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Ž.
Chemical Geology 168 2000 225–238
www.elsevier.comrlocaterchemgeo
Application of the improved regression method to derive DG0of
f
non-stoichiometric clay minerals and their correlations with
compositional parameters
Mahammad Kudrat a, Chandrika Varadachari b,), Kunal Ghosh a
aDepartment of Agricultural Chemistry and Soil Science, UniÕersity of Calcutta, 35 B.C. Road, Calcutta 700 019, India
bRaman Centre for Applied and Interdisciplinary Sciences, 16A Jheel Road, Calcutta 700 075, India
Received 23 March 1999; accepted 17 January 2000
Abstract
w
A curvilinear regression method earlier developed by us Varadachari, C., Kudrat, M., Ghosh, K., 1994. Evaluation of
x
standard free energies of formation of clay minerals by an improved regression method. Clays Clay Miner. 42, 298–307
Ž
0
.
was utilised here for deriving standard free energies of formation DGof a compositionally wide range of illites, smectites,
f
vermiculites and chlorites. The DG
0
values ranged from around y1131 to y1321 kcalrmol for illites, y1097 to y1328
f
kcalrmol for smectites, y1295 to y1351 kcalrmol for vermiculites and y1596 to y1983 kcalrmol for chlorites. Derived
DG
0
data were compared with available DG
0
data for compositionally similar minerals. In spite of some differences in their
ff
Ž.
compositions, the values were within a close range about "0.3–0.5% . Statistical analysis of the relationships between
DG
0
and ionic contents for the different clay groups were done. DG
0
of illites showed strong correlations with Fe
3
qand
f f
Ž.
3
qŽ. Ž.
3
q
VI Al octahedral Al ; the values became more negative with increasing VI Al and less negative with increasing
3
q4qŽ.
3
qŽ.Ž.
3
q3q2q2q
Fe in the structure. A regression equation involving Si , IV Al tetrahedral Al , VI Al , Fe , Fe , Mg and
q
20 3qŽ
K gave a high regression coefficient, rs0.998. DGof smectites were markedly influenced by the Fe content higher
f
3
q0.
2
q2qŽ
2
q0
Fe contents lowered yDGand that of chlorites by the Fe and Mg contents higher Fe lowered yDGand
f f
2
q.
0
higher Mg increased it ; vermiculites did not show strong influence of any of the structural ions on the DG.q2000
f
Elsevier Science B.V. All rights reserved.
Keywords: Illite; Smectite; Vermiculite; Chlorite; Free energy; Computation
1. Introduction
Theoretical and empirical methods for the evalua-
Ž0.
tion of standard free energies of formation DGf
provide a relatively simple and rapid means of ob-
)Corresponding author. Fax: q91-33-225-5358.
Ž.
E-mail address: champaka@satyam.net.in C. Varadachari .
taining DG0values for clay minerals, with a fair
f
degree of accuracy. A number of such methods have
been proposed. Theoretical methods are usually based
on the relationship between thermodynamic con-
stants and crystallochemical characteristics
Ž.
Babushkin et al., 1962; Slaughter, 1966 . In most
empirical methods, the DG0values are derived from
f
the sums of basic compositional units such as oxides
0009-2541r00r$ - see front matter q2000 Elsevier Science B.V. All rights reserved.
Ž.
PII: S0009-2 5 4 1 0 0 00 1 9 6- 0
()
M. Kudrat et al.rChemical Geology 168 2000 225–238226
Ž
and hydroxides Tardy and Garrels, 1974, 1976;
Nriagu, 1975; Mattigod and Sposito, 1978; Tardy
.
and Duplay, 1992 . Thus, in the polymer model
ŽNriagu, 1975; Mattigod and Sposito, 1978; Sposito,
.
1986 , clay minerals are treated as condensation
polymers of hydroxide solids. The DG0values are
f
obtained using previously known DG0values of the
f
corresponding hydroxides and derived DG0values,
r
i.e., standard free energy of polymerisation reaction
w00
Ž.0Ž
DGsÝDGproducts yÝDGhydroxide re-
rf f
.x0
actants . The DGvalues are in turn obtained by
rŽ.
establishing correlation equations. Sposito 1986
proposed an equation in which DG0is correlated to
r
the radii and valence of the cations, layer charge and
isomorphic substitutions. Results obtained by this
method compare well with experimental values
Ž.
Sposito, 1986; Hemingway and Sposito, 1996 . Kar-
Ž.
pov and Kashik 1968 provided a new approach to
this problem by their suggestion that regression pro-
cedures be incorporated in such derivations for ther-
modynamic parameters. By this statistical treatment,
errors in individual equations will partly cancel out
and reliability of the equations will be increased.
Ž.
Karpov and Kashik 1968 derived several linear
multiple regression equations relating DG0to
r
molecular volumes and stoichiometric increments.
Ž.
Chermak and Rimstidt 1989 utilised this concept
of multiple linear regression to determine the contri-
bution of oxide and hydroxide components to the
DG0of silicate minerals. Thus, the contributions of
fŽ. Ž. Ž
Al O , Al OH , SiO , Mg OH , K O, etc. i.e.,
23 3 2 2 2
.0
the various components of clay minerals to the DGf
of a selected group of silicates were determined by a
multiple linear regression technique. Using these
data, the DG0for a silicate was evaluated from a
f
weighted sum of the contributions of each oxide and
hydroxide component. Experimentally measured DG0
f
values differed from the predicted DG0values by
f
about 0.26%. The least-square approach was also
Ž.
advocated by Powell and Holand 1993 as a pre-
ferred method of calculating thermodynamic data of
silicate minerals. A novel approach was attempted by
Ž.
Chen 1975 , who incorporated the concept of curvi-
linear regression as well as the use of complex
Ž.
silicates in place of oxides and hydroxides for
0Ž.
evaluation of DG. According to Chen 1975 , a
f
complex silicate may be hypothetically formed from
various compounds ranging from simple oxides to
complex silicates. Thus, hypothetically the formation
Ž.
of kaolinite, Al Si O OH , may be represented as
225 4
Ž. Ž .
iAlOq2SiO q2H O, ii Al SiO qSiO q
23 2 2 2 3 2
Ž. Ž .
2H O, iii 2AlO OH q2SiO qH O, etc. For each
222
Ž. Ž . Ž . 0
combination, i , ii , iii , etc., the DGof the
f
individual component minerals are added to give the
0wŽ. 00
sum ÝDGe.g., for combination i ÝDGsDG
f,if,if
Ž. 0Ž. 0Ž.x
Al O q2DGSiO q2DGH O . Various
23 f 2 f 2
possible combinations are constructed in this man-
Ž.
0
ner, for a clay silicate mineral and the ÝDGare
f,i
computed. The values of ÝDG0are then arranged in
f,i
descending order and each is assigned an integral
Ž.
value xe.g., 0, 1, 2, 3, etc. , which represents the
0Ž
rank of the ÝDGi.e., the numerical distance of a
f,i
ÝDG0value along the ordinate in the exponential
f,i
.0
graph . Utilising the values of ÝDGand x,a
f,i
regression equation of the form:
ÝDG0saebxqc1
Ž.
f,i
is derived, where a,b, and care constants and the
value of cgives the DG0of the mineral. The value
fŽ.
of cis derived by solving Eq. 1 .
