 52.839
450 417.34 433.76 56.990
460 421.67 442.98 61.185
470 425.78 452.09 65.422
480 429.67 461.10 69.700
490 433.35 470.00 74.015
500 436.81 478.79 78.366
510 440.08 487.47 82.750
520 443.15 496.04 87.167
Note. Molecular weight of smectite is given in Table 4.
5468 H. Gailhanou et al. / Geochimica et Cosmochimica Acta 71 (2007) 5463–5473
Numerical integration was done using the trapezoid meth-
od, from the C0
p;mvalues at every degree.
Values for the heat contents H(T)H
0
(298.15) for
smectite MX-80, illite IMt-2 and mixed-layer ISCz-1 are
listed at selected temperatures in Tables 6–8.
Table 7
Molar heat capacities and derived thermodynamic functions of the
illite IMt-2 (corrected for impurities) at selected temperatures
T(K) C0
p;m
(J mol
1
K
1
)
S
0
(T)
(J mol
1
K
1
)
H
0
(T)H
0
(298.15)
(kJ mol
1
)
0 0.00 0.00 50.090
10 0.89 0.42 50.087
20 4.91 2.08 50.060
30 12.67 5.47 49.974
40 23.18 10.53 49.796
50 35.84 17.04 49.501
60 49.27 24.76 49.076
70 63.80 33.43 48.512
80 78.80 42.93 47.799
90 93.84 53.08 46.936
100 109.39 63.75 45.921
110 123.94 74.83 44.757
120 137.81 86.22 43.447
130 152.51 97.83 41.996
140 166.20 109.64 40.402
150 179.52 121.56 38.673
160 192.38 133.56 36.813
170 204.95 145.60 34.826
180 217.17 157.66 32.715
190 228.86 169.72 30.485
200 239.89 181.74 28.140
210 250.60 193.71 25.688
220 260.83 205.60 23.130
230 270.57 217.41 20.473
240 280.06 229.13 17.720
250 289.29 240.75 14.874
260 297.15 252.24 11.943
270 305.72 263.62 8.928
280 313.92 274.89 5.829
290 321.98 286.04 2.650
298.15 328.21 295.05 0
300 329.42 297.09 0.608
310 336.68 308.01 3.938
320 343.47 318.80 7.338
330 350.06 329.47 10.806
340 356.03 340.01 14.336
350 362.31 350.42 17.928
360 368.10 360.71 21.580
370 373.64 370.87 25.289
380 379.44 380.91 29.055
390 384.94 390.84 32.876
400 390.16 400.65 36.751
410 394.90 410.34 40.677
420 399.46 419.91 44.648
430 403.78 429.36 48.665
440 407.87 438.69 52.723
450 411.74 447.90 56.821
460 415.39 456.99 60.957
470 418.83 465.96 65.129
480 422.07 474.82 69.333
490 425.10 483.55 73.569
500 427.93 492.17 77.834
510 430.57 500.67 82.127
Note. Molecular weight of illite is given in Table 4.
Table 8
Molar heat capacities and derived thermodynamic functions of the
anhydrous mixed-layer ISCz-1 (corrected for impurities) at selected
temperatures
T(K) C0
p;m
(J mol
1
K
1
)
S
0
(T)
(J mol
1
K
1
)
H
0
(T)H
0
(298.15)
(kJ mol
1
)
00 0 48.404
10 0.33 0.11 48.403
20 3.85 1.21 48.385
30 10.82 4.00 48.314
40 20.60 8.42 48.158
50 32.41 14.26 47.894
60 45.48 21.32 47.505
70 59.25 29.36 46.982
80 73.52 38.19 46.318
90 88.09 47.69 45.510
100 103.22 57.74 44.556
110 117.50 68.23 43.454
120 131.28 79.06 42.209
130 145.86 90.15 40.822
140 159.60 101.46 39.294
150 172.95 112.93 37.631
160 185.76 124.50 35.837
170 198.23 136.14 33.917
180 210.20 147.81 31.875
190 221.79 159.49 29.715
200 232.84 171.14 27.442
210 243.51 182.76 25.060
220 253.82 194.33 22.573
230 263.50 205.83 19.986
240 273.05 217.25 17.303
250 282.17 228.58 14.527
260 290.10 239.79 11.667
270 298.75 250.91 8.722
280 306.74 261.91 5.695
290 314.63 272.81 2.589
298.15 320.79 281.62 0
300 321.94 283.61 0.595
310 328.64 294.26 3.845
320 335.50 304.81 7.166
330 342.17 315.23 10.555
340 348.53 325.54 14.008
350 354.74 335.73 17.524
360 360.69 345.81 21.100
370 366.29 355.77 24.735
380 371.88 365.61 28.425
390 377.64 375.34 32.173
400 383.20 384.97 35.977
410 388.53 394.50 39.836
420 393.65 403.92 43.747
430 398.57 413.25 47.708
440 403.30 422.46 51.717
450 407.87 431.58 55.773
460 412.28 440.59 59.874
470 416.54 449.50 64.018
480 420.66 458.32 68.204
490 424.65 467.03 72.431
500 428.52 475.65 76.697
510 432.27 484.17 81.001
520 435.92 492.60 85.342
Note. Molecular weight of mixed-layer is given in Table 4.
