Alkali metal-substituted bismuth-based perovskite compounds: A DFT study

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Original Article

Alkali metal-substituted bismuth-based perovskite compounds: A DFT

study

Nguyen Hoang Linh

a

, Nguyen Hoang Tuan

a

, Dang Duc Dung

a

, Phung Quoc Bao

b

,

Bach Thanh Cong

b

, Le Thi Hai Thanh

a,*

a_{School of Engineering Physics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Viet Nam}

b_{Faculty of Physics, VNU}_{e University of Science, 334 Nguyen Trai, Hanoi, Viet Nam}

a r t i c l e i n f o

Article history:
Received 10 April 2019
Received in revised form
18 June 2019

Accepted 30 June 2019
Available online xxx

Keywords:

Bismuthe based perovskite
Alkali metals

Density functional theory
O-vacancies

Photocatalyst

a b s t r a c t

In this study, we have performed density functional theory based calculations to investigate the effect of
alkali substituents M on the structure and electronic properties of (Bi0.5M0.5)TiO3 compounds with
M¼ Li, Na and K. When the ionic radius of the substituting M cation increases, the corresponding direct
band gap of (Bi0.5M0.5)TiO3also increases. The same trend is found for the O-deficient Bi0.5M0.5TiO
3-dcompounds, which were investigated by removing one Oxygen atom from the super cell creating an
O-vacancy in it. The presence of the O-O-vacancy breaks the local symmetry of the crystal structures and
generates excess electrons in the O-deficient compounds. This results in the appearance of an indirect
bandgap in Bi0.5Na0.5TiO3-d and Bi0.5K0.5TiO3-d, except for Bi0.5Li0.5TiO3-d that still exhibits a direct
bandgap. Excess electrons induce the defect states within the original bandgap of the stoichiometric
compounds and decrease the bandgap of the O-deficient compounds. In line with the electronic
cal-culations, effective mass calculations have provided a preliminary insight into the photocatalytic
per-formance of (Bi0.5M0.5)TiO3and reveal a positive impact of K cations on the photocatalytic activity.

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1. Introduction

Lead-based perovskite ceramics, e.g. lead zirconates and
tita-nates, have recently elicited considerable attention because of their
wide range of applications in sensors, piezoelectric devices,
ca-pacitors, etc.[1,2]. However, the toxicity of lead-based oxides
dur-ing the manufacturdur-ing and manipulation processes results in lead
pollution and other environmental problems. These problems can
be addressed by developing lead-free materials. (Bi0.5Na0.5)TiO3

(BNT) is considered one of the promising candidates for lead-free

perovskite materials to achieve such applications.

Since thefirst work of Smolenskii et al.[3]in 1960, BNT has been
intensively studied for their potential electronic applications.
Although BNT exhibits a large remanent polarization of 38.0

m

C=cm2_{at room temperature, its coercive}_{field can reach as high as}

7.3

m

V=mm[4], which is an obstacle in poling processes. Various
BNT-based solid solutions have been investigated to overcome this

obstacle. In consideration of the similarity in the chemical activities
of compounds, recent studies have focused on the solid solutions of
BNT and other alkali metal-substituted Bi-based perovskite
com-pounds, such as (Bi0.5K0.5)TiO3(BKT)[5,6]and (Bi0.5Li0.5)TiO3(BLT)

[7]. The high-performance ferroelectric properties of these
com-pounds are attributed to the presence of the 6s2lone pair of
elec-trons Bi3ỵ, which is similar to Pb2ỵin the perovskite structure[8,9].
This phenomenon suggests that the materials can support oxygen
reduction and redox reactions and introduce a potential application
as photocatalysts and ionic-conducting electrolytes. Although BNT
and its related compounds have elicited considerable attention as
multiferroic materials [10e12], the electronic properties of
(Bi0.5M0.5)TiO3(M¼ Li, Na, and K), which critically contribute to the

active photocatalytic reactions of these materials, remain poorly
understood.

