FIRST-PRINCIPLES STUDY ON STRUCTURAL STABILITY
OF Ba-DOPED BELITE
R. Sakurada, Akita National College of Technology, Japan
H. Mizuseki, Tohoku University, Japan
A. K. Singh, Indian Institute of Science,India
37th Conference on OUR WORLD IN CONCRETE & STRUCTURES: 29 - 31 August 2012,
Singapore
Article Online Id: 100037037
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37 Conference on Our World in Concrete and Structures
29-31 August 2012, Singapore
FIRST-PRINCIPLES STUDY ON STRUCTURAL STABILITY
OF Ba-DOPED BELITE
R. Sakurada*, H. Mizuseki†and A. K. Singh‡
*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, first-principles calculation, Ba, structural stability
Abstract. First-principles calculations based on density functional theory were
conducted to study structural stability of beta-form Belite (β-C2S) replacing one Ca
atom in CaOx polyhedron with one Ba atom. Emphasis is on the effect of structural
arrangement of atoms in CaOx polyhedron replaced by Ba atom on the change in
inter-atomic distance of CaOx polyhedron and formation energy of β-C2S.The
super-cell of 504 atoms (ax3, bx3, cx2) was employed in the substitution models by
Ba atom in this work.
Mean Ca-O bond length of CaOx polyhedron after replacing one Ca(1) atom having
sevenfold coordinates with one Ba atom provides 2.493Å for Ca(1)-O bond length
and 2.483Å for Ca(2)-O bond length in which Ca(2) atom has eightfold coordinates,
respectively. Ca(1)-O bond length in distorted pentagonal bi-pyramid CaOx
polyhedron having seven coordinates of oxygen is longer than Ca(2)-O bond length
in distorted anti-cube CaOx polyhedron having eight coordinates of oxygen.
Replacing Ca(1) atom having seven coordinates with Ba(1) atom results in a stretch
of Ba(1)-O bond length.
β-C2S substituted one Ba atom for Ca(1) atom lies in more stable state in total
energy compared with that substituted one Ba atom for Ca(2) atom. Formation
energy of β-C2S doped by Ba atom is approximately five times higher than that of
β-C2S doped by Sr atom. The higher is formation energy, the more difficultly the
foreign atom is doped into CaOx polyhedron. The bond valence of Ca(1) ion having
sevenfold coordinates is estimated to be +1.8 - +1.9 which value is obviously smaller
than exact valence of +2. It is assumed that the covalent exists in Ca(1)-[SiO4] unit as
an intermediate state during hydration with water molecule.
1 INTRODUCTION
Belite C2S (2CaO·SiO2) is one of four major cement clinker compounds of C3S (3CaO·SiO2), C2S
(2CaO·SiO2), C3A (3CaO·Al2O3) and C4AF (4CaO· Al2O3·Fe2O3). It has been generally known that there
is five polymorphs of α-form, α’H-form, α’L-form, β-form and γ-form in Belite by temperature of cement
clinker compounds during cooling process as shown in Figure1 and Table1.
†
Tohoku University,
‡
Indian Institute of Science
R. Sakurada, H. Mizuseki, and A. K. Singh
780-860℃
1160℃
1425℃
2130℃
γ-C2S
α’L-C2S
α’H-C2S
α-C2S
orthorhombic
orthorhombic
orthorhombic
hexagonal
～500℃
β-C2S
Solid solution
630-690℃
monoclinic
Figure 1 : Polymorphs of Belite
Table 1 : Lattice vectors of five polymorphs
Dicalcium Silicates
α-C2S Hexagonal
α'H-C2S Orthorhombic
α'L-C2S Orthorhombic
β-C2S Monoclinic
γ-C2S Orthorhombic
a,Å b,Å c,Å
deg.
5.579
7.150 γ=120
9.490 5.590 6.850
6.957 9.496 5.600
5.502 6.745 9.297 β=94.59
5.081 11.22 6.778
Beta-form Belite (β-C2S) is usually useful in ordinary Portland cement to reduce heat liberation
during hydrate reaction and to gain strength development at long-term age.
