World Journal of Nano Science and Engineering, 2011, 1, 62-66
doi:10.4236/wjnse.2011.12009 Published Online June 2011 (
Copyright © 2011 SciRes. WJNSE
Theoretical Study of Kaoli nite Structure; Energy
Minimization and Crystal Properties
Mohamed Salah Karmous
Département de physique, Faculté des Sciences de Sfax,
Route de la Soukra km 4 - B.P. n 802 3038 Sfax, Tunisie
Received April 19, 2011; revised April 25, 2011; accepted May 9, 2011
Computational energy minimization techniques have been used to study the structure and crystal properties
of kaolinite. The full elastic tensors of the sheet silicates of clay have been derived with first-principles cal-
culations based on density functional theory. All calculations were performed using GULP program.
Keywords: Kaolinite, GULP, Energy, Crystal Properties, Calculation, Elasticity
1. Introduction
Molecular modeling methods have been increasingly
used in the past decade to simulate a wide range of mate-
rials and to evaluate their microscopic stru cture, physical,
and thermodynamic properties. Clays and related layered
minerals are fine grained and poorly crystalline materials.
Large single crystals of clay minerals suitable for X-ray
refinement studies are lacking and therefore only a few
detailed structural characterizations exist [1-4]. Clay
minerals also possess low crystal symmetry and have a
unique chemistry that is characterized by a variety of
multicomponent substitutions in the tetrahedral and oc-
tahedral sheets. Depending upon the type of structural
substitution and net charge, the clay may become ex-
pandable and provide a suitable host for a variety of in-
Molecular computer simulations have become ex-
tremely helpful in providing an atomistic perspective on
the structure and behavior of clay minerals.
In other hand elastic properties of clay minerals are
almost unknown, mainly because of the difficulty pre-
sented by the intrinsic properties. Their small grain size
makes it is impossible to isolate an individual crystal of
clay large enough to measure acoustic properties [5]. So
far the effective elastic properties of clays have been
derived either by theoretical computation [6-8], by a
combination of theoretical and experimental investiga-
tions on clay-epoxy mixture [9] or by empirical extrapo-
lations from measurements on shales [10-12]. These de-
rived values of clay moduli show little agreement.
Kaolinite is a 1:1 layer clay composed of a repeating
layer of an aluminum octahedral (O) sheet and a silicon
tetrahedral (T) sheet. Interlayer hydroxyl groups extend
from the octahedral sheet into the interlayer region where
they form hydrogen bonds to basal oxygens of the op-
posing tetrahedral silicate sheet [13] (Figure 1).
In this paper a tentative of junction between energetic
and crystal properties of kaolinite is presented.
2. Methods
2.1. Energy Calculation
Energy minimizations were carried out using the pro-
gram GULP [15]. This utilizes interatomic potentials for
describing the interactions within the layered silicate
structure. The interatomic potentials used are given in
Table 1. A shell model [16] is used to describe the po-
larization of the O2 ions. All atoms have integral
charges except for the OH groups, whose component
atoms have partial charges [17] so as to reproduce the
dipole moment of the OH group [18]. Atom based
cut-offs to 12 Å are used for describing the two body
short range interactions and a Ewald summation tech-
nique is used for the dispersion and electrostatic interac-
tions [19].
2.2. Simulation Principle
The potential model describing the effective forces act-
ing between the atoms in the structure has the following
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Figure 1. Stacking polytypism in kaolinite; Only the Si4+
ions (dark) and the Al3+ (light) are shown for simplicity.
The view direction is perpendicular to the sheets and a
shading has been added to the lower Si4+ layer. The thin
lines denote the unit cell [14].
components [18].
A two-body short-range term describes repulsions
from electron cloud overlap and attractions due to dis-
persion and covalence. In this study we describe ca-
tion-O and the O-O interactions using a Buckingham
function: Usr = Aexp(r/ρ) C/r6, where the exponential
term describes the repulsive energy and the r6 term the
longer range attraction. The intramolecular OH interac-
tion is representedb y a Morse function: Usr = D{1
exp[β(r re)]}2, where r and r. are the observed and
equilibrium interatomic distances, respectively. Coulomb
forces are not included between atoms coupled by a
Morse potential, as it is assumed that this potential de-
scribes all components of the interactions between the
two atoms. As in many previous simulation studies on
silicates, the short range cation-cation interactions are
not significant and were therefore neglected.
A three-body short-range term describes angular de-
pendent covalent forces. A simple approach is to include
bond-bending terms about the tetrahedral cation of the
type: Uthb = 1/2Kthb(θ θ0)2. where Kthb is the harmonic
three-body force constant, and θ and θ0 are the observed
and ideal tetrahedral O-T-O bond angles, respectively.
A term to describe electronic po larizability is r equired
if dielectric and dynamic properties are to be modeled
accurately. In this stud y the shell model was used, which
provides a simple mechanical model of electronic pola-
rizability. The coreshell self energy is given by Us =
1/2Ksr2 where Ks is the harmonic spring constant and r is
the core-shell separation.
In Table 1 are represented all the potential used during
Table 1. Potential used in simulation.