In this work, we have performed density functional theory

(DFT)-based calculations to study the effects of thefirst three alkali
metals in Bi0.5M0.5TiO3(M¼ Li, Na, and K). BKT was reported to

have a tetragonal perovskite structure[13,14]. However, (1-x)BNTe
xBKT solid solutions exhibit a perovskite structure with a
rhom-bohedral R3c symmetry for x< 0.16e0.20[15,16]. Lin et al. reported
that the BNTeBKTeBLT solid solutions demonstrated a pure

* Corresponding author.

E-mail address:(L.T.H. Thanh).

Peer review under responsibility of Vietnam National University, Hanoi.

Contents lists available atScienceDirect

Journal of Science: Advanced Materials and Devices

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j s a m d

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perovskite structure without second phases[7]. This result suggests
that Kỵand Liỵdiffuse completely into the BNT lattices. When the
concentration of BLT is 0.10 and that of BKT is smaller than 0.15, the
ceramics still maintain a perovskite structure with a rhombohedral
symmetry. Hence, we assume the rhombohedral R3c structure of
BNT to investigate the effects of other alkali substituents, namely, K
and Li, on the structural and electronic properties of the substituted
compounds. The role of the O-vacancy as one of the important
factors that governs photocatalytic reactions in these materials is

also considered.

2. Computational details

In this study, all DFT calculations were performed in the
framework of the projector-augmented wave using the PWScf code
implemented in the Quantum ESPRESSO software package[17]. For
the exchange correlation energy, we adopted the generalized
gradient approximation using PerdeweBurkeeErnzerhof (PBE)
exchange-correlation functionals[18], which is sufficiently accurate
to describe the crystal structures and electronic properties of
perovskite compounds[19e22]. Plane-wave basis set cut offs for
the smooth part of the wave functions and the augmented density
were 80 Ry and 350 Ry, respectively. The MonkhorstePack scheme
was used to sample the Brillouin zone[23]. The structures were
fully relaxed with a mesh of 2 2  2. The mesh of k-space was
increased to 10 10  10 in the static and projected density of state
(PDOS) calculations. In the self-consistent calculations, the charge
difference between stoichiometric and O-deficient BLT, BNT, and
BKT was obtained from the L€owdin population analysis [24,25]

implemented in the Quantum ESPRESSO software package.
(Bi0.5M0.5)TiO3compounds (M¼ Li, Na, and K) were simulated

by the primitive cell of R3c with two Bi/M cations in the Wyckoff
symmetric position 2a, two Ti cations in 2a, and six O anions in 6a to
reduce computational resources (Fig. 1). The primitive cell of BNT
was assumed from the experimental lattice parameters[26,27], and
thus, a super cell of 2_{ 2  2 was obtained. The calculation results}
showed that the optimized lattice parameters of BNT are

compa-rable with those reported previously [21]. O-deficient (Bi0.5M0.5)

TiO3dcompounds with (M¼ Li, Na, and K) were each simulated by

removing one O atom from the super cell of the stoichiometric
compound, thereby creating an O-vacancy with a concentration of
2.083% (

d

¼ 0.0625) in it. The position of the vacancy in the
O-deficient compounds is the position corresponding to the
mini-mum total energy among the other equivalent positions of the
O-vacancy. (Bi0.5Li0.5)TiO3d, (Bi0.5Na0.5)TiO3d, and (Bi0.5K0.5)TiO3d

compounds are hereafter denoted as BLT_d, BNTd, and BKTd,

respectively. The optimized lattice parameters of (Bi0.5M0.5)TiO3

and (Bi0.5M0.5)TiO3dcompounds (M¼ Li, Na, and K) were obtained

from the minimum total energy (Table 1).

To obtain preliminary insights into the photocatalytic
perfor-mance of (Bi0.5M0.5)TiO3 compounds (M ¼ Li, Na, and K), the

effective mass of electrons (m*_e) and holes (m*_h) along various
di-rections were derived from calculations using thefitting parabolic
function method in the conduction band minimum (CBM) and the
valence band maximum (VBM) through the following equation:

m*¼ ±Z2 d

2_E

k

dk2

!1

; (1)

where k is the wave vector, and Ekis the energy that corresponds to

the wave vector k. The valid region of the parabolic approximation
for effective mass calculations is the energy curve within the energy
range of approximately 1% of the extreme, i.e., the VBM and CBM.