Thermodynamic properties of anhydrous smectite, illite and illite–smectite 5469
4.3. Entropies S
0
(T)
In the case of anhydrous minerals, no phase changes
were observed. Entropy of the minerals, S
0
(T), was calcu-
lated at any temperature, according to:
S0ðTÞ¼ZT
0
C0
p;m
TdT
(numerical integration with the trapezoid method, from the
C0
p;m/Tvalues at every degree). These entropy values are gi-
ven in Tables 6–8. Maximum deviations are obtained from
the deviations on C0
pvalues (see Section 4.1.2).
4.4. Entropies of formation at 298.15 K
The entropies of formation of the minerals from the con-
stitutive oxides were calculated considering the reactions of
formation of the minerals from oxides. In the same way, the
standard entropies of formation of the minerals were ob-
tained considering the reactions of formation of the miner-
als from the elements in their stable thermodynamic form in
standard conditions. Their values, obtained from the entro-
pies of the minerals, oxides and elements (Table EA-4 of
Electronic annex EA-4), are given in Table 10. The negative
values of the entropies of formation from oxides indicate an
ordering effect during the reaction of formation of the min-
eral from the constituent oxides. The values of standard
entropies of formation are obviously lower, mainly because
of the high entropy values of the gaseous references O
2
and
H
2
.
5. DISCUSSION
5.1. Comparison with previous work
The comparison between our data and other experi-
mental values is very limited. No previous low-tempera-
ture heat capacity data are available for smectite and
mixed-layer illite–smectite. Only Robie et al. (1976) car-
ried out heat capacity measurements at low temperatures
on illite from Marblehead. Heat capacities were measured
by adiabatic calorimetry from 15 to 380 K and were cor-
rected for the contribution of the 1.6% adsorbed water.
0 100 200 300 400 500 600
0
100
200
300
400
500
T
(
K
)
Cp,m
°
(J.mol
-1
.K
-1
)
smectite
illite
mixed-layer
Fig. 2. Comparison of the C0
p;mof the three anhydrous minerals
smectite MX-80, illite IMt-2 and mixed-layer ISCz-1.
Table 9
Analytical expressions of the molar heat capacities of the anhydrous minerals
Expression of molar heat capacity of minerals Trange (K)
Smectite MX-80 C
p,m
= 6.37093 10
4
T
3
0–15
C0
p;m= 48.1910–6.07063 ·10
1
T+ 1.52654 ·10
2
T
2
1.92243 ·10
2
T
0.5
+ 2.08514 ·10
3
T
2
15–40
C0
p;m=221.715 + 2.69388 T3.90554 ·10
3
T
2
+ 9.30988 10
2
T
0.5
1.24017 ·10
4
T
2
40–80
C0
p;m= 561.701–6.89634 ·10
1
T+ 3.48830 ·10
3
T
2
4.69837 ·10
3
T
0.5
+ 4.31281 10
5
T
2
80–150
C0
p;m= 379.403 + 6.90525 10
1
T4.11884 ·10
4
T
2
3.92645 ·10
3
T
0.5
+ 4.31306 ·10
5
T
2
150–298.15
C0
p;m= 871.493–2.08851 ·10
1
T+ 2.72944 ·10
4
T
2
8.84439 ·10
3
T
0.5
+ 4.31262 ·10
5
T
2
298.15–400
C0
p;m=660.406 + 2.41460 T1.74735 ·10
3
T
2
+ 7.27097 10
3
T
0.5
+ 4.31276 ·10
5
T
2
400–520
Illite IMt-2 C0
p;m= 2.91645 10
3
T
2.5
0–15
C0
p;m=221.063 + 3.70974 T– 1.47826 ·10
2
T
2
+ 7.86535 ·10
2
T
0.5
7.15459 ·10
3
T
2
15–50
C0
p;m=208.700 + 2.80152 T4.44904 ·10
3
T
2
+ 8.25060 ·10
2
T
0.5
2.73851 ·10
3
T
2
50–130
C0
p;m= 36.4649 + 1.93294 T2.44190 ·10
3
T
2
1.35852 ·10
3
T
0.5
+ 4.25529 ·10
5
T
2
130–210
C0
p;m= 514.278 + 3.38679 10
1
T5.20504 10
5
T
2
4.96021 10
3
T
0.5
+ 4.31269 10
5
T
2
210–298.15
C0
p;m= 674.639 + 2.74982 10