This method is apparently very promising and
versatile. It can be applied to any type of clay
mineral with fairly good results. However, various
stages in this method needed to be improved upon.
The assignment of rank, x, as proposed by Chen
Ž.
1975 was quite arbitrary, although choice of this
value is critical for obtaining DG0. A method for
f
solving the complex exponential equation was also
needed.
Keeping these aspects in view, Varadachari et al.
Ž.
1994 further modified and improved the curvilinear
Ž.
regression method Chen, 1975 . Particularly, they
proposed a method for assignment of xrankings
from the various possible combinations of xvalues
that can be computed. A method was also developed
Ž.
for solving the complex exponential Eq. 1 , which
involved an iterative least-squares fitting of data to
obtain DG0. Utilising each combination of x, the
f
least-squares fit regression curve was computed and
the residual error was obtained. The combination of
Ž.
xs with the least residual error best curve-fit was
selected; the corresponding value of cin the expo-
nential equation gave the DG0for the silicate min-
f
Ž.
eral. Varadachari et al. 1994 observed that the
()
M. Kudrat et al.rChemical Geology 168 2000 225–238 227
values of DG0obtained by this method are in better
f
agreement with the standard values than those ob-
tained by most other theoretical or experimental
means. Thus, where experimental determinations are
not convenient, the improved regression method pro-
vides a reliable and relatively rapid means of evalu-
ating DG0of any kind of clay mineral merely from
f
a knowledge of its chemical composition.
In this work, the improved regression method
Ž.
Varadachari et al., 1994 has been used for deriving
DG0values of a series of non-stoichiometric clays
f
belonging to the illite, smectite, vermiculite and
chlorite groups and having wide variations in chemi-
cal compositions. Such data are imperative for the
thermodynamic treatment of mineral equilibria,
which would enable a better understanding of the
differences in the nature of clay minerals in different
Ž.
geochemical environments Varadachari, 1992 . The
influence of structural ions on DG0values was also
f
investigated here, by multivariate statistical analysis.
It was hoped, thereby, to obtain a better understand-
ing of those ions, which have major influences on
the thermodynamic status of different groups of clay
minerals and, if possible, to deduce mathematical
expressions of such influences, which could be used
for further simpler derivations of DG0values.
f
2. Methodology
Clay minerals under different groups, viz., illite,
smectite, vermiculite and chlorite were mainly se-
Ž.
lected from Deer et al. 1965 and their structural
formulae were recorded. Clay minerals from each
group were selected to obtain a wide range of com-
positions, including a range of tetrahedral and octa-
hedral substitutions, interlayer charge, Fe and Mg
contents, etc. Structural formulae of the clay miner-
als illite, smectite and vermiculite are expressed here
Ž.
in terms of a half unit cell, i.e., O OH , and for
10 2
Ž.
chlorite in terms of O OH . Trace amounts of
10 8
2q4qŽ
Mn and Ti were ignored Weaver and Pollard,
.
1973 . However, in order to maintain charge neutral-
ity, these were substituted by equivalent amounts of
Feq2. Elemental formulae of the clay minerals were
represented by the major constituents, viz., Si4q,
Al3q,Fe
3q,Fe
2q,Mg
2qand Kq; in a few instances,
Naqand Kqwere also included.
The procedure followed for obtaining DG0values
f
of the clay minerals is given in detail by Varadachari
Ž.
et al. 1994 . The various stages of this procedure are
briefly as follows. Each mineral is first represented
in the form of combinations of various compounds.
Typical examples for the four clay mineral groups,
may be seen in Appendix A. For each combination,
the DG0of the individual component minerals are
f
then added to give the sum, ÝDG0. These values of
f,i
DG0for the component minerals were obtained from
fŽ. 0
Helgeson et al. 1978 ; the DGfor water was taken
f
Ž.
from Robie et al. 1978 .
The values of ÝDG0for a mineral are arranged
f,i
Ž.
in descending order as shown in Appendix A and
each is assigned an integral value x, which repre-
sents the rank of the ÝDG0. However, there are
f,i
many ways in which xvalues may be assigned to a
set of ÝDG0. All such combinations are computed
f,iŽ
using a ‘tree diagram’ procedure Varadachari et al.,
.
1994 . Essentially, the procedure is as follows. The
ÝDG0are arranged in order of increasing numerical
f,i
magnitude. The first ÝDG0value is assigned rank
f,i
xs0. The subsequent ÝDG0may have a rank
f,i
Ž. 0
xs0, 1 or 2. Rank xof the iq1thÝDGis G
f,i
Ž. 00
the xvalue for the ith ÝDG, i.e., ÝDGG
f,if,iq1
ÝDG0. The difference in x values for adjacent
f,i
ÝDG0is either 0,1 or 2. Thereby, various combina-
f,i
tions of xvalues for a set of ÝDG0is obtained.
f,i
This is diagrammatically represented as a ‘tree’. The
examples in Appendix A show the ÝDG0values
f,i
and their corresponding ranks x, for some clay
minerals. The combination of values shown there is
the best possible combination, which gives closest fit
in the exponential curve.
Ž.
Curve fitting and solving the Eq. 1 is done as
follows. For each combination of x, obtained as
Ž.
mentioned above, the exponential Eq. 1 is solved
by an iterative least-squares technique and the resid-
ual error is obtained. That combination, which shows
the best curve fitting, i.e., smallest residual error, is
Ž.
selected. The corresponding value of cin Eq. 1
gives the required value of DG0of the clay mineral.
f
The general nature of the curves may be seen in Fig.
1 and Appendix A.
The iterative least-squares method of solving the
Ž.
exponential Eq. 1 broadly consists in assuming
certain initial estimates of the constants, a,b,c, i.e.,
a,band c, and evaluating the error, Ý
´
2. At the
00 0 n
()
M. Kudrat et al.rChemical Geology 168 2000 225–238228
Fig. 1. Regression of ÝDG0values for some clay minerals.
f,i
completion of the first iteration, the values of a,b,
00
c, are replaced by revised values derived, and the
0
whole procedure is repeated again. This will lead to
another set of revised estimates of a,b, and c.At
each stage of the iterative procedure, Ý
´
2is evalu-
n
ated. The iterative process is continued until the
solution converges, i.e., Ý
´
2reaches a minimum;
n
the corresponding value of cgives DG0for the
f
mineral.
Ž
A computer program has been developed Kudrat
.
et al., 1999 , which can be utilised for obtaining
DG0of clay minerals. The input data required, are
f0Ž.
ÝDGvalues e.g., Appendix A . This program is
f,iŽ.
available for use Kudrat et al., 1999 . Here, all
computations were done on a IBM-RSr6000 work-
station using the above program. The DG0derived,
f
were utilised for studying the relations with struc-
tural ion contents. This included evaluation of corre-
lation coefficients between DG0and moles of indi-
f
vidual structural ions. Multiple correlation and re-
gression equations were also computed, which re-
lated DG0with more than one structural ion. For all
f
minerals, the amounts of tetrahedral and octahedral
Al3qwere computed from the unit cell formulae by
utilising the concept that the total tetrahedral occu-
pancy should be four, i.e., p mole Si4qqq mole
Al3qs4 in the tetrahedral layer; the remaining Al3q
Ž3q3q.3q
total Al ytetrahedral Al is the octahedral Al .