Trace impurities contained in β-C2S have direct effects upon structural stability of cement clinker
compound, combustibility of raw materials and hydraulic activity. It was reported in the study of G. C.
Lai et al.[1] that the kind of univalent and multivalent ions as trace impurities and their substitution rate
have close connection with the phase change of C2S.
Besides above experimental approach first-principles calculation at atomic level based on density
functional theory without any other assumptions have been firstly applied to explore theoretically
crystal stability and hydraulic activity of β-C2S and γ-C2S by R. Sakurada, A. K. Singh, Y. Kawazoe et
al.[2]. From this result Ca-Ca bond length less than 4Å of β-C2S is shorter than that of γ-C2S. The
Ca-Ca bond length may become a yardstick to estimate the hydraulic activity of calcium silicates.
These calculation results are agree well with the experimental one conducted by K. H. Jost et al.[3].
R. Sakurada, A. K. Singh, Y. Kawazoe et al. also [4] have reported the effect of substitution of Ca
atom by Sr atom as trace impurity of cement raw materials on the crystal stability and hydraulic activity
of β-C2S.
As mentioned above the first-principles study based on quantum mechanics and quantum
chemistry is useful tool to make clear theoretically crystal structure of solid at atomic level.
First-principles calculations based on Kohn-Sham equation is conducted by solving directly
Schrödinger’s equation at the quantum level without any other statistical assumptions,
phenomena-based parameters and fitting parameters as employed in the self-consistent-field discrete
variation Xα method. The first-principles calculations have been applied to develop the magnetism in
metal-doped silicon nanotubes[5], pristine silicon nanowires[6] and other nano-scale electronic
devices. The first-principles calculations, however, is not yet familiar in cement and concrete field.
Emphasis in this study is on the structural stability of beta-form Belite (β-C2S) replaced Ca atom in
CaOx polyhedron with Ba atom. The crystal stability is analyzed from the total energy of super-cell and
formation energy relating to structural arrangement of Ca, O, and Si atoms. And the bond valence of
Ca ion in CaOx polyhedron is estimated in Ca(1) atom having sevenfold coordinates and Ca(2) atom
having eightfold coordinates to make clear the behavior of Ca(1) and Ca(2) atoms in hydration
process. The super-cell sizing up to 504 atoms (ax3, bx3, cx2) is adopted in this work.
R. Sakurada, H. Mizuseki, and A. K. Singh
2 DENSITY FUNCTIONAL THEORY
First-principles calculation is based on density functional theory and norm-conserved
pseudo-potentials. The total energy of electron system is expressed as a functional of electronic
charge density ρ(r) at a particular point of r. The energy functional gives minimum value of energy at
ground state for real electronic charge density.
By applying variation principle to the total energy functional of the electronic charge density ρ(r),
Kohn-Sham equation in a similar form of Shrödinger equation can be easily obtained for one-electron
orbital in Equations (1) and (2).
 h2 2

 −
∇ + Veff (r )ψ i (r ) = ε iψ i (r )
 2m

Veff (r ) = Vext (r ) + ∫
ρ (r ′)
r− r′
(1)
dr ′ + µ xc [r ]
(2)
where h is Planck’s constant ( ћ = h/2π), m is mass of electron, ψi (r) denotes one-electron spatial orbital
for i =1,2,3,…….n,
ε i is Kohn-Sham orbital energies, Veff (r) is effective potential. and Vext (r) is effective
potential involving external potential, interaction potential between electrons and exchange-correlation
potential µxc[r] which is functional derivative of exchange-correlation energy Exc[ρ (r)]:
µ xc [r ] =
δE xc [ρ (r )]
δρ (r )
(3)
The solutions of Equation (1) can be easily founded by solving Shrödinger equation for
noninteracting particles moving under an effective potential Veff (r).
