Analysis of the local structure around Cr3+ centers in perovskite KMgF3 using both ab initio (DFT) and semi-empirical (SPM) calculations

Abstract

The local structure around Cr3+ centers in perovskite KMgF3 crystal have been investigated through the applications of both an ab-initio, density functional theory (DFT), and a semi empirical, superposition model (SPM), analyses. A supercell approach is used for DFT calculations. All the tetragonal (Cr3+–VMg and Cr3+–Li+), trigonal (Cr3+–VK), and CrF5O cluster centers have been considered with various structural models based on the previously suggested experimental inferences. The significant structural changes around the Cr3+ centers induced by Mg2+ or K+ vacancies and the Li substitution at those vacancy sites have been determined and discussed by means of charge distribution. This study provides insight on both the roles of Mg2+ and K+ vacancies and Li+ ion in the local structural properties around Cr3+ centers in KMgF3.

Full text

Analysis of the local structure around Cr
3+
centers in perovskite KMgF
3
using both ab initio (DFT) and semi-empirical (SPM) calculations
Y. Emül
a
, D. Erbahar
b,c
, M. Açıkgöz
a,
⇑
a
Bahcesehir University, Faculty of Arts and Sciences, Besiktas Campus, 34349 Besiktas/Iıstanbul, Turkey
b
Department of Physics, Gebze Institute of Technology, 41400 Gebze, Kocaeli, Turkey
c
IMN, CNRS UMR6502, Universite de Nantes, 44300 Nantes, France
article info
Article history:
Received 18 August 2014
In final form 1 October 2014
Available online 13 October 2014
Keywords:
Ab-initio calculation
DFT
Cr
3+
SPM
KMgF
3
abstract
The local structure around Cr
3+
centers in perovskite KMgF
3
crystal have been investigated through the
applications of both an ab-initio, density functional theory (DFT), and a semi empirical, superposition
model (SPM), analyses. A supercell approach is used for DFT calculations. All the tetragonal (Cr
3+
–V
Mg
and Cr
3+
–Li
+
), trigonal (Cr
3+
–V
K
), and CrF
5
O cluster centers have been considered with various structural
models based on the previously suggested experimental inferences. The significant structural changes
around the Cr
3+
centers induced by Mg
2+
or K
+
vacancies and the Li substitution at those vacancy sites
have been determined and discussed by means of charge distribution. This study provides insight on both
the roles of Mg
2+
and K
+
vacancies and Li
+
ion in the local structural properties around Cr
3+
centers in
KMgF
3
.
Ó2014 Elsevier B.V. All rights reserved.
1. Introduction
Fluoroperovskite ABF
3
crystals have been investigated inten-
sively by both experimental and theoretical methods due to being
convenient hosts for rare-earth (RE) and transition metal (TM)
impurity ions. Most of these ABF
3
crystals have been studied in
terms of spectroscopic properties [1–5] and the presence of several
centers were reported especially in the structure of TM ion doped
ABF
3
crystals. EPR spectra were investigated in many studies for
the tetragonal centers [2,3,6,7] and the trigonal centers [3,5,8,9].
Also, charge compensation mechanism was studied [10]. Particu-
larly, a great interest has been devoted to Cr
3+
-doped ABF
3
crystals
for their applications to be tunable solid-state lasers [1].
As the results of EPR and ENDOR studies [6,7,11,12] performed
for different ABF
3
-type fluorine perovskite compounds, where A
and B are the monovalent and divalent cations, respectively, sev-
eral centers were reported for the transition metal ions Cr
3+
and
Fe
3+
. It is well known that Cr
3+
or Fe
3+
ions in the ABF
3
crystals
locate to the divalent cations B
2+
. However, this location requires
a charge compensation in the local structure since this substitu-
tional impurity creates an excess positive charge. This compensa-
tion can take place in several mechanisms, which can result in
different Cr
3+
centers with different symmetries; cubic, trigonal
or tetragonal symmetry.
(i) Cubic symmetry center
(ii) Tetragonal symmetry center
(1) CrF
5
O cluster (see Fig. 7 in Section 3.3).
(2) Cr
3+
–V
B
: associated with a cation vacancy at the nearest
divalent cation B
2+
site (see Fig. 4a in section 3.1)
(3) Cr
3+
–Li
+
: associated with a Li
+
ion located at the nearest
B
2+
site (see Fig. 4b in Section 3.1).
(iii) Trigonal symmetry center: associated with a nearest neigh-
bor cation vacancy (K
+
vacancy) along [111]-axis (trigonal
axis) (see Fig. 6a in Section 3.2).
Although several symmetry reductions around the Cr
3+
centers
have been reported for A
2
BF
4
-type fluorine crystals, such as ortho-
rhombic and monoclinic in K
2
ZnF
4
[13], there is no report for the
existence of such symmetry reduction in ABF
3
-type crystals. Fur-
thermore, structural changes around these centers can take place
in various cases inducing changes in the ligand bond lengths and
angular positions of the ligands (R
i
,h
i
,
u
i
) with respect to the sym-
metries of the Cr
3+
centers.
Three Cr
3+
centers were reported by Patel et.al. [3]. Two of them
as tetragonal and the other one as trigonal were assigned. It was
suggested in [3] that divalent cation vacancies in the presence of
O
2
ions instead of one of the axial F ions or with other impurities
on the tetragonal axis were considered for the tetragonal centers,
while K
+
vacancies were attributed to the trigonal Cr
3+
center. A
different tetragonal center was found experimentally [7] in
http://dx.doi.org/10.1016/j.chemphys.2014.10.003
0301-0104/Ó2014 Elsevier B.V. All rights reserved.
⇑
Corresponding author. Tel.: +90 212 3810307; fax: +90 212 3810300.
E-mail address: macikgoz@bahcesehir.edu.tr (M. Açıkgöz).
Chemical Physics 444 (2014) 52–60
Contents lists available at ScienceDirect
Chemical Physics
journal homepage: www.elsevier.com/locate/chemphys