3. Results and discussion

3.1. Stoichiometric (Bi0.5M0.5)TiO3compounds

3.1.1. Crystal structures

Table 1presents the effect of the alkali metal substitution on the
crystal lattice properties of Bi0.5M0.5TiO3(M¼ Li, Na, and K). The

super cell of (Bi0.5M0.5)TiO3expands as the ionic radius of M

in-creases. The lattice parameters of the rhombohedral BKT structure
is larger than those of the tetragonal BKT arrangement[13]. This
difference can explain the effect of K in decreasing the grain size of
the BNT-based ceramics[28e30]. The rhombohedral BLT exhibits
smaller lattice parameters as compared to the rhombohedral BNT.

This result is consistent with the experimental observation [7]

wherein the grain size of BNT-based ceramics becomes smaller
when the concentration of Li is increased. The tilting of the
octa-hedral [TiO6] due to the difference in the ionic size of A-site cations

results in the unequal values of the

a

,

b

, and

g

angles. However, the
differences in the values of the

a

,

b

, and

g

angles are smaller than
approximately 5%, thereby indicating that the rhombohedral
structure of the Bi0.5M0.5TiO3compounds remains unchanged.

The alkali substituents M (M¼ Li, Na, and K) exert no
signifi-cant effect on the bond length, r_TieO, between the Ti cations and
the nearest O anions of (Bi0.5M0.5)TiO3, which is presented by the

average values of 1.89, 1.87, and 1.86 Å for BLT, BNT, and BKT,
respectively. The same conclusion can be drawn for the bond
length, rBieO, between the Bi cations and the nearest O anions of

the (Bi0.5M0.5)TiO3compounds. The BieO bonds expand, whereas

the TieO bonds are shortened under the effect of the alkali
sub-stituents M. The alkali subsub-stituents M exert a significant effect on
the bond length between the alkali M cation and the O anions: the

Fig. 1. The optimized 2 2  2 super cell of (Bi0.5M0.5)TiO3with M¼ Li, Na, and K.

Blue, purple and redfilled spheres represent the Ti, Bi cations and the O anion,
respectively. The substituents M are represented by the greenfilled sphere. The
po-sition where an O anion is removed creating an O-vacancy is marked in thefigure.

Table 1

Optimized lattice parameters and bond lengths of the cations (Bi, Ti and M) and the
nearest O anions with M¼ Li, Na and K in the corresponding stoichiometric
(Bi0.5M0.5)TiO3and O-deficient (Bi0.5M0.5)TiO3-dcompounds.

Stoichiometric materials O-deficient materials

BLT BNT BKT BLT-d BNT-d BKT-d

a (Å) 5.04 5.17 5.18 4.91 5.15 5.36

b/a 1.01 1.00 1.00 0.97 1.00 0.97

c/a 1.00 0.98 1.01 1.03 0.99 1.00

a() 58.85 58.37 61.47 58.49 58.25 60.21

b(₎ _60.15 _60.24 _59.99 _60.56 _59.82 _57.64

g(₎ _59.77 _60.56 _60.46 _60.67 _59.06 _60.17

rBi-O(Å) 2.20 2.22 2.27 2.16 2.21 2.30

rM-O(Å) 1.77 1.98 2.26 1.69 1.97 2.33

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larger the ionic radius of the substituents M, the larger the bond
length r_MeO. This phenomenon is a consequence of the different
electron screening and repulsion between the Bi/M cations and

the O anions. In this case, a large substituent M ion enhances the
electron screening effect in the MeO interaction, thereby
elon-gating the MeO bond length. This phenomenon also increases the
repulsion to the Bi cation at an equivalent site. The repulsion
between the Bi/M cations and the O anions expands the super cell,
as shown inTable 1. However, the substituent M exerts an
insig-nificant effect only on the structural properties of the (Bi0.5M0.5)

TiO3compounds, which is in good agreement with the

observa-tion of Gr€oting et al.[31].