The statistical calculations were done on a personal
computer using Statgraf Software Package.
3. Results and discussion
(0)
3.1. Standard free energy of formation
D
GÕalues
f
3.1.1. Illites
Ž0.
Standard free of formation DGdata derived
f
here for a wide range of illite compositions are
shown in Table 1. Experimental and theoretically
derived data available in the literature for illites of
similar compositions are also included in Table 1.
The footnote includes available data for other illites.
0Ž.
Values of DGfor illites Table 1 range from
f
y1131.41 kcalrmol for Glauconite to y1321.05
kcalrmol for Illite II. The range is wide because of
the wide compositional range of materials studied,
including a range of tetrahedral substitutions, inter-
layer charges, Fe3qand Mg2qcontents, etc. For
Ž.
example., Illite II a hydromuscovite , which is a
dioctahedral illite with high tetrahedral substitution,
0Ž.
has a high negative DGy1321.05 kcalrmol ;
f
Illite VI, which also has high tetrahedral charge but
Ž2q.
is trioctahedral high Mg content , has a much
0Ž.
less negative DGvalue y1243.91 kcalrmol .
f
Glauconite, an iron-rich illite has an even less nega-
0Ž.
tive DGvalue y1131.41 kcalrmol .
f
()
M. Kudrat et al.rChemical Geology 168 2000 225–238 229
Table 1
Computed standard free energies of formation DG0,aand bvalues of illite minerals and data available for comparable compositions
f
Ž. Ž. Ž . Ž . Ž. Ž.
Other data: Fithian Illite Si IV Al VI Al Mg K Na C O OH : y1319.7 Reesman, 1974 . Goose Lake Illite Si IV Al VI Al -
3.46 0.54 1.65 0.4 0.60 0.05 0.07 10 2 3.65 0.35 1.58
Ž . Ž . Ž. Ž. 3qŽ. Ž
Fe Mg K O OH : y1265.3 Rouston and Kittrick, 1971 . Beavers Bend Si IV Al VI Al Fe Mg K Na O OH : y1250.5 Huang and Keller,
0.24 0.15 0.59 10 2 3.48 0.52 1.43 0.42 0.16 0.6 0.04 10 2
.Ž.Ž. Ž.Ž. Ž.Ž.
1973 . Grundy Si IV Al VI Al Mg Na K O OH : y1322.7 Reesman, 1974 . Marblehead Si IV Al VI Al Mg Ca -
3.22 0.78 1.9 0.24 0.04 0.56 10 2 3.58 0.42 1.60 0.40 0.05
Ž. Ž .
Na K O OH : y1310.8 Reesman, 1974 .
0.03 0.69 10 2
0
wŽ.xŽ.
Illites studied here Analytical data source: Deer et al. 1965 DGkcalrmol ab
f
2q
Ž . Ž. Ž. Ž .
1. Illite I: Hydromuscovite Japan Si IV Al VI Al Fe Mg K Na O OH y1318.43 60.92729 y0.96916
3.12 0.880 1.667 0.12 0.30 0.899 0.14 10 2
3q2q
Ž . Ž. Ž. Ž .
2. Illite II: Hydromuscovite S. Wales Si IV Al VI Al Fe Fe Mg K O OH y1321.05 52.62718 y0.59889
3.10 0.900 1.960 0.036 0.052 0.066 0.676 10 2
2q
Ž . Ž. Ž. Ž .
3. Illite III: Yellow Sericite Virginia Si IV Al VI Al Fe Mg Na K O OH y1313.84 57.39148 y0.8957
3.283 0.717 1.708 0.08 0.22 0.06 0.933 10 2
3q2q
Ž . Ž. Ž. Ž .
4. Illite IV: Illitic Material Illinois Si IV Al VI Al Fe Fe Mg K O OH y1281.28 54.02618 y0.9579602
3.375 0.625 1.476 0.225 0.15 0.28 0.935 10 2
3q2q
Ž . Ž. Ž. Ž .
5. Illite V: Illitic Material Illinois Si IV Al VI Al Fe Fe Mg K O OH y1280.33 46.36889 y0.89953
3.365 0.635 1.359 0.26 0.09 0.42 0.758 10 2
3q2q
Ž . Ž. Ž. Ž .
6. Illite VI: Trioctahedral Illite Scottish clay Si IV Al VI Al Fe Fe Mg K O OH y1243.91 35.08223 y0.705341
3.013 0.987 0.784 0.698 0.264 0.813 0.387 10 2
3q
Ž.wŽ.xŽ. Ž. Ž .
7. Illite VII: Illite Fithian Nriagu 1975 Si IV Al VI Al Fe Mg K O OH y1274.73 43.72045 y0.806652
3.51 0.490 1.540 0.29 0.19 0.62 10 2
Ž.wxŽ. Ž. Ž .
8. Illite Average Weaver and Pollard, 1973 Si IV Al VI Al Mg K Na O OH y1302.35 45.14204 y0.640779
3.56 0.440 1.740 0.26 0.55 0.15 10 2
3q2q
Ž . Ž. Ž. Ž .
9. Glauconite: Glauconite New Zealand Si IV Al VI Al Fe Fe Mg K O OH y1131.41 20.70951 y1.02875
3.82 0.180 0.110 1.266 0.22 0.505 0.602 10 2
0Ž.
Data from other sources for Illites of comparable composition DGkcalrmol Reference
f
a3qb
Ž. Ž. Ž .wx
10. Fithian Illite Si IV Al VI Al Fe Mg K O OH Composition comparable to Illite VII y1270.6 Rouston
3.51 0.49 1.54 0.29 0.19 0.64 10 2 Ž.
and Kittrick 1971
3qc
Ž. Ž. Ž .wx
11. Fithian Illite Si IV Al VI Al Fe Mg K O OH Composition comparable to Illite VII y1278.8 Tardy and
3.51 0.49 1.54 0.29 0.19 0.64 10 2 Ž.
Garrels 1974
3qc
Ž. Ž. Ž .wx
12. Fithian Illite Si IV Al VI Al Fe Mg K O OH Composition comparable to Illite VII y1273.2 Chermak and
3.51 0.49 1.54 0.29 0.19 0.64 10 2 Ž.
Rimstidt 1989
b
Ž. Ž. Ž .wx Ž.
13. Illite Si IV Al VI Al Mg K O OH Composition comparable to Illite Average y1300.95 Helgeson 1969
3.5 0.5 1.8 0.25 0.6 10 2 b
Ž. Ž. Ž . Ž .
14. Rock Island Si IV Al VI Al Mg Ca Na K O OH y1307.3 Reesman 1974
3.57 0.43 1.69 0.34 0.03 0.03 0.59 10 2
wx
Composition comparable to Illite Average 3q2qb
Ž. Ž. Ž .
15. Kettleman North Dome Si IV Al VI Al Fe Fe Mg Ca Na K O OH y1320.9 Merino and
3.06 0.94 1.94 0.055 0.008 0.13 0.001 0.095 0.61 10 2
wx ŽŽ.
Composition comparable to Illite II at 1008C Ransom 1982
.
and 150 bar
aChemical formula show excess qve charge of 0.02.
bExperimentally determined values.
cTheoretically derived values.