KMgF
3
:Cr
3+
system with quite large axial zero-field splitting (ZFS)
parameter (ZFSP) D(2167 10
4
cm
1
). By calculating the EPR
parameters from crystal-field theory Zhou et al. characterized the
tetragonal centers for Cr
3+
–V
B
and Cr
3+
–Li
+
cases [14] and from
the high order perturbation formulas Zheng et.al studied the trigo-
nal centers for Cr
3+
–V
c
case [15] in Cr
3+
-doped fluoroperovskites
ABF
3
. The local structure of the trigonal Cr
3+
center in KMgF
3
was
previously studied by Zheng using Macfarlane’s high order pertur-
bation formulas [16]. Also, the spin-Hamiltonian parameters and
the local structure around the CrF
5
O
4
cluster center were theoret-
ically investigated by Yang [17] using complete diagonalization
method (CDM) and the microscopic spin Hamiltonian theory calcu-
lations for Cr
3+
doped KMgF
3
crystal.In general ABF
3
crystals pos-
sess two different cation sites to be principally introduced by a
cation transition metal or rare-earth impurities: A
+
with coordina-
tion number 12 and B
2+
with coordination number 6. The detailed
crystallographic data about KMgF
3
were given in [18]. The lattice
parameter aof pure KMgF
3
at room temperature is 0.3973 nm.
The ABF
3
crystals have cubic space symmetry O
1
h
(Pm3m) (No.
221). The atomic coordinates of the atoms in KMgF
3
crystal are:
K(0, 0, 0); Mg(0.5, 0.5, 0.5), and F(0, 0, 0.5) with site symmetries
O
h
,O
h
, and D
4h
, respectively. The ligand bond lengths and angular
positions of F
-
ligands (R
i
,h
i
,
u
i
) in the [M–F
6
]
x
cluster for Mg sites
in KMgF
3
are: (0.2029 nm, 90°,0°), (0.2029 nm, 180°,0°) for the
axial ligands and (0.2029 nm, 90°,90°), (0.2029 nm, 90°, 180°),
(0.2029 nm, 90°, 270°), (0.2029 nm, 90°,0°) for the equatorial
ligands. Also, another ligand bond length (0.1993 nm) was sug-
gested by [19]. The supercell of 135 ions of KMgF
3
used in our
DFT calculations is depicted in Fig. 1 at room temperature.
In spite of the fact that several investigations were devoted to
understand the influence of a transition metal ion on the structure
of KMgF
3
crystal, a comprehensive study is still required to have
fulfilling knowledge of substitution mechanism for all reported
Cr
3+
centers in KMgF
3
. In this study, we have investigated the local
structure around all the potentially possible Cr
3+
centers by DFT
calculations. Obtaining the structural parameters from DFT, we
use superposition model (SPM) to calculate the ZFSPs for the Cr
3+
centers. The importance of this study arises from this combination
of DFT and SPM calculations, to best our knowledge, as the first
study in literature, to determine local structural picture around
TM ion centers. We have considered all the possible cases, which
are mentioned in literature, for the role of the Cr
3+
ions in the
structure of Cr
3+
doped KMgF
3
crystal.
The organization of this paper is as follows. A brief description
of our computational method and calculation details are presented
in Section 2.1. The details of the SPM analysis are outlined in Sec-
tion 2.2. The results and the discussion of our results are presented
on Section 3beginning by tetragonal Cr
+3
center in Section 3.1 fol-
lowed by trigonal Cr
+3
centers in Section 3.2 and the CrF
5
O
4-
center