3.1.2. Electronic structures

As shown inFig. 2, BLT, BNT, and BKT compounds have direct
bandgaps of 1.68, 1.72, and 2.05 eV, respectively, at the critical point

G

(0, 0, 0) in the reciprocal space. This result correlates with an
in-crease in the ionic radius of the M cation at the A-sites from Li to K.
The corresponding bandgap of the (Bi0.5M0.5)TiO3compounds also

increases. BKT presents the largest bandgap, whereas BLT has the
smallest bandgap. The direct bandgap obtained here for BNT and
BKT is comparable with that reported in [32,33]. This finding

implies that the substitution of large alkali elements shifts the
bandgap energy of the (Bi0.5M0.5)TiO3compounds toward the

ul-traviolet range.

Fig. 2shows the contribution of each cation and anion in the
calculated PDOS of BLT, BNT, and BKT. The contributions of the
p-orbitals of Bi, d-orbital of Ti, and p-orbital of O are significant within
the low-energy range. The hybridization of the Ti d-orbital and the
O p-orbital occurs within the low-energy range of
approximately 6 eV in all three compounds. The high energy
range, particularly near the Fermi level, is predominantly occupied
by the s-orbitals of Bi. Ganose et al.[34]demonstrated the
insig-nificant role of the Bi d-electrons in the BieO/halide interaction
considering the electroneelectron interactions using the screened
hybrid functional, relativistic effects, and spin_{eorbit coupling. The}
optimal contribution of Bi in this interaction originates from its
s-and p-electrons, which is consistent with our results. The s-orbitals
of the Li cations contribute the most to the PDOS within the
low-energy range. By contrast, the majority of the p-orbitals of the Na
cations contribute to PDOS within the high-energy range. In the
case of BKT, the 3d states exhibit lower energy than the 4s states
under the effect of the crystalfield despite of the outer shell of the
4s states of K, and thus, can be occupiedfirst. The d-orbitals of the K

Fig. 2. Projected density of states (PDOS) and the corresponding band structures alongG- Ze L -G- F path in the reciprocal space of the stoichiometric (Bi0.5M0.5)TiO3with M¼ Li,

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ions share the hybridization with the p-orbitals of the O cations
within the energy range near the Fermi level. That is, the presence
of K pulls the d states into the VBM and increases the density near
to the Fermi level. The major occupation by the Bi/M cation orbitals
near the Fermi level indicates that the activity of the (Bi0.5M0.5)TiO3

(M¼ Li, Na, and K) compounds for photocatalytic performance
strongly depends on the types of cations at A-sites.

Considering the symmetry of the rhombohedral crystal
struc-ture and the electronic band strucstruc-ture of (Bi0.5M0.5)TiO3(M¼ Li, Na,

and K), the directions along the [111], [010], and [110] at the VBM
and CBM of

G

(0, 0, 0) are selected. In these compounds, we cannot
obtain the degenerated states at the extremum of VBM and CBM.
The results are presented inTable 2.

The results inTable 2 indicate that the effective mass of the
charge carriers (electrons and holes) in the BLT, BNT, and BKT
compounds in CBM and VBM is heavier than those in the
well-known photocatalysts TiO2[35,36]and In2O3[37]. Light holes are

associated with a steep band, whereas heavy holes correspond to a
flat band. A heavier effective mass of the holes indicates that the
density of states of these holes will be larger than that of the lighter
ones. However, the larger the effective mass of the photo-generated
carriers, the slower the transfer rate. The hole effective mass m*_h
along the [111] direction is noticeably larger than that along the
[010] and [110] directions for the BLT, BNT, and BKT compounds.
That is, the small effective masses of the holes along the [010] and
[110] directions provide an easy transfer channel. In particular, the
[010] direction is the easiest direction for the transfer of holes with
the smallest effective mass m*_hin all three compounds. This
direc-tion leads to a high oxidadirec-tion activity, thereby suggesting that the
{010} surface of BLT, BNT, and BKT will exhibit higher photocatalytic
activities than those of other orientations. The effective mass of
electrons m*_e along the [111] direction from the

G

(0, 0, 0) of the
CBM is also larger than those along the [010] and [110] directions

for the BLT, BNT, and BKT compounds. However, the effective mass
of electrons is smallest along the [110] direction in BLT and BNT,
whereas it is smallest along the [010] direction in BKT. The effective
masses of holes, m*_h, and electrons, m*_e, show the smallest values
correlating with the fastest carrier transfer in BKT. This feature may
result from the effect of K in the rhombohedral BKT: it pulls the
d states down close to the VBM, enhances the dispersion of the VBM
and the CBM, thereby decreasing the effective mass, and promotes

the carrier transfer. The same mechanism was also reported to
govern the enhancement of the photocatalytic performance of
silver-based oxides[38].