3
COMPUTATIONAL MODELS OF β-C2S DOPED BY Ba ATOM
5
Beta-form Belite (β-C2S) crystal belongs monoclinic space group P21/n (C 2h) with lattice constants
[3] of a = 5.502Å, b = 6.745Å, c = 9.297Å, and the monoclinic angle is 94.59° from X-ray diffraction
analysis as tabulated in Table1. Pure β-C2S without doping of foreign atoms is composed of two kinds
of CaOx polyhedra and SiO4 tetrahedron : 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 Figure2. The atom coordinates of the monoclinic unit cell are tabulated in Table2.
Table 2 : Atomic coordinates for β-C2S
atom
Ca(1)
Ca(2)
Si
O(1)
O(2)
O(3)
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
Seven Ca-O bonds
Eight Ca-O bonds
Four Si-O bonds
Figure 2 : CaOx polyhedron and SiO4 tetrahedron
R. Sakurada, H. Mizuseki, and A. K. Singh
The
first-principles
calculations
were
conducted in the super-cell consisting of 504
atoms (a×3, b×3, c×2) to find the effect of doping
of Ba atom into CaOx polyhedron and the
coordinates of Ca atom replaced by Ba atom on a
change in structural stability and formation energy
related to structural arrangement of atoms of
β-C2S. The bond valence of Ca ion in CaOx
polyhedron
was
estimated
to
explore
the
hydration process. Figure3 illustrates the β-C2S
substituted one Ba for Ca(1) atom.
The first-principles calculations followed by
Figure 3 : Doping configuration of β-C2S
doped by Ba atom
Equations (1)-(3) were carried out using Vienna
ab-initio simulation package, VASP [7] for above
computational models of β-C2S. The calculations were performed using a plane wave method
employing the PAW pseudopotentials for Ca, Si and O atoms, and the generalized gradient
approximation (GGA) for the exchange-correlation potential in Equation (3) was employed.
-4
The convergence in energy is set up at 10 eV, and the cutoff energy at 400eV for plane-wave basis
in this work. Г-point sampling and k-point sampling (1×1×1) was used for calculations.
4
RESULTS AND DISCUSSIONS
Mean Ca-O bond length less than 3Å of all CaOx polyhedra after replacing one Ca atom with one
dopant X (Ba atom, Sr atom) are tabulated in Table 5. The doping concentration is 0.2 percent because
only one dopant of Ba atom or Sr atom is substituted for Ca atom in β-C2S composing of 504 atoms.
Ca(1) in Table 5 denotes the Ca atom having seven coordinate of oxygen and Ca(2) for having eight
coordinate of oxygen.
For β-C2S in which one Ca(1)Ox polyhedron having seven coordinate of oxygen is doped by one Ba
atom mean Ca-O bond length of CaOx polyhedron excluding Ba(1)Ox polyhedron exhibits 2.493Å for
Ca(1)-O bond length and 2.483Å for Ca(2)-O bond length, respectively. On the other hand, for β-C2S in
which one Ca(2)Ox polyhedron having eight coordinate of oxygen is doped by one Ba atom mean
Ca-O bond length of CaOx polyhedron gives 2.491Å for Ca(1)-O bond length and 2.483Å for Ca(2)-O
bond length, while Ca-O bond length in pure Belite without a dopant provides 2.494Å for Ca(1)-O bond
length and 2.484Å for Ca(2)-O bond length.
For the doping cases of one Sr atom a similar tendency is evident in Ca-O bond length. The Ca-O
bond length does not depend on the kind of dopants of Ba or Sr atoms. Mean Si-O bond length of SiO4
tetrahedra is 1.642Å for all of calculation models : 1Ba-7, 1Ba-8, 1Sr-7 and 1Sr-8. It can be considered
Table 5 : Ca-O bond length and Si-O bond length
Computational Model No.
Inter-atomic bond length
Dopant X
Doping mumber of atom X
Coordination number of XOx polyhedron
Concentration of dopant X, %
Mean Ca(1)-O bond length(<3Å) of Ca(1)Ox polyhedra, Å
Mean Ca(2)-O bond length(<3Å) of Ca(2)Ox polyhedra, Å
Mean Si-O bond length(<3Å) of SiO4 tetrahedra, Å
1Ba-7
1Ba-8
1Sr-7
1Sr-8
Ba
1
7
0.2
2.493
2.483
1.642
Ba
1
8
0.2
2.491
2.483
1.642
Sr
1
7
0.2
2.493
2.484
1.642
Sr
1
8
0.2
2.493
2.484
1.642
Without
doping
2.494
2.484
1.642
R. Sakurada, H. Mizuseki, and A. K. Singh
Table 6 : Ca-O bond length change rate
Computational Model No.