1
T2.84661 10
4
T
2
7.04421 10
3
T
0.5
+ 4.31264 10
5
T
2
298.15–510
Mixed-layer ISCz-1 C
p,m
= 3.36271 ·10
5
T
4
0–15
C0
p;m=93.2710 + 1.63848 T2.55743 ·10
3
T
2
+ 3.16665 ·10
2
T
0.5
15–50
C0
p;m= 65.3683 + 1.16861 T+ 8.01563 ·10
4
T
2
8.72912 ·10
2
T
0.5
50–150
C0
p;m=1.66809 10
3
+ 3.06285 T6.76587 ·10
6
T
2
+ 2.06041 ·10
4
T
0.5
150–210
C0
p;m= 2.56271 10
2
+ 5.17534 ·10
1
T1.56000 ·10
6
T
2
1.24733 ·10
3
T
0.5
210–298.15
C0
p;m= 6.38637 10
2
+ 1.28869 ·10
1
T9.32104 ·10
3
T
2
6.14995 ·10
3
T
0.5
298.15–520
Table 10
Entropies of formation from oxides DS
0f/ox
(298.15 K) and stan-
dard entropies of formation DS
0f
(298.15 K) of the anhydrous
minerals smectite MX-80, illite IMt-2 and mixed-layer ISCz-1
Minerals DS
0f/ox
(J mol
1
K
1
)DS
0f
(J mol
1
K
1
)
Smectite MX-80 24.5 (±1.4) 1243.3 (±0.9)
Illite IMt-2 29.1 (±3.6) 1257.6 (±0.9)
Mixed-layer ISCz-1 30.1 (±2.8) 1258.0 (±0.9)
5470 H. Gailhanou et al. / Geochimica et Cosmochimica Acta 71 (2007) 5463–5473
The liquid/solid transition of water in the adsorbed state
was assumed to be at 273 K (as for bulk water), and dif-
ferent C
p
corrections were applied above and below this
temperature. The sample was considered to be a pure
illite solution, for which the ideal composition should
be K
0.75
(Al
1.75
Mg
0.25
)(Si
3.5
Al
0.5
)O
10
(OH)
2
. No impurity
phases like those we have detected (silica, microcline, ru-
tile and kaolinite) were considered. Robie et al. (1976)
considered the solid solution Marblehead illite as a com-
bination of the so-defined ‘ideal illite’ and other mineral
phases, which were considered ‘impurities’. The amounts
of these impurities were deduced from the constitutive
oxide compositions of the raw sample, which were deter-
mined by chemical analyses, and from the ideal composi-
tion of illite. The resulting excess oxides were combined
into mineral phases describing the non-stoichiometries
in the various elements. This method requires as many
‘impurities’ as elements. The mineral impurities were cho-
sen based on the heat capacity data available at low tem-
peratures. In order to obtain the heat capacity of the
ideal illite, the additivity rule for C
p
was assumed, and
the impurity corrections were simply applied. Unfortu-
nately, the nature of these mineral phases and their heat
capacities were not specified in the original paper. The
difference between the corrected and the raw heat capac-
ities is about 12% at 50 K and decreases to 5% at 300 K.
Finally, from the heat capacities of the ideal illite, the
thermodynamic functions S
0
(T), H
0
(T)H
0
(0) and
(G(T)H
0
(0))/Twere determined at selected
temperatures.
Comparisons between the heat capacity and entropy
functions of the illite IMt-2 and the ideal illite from Ro-
bie et al. (1976) are given in Fig. 3. There is a relatively
good agreement between the functions obtained for both
illites, as the relative deviation decreases progressively
from 15% at 50 K to 4% at 200 K and 0.5% at
298.15 K. Consequently, only a deviation of 6% is ob-
served between the entropy values at 298.15 K. However,
these differences are higher than the absolute errors for
heat capacities given in Section 4.1.2 for the illite IMt-2
and higher than that estimated at 1.5% at 50 K and
0.5% at 300 K for the ideal illite of Robie et al. (1976).