()
M. Kudrat et al.rChemical Geology 168 2000 225–238230
In contrast, experimental data are available for a
Ž.
much narrower compositional range Table 1 . The
available range of DG0values is also, thereby, not
f
as wide as those derived here. The experimentally
derived value for Fithian Illite, y1270.6 kcalrmol
Ž.
Rouston and Kittrick, 1971 is close to that derived
Ž.
here y1274.73 kcalrmol . Other theoretically de-
rived values for the same mineral are y1278.8 and
Ž
y1273.2 kcalrmol Tardy and Garrels, 1974; Cher-
.
mack and Rimstidt, 1989, respectively . Experimen-
Ž.
tal values for an illite Helgeson, 1969 and a Rock
Ž.
Island Illite Reesman, 1974 viz., y1300.98 and
y1307.3 kcalrmol, respectively, are comparable to
the derived value for the compositionally similar
Ž.
mineral, Illite Average viz., y1302.35 kcalrmol,
Ž.
respectively. Similarly, Illite II derived here and
Ž
Kettleman North Dome Illite Merino and Ransom,
.
1982 , which are compositionally similar have very
close DG0values viz., y1321.05 and y1320.9
fŽ.
kcalrmol, respectively Table 1 .
Data for other Illites whose compositions are not
Ž
much comparable are also shown in Table 1 foot-
.
note . These values only serve to show the average
spread of the data and can be used for very rough
comparisons, if necessary.
3.1.2. Smectites
The DG0values for different types of smectites
f
are shown in Table 2. Here too, minerals of a wide
range of compositions have been taken for study.
Thereby, the range of DG0values obtained is also
fŽ. 0
wide. Overall, it is seen Table 2 that the DGf
values for montmorillonites and beidellites are mostly
in the range y1250 to 1290 kcalrmol; for saponites
this is somewhat higher, above the y1300 kcalrmol
range; the iron-rich member, nontronite, has a very
Ž.
low negative value y1097.79 kcalrmol . Such rela-
Ž. 0
tively lower numerical values for DGwere also
f
Ž.
observed in iron-rich illites Table 1 .
Experimental data from literature show that Belle
Fourche and Castle Rock montmorillonites, which
are nearest in composition to Montmorillonite V
0Ž.
have comparable DGvalues Table 2 . Beidellite I
fŽ
may, similarly, be compared with K-Beidellite Misra
.
and Upchurch, 1976 and Beidellite III may be com-
Ž
pared to Mg-Beidellite Chermak and Rimstidt,
.0
1989 . Differences in the DGare around y6 and
f
y5 kcalrmol, respectively; considering the range of
experimental errors and the differences in composi-
tions of the minerals, the DG0values are within a
f
very narrow range. Few other experimental data are
added as a footnote to Table 2.
3.1.3. Vermiculites
Computed values of DG0of six vermiculites are
f
shown in Table 3. Unlike illites and smectites, DG0
f
values for vermiculites appear less scattered. This
may be attributed to the fact that the vermiculites
Ž.
have smaller variations in composition Table 3 .
Overall, the DG0values are more negative than
f
those for montmorillonites, i.e., mostly around and
above the value 1300. Not many experimental values
Ž.
are available for vermiculites. Kittrick 1973 ob-
served that vermiculites are probably fast forming,
unstable intermediates and, therefore, their DG0val-
f
ues could not be evaluated by dissolution methods.
Ž. 0
Nriagu 1975 derived the DGvalue for a Montana
f
vermiculite whose composition is comparable to that
of Vermiculite I; the DG0values differ by only
f
Ž. Ž.
about 4 kcalrmol Table 3 . Henderson et al. 1976
evaluated the DG0for a Ca-vermiculite as y1303.7
f
kcalrmol; a similar mineral has not been studied
here.
3.1.4. Chlorites
The widest range of DG0values is shown by the
f
Ž.
chlorites Table 4 ; the values range from y1596.17
kcalrmol for Thuringite to y1983.78 kcalrmol for
Corundophilite; wide variations in the DG0values
f
may be attributed to the large compositional differ-
ences amongst the minerals studied. The minerals
Ž.
Thuringite, Chamosite II and Daphnite Table 4 ,
which have high Fe contents have the lowest range
of negative values of DG0, whereas minerals rich in
fŽ
Mg and low in Fe have the largest values e.g.,
.
Corundophilite and Clinochlore I . Such composi-
tional dependencies of DG0values have also been
f
observed earlier with the other clay groups studied
Ž.
Tables 1–3 .
Ž
Experimental data for a Vermont chlorite Kit-
.
trick, 1982 can at best be compared to Klementite I.
Their respective DG0values are also comparable. A
f
chlorite from New Mexico, also studied by Kittrick
Ž.
1982 may be compared to Chamosite I; their com-
positions and DG0values are fairly close. The DG0
ff
Ž.
for chlorites reported by Nriagu 1975 , Hemingway
()
M. Kudrat et al.rChemical Geology 168 2000 225–238 231
Table 2
Ž0.
Computed standard free energies of formation DG,aand bvalues of smectite minerals and data available for comparable compositions
f
Ž. Ž. 3qq Ž . Ž. Ž. Ž .
Other data: Aberdeen Si IV Al VI Al Fe Mg M : y1225.15 Kittrick, 1971 . Belle Fourche Si IV Al VI Al Fe Mg K O OH :
3.82 0.18 1.29 0.335 0.445 0.83 3.785 0.215 1.575 0.14 0.305 0.46 10 2
Ž . Ž. Ž. 3qŽ. Ž .
y1330.2 Peryea and Kittrick, 1986 . Clay Spur Si IV Al VI Al Fe Mg Ca Na K O OH : y1248.4 Huang and Keller, 1973 .
3.93 0.07 1.52 0.24 0.33 0.19 0.02 0.02 10 2
0
wŽ.xŽ.
Smectites studied here Analytical data source: Deer et al., 1965 DGkcalrmol ab
f
3q
Ž . Ž. Ž. Ž .
1. Montmorillonite I: Pink New Mexico Si IV Al VI Al Fe Mg K O OH y1296.36 59.74017 y0.1690361
4.04 0.00 1.410 0.07 0.5 0.4 10 2
3q
Ž . Ž. Ž. Ž .
2. Montmorillonite II: Montmorillon France Si IV Al VI Al Fe Mg K O OH y1271.69 21.78810 y0.2056358
3.905 0.095 1.685 0.046 0.365 0.172 10 2
3q2q
Ž . Ž. Ž. Ž .
3. Montmorillonite III: Dark Coloured Mississippi Si IV Al VI Al Fe Fe Mg K O OH y1268.62 53.69000 y0.1877527
3.845 0.155 1.355 0.32 0.07 0.31 0.37 10 2
3q2q
Ž . Ž. Ž. Ž .
4. Montmorillonite IV: Venezia Si IV Al VI Al Fe Fe Mg K O OH y1277.21 38.58842 y0.146039
3.80 0.200 1.355 0.155 0.09 0.625 0.24 10 2
3q
Ž . Ž. Ž. Ž .
5. Montmorillonite V: White Transylvania Si IV Al VI Al Fe Mg K O OH y1273.99 27.43043 y0.1412989
3.73 0.270 1.530 0.180 0.5 0.14 10 2
3q
Ž . Ž. Ž. Ž .