in Section 3.3. Some concluding remarks are given in Section 4.
2. Theoretical remarks
2.1. DFT
Computational details: our geometry optimization and total
energy calculations are based on the density functional theory
[20,21] within the generalized gradient approximation (GGA), as
implemented in the SIESTA [22,23] code. We used the Perdew–
Burke–Ernzerhof parametrization for the exchange–correlation
functional and a double-fbasis set augmented by polarization
orbitals. The interaction between the core and valence electrons
is handled by Troullier–Martins norm-conserving pseudopoten-
tials [24] in their fully separable form [25].
Previously, the structure around similar types of impurity cen-
ters have been investigated by DFT using a cluster of atoms around
the impurity centers [26]. That method would of course constrain
the atoms on the outer surfaces of the cluster to ideal lattice posi-
tions and introduce point charge centers to necessary places out-
side the cluster to simulate the effect of the rest of the lattice
[27]. However, we find it more appropriate to do our calculations
in the frame of supercell approach since we think that this would
not only include the electron correlation from the rest of the struc-
ture but also take into account the exchange energy in a more real-
istic manner. Thus, in our calculations we use a 3 33 supercell
constructed from the conventional KMgF
3
cubic unit cell for mod-
eling the isolated defect and substitution centers which have more
than 12 Å distance in between in the periodic structure.
We used a 8 k-point sampling which converges to less than
0.01 meV in the described cell. Charge density and potentials were
determined on a real-space mesh that corresponds to the plane
wave cutoff energy of 200 Ry. Experimental lattice constants were
used for calculating the structures to achieve comparable results to
experimental ZFSP values. Optimized geometries were obtained in
a conjugate-gradient algorithm until all force components on each
atom were less than 0.001 eV/Ang. All the structure optimizations
were initiated by small perturbations to break the symmetry dur-
ing the relaxation processes to avoid possible local minima on the
energy surfaces. To calculate the different contributions of differ-
ent structural distortions on ZFSPs, certain constraints on the posi-
tion of atoms were imposed to calculate the corresponding
structural and energetic changes. Those constraints are explained
in detail in the Section 3. The amount of charge residing on differ-
ent atomic orbitals was calculated by a Mulliken population
analysis.
2.2. SPM analysis
It is known that the cubic symmetry around the substitutional
Mg
2+
sites of the undoped KMgF
3
crystal lowers to tetragonal or
trigonal symmetry by means of a tetragonal or trigonal distortion,
respectively. The ZFS can be analyzed with only ZFSP b
0
2
¼Dfor
these two symmetries of Cr
3+
ions (3d
3
), even though different
symmetry cases (tetragonal I (D
4
,C
4v
,D
2d
,D
4h
), tetragonal II (C
4
,
S4, C
4h
), trigonal I (D
3
,C
3v
,D
3d
), and trigonal II (C
3
,C
3i
)) can be
possible.
Fig. 1. Supercell of 135 atoms used in DFT calculations in Cr
3+
doped KMgF
3
.
Y. Emül et al. / Chemical Physics 444 (2014) 52–60 53