Inter-atomic bond length change rate
Dopant X
Doping mumber of atom X
Coordination number of XOx polyhedron
Concentration of dopant X, %
Ca-O bond length change rate of CaOx polyhedron
due to substitution of dopant X, %
Ca-O bond length (<3Å) of CaOx polyhedron
before substitution of dopant X, Å
X-O bond length (<3Å) of XOx polyhedron
after substitution of dopant X, Å
1Ba-7
1Ba-8
1Sr-7
1Sr-8
Ba
1
7
0.2
-7.8
Ba
1
8
0.2
-6.6
Sr
1
7
0.2
-3.4
Sr
1
8
0.2
-2.6
2.493
2.484
2.493
2.484
2.688
2.647
2.579
2.549
Table 7(a) : Ca-O bond length of CaOx polyhedra connecting to BaOx polyhedron in which
one Ca(1) atom having sevenfold coordinates is replaced by one Ba atom
Ca-O bond length
Belite after doping of Ba atom
Belite before doping of Ba atom
Ca atom No. of CaOx
Ca-O bond length
Ca-O bond length
change rate
Bond type of
Ca atom No. of
polyhedra binding with CaOx polyhedra withof CaOx polyhedra CaOx polyhedra of CaOx polyhedra ([3]-[2]) / [3]
Ba(1)Ox polyhedron[1] Ba(1)Ox polyhedron (<3Å), Å [2]
corresponding to [1]
(<3Å), Å [3]
%
2.506
-0.47
Ca25 7Ca-O bonds
Common corners
Ca25
2.494
2.467
1.08
Ca28 7Ca-O bonds
Common corners
Ca28
2.494
2.517
-0.98
Ca66 7Ca-O bonds
Common edges
Ca67
2.493
2.504
-0.44
Ca68 7Ca-O bonds
Common edges
Ca69
2.493
2.489
-0.18
Ca80 8Ca-O bonds
Common faces
Ca81
2.484
2.493
-0.37
Ca105 8Ca-O bonds
Common edges
Ca106
2.484
2.502
-0.72
Ca116 8Ca-O bonds
Common faces
Ca117
2.484
2.471
0.54
Ca122 8Ca-O bonds
Common corners
Ca123
2.484
2.477
0.29
Ca133 8Ca-O bonds
Common corners
Ca134
2.484
2.493
-0.35
Ca135 8Ca-O bonds
Common edges
Ca136
2.484
2.475
0.35
Ca141 8Ca-O bonds
Common corners
Ca142
2.484
Table 7(b) : Ca-O bond length of CaOx polyhedra connecting to BaOx polyhedron in which
one Ca(2) atom having eightfold coordinates is replaced by one Ba atom
Ca-O bond length
Belite after doping of Ba atom
Belite before doping of Ba atom
Ca atom No. of CaOx
Ca-O bond length
Ca-O bond length
change rate
Bond type of
Ca atom No. of
polyhedra binding with CaOx polyhedra withof CaOx polyhedra CaOx polyhedra of CaOx polyhedra ([3]-[2]) / [3]
Ba(2)Ox polyhedron[1] Ba(2)Ox polyhedron (<3Å), Å [2]
corresponding to [1]
(<3Å), Å [3]
%
2.501
-0.27
Ca10 7Ca-O bonds
Common corners
Ca10
2.494
2.497
-0.13
Ca12 7Ca-O bonds
Common edges
Ca12
2.494
2.485
0.33
Ca40 7Ca-O bonds
Common corners
Ca40
2.493
2.487
0.25
Ca46 7Ca-O bonds
Common edges
Ca46
2.493
2.507
-0.53
Ca48 7Ca-O bonds
Common corners
Ca48
2.494
2.481
0.47
Ca69 7Ca-O bonds
Common corners
Ca69
2.493
2.503
-0.78
Ca106 8Ca-O bonds
Common faces
Ca106
2.484
2.477
0.28
Ca117 8Ca-O bonds
Common edges
Ca117
2.484
that there is no effect of replacing of only one Ba
or Sr atoms on the distortion of SiO4 tetrahedra.