Within the whole temperature range, the values obtained
for the ideal illite are lower than the values for the illite
IMt-2. A first possible explanation for this would be that
the heat capacities of the ideal illite were not corrected
for contributions of other phases present in the Marble-
head sample, which led to an underestimation of the heat
capacities of the ideal illite. Second, it is clear that the
additivity law approximates the C
p
function to some per-
cent. In such an approximation, it is implicitly assumed
that the harmonic (and for higher temperatures, anhar-
monic) vibrations are additive. Although the metal–oxy-
gen pair contribution to vibrational entropy is
important, the cooperative phonon effect accounts for a
few percent. In other words (and as an example), a mag-
nesium atom in a clay octahedral site cannot vibrate rel-
ative to the other entities in the same way it does in an
ionic MgO or MgFe
2
O
4
structure. Moreover, as Robie
et al. (1976) mentioned for various muscovites, the iron
ions can explain noteworthy differences for low tempera-
ture C
p
.
5.2. Application for predicting models of thermodynamic
properties
Several predicting models of heat capacities and entro-
pies were developed for silicates and oxide minerals; these
models were reviewed by Holland (1989). Generally, the
mineral properties were estimated by summing the fictive
thermodynamic properties of its constituents, which were
different depending on the refinement of the models (Lati-
mer, 1951; Fyfe et al., 1958; Robinson and Haas, 1983; Hol-
land, 1989). In these predicting models, very few data on
clay minerals were used to calculate the fictive properties
of the constituents because of a lack of data for these min-
erals, so these models may be unreliable for accurate esti-
mations of the thermodynamic properties of clay
minerals. The present study aims at providing new data
on clay minerals to improve or validate these predicting
models for clay minerals. A further goal would be to ac-
quire sufficient data on end-members clays in order to take
into account most of the chemical and structural variabili-
ties among clays.
0 100 200 300 400 500 600
0
100
200
300
400
500
600
T
(K)
S
°
(J.mol
-1
.K
-1
)
illite IMt-2
ideal illite (Robie et al., 1976)
a
b
0 100 200 300 400 500 600
0
100
200
300
400
500
T
(K)
C
p,m
°
(J.mol
-1
.K
-1
)
illite IMt-2
ideal illite (Robie et al., 1976)
Fig. 3. Comparison of the thermodynamic properties of the illite
IMt-2 and the ‘ideal illite’ K
0.75
(Al
1.75
Mg
0. 25
)(Si
3.5
Al
0.5
)O
10
(OH)
2
from Robie et al. (1976): (a) heat capacity functions C0
p;m(T) and (b)
entropy functions S
0
(T).
Thermodynamic properties of anhydrous smectite, illite and illite–smectite 5471
This calorimetric study provided the heat capacities
and derived thermodynamic functions of a smectite, an il-
lite and a mixed-layer illite–smectite from 0 to 520 K (at
1 bar). However, heat contents and entropies of forma-
tion data are not sufficient to describe the stability of
minerals under definite conditions of pressure, tempera-
ture and chemical potentials. This work is a first stage
for our final objective. The second stage aims to obtain
the standard enthalpies of formation of the anhydrous
minerals using isothermal calorimetry of dissolution at
298.15 K. Finally, from these results, all the thermody-
namic functions of these minerals in their anhydrous state
may be obtained from 0 to 520 K and at standard pres-
sure. These calorimetric methods are being used to study
these minerals in highly hydrated states as well. In the
same way as for heat capacity and entropy, these new
data about clay minerals will be used to validate predict-
ing models for the Gibbs free energies of clays, such as
those performed by Vieillard (2000, 2002).
ACKNOWLEDGMENTS
We thank C. Alba-Simionesco and F. Brunet for their contri-
butions to the first measurements carried out by adiabatic calo-
rimetry in Orsay. Financial support from the French Radioactive
Waste Management Agency (ANDRA, N. Michau), the French
Geological Survey (BRGM) and the French National Council
for Scientific Research (CNRS) is gratefully acknowledged. This
work was performed as part of a Ph.D. Thesis (H. Gailhanou,
Univ. Paul Ce
´zanne, Marseille), under ANRT-ANDRA-
BRGM-CNRS-University Agreement.
APPENDIX A. SUPPLEMENTARY DATA
Entropy data of oxides and elements (Electronic annex
EA-4, Table EA-4) used for the calculation of the entropies
of formation of minerals, were provided by Cox et al.
(1989) and Chase (1998). Supplementary data associated
with this article can be found, in the online version, at
doi:10.1016/j.gca.2007.09.020.
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Associate editor: David J. Wesolowski
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