The energy levels of the ground spin state of transition metal
Cr
3+
ions doped in ABF
3
type crystals can be described by the spin
Hamiltonian (SH) including the Zeeman electronic terms and the
ZFS terms [27–29]:
H¼g
jj
bB
z
S
z
þg
?
bðB
x
S
x
þB
y
S
y
ÞþDS
2
z
1
3SðSþ1Þ

ð1Þ
where bis Bohr magneton, B– the applied magnetic field, g– the
spectroscopic splitting factor, S– the effective spin operator. The
ZFSP Din Eq. (1) can be predicted using superposition model
(SPM) [30–33]. The explicit SPM expressions of the ZFSP Dhave
been derived by following the general definitions for the SPM quan-
tities outlined recently in [34,35] for a sixfold coordinated Cr
3+
cen-
ter with tetragonal symmetry in KMgF
3
[34–36]:
D¼b
0
2
¼

b
F
2
2
R
0
R
ax

t
F
2
X
2
i¼1
ð3 cos
2
h
i
1Þþ R
0
R
eq

t
F
2
X
6
i¼3
ð3 cos
2
h
i
1Þ
"#
ð2Þ
as follows for a Cr
3+
center with trigonal symmetry:
D¼b
0
2
¼3
b
F
2
2
R
0
R
1

t
F
2
ð3 cos
2
h
1
1Þþ R
0
R
2

t
F
2
ð3 cos
2
h
2
1Þ
"#
ð3Þ
and for a CrF
5
O cluster center with tetragonal symmetry:
D¼b
0
2
¼

b
O
2
2
R
0
R
ax

t
O
2
ð3 cos
2
h
O
1Þ
þ

b
F
2
2
R
0
R
ax

t
F
2
ð3 cos
2
h
F
1Þþ R
0
R
eq

t
F
2
X
4
i¼1
ð3 cos
2
h
i
1Þ
"#
ð4Þ
where R
0
is the reference distance. (R
i
,h
i
,
u
i
) are the coordinates for
the ligand i.
b
O
2
and 
b
F
2
are the intrinsic parameters and t
O
2
and t
F
2
are
adjustable power-law exponents for O and F ligands, respectively.
These parameters, utilized as adjustable parameters in SPM calcula-
tions, and R
0
can be grouped as SPM model parameters to calculate
ZFSPs [37].
Previously, we obtained superposition model (SPM) parameters
consisting of intrinsic parameters (IPs) b
2
ðR
0
Þand t
2
and the refer-
ence distance R
0
for Cr
3+
ions in fluorine ligand systems (Cr–F com-
bination) by combining the EPR data and the crystallographic data
of Cr
3+
ions in several crystals [38]. The values of the SPM param-
eters obtained in [38] are: b
2
ðR
0
Þ= (46,770 ± 800) 10
4
cm
1
and
t
2
=0.24 ± 0.03 with R
0
= 0.2113 nm. These SPM parameters have
been adopted for the all central cases. In the calculations, we have
also adopted R
0
= 0.1993 nm [19], which is the ligand distances of
the F