Ca-O bond length less than 3Å of CaOx polyhedra before and after replacing one Ca atom with one
dopant X (Ba atom, Sr atom) are tabulated in Table 6. The Ca-O bond length change rate λ caused by
the substitution of dopant X (Ba atom, Sr atom) for Ca atom is defined in this study as
λ = [(Ca-O) – (X-O)] / (Ca-O)
(4)
R. Sakurada, H. Mizuseki, and A. K. Singh
in which Ca-O is Ca-O bond length before doping and X-O is X-O bond length after doping,
respectively.
Ca(1)-O bond length before replacing of one Ba atom becomes 2.493Å, while Ba(1)-O bond length
after replacing of Ba atom becomes 2.688Å in the BaOx polyhedron having seven coordinates of
oxygen. The Ca-O bond length change rate leads to -7.8% resulting in a stretch of BaOx polyhedron.
And -6.6% stretch of BaOx polyhedron is found in model of 1Ba-8 in which Ca(2) atom having eight
coordinates of oxygen is replaced by Ba atom. For models of 1Sr-7 and 1Sr-8 a similar tendency is
found in Ca-O bond length change rate, however, the Ca-O bond length change rate becomes
approximately one-half of that in models of 1Ba-7 and 1Ba-8.
Table 7(a) tabulates Ca-O bond length change rate of CaOx polyhedra connecting directly with BaOx
polyhedron having seven Ba-O bonds. In Table 7(a) Ca28, for instance, connecting with BaOx
polyhedron by common corners exhibits 1.08% shrink after doping of Ba atom. Ca67 connecting with
BaOx polyhedron by common edges provides 0.98% extension in Ca-O bond length after doping of Ba
atom. Mean Ca-O bond length change rate of CaOx polyhedra connecting directly with BaOx
polyhedron having seven Ba-O bonds is -0.11%.
In Table 7(b) Ca-O bond length change rate of CaOx polyhedra connecting with BaOx polyhedron
having eight Ba-O bonds ranges between –0.78% and 0.47%, and the mean change rate is found
-0.05%. CaOx polyhedra connecting with BaOx polyhedron exhibit less difference of Ca-O bond length
Table 8(a) : Ca-O bond length of CaOx polyhedra connecting to SrOx polyhedron in which
one Ca(1) atom having sevenfold coordinates is replaced by one Sr atom
Ca-O bond length
Belite after doping of Sr atom
Belite before doping of Sr atom
Ca-O bond length
Ca-O bond length
change rate
Ca atom No. of CaOx
Bond type of
Ca atom No. of
polyhedra binding with CaOx polyhedra with of CaOx polyhedra CaOx polyhedra of CaOx polyhedra ([3]-[2]) / [3]
corresponding to [1]
(<3Å), Å [3]
%
Sr(1)Ox polyhedron[1] Sr(1)Ox polyhedron (<3Å), Å [2]
2.501
2.494
-0.28
Ca25 (7Ca-O bonds)
Common corners
Ca25 (7Ca-O bonds)
2.479
2.494
0.62
Ca28 (7Ca-O bonds)
Common corners
Ca28 (7Ca-O bonds)
2.504
2.494
-0.39
Ca66 (7Ca-O bonds)
Common edges
Ca67 (7Ca-O bonds)
2.498
2.494
-0.15
Ca68 (7Ca-O bonds)
Common edges
Ca69 (7Ca-O bonds)
2.485
2.484
-0.05
Ca80 (8Ca-O bonds)
Common faces
Ca81 (8Ca-O bonds)
2.484
2.484
-0.02
Ca103 (8Ca-O bonds)
Common corners