6. Beidellite I: Colorado Si IV Al VI Al Fe Mg Na K O OH y1251.74 45.39073 y0.2615
3.58 0.420 1.390 0.5 0.08 0.15 0.44 10 2
3q
Ž . Ž. Ž. Ž .
7. Beidellite II: Idaho Si IV Al VI Al Fe Mg K O OH y1289.12 77.1002 y1.12170
3.46 0.540 1.960 0.04 0.02 0.50 10 2
3q2q
Ž . Ž. Ž. Ž .
8. Beidellite III: Ukraine Si IV Al VI Al Fe Fe Mg K O OH y1250.86 36.39224 y0.9356344
3.54 0.460 1.615 0.33 0.08 0.10 0.265 10 2
3q2q
Ž . Ž. Ž. Ž .
9. Saponite I: White Soapy Transvaal Si IV Al VI Al Fe Fe Mg K O OH y1328.93 31.08443 y0.730785
3.615 0.355 0.00 0.03 0.03 3.16 0.005 10 2
3q
Ž . Ž. Ž. Ž .
10. Saponite II: Utah Si IV Al VI Al Fe Mg K O OH y1322.28 36.31517 y0.55854
3.745 0.255 0.085 0.015 2.875 0.205 10 2
3q2q
Ž . Ž. Ž. Ž .
11. Nontronite: Green Yellow Washington Si IV Al VI Al Fe Fe Mg Ca O OH y1097.79 8.304284 y0.9200576
3.46 0.540 0.010 1.92 0.03 0.12 0.225 10 2
3q
Ž . Ž. Ž. Ž .
12. Sauconite: Reddish Brown Wisconsin Si IV Al VI Al Fe Mg K O OH y1302.39 32.8763 y0.113837
3.39 0.610 0.680 0.23 1.69 0.20 10 2
0Ž.
Data from other sources for smectites of comparable composition DGkcalrmol Reference
f
a
Ž. Ž. Ž .
13. Belle Fourche Si IV Al VI Al Fe Mg O OH y1266.7 Peryea and
3.785 0.215 1.575 0.14 0.535 10 2
wx Ž.
Composition comparable to montmorillonite V Kittrick 1986
3qa
Ž. Ž. Ž . Ž.
14. Castle Rock Si IV Al VI Al Fe Mg O OH y1275.0 Weaver et al. 1976
3.68 0.32 1.52 0.14 0.67 10 2
wx
Composition comparable to montmorillonite V
3qb
Ž. Ž. Ž . Ž.
15. Castle Rock Si IV Al VI Al Fe Mg O OH y1274.0 Sposito 1986
3.68 0.32 1.52 0.14 0.67 10 2
wx
Composition comparable to montmorillonite V
3q2qb
Ž. Ž. Ž .
16. Mg-Beidellite Si IV Al VI Al Fe Fe Mg K Ca Na O OH y1245.6 Chermak and
3.55 0.45 1.41 0.415 0.055 0.34 0.095 0.01 0.07 10 2
wx Ž.
Composition comparable to Beidellite III Rimstidt 1989
3q2qa
Ž. Ž. Ž .
17. K-Beidellite Si IV Al VI Al Fe Fe Mg K Ca Na O OH y1245.7 Misra and
3.55 0.45 1.41 0.415 0.055 0.205 0.365 0.01 0.07 10 2
wx Ž.
Composition comparable to Beidellite I Upchurch 1976
aExperimentally determined values.
bTheoretically derived values.
()
M. Kudrat et al.rChemical Geology 168 2000 225–238232
Table 3
Ž0.
Computed standard free energies of formation DG,aand bvalues of vermiculite minerals and data available for comparable compositions
f
3qŽ. aŽ. Ž.Ž .
Other data: Idealised vermiculite Si Al Mg Fe O OH : y1367.9 Nriagu, 1975 . Ca-vermiculite Si Al Ca O OH : y1303.7 Henderson et al., 1976 .
2.95 1.1 3 0.5 10 2 3.3 2.7 0.35 10 2
0
wŽ.xŽ.
Vermiculites studied here Analytical data source: Deer et al. 1965 DGkcalrmol ab
f
3q2q
Ž . Ž. Ž. Ž .
1. Vermiculite I: Greenish Yellow North Carolina Si IV Al VI Al Fe Fe Mg O OH y1330.76 35.24387 y0.3736903
2.905 1.095 0.495 0.166 0.215 2.341 10 2
3q2q
Ž . Ž. Ž. Ž .
2. Vermiculite II: Pale Yellow Green Maryland Si IV Al VI Al Fe Fe Mg O OH y1344.31 39.60596 y0.4060366
2.84 1.160 0.125 0.26 0.077 2.924 10 2
3q2q
Ž . Ž. Ž. Ž .
3. Vermiculite III: Pennsylvania Si IV Al VI Al Fe Fe Mg O OH y1311.04 42.43549 y0.2006031
2.72 1.280 0.220 0.46 0.30 2.32 10 2
3q2q
Ž . Ž. Ž. Ž .
4. Vermiculite IV: Olive-Green Brown Finland Si IV Al VI Al Fe Fe Mg O OH y1351.64 55.02105 y0.1967631
2.616 1.280 0.000 0.346 0.249 3.08 10 2
3q2q
Ž . Ž. Ž. Ž .
5. Vermiculite V: Yellowish Brown Maryland Si IV Al VI Al Fe Fe Mg O OH y1297.71 35.89775 y0.4242093
2.885 1.010 0.000 0.66 0.055 2.67 10 2
3q2q
Ž . Ž. Ž. Ž .
6. Vermiculite VI: Green Nickeliferous North Carolina Si IV Al VI Al Fe Fe Mg O OH y1295.89 32.61073 y0.3899279
2.805 1.195 0.250 0.165 0.76 2.215 10 2
0Ž.
Data from other sources for vermiculites of comparable composition DGkcalrmol Reference
f
2q3qa
Ž. Ž.wxŽ.
7. Montana Si IV, VI Al Mg Fe Fe Ca O OH Composition comparable to Vermiculite I y1326.9 Nriagu 1975
2.91 1.14 2.71 0.02 0.46 0.06 10 2
aTheoretically derived values.
()
M. Kudrat et al.rChemical Geology 168 2000 225–238 233
Table 4
Ž0.
Computed standard free energies of formation DG,aand bvalues of chlorite minerals and data available for comparable compositions
f
Ž. Ž. 3q2qŽ. aŽ . Ž. Ž. 2qŽ. a
Other data: Quebec Si IV Al VI Al Fe Fe Mg O OH : y1879.84 Kittrick, 1982 . MichiganSi IV Al VI Al Fe Mg O OH : y1741.52
2.99 1.01 1.39 0.21 0.57 3.52 10 8 2.47 1.53 1.66 3.29 1.05 10 8
Ž. Ž.
aŽ.
2qŽ. bŽ.
Kittrick, 1982 . Chamosite Si Al Fe O OH : y1551.63 Saccocia and Seyfried, 1993 . Chlorite Si Al Mg Fe O OH : y1870.3 Nriagu, 1975 . Chlorite
32510 8 32 41.010 8
2qŽ. Ž . Ž. aŽ.