The preceding results suggest that BKT can be considered an
optimal catalyst for photocatalytic reactions among the (Bi0.5M0.5)

TiO3compounds (M¼ Li, Na, and K) despite of the large bandgap.

However, the presence of the O-vacancy is considered a critical
factor for active photocatalytic reactions[39,40]. In the subsequent
section, we discuss the effect of the O-vacancy in the O-deficient
(Bi0.5M0.5)TiO3d(M¼ Li, Na, and K) compounds.

3.2. Oxygen-deficient (Bi0.5M0.5)TiO3dcompounds

3.2.1. Crystal structures

In studying the effect of the O-vacancy on the crystal structures
of the (Bi0.5M0.5)TiO3d(M¼ Li, Na, and K) compounds, denoted as

BLT_d, BNTd, and BKTd, we observed the following major changes:

the crystal lattice of BKT_dexpands as the crystal lattice of BLTd

and that of BNT_dis compressed.

As shown inTable 1, the O-vacancy exerts a noticeable effect on
the crystal structure of BLT_d. The decrease in the lattice parameters

of BLT_dresults from the slight distortion of the octahedral [TiO6]

and the shortening of the bond lengths of the cations at the A-site,
namely, Bi and Li, and the nearest O anions, thereby breaking the
equality of the lattice parameters. However, the tilting of the
octahedral [TiO6] cannot be detected in the O-deficient BLTd

compounds. The O-vacancy also slightly reduces the lattice
pa-rameters of BNT_d, and no significant change of crystal structure is

observed. The decrease is induced by the reduction in the lengths of
the BieO bond in the O-deficient BNTddue to the O-vacancy. The

octahedral [TiO6] of BNTdpresents no notable distortion but the

slight tilting under the effect of the O-vacancy, especially near to
the O-vacancy. By contrast, the lattice of BKT_dshows an expansion

indicated by an increase in the lattice parameters that is consistent
with the reduction in the interaction between the A-site cations,
such as Bi and K, and the O anions, thereby resulting in the

elon-gation of Bi/KeO bond lengths. The octahedral [TiO6] of BKTdalso

exhibits a notable distortion, and the equality of the lattice
pa-rameters is broken, which is similar to the case of BLTd. The

O-vacancy in BKT_ddoes not only cause the distortion but also the

tilting of the octahedral [TiO6], as reflected by the unequal values of

the

a

,

b

, and

g

angles. This finding indicates that the crystal
structure of the O-deficient BKTd exhibits a more tetragonal

character than that of the stoichiometric BKT.

3.2.2. Electronic structures

Removing an O atom in a stoichiometric (Bi0.5M0.5)TiO3

com-pound not only breaks the local symmetry of the crystal structure,
but also generates excess electrons in the corresponding O-de
fi-cient (Bi0.5M0.5)TiO3dcompound. As a consequence, the presence

of an O-vacancy significantly affects the electronic structure of
(Bi0.5M0.5)TiO3d. First of all, the appearance of the defect states

reduces the bandgap of all three compounds. The dependence of
the bandgap width on the ionic radii of the substituted elements
remains the same as that in the stoichiometric (Bi0.5M0.5)TiO3

compounds. While all the stoichiometric compounds show a direct

energy bandgap structure, the corresponding band structures of
the O-deficient (Bi0.5M0.5)TiO3dmaterials present a direct bandgap

for BLT_dand an indirect bandgap for BNTdand BKTd. In the

O-deficient BLTdcompound, the extremum of the valence band and

the conduction band shift from the

G

(0, 0, 0) to the Z (½, ½, ½)
point, and the direct bandgap is reduced to 0.50 eV. BNT_dand

BKT_d exhibit indirect bandgaps of 1.25 eV and 1.27 eV,

respectively.