Ca142 (8Ca-O bonds)
2.486
2.484
-0.08
Ca105 (8Ca-O bonds)
Common corners
Ca104 (8Ca-O bonds)
2.492
2.484
-0.32
Ca116 (8Ca-O bonds)
Common edges
Ca106 (8Ca-O bonds)
2.478
2.484
0.23
Ca122 (8Ca-O bonds)
Common faces
Ca117 (8Ca-O bonds)
2.480
2.484
0.15
Ca133 (8Ca-O bonds)
Common corners
Ca123 (8Ca-O bonds)
2.487
2.484
-0.12
Ca135 (8Ca-O bonds)
Common corners
Ca134 (8Ca-O bonds)
2.479
2.484
0.21
Ca141 (8Ca-O bonds)
Common edges
Ca136 (8Ca-O bonds)
Table 8(b) : Ca-O bond length of CaOx polyhedra connecting to SrOx polyhedron in which
one Ca(2) atom having eightfold coordinates is replaced by one Sr atom
Ca-O bond length
Belite after doping of Sr atom
Belite before doping of Sr atom
Ca atom No. of CaOx
Ca-O bond length
Ca-O bond length
change rate
Bond type of
Ca atom No. of
polyhedra binding with CaOx polyhedra withof CaOx polyhedra CaOx polyhedra of CaOx polyhedra ([3]-[2]) / [3]
Sr(2)Ox polyhedron[1] Sr(2)Ox polyhedron (<3Å), Å [2]
corresponding to [1]
(<3Å), Å [3]
%
2.496
2.494
-0.08
Ca10
Ca10 (7Ca-O bonds)
Common corners
2.495
2.494
-0.03
Ca12 (7Ca-O bonds)
Common edges
Ca12
2.502
2.494
-0.32
Ca28 (7Ca-O bonds)
Common faces
Ca28
2.490
2.493
0.12
Ca40 (7Ca-O bonds)
Common corners
Ca40
2.490
2.493
0.13
Ca46 (7Ca-O bonds)
Common edges
Ca46
2.498
2.494
-0.17
Ca48 (7Ca-O bonds)
Common corners
Ca48
2.490
2.493
0.13
Ca63 (7Ca-O bonds)
Common faces
Ca63
2.489
2.494
0.20
Ca69 (7Ca-O bonds)
Common corners
Ca69
2.489
2.484
-0.20
Ca100 (8Ca-O bonds)
Common faces
Ca100
2.491
2.484
-0.28
Ca106 (8Ca-O bonds)
Common faces
Ca106
2.480
2.484
0.16
Ca117 (8Ca-O bonds)
Common edges
Ca117
R. Sakurada, H. Mizuseki, and A. K. Singh
change rate by the connection kind of common corners, common edges and common faces.
Ca-O bond length change rate of CaOx polyhedra connecting directly with SrOx polyhedron having
seven and eight Sr-O bonds were tabulated in Table 8(a) and 8(b), respectively. Mean Ca-O bond
length change rate gives 0.02% in elongation for CaOx polyhedra connecting with BaOx polyhedron
having seven coordinates of oxygen and 0.03% in elongation for CaOx polyhedra connecting with BaOx
polyhedron having eight coordinates of oxygen. This Ca-O change rate for Sr doping case is smaller
than that for Ba doping case. In every doping case Ca-O bond length change rate does not depend on
connection kind of atoms such as common corners, common edges and common faces.
The total energy, energy at HOMO and LUMO, and formation energy are summarized in Table 9.
HOMO (highest occupied molecular orbit) and LUMO (lowest unoccupied molecular orbit) are energy
levels of frontier molecular orbits. The total energy gives -3642.58eV for β-C2S substituted one Ba atom
for Ca(1) atom having seven Ca-O bonds and -3642.27eV for β-C2S substituted one Ba atom for Ca(2)
atom having eight Ca-O bonds, respectively.