Two body short range interactiona
Atom 1 Atom 2 Potential A/eV ρC/eVÅ6 References
Al1 c O1 s Buckingham 1460 0.299 0.00 [17]
O2 c Al1 c Buckingham 1140 0.299 0.00 [17]
Si1 c O1 s Buckingham 1280 0.321 10.7 [17]
O2 c Si1 c Buckingham 984 0.321 10.7 [17]
O1 s O1 s Buckingham 22800 0.149 27.9 [17]
O2 c O1 s Buckingham 22800 0.149 27.9 [17]
O2 c O2 c Buckingham 22800 0.149 27.9 [17]
H1 c O1 s Buckingham 312 0.250 0.00 [17]
Morse potential
Atom 1 Atom 2 Potential De/eV β1 re/Å References
H1 c O2 c Morse-Coulomb 7.05 2.20 0.949 [17]
Shell model interaction
Atom 1 Atom 2 Potential Ks/eVÅ2 References
O1 c O1 s Spring 74.90 [17]
Three body interaction
Atom 1 Atom 2 Atom3 Kthb/eV rad2 θ/° References
Si1 c O1 s O1 s 2.097 109.470 [17]
Al1 c O2 c O1 s 2.097 109.470 [17]
Copyright © 2011 SciRes. WJNSE
this work.
2.3. Elastic Constant
The calculation of elastic constants is potentially very
useful, since the full tensor has only been measured ex-
perimentally for a very small percentage of all known
solids. This is primarily because the practical determina-
tion typically requires single crystals with a size of a few
micrometers at least.
The elastic constant tensor C, is calculated analytically
using standard procedures, which require the prior cal-
culation of the second derivatives of the total lattice
energy with respect to the six bulk strain components and
with respect to atomic coordinates.
The elastic constants were calculated using GULP
3. Results and Discussion
In Table 2, energetic simulation of structural properties
of kaolinite is presented.
The value of kaolinite total lattice energy obtained is
equal to 827.41650215 eV, primitive cell volume is
321.304389Å3. This result is near to energy values found
in previous works [20]. The lowest total energy structure
obtained from these calculations was that which started
from the experimental structures reported by Neder et al.
[20] and by Bish [2], i.e., both initial structures yield
essentially identical final structures with the same total
energy, the same internal bond lengths, and unit cell vo-
lumes that differ by only 0.025% (Table 2), this differ-
ence is due to hydroxyl (OH) orientation in interlayer
region of kaolinite structure.
Lattice parameters a and b fr om S a to et al. (2005) [21]
are shorter and agree better with experiment than those
of the present work, while the opposite is true for the c
parameter. This means that our calculations predict a
smaller sheet separation, but larger lattice parameters in
the planes.
Elastic constant was calculated using structural para-
meter listed in Table 2, the results are summarized on
Table 3, and are compared to many works.
The qualitative study of the table shows:
C11~ C22 >> C33.
C12 differs significantly fro m bibliograph ic value.
C23 ~ C13
C15 and C46 is diffe rent to zero.
These values of elastic constant reflect the hexagonal-
ly symmetric structure.
Differences in other elastic constan ts are either related
to this or the difference of the density value, concentra-
tion and arrangement of defects ([14] and [22]).
Table 2. Structural properties derived from simulations of
Cell structure
(this work) Observed
(Bish) [2] Observed
(Neder) [21] Observed
(Sato) [22]
a axis (Å) 5.149 5.153 5.154 5.144
b axis (Å) 8.934 8.941 8.942 8.924
c axis (Å) 7.384 7.390 7.401 7.587
α angle (deg) 91.93 91.92 91.69 91.08
β angle (deg) 105.0420 105.046 104.61 104.60
γ angle (deg) 89.9710 89.79 89.82 89.86
ρ (g/cm3) 2.668652 - 2.599 2.544
Table 3. Calculated elastic constant.
Elastic constant Sato [22] Militizer [14] This work
C11 178.5 ± 8.8 169.1 209.0343
C22 200.9 ± 12.8 179.7 209.6761
C33 32.1 ± 2.0 81.1 68.4720
C44 11.2 ± 5.6 17.0 12.4953
C55 22.2 ± 1.4 26.6 6.7199
C66 60.1 ± 3.2 57.6 50.1239
C12 71.5 ± 7.1 66.1 126.0545
C13 2.0 ± 5.3 15.4 16.8481
C14 –0.4 ± 2.10.4 2.9326
C15 –41.7 ± 1.434.00.9305
C16 –2.3 ±
C23 –2.9 ± 5.7 10.2 19.1547
C24 –2.8 ± 2.73.4 1.6428
C25 –19.8 ± 0.616.1 0.0802
C26 1.9 ± 1.50.1 9.0795
C34 –0.2 ±
C35 1.7 ± 1.8 6.72.9557
C36 3.4 ±
C45 –1.2 ±
C46 –12.9 ± 2.412.4 2.2793
C56 0.8 ± 0.7 1.1 3.6822
The calculated elastic constant tensors indicate that the
a direction is slightly more flexible than the b direction.
The calculated elastic constant tensor along c is much
Copyright © 2011 SciRes. WJNSE
lower than the constants c alculated along a and b consis-
tent with the crystal structure of kaolinite [22].
4. Conclusions
In summary, these calculations have shown that the
computational techniques are a useful tool for investi-
gating clay structures and mechanical properties. Pre-
dicting the mechanical properties of minerals that are
difficult to obtain experimentally because of their small
particle size (typically <2 micrometers).
5. Acknowledgements
Dr KARMOUS Mohamed Salah is grateful to Dr David
S Coombes for his helpful discussion. Dr Julian Gale
(Imperial College, University of London) is also grate-
fully acknowledged for providing GULP and for useful
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