Table 2

Calculated effective mass of electrons (m*e) and holes (m*h) for the corresponding

stoichiometric (Bi0.5M0.5)TiO3and O-deficient (Bi0.5M0.5)TiO3-d(M¼ Li, Na and K)
compounds obtained from parabolicfitting (Eq.(1)) to the VBM and CBM along the
selected directions at the extremum of VBM and CBM in the reciprocal space of the
corresponding (Bi0.5M0.5)TiO3and (Bi0.5M0.5)TiO3-dcompounds with m0as the

free-electron mass.

VBM Direction m*

h=m0 CBM Direction m*e=m0

BLT G(0, 0, 0) [111] 2.22 G(0, 0, 0) [111] 2.26

[010] 1.47 [010] 1.03

[110] 1.47 [110] 0.92

BNT G(0, 0, 0) [111] 2.54 G(0, 0, 0) [111] 1.69

[010] 0.74 [010] 0.67

[110] 1.08 [110] 0.51

BKT G(0, 0, 0) [111] 1.33 G(0, 0, 0) [111] 1.28

[010] 0.77 [010] 0.37

[110] 0.73 [110] 0.88

BLT-d Z (½, ½, ½) [111] 7.42 Z (½, ½, ½) [111] 5.79

[101] 1.92 [101] 1.88

BNT-d F (½, ½, 0) [110] 5.66 G(0, 0, 0) [111] 1.75

[010] 0.67

[110] 0.81

BKT-d Z (½, ½, ½) [111] 2.08 G(0, 0, 0) [111] 1.37

[101] 15.85 [010] 0.44

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The charge analysis inTable 3shows the charge redistribution of
the excess electrons related to the O-vacancy in the O-de_ficient
(Bi0.5M0.5)TiO3d compounds compared with the stoichiometric

(Bi0.5M0.5)TiO3. These excess electrons occupy the defect states near

the Fermi energy level in the original bandgap of the fully
oxygenated (Bi0.5M0.5)TiO3compounds, as illustrated inFig. 3. The

O anions do not exhibit a clear contribution to the charge
redis-tribution of the excess electrons in all the three compounds. In
BLT_d, excess electrons are mostly distributed in the Li cations due

to their high electron affinity. The gained charges in the Li cations of
BLT_dare delocalized in the wide bands of the s-orbitals of Li

cat-ions, particularly those in the nearest neighborhood to the
O-va-cancy. This situation broadens the distribution of the excess
electrons at the low energy range, reduces the defect states near the

Fermi level and pulls the electrons of the VBM and the CBM toward
the close neighborhood of the Fermi level. Besides, the broken local
symmetry at the O-vacancy's position makes the Ti cations, which
are nearest to the O-vacancy, gain a few charges. Despite of the
charge redistribution, the crystal structure of BLTdis observed only

with the modification of bond lengths, especially the bonds
be-tween Bi/Li cations and O anions. Accordingly, the O-deficient BLTd

compounds still exhibit a direct bandgap but the extremum bands
shift to the Z (½, ½, ½) point.

On the contrary, both of BNT_dand BKTdexpose the slight

tilting of the octahedral [TiO6], especially near to the position of the

O-vacancy; and that results in an indirect bandgap in these
com-pounds. The O-deficient BNTdcompound exhibits the

redistribu-tion of the excess electrons mostly in the Bi and Ti caredistribu-tions, which

Table 3

Charge gain/loss (±DQ ) in unit of (e) by Bi, M, Ti and O (M¼ Li, Na and K) in O-deficient (Bi0.5M0.5)TiO3-dcompounds as compared with the stoichiometric (Bi0.5M0.5)TiO3ones.

Plus/minus signs represent gained/lost charges.

