EFFECT OF DOPING POSITION OF Sr ATOM
ON CRYSTAL STABILITY OF BETA-FORM BELITE
R. Sakurada*, Akita National College of Technology, Japan
A. K. Singh, Indian Institute of Science
Y. Kawazoe, Tohoku University
36th Conference on OUR WORLD IN CONCRETE & STRUCTURES: 14 - 16 August 2011,
Singapore
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36 Conference on Our World in Concrete & Structures
Singapore, August 14-16, 2011
EFFECT OF DOPING POSITION OF Sr ATOM
ON CRYSTAL STABILITY OF BETA-FORM BELITE
R. Sakurada*, A. K. Singh† and Y. Kawazoe‡
*Department of Civil Engineering
Akita National College of Technology
1-1, Bunkyo-cho, Iijima, Akita City, Akita Prefecture, Japan 011-8511
e-mail : < [email protected] > webpage : http://www.akita-nct.ac.jp
Keywords: Belite, Ab-initio calculation, crystal structure, hydraulic activity
Abstract. Ab-initio calculations made theoretically clear the effect of the substitution
position of Sr atoms for Ca atoms in CaOx polyhedra on the stability and hydraulic
activity of beta-form Belite, β-C2S. The unit cell of 28 atoms was employed to the
substitution models for higher concentration of 7.1% by Sr atoms in this work. The
β-C2S in higher doping rate of 7.1% by Sr atoms lies energetically in more unstable
than that in doping rate of 3.6% by Sr atoms. The β-C2S substituted two Sr atoms for
Ca(1) atoms having seven Ca-O bonds lies in more stable state than that substituted
one Sr atom for Ca(1) atom having seven Ca-O bonds and one Sr atom for Ca(2) atom
having eight Ca-O bonds. The mean HOMO-LUMO energy gap is 5.30 eV for β-C2S
substituted two Sr atoms for Ca(1) atoms having seven Ca-O bonds and 5.25 eV for
β-C2S substituted one Sr atom for Ca(1) atom having seven Ca-O bonds and one Sr
atom for Ca(2) atom having eight Ca-O bonds, reflecting a typical feature of insulators.
The substitution of Sr atom for Ca(1) atom having seven Ca-O bonds makes the Ca-Ca
bond length of the β-C2S shorter than the substitution of Sr atom for Ca(2) atom having
eight Ca-O bonds. The shorter Ca-Ca bond length is favorable to a higher hydraulic
activity of the β-C2S.
1 INTRODUCTION
The α-form, α’H-form, α’L-form, β-form and γ-form in Belite C2S (2CaO·SiO2) represent the
polymorphs of Belite by the temperature of the cement clinker compounds during cooling
process as shown in Table1. Ordinary Portland cement usually contains β-form Belite
(β-C2S) that reacts slower with water and results in lowest rate of heat evolution in four major
compounds of C3S, C2S, C3A, and C4AF. The β-C2S contributes to gain strength
development in long-term age and to reduce heat liberation during hydrate reaction.
Moreover, trace impurities contained in β-C2S play an important roll in crystal structural
stability and hydraulic activity. The experimental approach on the effect of trace impurities on
the phase change of clinker minerals has been reported by G. C. Lai et. al [1]. In the report
the phase change of Belite (C2S) depends on the kind of univalent and multivalent ions and
their substitution rate. In addition to the experimental approach the numerical calculation
†
based on only quantum mechanics without any other
Indian Institute of Science
‡
assumptions is needed to explore theoretically the stability of
Tohoku University
R. Sakurada, A. K. Singh and Y. Kawazoe
Table1 Lattice vectors of Belite polymorphs
Belite crystal and the mechanism of
hydraulic activity of calcium silicate
Dicalcium Silicates
a,Å b,Å c,Å
deg.
compounds at the atomic level.
α-C2S Hexagonal
5.579
7.150 γ=120
The theoretical approach from α' -C S Orthorhombic 9.490 5.590 6.850
H 2
quantum mechanics and quantum α'L-C2S Orthorhombic 6.957 9.496 5.600
chemistry calculations is a powerful tool β-C2S Monoclinic
5.502 6.745 9.297 β=94.59
γ-C
S
Orthorhombic
5.081
11.22 6.778
to clarify theoretically the crystal structure
2
of the solid at atomic level. Ab-initio
calculations using Kohn-Sham equation based on density functional theory is conducted by
solving directly Schrödinger’s equation at the quantum level. This approach employs no
statistical assumptions of fitting parameters as seen in the self-consistent-field discrete
variation Xα method (DV-Xα method) and phenomena-based parameters.