Si Al Mg Fe O OH : y1938.2 Nriagu, 1975 . Oaphnite Si Al Fe O OH : y1600.7 Bryndzia and Scott, 1987 .
3 2 4.8 0.2 10 8 3 2 5 10 8
0
wŽ.xŽ.
Chlorites studied here Analytical data source: Deer et al. 1965 DGkcalrmol ab
f
2q
Ž . Ž. Ž. Ž .
1. Klementite I: Dark Olive Green Belgium Si IV Al VI Al Fe Mg O OH y1859.21 53.02806 y0.3797
2.726 1.274 1.580 1.192 3.075 10 8
2q
Ž . Ž. Ž. Ž .
2. Klementite II: Brown Transvaal Si IV Al VI Al Fe Mg O OH y1783.26 28.53640 y1.23825
2.725 1.275 1.579 1.915 2.354 10 8
3q2q
Ž . Ž. Ž. Ž .
3. Thuringite: Dark Olive Green Thuringia Si IV Al VI Al Fe Fe Mg O OH y1596.17 34.5008 y0.16159
2.417 1.586 0.828 0.76 3.687 0.718 10 8
2q
Ž . Ž. Ž. Ž .
4. Chamosite I: Green Oolitic Gloucestershire Si IV Al VI Al Fe Mg K O OH y1752.74 69.55933 y0.1084398
2.874 1.126 1.213 2.826 1.889 0.057 10 8
2q
Ž . Ž. Ž. Ž .
5. Chamosite II: Yellow Green Thuringia Si IV Al VI Al Fe Mg O OH y1615.21 19.70844 y0.24484
3.050 0.950 1.228 3.871 0.762 10 8
3q
Ž . Ž. Ž. Ž .
6. Corundophilite: Quebec Si IV Al VI Al Fe Mg O OH y1983.78 67.354 y0.2282
2.467 1.533 1.179 0.034 4.947 10 8
3q2q
Ž . Ž. Ž. Ž .
7. Daphnite: France Si IV Al VI Al Fe Fe Mg K O OH y1626.94 64.3534 0.31499
2.530 1.470 1.395 0.057 4.081 0.416 0.12 10 8
Ž . Ž. Ž. Ž .
8. Clinochlore I: Colourless–Pale Green Montana Si IV Al VI Al Mg K O OH y1969.94 71.25687 y0.2741372
2.915 1.085 0.841 5.202 0.158 10 8
3q2q
Ž . Ž. Ž. Ž .
9. Clinochlore II: Silver White–Pale Green New Zealand Si IV Al VI Al Fe Fe Mg O OH y1870.91 31.50613 y0.5611323
3.042 0.958 0.668 0.33 0.29 4.692 10 8
2q
Ž . Ž. Ž. Ž .
10. Clinochlore III: Japan Si IV Al VI Al Fe Mg O OH y1821.34 49.69649 y0.44675
2.973 1.027 1.083 1.637 3.252 10 8
Ž. Ž.
11. Chlorite idealised Si Al Mg O OH y1953.28 57.07883 y0.32814
32 510 2
0Ž.
Data from other sources for chlorites of comparable composition DGkcalrmol Reference
f
3q2qa
Ž. Ž. Ž .wxŽ.
12. Vermont Si IV Al VI Al Fe Fe Mg O OH Composition comparable to Klementite I y1861.68 Kittrick 1982
2.97 1.03 1.44 0.07 0.99 3.24 10 8
2q3qa
Ž. Ž. Ž .wxŽ.
13. New Mexico Si IV Al VI Al Fe Mg Fe O OH Composition comparable to Chamosite I y1748.45 Kittrick 1982
2.84 1.16 1.75 2.61 1.16 0.12 10 8 b
Ž. Ž.wŽ.xŽ.
14. Chlorite Mg Si Al Mg O OH Composition same as cholorite idealised y1955.40 Nriagu 1975
32 510 8 b
Ž.wŽ.xŽ.
15. Clinochlore Si Al Mg O OH Composition same as cholorite idealised 1948.85 Henderson et al. 1976
32 510 8 a
Ž.wŽ.xŽ.
16. Chlorite Si Al Mg O OH Composition same as cholorite idealised y1961.70 Helgeson et al. 1978
32 510 8
aExperimentally determined values.
bTheoretically derived values.
()
M. Kudrat et al.rChemical Geology 168 2000 225–238234
Ž. 0
and Sposito 1996 are very close to the DGvalue
f
derived here, for a chlorite of the same composition
Ž.
Table 4 . Other data included in the footnote give
the general trends in the experimentally derived val-
ues. The range of values are also comparable.
Overall, the derived data indicate trends in the
variations of DG0with contents of certain ionic
f
constituents; their influence on DG0appears to be
f
positive with some ions and negative with others.
Comparison with other experimental and theoretical
Ž.
data show fairly small deviations 0.3–0.5% be-
tween minerals, which are compositionally similar
Ž.
but not necessarily the same . Comparison of the
DG0values obtained by the improved regression
f
method, with the DG0values obtained by calorimetic
f
methods gives very good agreement between the
Ž.
values Varadachari et al., 1994 , e.g., with kaolinite,
muscovite, pyrophylite, phlogopite, sepiolite, etc.;
Ž
deviations are of the order of 1–2 kcalrmol 0.08–
.
0.16% . For non-stoichiometric clays, deviations may
be higher since the experimental values, which are
based on solubility measurements, are less accurate
than calorimetrically derived values.
3.2. Correlations with compositional parameters
3.2.1. Illites
Ž.2q
Statistical analysis shows Table 5 that Fe and
Kqcontents have no influence on the DG0of illites;
f
there is a weak correlation with Mg2q,Si
4q, and
Ž. 3qŽ3q.
IV Al tetrahedral Al . On the other hand,
0Ž. 3qŽ
DGis strongly correlated to both VI Al oc-
f3q.3q
tahedral Al as well as Fe . Simple linear regres-
sion equations for structural ions, which showed
r)0.5 were computed and are presented in Table 6.
It is seen that DG0vs. Fe3qshows a high regression
f
Ž2.03q
coefficient rs0.96 followed by DGvs. Al
f
Ž2.
rs0.917 . The data suggest that with an increase
in the Fe3qcontent, the DG0of illite becomes less
f
Ž. 3q
negative whereas with an increase in VI Al , the
DG0becomes more negative. Multivariate regression
f4qŽ. 3qŽ. 3q3q
analysis with Si , IV Al , VI Al , Fe ,
Mg2qand Kqall together vs. DG0gave r2s0.998
f
and an error of "1.486 kcalrmol. This suggests that
it may be possible to predict DG0of illites with a
f
good accuracy by using multiple linear regression
Ž.
coefficient values Table 6 from a knowledge of
their structural formulae. This can open up a new
approach for empirical evaluation of DG0of illites.
f
3.2.2. Smectites
Ž.
Values of correlation coefficients Table 5 reveal
that amongst the structural ions, only Fe3qhas a
significant effect on DG0. With an increase in Fe3q
f
content, the DG0value becomes less negative. Mul-
f
tivariate regression with the three variables Fe3q,
Mg2qand Kqtaken together, shows a fairly high
Ž2.
value regression coefficient rs0.967 with an
Ž.
error of "6.355 kcalrmol Table 6 . Thus, the
content of Fe3q,Mg
2qand Kqin a smectite deter-
mines to a large extent its DG0value and may be
f
utilised for evaluating it with a fair degree of accu-
racy.