DQBi1st DQBi2nd DQBi3rd DQM1st DQM2nd DQM3rd DQTi1st DQTi2nd DQTi3rd DQO

BLT-d 0.06 0.06 0.16 0.17 0.13 0.12 0.03 0.05 0.1 0.03

BNT-d 0.11 ~0.00 ~0.00 ~0.00 ~0.00 0.02 0.14 0.01 0.01 ~0.00

BKT-d 0.19 0.1 0.08 0.06 0.08 0.07 0.07 0.03 0.04 0.01

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are nearest to the O-vacancy, namely, in Bi1st and Ti1st. The Na

cations appear to stand apart from the redistribution of the excess
electrons without gaining/losing any charge. These excess electrons

occupy the defect states of the s-orbitals of Bi cations and the
d-orbitals of the Ti cations next to the Fermi level in the PDOS of
BNT_d(Fig. 3). The defect states exhibit a slight hybridization with

the p-orbitals of the O anions. Similar to BNT_d, BKTdalso

pre-dominantly shows the redistribution of the excess electrons in the
Bi and Ti cations, especially the Bi1stand Ti1st. However, the excess

charges in BKT_dare located not only in the Bi cation nearest to the

O-vacancy but also in other Bi cations, which are second and third
nearest to the O-vacancy, namely, Bi2ndand Bi3rd. The excess

elec-trons induce the defect states that primarily correspond to the
p-orbitals of the Bi cations in the PDOS of BKT_d. This condition also

reduces the charge gained by the Ti1stcation and results in small

defect states in the PDOS of the Ti cation in BKT_d. The clear defect

states induced by the O-vacancy in BNTdand BKTdcan act as an

electron or a hole trap that enhances the lifetime of the
photo-generated electronehole pairs.

In the radiative recombination process of the photogenerated
electrons and holes, the excited electrons degenerate from
con-duction to valence bands and release photons. In indirect bandgap
semiconductors, the excited electrons should satisfy the transition

selection rule of momentum conservation, which is presented in
the following formulas:

Eg Z

u

photon; (2)

Zk0_e Zke¼ ±Zqphonon; (3)

where k0_eand ke are the electron wave vectors at VBM and CBM,

respectively; and qphononis the wave vector of the assisted phonons.

For the direct bandgap, k0_e¼ keindicates that an electron emits only

one photon for the recombination of the photogenerated charge
carriers. However, the recombination of the photoexcited electrons
and holes in an indirect bandgap semiconductor requires the
assistance of phonons because k0_eskein such semiconductor. The

excited electrons will experience difficulty in directly recombining
with holes. This phenomenon is the reason why the lifetime of the
photogenerated electronehole pairs is increased in an indirect
bandgap semiconductor. Similar arguments can be applied to
explain why the indirect bandgap anatase exhibits better
photo-catalytic activity than the direct bandgap rutile[41,42]. This
con-dition clarifies the previous arguments of the role of defect states in
the O-deficient BNTdand BKTdas an electronehole trap to hinder

the direct recombination of photogenerated electronehole pairs.
The corresponding band structures of the BKT_dcompounds

pre-sent a“seem-to-be” flat band as a consequence of the d-states of K
cations, thereby indicating a high density of states immediately
below the Fermi level. This finding implies that the indirect
bandgap compounds BNT_dand BKTdmay exhibit better

photo-catalytic performance than the direct bandgap compound BLT_d

through the obvious appearance of defect states.

Table 2 illustrates that the O-vacancy strongly increases the
effective mass of holes compared with that in the stoichiometric
(Bi0.5M0.5)TiO3 compounds. For the O-deficient BLTdcompound,

we observe an enlargement of the effective mass of holes, m*_h, and
electrons, m*e; along the [111] direction at the VBM and CBM of Z (½,

½, ½), respectively. The heavier carriers correlate with a slower
transfer of carriers, and thus, can increase the probability of the
electronehole recombination. BLTd is unsuitable for

photo-catalytic activities despite the small bandgap. The O-deficient
BNT_d compound presents smaller values than the BLTd

com-pound for the effective masses of holes, m*_h, at the VBM of F (½, ½, 0)

and electrons, m*_e, at the CBM of

G

(0, 0, 0), thereby indicating a
higher carrier transfer rate. In particular, the effective masses of
electrons m*_ealong the [010] and [110] directions at