The ab-initio numerical simulation, that is called first-principles calculation in other words,
has been progressively used to develop the nano-scale electronic devices and the carbon
materials: magnetism in metal-doped silicon nanotubes [2], pristine silicon nanowires [3] and
magnetic behavior of Mn clusters [4]. R. Sakurada, A. K. Singh, Y. Kawazoe et.al [5] have
firstly reported the ab-initio calculations study on the crystal stability of β-C2S and γ-C2S. This
work elucidated that β-C2S lies in more unstable state in the total energy of crystal than γ-C2S,
and that Ca-Ca inter-atomic distance of β-C2S, which is strongly relevant to the hydraulic
activity of calcium silicates, is shorter than that of γ-C2S. They also [6], [7] have reported the
effect of substitution of Ca atom by Ba or Sr atom as trace impurity of cement raw materials
on the crystal stability and hydraulic activity of β-C2S.
The authors present the results of ab-initio calculations based on quantum mechanics
theory of the β-C2S crystal and of the crystal stability and the hydraulic activity of β-C2S
analyzed from the converged crystal structure. Emphasis in this work is on the effect of the Sr
atom doping position on the stability of β-C2S crystal. To find a change in crystal structure of
beta-form Belite substituted two Sr atoms for Ca atoms having seven or eight Ca-O bonds at
higher doping concentration the stability was estimated by the total energy of β-C2S crystal,
and the Ca-Ca bond length was chosen as a yardstick for making reliable prediction of the
hydraulic activity of β-C2S. The unit cell sizing up to 28 atoms (ax1, bx1, cx1) is adopted in
this work.
2 DENSITY FUNCTIONAL THEORY
First-principles molecular dynamics is based on the density functional theory and the
norm-conserved pseudopotentials. The density functional theory has been most popular for
calculation of the electronic structure of many-body systems. The total energy of electron
system E[ρ(r)] is expressed as a functional of electronic charge density ρ(r) at a particular point
of r in Eq.(1). This energy functional E[ρ(r)] gives the minimum value of energy in ground-state
for the real electronic charge density. The electronic charge density at the exact ground-state
ρ(r) is given by Eq.(2).
E [ρ (r )] = T [ρ (r )] + ∫ Vext (r )ρ (r )dr +
1 ρ (r )ρ (r ′)
drdr ′ + E xc [ρ (r )]
2 ∫∫ r − r ′
(1)
R. Sakurada, A. K. Singh and Y. Kawazoe
n
ρ (r ) = ∑ ψ i (r )
2
(2)
i =1
Here “ r “ indicates coordinate vector in the real space, ψi (r) denotes the one-electron spatial
orbitals for i =1,2,3,…….n, and Vext (r) is electron-nucleus attraction potential. The terms on
right-hand side of Eq.(1) are the kinetic energy of a system of non-interacting electrons, the
potential energy by electron-nucleus attraction, the Coulomb interaction energy between the
total charge distribution and the exchange-correlation energy of the system, respectively.
By applying the variation principle to the total energy functional E[ρ(r)] of the electronic
charge density ρ(r) in Eqs.(1)-(2), the Kohn-Sham equation in a similar form of the Shrödinger
equation can be easily obtained for the one-electron orbital in Eqs.(3)-(4)
 h2 2

 −
∇ + Veff (r )ψ i (r ) = ε iψ i (r )
 2m

Veff (r ) = Vext (r ) + ∫
ρ (r ′)
r− r′
dr ′ + µ xc [r ]
(3)
(4)
where h is Planck’s constant ( ћ = h/2π), m is mass of electron, ε i are the Kohn-Sham orbital
energies, and Vext (r) is effective potential involving the external potential, interaction potential
between electrons and the exchange-correlation potential µxc[r] which is the functional
derivative of the exchange-correlation energy Exc[ρ (r)]:
µ xc [r ] =
δE xc [ρ (r )]
δρ (r )
(5)
The solutions of Eq.(3) can be easily founded by solving the Shrödinger equation for
noninteracting particles moving under an effective potential Veff (r).