3.2.3. Vermiculites
Unlike illites and smectites, the DG0of vermi-
f
culites do not appear to be significantly influenced
by the contents of structural ions; only Mg2qshows
0Ž.
moderate correlation with DGTable 5 . The pre-
f
dictability of DG0is consequently low.
f
3.2.4. Chlorites
Strong correlations are seen between DG0and
f
both Fe2qas well as Mg2q. With increasing Mg2q
content, the DG0of chlorites become more negative
f
whereas increase in Fe2qcauses DG0to become
f
Ž.
less negative Table 5 . Univariate and multivariate
regression analysis gave the highest r2s0.950 for
Table 5
Ž0.
Correlation coefficients between standard free energies of formation DGand contents of individual ionic species
f
4q3q3q3q2q2qq
Ž. Ž.
Mineral Si IV Al VI Al Fe Fe Mg K
Illite 0.619 y0.619 y0.965 0.982 0.068 0.580 y0.251
Smectite y0.309 0.023 y0.082 0.958 0.176 y0.468 y0.354
Vermiculite 0.379 y0.349 0.076 0.334 0.436 y0.722 –
Chlorite y0.159 0.133 0.146 0.387 0.975 y0.969 y0.412
()
M. Kudrat et al.rChemical Geology 168 2000 225–238 235
Table 6
Ž0.
Regression between standard free energies of formation DGand structural ion contents of the clay minerals
f
2
Mineral Regression Independent variable Regression parameter rMean error
Constant Coefficient
03q3q
Illite DGvs. Fe Fe y1316.547 136.845 0.960 7.598
f
02q2q
DGvs. Mg Mg y1327.618 156.967 0.241 31.231
f
03q3q
Ž. Ž.
DGvs. VI Al VI Al y1139.382 y100.036 0.917 13.629
f
04q4q
DGvs. Si Si y1752.200 142.660 0.295 34.285
f
03q3q
Ž. Ž.
DGvs. IV Al IV Al y1181.386 y142.831 0.296 34.252
f
04q
DGvs. Si , y15006.830 0.997 1.486
f3q4q
Ž.
IV Al , Si 3447.258
3q3q3q
ŽŽ.
VIAl Fe IV Al 3409.683
2q3q
Ž.
and Mg VI Al y39.083
3q
Fe 84.283
2q
Mg y20.294
04q
DGvs. Si , y760.988 0.998 1.476
f34q
Ž.
IV Al , Si y136.083
3q3q3q
Ž. Ž.
VI Al , Fe , IV Al y199.541
2q2qq 3q
Ž.
Fe , Mg and K VI Al 4.128
3q
Fe 119.680
2q
Fe 26.879
2q
Mg 26.469
q
K 22.564
03q3q
Smectite DGvs. Fe Fe y1302.515 107.269 0.918 12.280
f3q
Fe y1279.230 94.980 0.967 6.355
03q2qq 2q
DGvs. Fe , Mg K Mg y15.779
fq
Ky31.882
02q2q
Vermiculite DGvs. Mg Mg y1196.873 y48.223 0.520 11.920
f
02q2q2q
DGvs. Mg , Fe Mg y1198.375 1.089 0.201 11.855
f2q
Fe y47.760
02q2q
Chlorite DGvs. Fe Fe y1955.132 85.602 0.950 23.832
f
02q2q
DGvs. Mg Mg y1582.555 y75.309 0.938 28.136
f
02q2q2q
DGvs. Fe , Mg Fe y1885.020 69.645 0.937 23.253
f2q
Mg y14.280
DG0vs. Fe2q;r2is reduced to 0.937 when Fe2q
f2qŽ.
and Mg are considered together Table 6 . Appar-
ently for chlorites, the Fe2qcontent itself will suf-
fice to provide a fair idea of its DG0value.
f
3.3. Implications
The influence of compositional changes on the
DG0of clay minerals, although an accepted fact, has
f
not been defined clearly in quantitative terms. The
correlations observed here clearly bring out the sig-
nificant influence of some structural ions and the
poor influence of others, on the DG0values. Thus,
f
DG0of illites is strongly influenced by octahedral
f
Al3qand Fe3qbut not by its Kqcontent. Broadly
generalised, this would imply that increasing levels
Ž. 3q3q
of VI Al and reducing levels of Fe in illites
will increase their stability and favour neoformation
from solution. Similarly with smectites, the single
most important influence on DG0is the content of
f
Fe3q; smectites with higher contents of Fe3qare
likely to be less stable than with lower Fe3q. Chlo-
rites, on the other hand, are thermodynamically
favoured on increasing Mg2qbut stability reduces
with higher levels of Fe2q. Vermiculites have appar-
ently a more complex relationship of their DG0with
f
composition; none of the ions show any dominant
influence on the DG0value. It would appear from
f
()
M. Kudrat et al.rChemical Geology 168 2000 225–238236
Appendix A. ÝDG0and the rankings of the combinations for some clay minerals
f,i0Ž. Ž.
ÝDGkcalrmol Rank x
f,i
3q2q
Ž. Ž. Ž. Ž .
1 Illite II: Si . IV Al VI Al Fe Fe Mg K O OH
3 10 0.900 1.960 0.036 0.052 0.066 0.676 10 2
1 3.10SiO q1.43Al O q0.018Fe O q0.052FeOq0.066MgOq0.338K OqHO y1268.446 0
223 23 22
2 0.676KAlSiO q1.092Al O q0.018Fe O q0.052FeOq0.033Mg SiO q2.391SiO qHO y1303.519 2
42323 24 22
3 0676KAlSi O q1.092Al O q0.018Fe O q0.052FeOq0.066MgSiO q1.006SiO qHO y1306.502 2
38 23 23 3 2 2
Ž.
4 0.676KAl Si O OH q0.416Al O q0.066MgSiO q0.052FeSiO q0.018Fe O q0.954SiO q0.324H O y1312.994 3
3310 2 23 3 3 23 2 2
Ž. Ž.
5 0.676KAl Si O OH q0.416Al Si O OH q0.066MgOq0.052FeOq0.018Fe O q0.24SiO y0.508H O y1315.706 4
3310 2 2 25 4 23 2 2
Ž. Ž.
6 0.676KAl Si O OH q0.416Al Si O OH q0.066MgSiO q0.052FeSiO q0.122SiO q0.018Fe O y0.508H O y1316.373 4
3310 2 2 25 4 3 3 2 23 2
Ž.
7 0.676KAlSi O q0.536Al Si O OH q0.556Al O q0.018Fe O q0.052FeOq0.066MgOy0.072H O y1318.478 5
38 2 25 4 23 23 2
0y0.59889x
Regression equation: ÝDGsy1321.0529q52.62718e
f,i
3q2q
Ž. Ž. Ž. Ž .
2 Montmorillonite IV: Si IV Al VI Al Fe Fe Mg K O OH
3.80 0.200 1.355 0.155 0.09 0.625 0.24 10 2
1 3.80SiO q0.7775Al O q0.0775Fe O q0.09FeOq0.625MgOq0.12K OqHO y1239.283 0
22323 22
Ž.