β-C2S substituted one Ba atom for Ca(1) atom lies in more stable state in total energy compared with
that substituted one Ba atom for Ca(2) atom. The total energy of β-C2S doped by Sr atom shows a
similar tendency with that of β-C2S doped by Ba atom. HOMO-LUMO energy gap ranges between
4.97eV to 4.99eV for all of doping cases. The higher value of around 5eV obviously reflects charge
distribution as a typical insulator.
Formation energy defined as the energy difference between the energy content of the products and
the reactants relate closely to the structural arrangement of atoms due to the various chemical bonds.
Formation energy of β-C2S substituted Ba atom for Ca atom is approximately five times higher than
that of β-C2S substituted Sr atom for Ca atom. The higher is formation energy, the more difficultly the
foreign atom is doped into CaOx polyhedron. These formation energy shows that the substitution of Sr
atom with Ca atom is easier than the substitution of Ba atom with Ca atom and that the doping into
CaOx polyhedron having seven Ca-O bonds is easier than that into CaOx polyhedron having eight
Ca-O bonds.
Ba atom having a body-centered cubic structure provides chemically similar property to Ca atom, Sr
atom and Mg atom. The atomic radius of Ba atom is 222pm that is similar to Ca atom. Sr atom in
atomic number of 38 is an alkaline earth metal, and its crystal structure belongs to face-centered cubic.
The atomic radius of Sr atom is 215pm that is similar to Ca atom of 197pm. Besides Sr atom in
oxidation of +2 replaces easily with Ca atom of an oxidation of +2.
Both atoms of Sr and Ba belong to alkaline earth metal are similar features to Ca atom in an oxidation
of +2 and an atomic radius of around 200pm. In particular Sr atom has a feature to substitute easily
with Ca atom. This fact causes lesser formation energy of Sr-doped β-C2S in comparison with
Ba-doped β-C2S.
Bond valence Vi of Ca ion in CaOx polyhedron can be estimated by summing up of all the valences
vij between Ca atom i and O atom j. The bond valence Vi for solids is defined by following empirical
expression [8]:
R. Sakurada, H. Mizuseki, and A. K. Singh
Table 10 : Bond valence of Ca ion in CaOx polyhedra connecting with XOx polyhedron
CaOx polyhedra connecting with XOx polyhedron
after doping of X atom
Coordination number Mean value
Mean value of
of CaOx polyhedra
of Ca-O, Å
bond valence for Ca ion
Ba(1)Ox
1Ba-7
Ba
-3642.58
7
2.50
1.88
8
2.49
2.06
Ba(2)Ox
1Ba-8
Ba
-3642.27
7
2.49
1.92
8
2.49
2.07
Sr(1)Ox
1Sr-7
Sr
-3643.31
7
2.50
1.88
8
2.49
2.06
Sr(2)Ox
1Sr-8
Sr
-3643.27
7
2.49
1.92
8
2.49
2.07
Ba(1)Ox polyhedron = 7 Ba-O bonds, Ba(2)Ox polyhedron = 8 Ba-O bonds
Sr(1)Ox polyhedron = 7 Sr-O bonds, Sr(2)Ox polyhedron = 8 Sr-O bonds
Ca(1)Ox polyhedron = 7 Ca-O bonds, Ca(2)Ox polyhedron = 8 Ca-O bonds
XOx
Computational Dopant X
Total energy
Model No.
polyhedron
eV
vij = exp [ (Rij-dij) / B ]
(5)
Vi = Σj vij
(6)
where Rij is the bond valence parameter between pairs of atom, Ca atom i and O atom j in CaOx
polyhedron (=1.967Å), dij is the obtained Ca-O bond length for each oxygen j, and B is universal
constant equal to 0.37Å.
The bond valence of Ca ion in model 1Ba-7, in which one Ca(1) atom having seven Ca-O bonds is
replaced by one Ba atom, are estimated to be +1.8 for Ca(1) atom of CaOx polyhedron having seven
coordinates of oxygen and +2.0 for Ca(2) atom of CaOx polyhedron having eight coordinates of oxygen
as listed in Table 10. The bond valence of Ca ion in model 1Ba-8, in which one Ca(2) atom having eight
Ca-O bonds is replaced by one Ba atom, are estimated to be +1.9 for Ca(1) atom of CaOx polyhedron
having seven coordinates of oxygen and +2.0 for Ca(2) atom of CaOx polyhedron having eight
coordinates of oxygen. For Sr-doping cases we find less difference with the Ba-doping cases.