3 COMPUTATIONAL MODELS OF β-C2S
β-C2S compound crystallizes in monoclinic space group P21 /n (C52h) with lattice constants of
am = 5.502 Å, bm = 6.745 Å, cm = 9.297 Å, and the monoclinic angle is 94.59° from X-ray
diffraction analysis [8]. β-C2S without substitution of foreign atoms is composed of two kinds of
CaOx polyhedra as Ca(1)Ox polyhedron in which Ca(1) atom having seven Ca-O bonds and
Ca(2)Ox polyhedron in which Ca(2) atom having eight Ca-O bonds and SiO4 tetrahedron as
shown in Figure1. The atom coordinates of the monoclinic unit cell are tabulated in Table2.
The calculation for the unit cell consisting of 28 atoms (a×1, b×1, c×1) was conducted to find
the effect of Sr atom doping position in CaOx polyhedra and doping concentration of Sr atom on
a change in crystal structure and stability of β-C2S. Figure2 illustrates the substitution models of
Sr atoms. #1 in Figure2 indicates the β-C2S substituted one Sr for Ca(1) atom.
The substitution of two Sr atoms for two Ca atoms is conducted in the following calculation
models. Seven combinations of one Ca(1) atom (No.1) and the rest of independent seven Ca
atoms (No.2-No.8) within unit cell were chosen as doping position : #1-2, #1-3, #1-4, #1-5, #1-6,
R. Sakurada, A. K. Singh and Y. Kawazoe
Seven Ca-O bonds
Eight Ca-O bonds
Table2 Atomic coordinates for β-C2S
atom
Ca(1)
Ca(2)
Four Si-O bonds
Si
O(1)
O(2)
Figure1 Ca(1)Ox polyhedron having seven Ca-O bonds,
O(3)
bonds, Ca(2)Ox polyhedron having eight Ca-O
O(4)
x
0.2738
0.2798
0.2324
0.2864
0.0202
0.4859
0.1558
y
0.3428
0.9976
0.7814
0.0135
0.7492
0.6682
0.6710
z
0.5694
0.2981
0.5817
0.5599
0.6919
0.6381
0.4264
bonds and SiO4 tetrahedron
#1
#1-2
#1-5
Figure2 Doping configurations of β-C2S in #1, #1-2 and #1-5
#1-7, #1-8, where No.1-No.4 Ca atoms indicate Ca(1) atom having seven coordinates and
No.5-No.8 Ca atoms indicate Ca(2) atom having eight coordinates.
For the computational models of β-C2S, the ab-initio calculations of Eqs.(3)-(5) in former
Section 2 were carried out using Vienna ab-initio simulation package, VASP[9]. The calculations
were performed using a plane wave method employing the ultrasoft pseudopotentials for Ca, Si
and O atoms, and the generalized gradient approximation (GGA) for the exchange-correlation
potential in Eq.(5) was employed.
Calculations were performed by setting up the convergence in energy at 10- 4 eV and the
cutoff energy at 400 eV for plane-wave basis. Г-point sampling and k-point sampling (1×1×1)
was used for calculations.
R. Sakurada, A. K. Singh and Y. Kawazoe
4 RESULTS AND DISCUSSIONS
The total energy and the Ca-Ca inter-atomic bond length of the unit cell of β-C2S substituted one
Sr atom for Ca atom is listed with no substitution case in Table3. The Ca-Ca bond length is given in
the distance less than 4 Å to the neighboring Ca atoms for all of independent Ca atoms within unit
cell. The replaced Ca atoms are Ca(1) atom having seven Ca-O bonds and Ca(2) atom having eight
Ca-O bonds.
The mean total energy of #1-2, #1-3 and #1-4 provides -200.97 eV for β-C2S substituted two Sr
atom for Ca(1) atoms having seven Ca-O bonds, and that of #1-5, #1-6, #1-7 and #1-8 is
–200.89 eV for β-C2S substituted one Sr atom for Ca(1) atom having seven Ca-O bonds and one Sr
atom for for Ca(2) atom having eight Ca-O bonds, while the undoped pure β-C2S gives –195.56 eV.