2 1.555Al OH q0.3125Mg SiO q0.12K Oq0.0775Fe O q0.09FeOq3.4875SiO y1.3325H O y1243.545 1
3242 23 22
Ž.
3 0.7775Al Si O OH q0.3125Mg SiO q0.12K Oq0.0775Fe O q0.09FeSiO q0.2875SiO q0.2225H O y1248.698 2
24102242 23322
Ž.
4 0.24KAlSi O q0.6575Al Si O OH q0.625MgOq0.0775Fe O q0.09FeSiO q0.36SiO q0.3425H O y1256.273 4
38 2 410 2 23 3 2 2
5 0.24KAlSi O q0.6575Al SiO q0.0775Fe O q0.625MgSiO q0.093FeSiO q1.7075SiO qHO y1258.921 5
38 2 5 23 3 3 2 2
Ž.
6 0.24KAlSiO q0.6575Al Si O OH q0.3125Mg SiO q0.0775Fe O q0.09FeSiO q1.8425SiO q0.315H O y1261.730 6
42254 2423 3 22
Ž.
7 0.24KAlSi O q0.6575Al Si O OH q0.625MgSiO q0.0775Fe O q0.09FeSiO q1.05SiO y0.315H O y1263.285 7
38 2 25 4 3 23 3 2 2
03qy0.146039x
Regression equation: ÝDGsy1277.21 38.58842e
f,i
3q2q
Ž. Ž. Ž. Ž .
3 Vermiculite V: Si IV Al VI Al Fe Fe Mg O OH
2.885 1.010 0.000 0.66 0.055 2.67 10 2
1 2.885SiO q0.505Al O q0.33Fe O q0.055FeOq2.67MgOqHO y1261.823 0
22323 2
2 0.505Al SiO q1.335Mg SiO q0.33Fe O q0.055FeOq1.045SiO qHO y1282.259 2
25 24 23 2 2
Ž.
3 0.505Al Si O OH q1.335Mg SiO q0.33Fe O q0.055FeOq0.54SiO y0.01H O y1286.745 3
225 4 2 4 23 2 2
Ž.
4 0.70Mg Si O OH q0.505Al O q0.33Fe O q0.085Mg SiO q0.4MgOq0.055FeOq0.3H O y1288.737 3
3410 2 23 23 2 4 2
Ž. Ž.
5 0.80Mg Si O OH q0.505Al O OH q0.33Fe O q0.055FeSiO q0.22SiO q0.27MgOy1.61H O y1293.216 5
325 4 25 4 23 3 2 2
Ž. Ž.
6 0.505Al Si O OH q0.89Mg Si O OH q0.33Fe O q0.055FeOq1.79H Oq0.095SiO y1296.138 7
2254 3254 23 2 2
Ž.
7 0.505Mg Al Si O OH q0.145MgSiO q0.33Fe O q0.055FeSiO q1.17SiO y1.02H O y1296.354 8
52310 8 3 23 3 2 2
0y0.4242093x
Regression equation: ÝDGsy1297.714q35.89775e
f,i2q
Ž. Ž. Ž. Ž .
4 Chamosite II: Si IV Al VI Al Fe Mg O OH
3.050 0.950 1.228 3.871 0.762 10 8
1 3.050SiO q1.089Al O q3.871FeOq0.762MgOq4H O y1595.435 0
223 2
2 1.089Al SiO q0.762MgSiO q1.199SiO q3.871FeOq4H O y1603.299 2
25 3 2 2
3 1.089Al SiO q1.9355Fe SiO q0.0255Mg SiO q0.711MgOq4H O y1607.867 4
25 24 24 2
Ž.
4 1.089Al Si O OH q0.762MgSiO q0.11SiO q3.871FeOq1.822H O y1610.528 6
225 4 3 2 2
Ž. Ž. Ž.
5 0.254Mg Si O OH q1.017Al Si O OH q0.144A1OOHq3.871Fe OH y2.231H O y1611.311 7
3410 2 225 4 2 2
Ž. Ž. Ž.
6 0.254Mg Si O OH q1.089Al Si O OH q0.364Fe SiO q3.143Fe OH y1.829H O y1613.435 9
3254 2254 24 2 2
Ž.
7 0.762MgAl O q0.327Al Si O OH q1.9355Fe SiO q0.4605SiO q3.346H O y1613.815 11
24 2 25 4 2 4 2 2
0y0.24484x
Regression equation: ÝDGsy1615.211q19.70844e
f,i
()
M. Kudrat et al.rChemical Geology 168 2000 225–238 237
the data that the DG0of different types of clay
f
minerals are not influenced in the same manner by
various ionic species; the extent of their influence
differs widely. The data offer a simple and quantified
view of such relationships.
Apart from this, an offshoot of the statistical
interrelationships is the derivation of simple linear
equations, which may also be utilised for obtaining
DG0values with fairly good accuracy for illites. A
f
rough approximation of DG0of smectites or chlo-
f
rites can also be obtained.
4. Summary and conclusion
Ž0.
Standard free energy of formation DGvalues
f
were computed for a large number of illites, smec-
tites, vermiculites and chlorites using an improved
Ž
curvilinear regression method Varadachari et al.,
.
1994 . All the clay groups showed a fairly wide
range of DG0values, except vermiculite, which had
f
DG0within a relatively narrower range. Chlorite
f
showed the largest variations in DG0; this is appar-
f
ently related to the wide compositional differences
amongst the chlorite minerals.
Analysis of the relationships between DG0and
f
structural ion contents revealed interesting trends. It
was observed that the DG0of some clay groups are
f
correlated to their structural ion content. Moreover,
not all ions influence the DG0values; only certain
f
ions have a pronounced effect in increasing or de-
creasing DG0. Such correlations are most marked
f
with illites. The DG0of illites are strongly corre-
f
3qŽ. 3q
lated to their Fe and VI Al contents. A multi-
4qŽ.
ple linear regression equation involving Si , IV
3qŽ. 3q3q2q2qq
Al , VI Al , Fe , Fe , Mg and K could
give excellent fit, with an r2s0.998 and an error of
"1.476 kcalrmol. Similarly, smectites showed good
correlation between their Fe3qcontents and DG0;a
f
multiple regression equation involving Fe2q,Mg
2q
and Kqcontents can give a fair estimate of DG0.
f
Vermiculites, in contrast, showed no strong correla-
tion between DG0and various structural ions. The
f
Fe3qand Mg2qcontents in chlorites showed strong
influences on DG0, with the former causing it to
f
become less negative and the latter, more negative at
increasing ionic levels. It appears that Fe2qcontent
alone can give an approximate idea of the DG0of
f
chlorites.
This study shows that it may be possible to quite
accurately predict DG0values of illites from a sim-
f
ple linear regression equation such as derived here.
Fair or good predictions may also be made with
smectites and chlorites. By incorporating more data,
predictability for these minerals may possibly be
further improved. This investigation reveals the im-
mense potential of the improved regression method
of evaluating DG0; it also shows how the latter
f
technique can be used for deriving simpler methods
of computing DG0of clay minerals.
f
Acknowledgements
The authors are grateful to CSIR, New Delhi,
ISROrRRSSC, Bangalore and Dehra Dun for their
support.
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