The bond valence of Ca(1) ion for +1.8 - +1.9 is obviously smaller than exact bond valence of +2.0,
while the bond valence of Ca(2) ion becomes equal to exact bond valence of +2.0. From the charge
neutrality K. Mori et al.[9] pointed out that the bond valence less than +2.0 for Ca(1) ion receives
1.87
exceeding charge from SiO4 tetrahedron in the intermediate unit of Ca
3.87+
-[SiO4]
during hydration. It
can be estimated that the existence of intermediate Ca(1)-[SiO4] unit during hydration seems to be
1.9+
most probable from the results of first-principles calculation as shown in Ca
3.9+
- [SiO4]
unit and that
covalent exists in Ca(1)-[SiO4] unit.
Table 9 : Formation energy of β-C2S doprd by Ba atom, and by Sr atom
Computational Model No.
Energy
Dopant X
Doping mumber of atom X
Coordination number of XOx polyhedron
Concentration of dopant X, %
Formation energy, eV
Total energy, eV
HOMO, eV
LUMO, eV
HOMO-LUMO energy gap, eV
1Ba-7
1Ba-8
1Sr-7
1Sr-8
Ba
1
7
0.2
2.34
-3642.58
3.01
8.00
4.99
Ba
1
8
0.2
2.65
-3642.27
3.03
8.00
4.97
Sr
1
7
0.2
0.42
-3643.31
3.00
7.99
4.99
Sr
1
8
0.2
0.46
-3643.27
3.00
7.99
4.99
R. Sakurada, H. Mizuseki, and A. K. Singh
5 CONCLUSIONS
From the previous results and discussions, following conclusions can be made:
(1) Mean Ca-O bond length of CaOx polyhedra in β-C2S after replacing one Ca(1) atom having seven
coordinates with one Ba atom provides 2.493Å for Ca(1)-O bond length and 2.483Å for Ca(2)-O bond
length in which Ca(2) has eight coordinates, respectively.
β-C2S after replacing one Ca(2) having eight coordinates with one Ba atom gives a similar tendency
to Ca(1) atom substituting case. Ca(1)-O bond length in distorted pentagonal bi-pyramid CaOx
polyhedra having seven coordinates of oxygen is longer than Ca(2)-O bond length in distorted
anti-cube CaOx polyhedra having eight coordinates of oxygen.
(2) Replacing one Ca(1) atom in CaOx polyhedron having seven coordinates of oxygen with one Ba
atom induces 7.8% increase in Ba(1)-O bond length against original Ca(1)-O bond length. For
replacing one Ca(2) atom in CaOx polyhedron having eight coordinates of oxygen with one Ba atom
6.7% increase in Ca(2)-O bond length is found.
(3) β-C2S substituted one Ba atom for Ca(1) atom lies in more stable state in total energy compared
with that substituted one Ba atom for Ca(2) atom. The total energy of β-C2S doped by Sr atom shows a
similar tendency with that of β-C2S doped by Ba atom. HOMO-LUMO energy gap is 4.99eV for β-C2S
substituted one Ba atom for one Ca atom and for β-C2S substituted one Sr atom for one Ca atom
Formation energy of β-C2S substituted Ba atom for Ca atom is approximately five times higher than
that of β-C2S substituted Sr atom for Ca atom. The higher is formation energy, the more difficultly the
foreign atom is doped into CaOx polyhedron.
(4) The bond valence of Ca ion in CaOx polyhedron are estimated to be +1.8 - +1.9 for Ca(1) atom
having seven coordinates and +2.0 for Ca(2) atom having eight coordination, respectively. The bond
valence of +1.8 - +1.9 in Ca(1) ion is obviously smaller than exact bond valence of +2.0. This implies
that covalent exists in Ca(1)-[SiO4] unit as a intermediate state during hydration with water molecule.
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.
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