The β-C2S substituted two Sr atoms for Ca(1) atoms having seven Ca-O bonds lies in stable state
compared with that substituted one Sr atom for Ca(1) atom having seven Ca-O bonds and one Sr
atom for for Ca(2) atom having eight Ca-O bonds. It is worth to mention that the total energy of
β-C2S substituted by one Sr atom, which doping concentration is equivalent to 3.6%, lies in more
stable state than β-C2S with substitution of two Sr atoms, which doping concentration is equivalent
to 7.1%, and without substitution. Thus higher doping percentage of 7.1% by Sr atom makes the
crystal structure of β-C2S unstable.
The mean HOMO-LUMO energy gap of #1-2, #1-3, and #1-4 is given in 5.30 eV for β-C2S
substituted two Sr atoms for Ca(1) atoms having seven Ca-O bonds, and that of #1-5, #1-6, #1-7
and #1-8 is 5.25 eV for β-C2S substituted one Sr atom for Ca(1) atom having seven Ca-O bonds and
one Sr atom for Ca(2) atom having eight Ca-O bonds, while β-C2S substituted one Sr atom for Ca(1)
atom having seven Ca-O bonds gives 5.21 eV. The β-C2S doped by Sr atoms reflects the charge
distribution of β-C2S as a typical insulator.
The mean Ca-Ca bond lengths are found to be 3.542 Å for β-C2S substituted one Sr atom for
Ca(1) atom of the calculation models of #1-2, #1-3, and #1-4 and 3.552 Å for β-C2S substituted one
Sr atom for Ca(1) atom and Ca(2) atom of the calculation models of #1-5, #1-6, #1-7 and #1-8,
respectively. For higher doping concentration of Sr atoms in CaOx polyhedra, the substitution of
Ca(1) atom having seven Ca-O bonds in CaOx polyhedra provides shorter mean Ca-Ca bond length
of β-C2S in comparison with the case of substitution of Ca(2) atom having eight Ca-O bonds in CaOx
polyhedra. K. H. Jost, B. Ziemer and R. Seydel [8] reported that the shorter Ca-Ca bond length was
favorable to hydration with water from the experimental results of hydraulic active Alite C3S and
Belites. The reported experimental values of the Ca-Ca bond lengths are 3.40 Å for CaO, 3.47 Å for
Table3 Total energy and Ca-Ca bond lengths of β-C2S for doping concentrations
of 3.6% and 7.1%
Substituiton Doping concentration
model #
of Sr atom, %
#1
3.6
#1-2
7.1
#1-3
7.1
#1-4
7.1
#1-5
7.1
#1-6
7.1
#1-7
7.1
#1-8
7.1
without subst.
0.0
Total energy, eV
-201.69
-200.97
-200.96
-201.00
-200.87
-200.92
-200.87
-200.90
-195.56
Ca-Ca bond length
less than 4Å, Å
3.552
3.553
3.538
3.536
3.546
3.542
3.555
3.566
3.560
HOMO-LUMO
energy gap, eV
5.21
5.28
5.31
5.29
5.28
5.27
5.22
5.23
5.77
R. Sakurada, A. K. Singh and Y. Kawazoe
Table4 Total energy and Ca-Ca bond lengths of β-C2S for possible doping configurations
SrOx polyhedra connecting model
2Sr-771
2Sr-772
2Sr-781
2Sr-782
Bond length change rate and total energy
Mean Sr(1)-O bond length change rate of Sr(1)Ox polyhedra, %
Isolated
-3.610
Edge to edge Edge to edge Face to face
-3.627
-3.598
-3.925
Mean Sr(2)-O bond length change rate of Sr(2)Ox polyhedra, %
-3.529
-3.650
-2.249
-2.944
Mean Si-O bond length (<3Å) change rate of SiO4 tetrahedra
0.125
0.094
0.088
0.090
-3642.62
3.5589
3.5579
0.028
-3642.61
3.5589
3.5579
0.030
-3642.59
3.5589
3.5588
0.005
-3642.61
3.5589
3.5582
0.020
Without
substitution
bridging with SrOx polyhedra, %
Total energy, eV
Mean Ca-Ca bond length (<4Å) before substitution, Å
Mean Ca-Ca bond length (<4Å) after substitution, Å
Mean Ca-Ca bond length change rate, %
-3644.02
3.5589
0.000
Sr(1) is bounded by seven O atoms. Sr(2) is bounded by eight O atoms.