G

(0, 0, 0) are
smaller than those along the [111] direction. This variation indicates
that the transfer of excited electrons to the active sites is easier

along the [010] and [110] directions, thereby suggesting a higher
reduction activity. The O-deficient BKTd exhibits a similar

behavior to the case of BNT_d: the [010] direction with the smallest

effective mass of electrons m*_eis the most favorable channel for the
electron transfer. Therefore, similar predictions may be made for
the stoichiometric (Bi0.5M0.5)TiO3compounds. The {010} surface of

BNT_dand BKTdwill exhibit higher photocatalytic activities than

the other surfaces. As previously mentioned, the band structure of
BKT_dshows a“flat” band and that leads to relatively large values of

the effective masses of holes m*_h along the [101] direction at the
VBM of Z (½, ½, ½) and of electrons m*

ealong the [110] direction at

the CBM of

G

(0, 0, 0). This condition allows creating a carrier
transfer channel with a high density and a small transfer rate,
which becomes an efficient trap for the photon-generated holes
and electrons. Accordingly, the BKT_d compound can be more

efficient for photocatalytic reactions than BLTd and BNTd

although it exhibits the largest bandgap among the three
com-pounds. The BKT_dcompound is confirmed as a good candidate for

photocatalytic applications by the experiments of Bac et al.[33].

The carrier effective masses in these compounds can be
com-parable with those in the anatase/rutile TiO2 [41] and Ag3PO4

compound[38]: they are larger than those of anatase/rutile TiO2

but smaller than those of the Ag3PO4 compound. This finding

suggests that the O-deficient (Bi0.5M0.5)TiO3dcompounds can be

less photocatalytically active than anatase/rutile TiO2but possess a

stronger oxidation power as compared to the Ag3PO4compound.

This information attracts new attention to conduct further research
on the photocatalytic applications of the (Bi0.5M0.5)TiO3compounds

with (M¼ Li, Na, and K). Since the photocatalytic performance of a
catalyst depends on many practical conditions, a rigorous study of
the carrier mobility in these compounds is necessary to realize their
photocatalytic performance. The current study only provides
pre-liminary insights into the electronic structure and related
photo-catalytic performance of the (Bi0.5M0.5)TiO3system with (M¼ Li,

Na, and K).

4. Conclusion

We have studied the structural and electronic properties of
(Bi0.5M0.5)TiO3and (Bi0.5M0.5)TiO3d(M¼ Li, Na, and K) compounds

using DFT calculations. Wefind that the larger the ionic radius of
the substituent cations, the larger the bandgaps of the compounds.
The results show that the lithium-substituted bismuth titanate
perovskite compound exhibits the smallest bandgap among the
three studied compounds for both of stoichiometric and O-de
fi-cient materials. The occurrence of the O-vacancy has an influence
on the crystal structures of O-deficient (Bi0.5M0.5)TiO3d

com-pounds (M¼ Li, Na, and K), particularly the local symmetry
sur-rounding the O-vacancy. While BLT_d compound is observed

mostly with the modification of the bond lengths and no tilting of
the octahedral [TiO6], BNTdand BKTdcompounds expose the

tilting of octahedral [TiO6]. As a result, the O-vacancy transforms

the bandgap of the O-deficient (Bi0.5M0.5)TiO3d compounds

(M¼ Na, K) into indirect ones, except for BLTdthat still retains a

direct bandgap one. The presence of an O-vacancy not only breaks
the local symmetry of the crystal structure of the stoichiometric
(Bi0.5M0.5)TiO3compound, but also generates the excess electrons

in the corresponding O-deficient (Bi0.5M0.5)TiO3dcompound and

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electronic structure calculations imply that BLTdis unsuitable for

photocatalytic reactions although it presents the smallest bandgap
among the three compounds. Thisfinding is confirmed by the large

effective mass of the carriers, which corresponds to a slow transfer
rate. The effective mass analysis also suggests that the {010} surface
can exhibit higher photocatalytic activities than the other surfaces
in the stoichiometric and O-deficient BNT and BKT compounds.
Furthermore, the electronic structure and calculated effective mass
analyses yield the positive effect of the K cations on the
photo-catalytic performance in both the stoichiometric and O-deficient
compounds.

Acknowledgement

This research was funded by project T2017-TT-011 from the
Basic Research of Hanoi University of Science and Technology 2017.
Structurefigures were plotted using the VESTA package[43].

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