(a) Converged geometry of 2Sr-771
consisting of 504 atoms
(b) Is olated SrOx polyhedra and bridging CaOx
polyhedra
Figure3 Converged geometry of 2Sr-771 with bridged CaOx polyhedra
and SiO4 tetrahedra
C3S, 3.58 Å for β-C2S and 3.75 Å for γ-C2S [8].
From these results, the replacement of Ca(1) atom having seven Ca-O bonds with Sr atoms
makes the crystal structure of β-C2S stable and simultaneously shorten the mean Ca-Ca bond
length relating closely to the hydraulic activity of β-C2S.
In addition to the doping concentration of Sr atoms as mentioned before, the kinds of CaOx
polyhedra connection might be relevant to the crystal structure stability and Ca-Ca inter-atomic
distance of β-C2S after replacing Ca atoms with Sr atoms. R. Sakurada, A. K. Singh and Y. Kawazoe
have investigated the relationship between the kinds of CaOx polyhedra connection and crystal
stability of β-C2S [10] as tabulated in Table4.
2Sr-771 replaces two Ca(1) atoms having seven Ca-O bonds in central site of β-C2S with Sr
atoms as shown in Figure3. 2Sr-772 forms edge to edge bond between two Sr(1)Ox polyhedra
having seven Sr(1)-O bonds. 2Sr-781 replaces one Ca(1) atom having seven Ca-O bonds and one
Ca(2) atom having eight Ca-O bonds with Sr atoms, respectively. 2Sr-782 forms face to face bond
between Sr(1)Ox polyhedron and Sr(2)Ox polyhedron.
R. Sakurada, A. K. Singh and Y. Kawazoe [10] reported that the total energy of four CaOx
polyhedra connecting models were -3642.62 eV for 2Sr-771, –3642.61 eV for 2Sr-772, –3642.59 eV
for 2Sr-781, –3642.61 eV for 2Sr-782, and -3644.02 eV for without substitution, respectively. Less
difference in the total energy among 2Sr-771, 2Sr-772 and 2Sr-782 computational configurations
was found, however, 2Sr-781 forming edge to edge bond between Sr(1)Ox polyhedron and Sr(2)Ox
R. Sakurada, A. K. Singh and Y. Kawazoe
polyhedron lies in most unstable state in total energy of the crystal. 2Sr-771 where two Sr(1)Ox
polyhedra are isolated without edge to edge bond or face to face bond lies in most stable state
among four computational configurations. Same behavior was found in the higher doping
concentration cases as shown in Table 3.
A stretch of SrOx polyhedra due to entering of the Sr atom into CaOx polyhedra was found in
β-C2S crystal. On the other hand, all of SiO4 tetrahedra connecting with SrOx polyhedra shrinks as
shown in Si-O bond length change rate ranging from 0.088% to 0.125%.
From the calculation result of super cell of 504 atoms [10], same tendency is found that the mean
Ca-Ca bond length in β-C2S crystal depends on the doping position of Sr atoms in CaO x polyhedra.
The Ca-Ca bond lengths after doping of Sr atoms in 2Sr-771 and 2Sr-772 having seven Sr(1)-O
bonds are shorter than that in 2Sr-781 and 2Sr-782 having seven Sr(1)-O bonds and eight Sr(2)-O
bonds.
The key to a stability and Ca-Ca bond length of β-C2S is whether a doping position of Sr atom is
in CaOx polyhedra forming distorted bipyramid of seven Ca-O bonds or in CaOx polyhedra forming
anticube of eight Ca-O bonds (Ref. Figure1).
5 CONCLUSIONS
Based on the previous results and discussions, following conclusions can be conducted:
(1) β-C2S in higher doping rate of 7.1% by Sr atoms of the calculation models of #1-2 - #1-8
energetically lies in more unstable than β-C2S in doping rate of 3.6% by Sr atoms of the
calculation model of #1. β-C2S substituted two Sr atoms for Ca(1) atoms having seven Ca-O
bonds of the calculation models of #1-2, #1-3 and #1-4 lies in more stable state than that
substituted one Sr atom for Ca(1) atom having seven Ca-O bonds and one Sr atom for Ca(2)
atom having eight Ca-O bonds of the calculation models of #1-5, #1-6, #1-7 and #1-8.
(2) The substitution of Sr atom for Ca(1) atom having seven Ca-O bonds of the calculation
models of #1-2, #1-3 and #1-4 contributes to shorten the Ca-Ca bond length of the β-C2S
compared with the substitution of Sr atom for Ca(2) atom having eight Ca-O bonds of the
calculation models of #1-5, #1-6, #1-7 and #1-8.
(3) The mean HOMO-LUMO energy gap is 5.30 eV for β-C2S substituted two Sr atoms for
Ca(1) atoms having seven Ca-O bonds and 5.25 eV for β-C2S substituted one Sr atom for
Ca(1) atom having seven Ca-O bonds and one Sr atom for Ca(2) atom having eight Ca-O
bonds, while β-C2S substituted one Sr atom for Ca(1) atom having seven Ca-O bonds gives
5.21 eV.
(4) The doping position of Sr atom in CaOx polyhedra plays an important role on the crystal
stability and the shortening of Ca-Ca inter-atomic bond length relating closely to the hydraulic
activity of β-C2S. This result was coincided to the ab-initio calculation using super cell sizing up
to 504 atoms where the effect of the kinds of connection of CaOx polyhedra on the stability of
β-C2Scrystal was investigated.
The authors would like to gratefully acknowledge the supercomputing resources from the
Center for Computational Materials Sciences of the Institute for Materials Research, Tohoku
University. One of the authors, Prof. Yoshiyuki Kawazoe is supported by the CREST project
headed by Prof. Motoko Kotani.
REFERENCES
[1] G. C. Lai, T. Nojiri, and K. Nakano, Studies of the Stability of β-Ca2SiO4 Doped by Minor Ions,
Cement and Concrete Research, Vol.22, pp.743-754 (1992).
[2] A. K. Singh, V. Kumar, and Y. Kawazoe, Metal encapsulated nanotubes of silicon and
R. Sakurada, A. K. Singh and Y. Kawazoe
germanium, Journal of Materials Chemistry, Vol.14, pp.555-563 (2004).
[3] A. K. Singh, V. Kumar, R. Note, and Y. Kawazoe, Pristine Semiconducting [110] Silicon
Nanowires, Nano Letters, Vol.5, No.11, pp.2302-2305 (2005).
[4] T. M. Briere, M. H. F. Sluiter, V. Kumar, and Y. Kawazoe, Atomic structures and magnetic
behavior of Mn clusters, Physical Review B66, pp.064412-1-064412-6 (2002).
[5] R. Sakurada, A. K. Singh, T. M. Briere, M. Uzawa, and Y. Kawazoe, Crystal Structure
Analysis of Dicalcium Silicates by Ab-initio Calculation, 32nd Conf. on Our World in Concrete
& Structures, Vol.26, pp.407-412 (2007).
[6] R. Sakurada, A. K. Singh, M. Uzawa, and Y. Kawazoe, First-Principles Calculation of
Beta-Form Belite Substituted with Trace Impurity, 34th Conf. on Our World in Concrete &
Structures, Vol.28, pp.297-304 (2009).
[7] R. Sakurada, A. K. Singh, M. Uzawa, and Y. Kawazoe, First-Principles Study on Crystal
Structure of Beta-Form Belite, The 4th Asian Particle Technology Symposium, pp.691-696
(2009).
[8] K. H. Jost, B. Ziemer, and R. Seydel, Redetermination of the Structure of β-Dicalcium
Silicate, Acta Crystallographica, B33, pp.1696-1700 (1977).
[9] G. Kresse, and J. Furthmüller, Efficient iterative schemes for ab initio total-energy
calculations using a plane-wave basis set, Physical Review B, Vol.54, No.16, pp.11169-11186
(1996).
[10] R. Sakurada, A. K. Singh, and Y. Kawazoe, First-Principles Study on Structural Properties
of Bata-Form Belite, 35th Conf. on Our World in Concrete & Structures, Vol.29, pp.391-396
(2010).