ions to the central Mg
2+
ion in the cubic symmetry.
3. Results and discussion
As mentioned before, for the role of Cr
3+
ions in KMgF
3
, several
structural mechanisms were suggested as results of experimental
findings. Two of them are related with the tetragonal centers,
which have a potential to appear in the form of Cr
3+
–V
B
,Cr
3+
–Li
+
,
or CrF
5
O cluster. On the other hand, the other mechanism can be
attributed to a trigonal center with a K
+
vacancy along [111]-axis.
Using EPR as an experimental technique or SPM as an theoretical
calculation method, we cannot identify the presence and occur-
rence of such cation vacancies. For this purpose, ab initio methods,
such as the density functional theory (DFT) to see the mechanism
related with any vacancy for the charge compensation, are
required. After getting the structural properties around the Cr
3+
centers in terms of the structural parameters Rand hfrom DFT
calculations, we have used them in SPM calculations as input
parameters to obtain the ZFSPs for each case. Our results are pre-
sented in the following sections.
3.1. Tetragonal Cr
3+
centers
In the frame of tetragonal symmetry, two tetragonal Cr
3+
cen-
ters are created in the structure of Cr
3+
doped KMgF
3
;Cr
3+
–V
B
cen-
ter with an Mg vacancy and Cr
3+
–Li
+
center with Mg–Li
substitution at the nearest Mg
2+
site, by supplying the required
charge compensation. These centers are based on the tetragonal
distortions characterized by the displacement of the F ligands,
which can be associated with different contributions from several
structural changes. Thus, we have carried out the calculations for
both DFT and SPM by following five steps: Step-I: One of the axial
F, F
1
ax
, (nearer to Mg vacancy) is free to move; Step-II: The other
axial F, F
2
ax
, is free to move; Step-III: Only equatorial F ligands,
F
eq
, are free to move; Step-IV: All ions including central Cr ion
are free to move; Step V: Cr ion is frozen but all F ligands are free
to move. The results of DFT calculations are put together in Table 1.
It is seen from Table 1 that for the cases including the displace-
ment of axial F ligands along C
4
axis ligand distances of the axial F
ions get smaller, i.e. they move towards the central Cr
3+
ion. As
expected, the displacement of the axial F nearer to Mg vacancy is
more than that of the other axial F due to the decrease in the elec-
trostatic attraction between the F ligand and Mg vacancy or Li
+
ion
in the Mg
2+
site. Our calculated energies of the constrained struc-
ture and their comparison with the relaxed structure energy sug-
gest that the biggest contribution to relaxation energy comes
from the relaxation of Cr atom in the impurity. Also, as another
expected result, the displacements of the ligands in Mg vacancy
case are larger than those in Mg–Li substitution case, which is
accordance with the role of the effective charges in electrostatic
interaction. These obtained values of the ligand distances yield
quite large distortions for F
1
ax
ligand (e.g. around 8.5% for Cr
3+
–V
B
and 5.6% for Cr
3+
–Li
+
in Step-IV), whereas a more smaller distortion
Table 1
The results of DFT calculations for the tetragonal Cr
3+
centers in the presence of Mg
vacancy case and Li substitution into Mg vacancy case. Energy values are given with
respect to the most stable structure, which is of course the unconstrained structure.
The Mulliken charge distributions on different molecular orbitals of Cr and F ligands
in units of electron charge are also given for all steps. Calculated values of the
distances (R) are given in nm and the angles in degree. R
i
and h
i
values are the polar
coordinates of the ligands with respect to central Cr
3+
ion.
Parameters Step-I Step-II Step-III Step-IV Step-V
Mg vacancy case
Energies (eV) +1.9851 +2.5701 +1.9457 0.0 +1.1839
4s (Cr) tot. e 0.294 0.293 0.311 0.324 0.321
3d (Cr) tot. e 4.120 4.104 4.140 4.086 4.150
2p (F
1
ax
)5.487 5.521 5.532 5.507 5.509
2p (F
2
ax
)5.736 5.690 5.739 5.657 5.726
2p (F
eq
) 5.715 5.717 5.693 5.646 5.694
F
eq
-z-axis angel 89.9997 89.9997 89.9997 90.0000 89.9997
F
1
ax
-Cr dist. 0.180109 0.212408 0.212408 0.180960 0.180948
F
2
ax
-Cr dist. 0.212408 0.192749 0.212408 0.192256 0.201741
F
eq
-Cr dist. 0.212409 0.212409 0.193346 0.192176 0.193757
Mg–Li substitution case
Energies (eV) +1.5134 +1.8835 +1.2147 0.0 +0.6002
4s (Cr) tot. e 0.296 0.294 0.312 0.308 0.323
3d (Cr) tot. e 4.114 4.104 4.126 4.139 4.154
2p (F
1
ax
)5.559 5.629 5.622 5.620 5.587
2p (F
2
ax
)5.733 5.682 5.729 5.705 5.709
2p (F
eq
) 5.716 5.719 5.687 5.684 5.697
F
eq
-z-axis angel 89.9997 89.9997 89.9997 89.9999 89.9997
F
1
ax
-Cr dist. 0.181475 0.212408 0.212408 0.186862 0.183644
F
2
ax
-Cr dist. 0.212408 0.192111 0.212408 0.197787 0.194601
F
eq
-Cr dist. 0.212409 0.212409 0.192908 0.193662 0.193926
54 Y. Emül et al. / Chemical Physics 444 (2014) 52–60

(e.g. less than 5.8% for Cr
3+
–V
B
and just 0.11% for Cr
3+
–Li
+
in Step-
IV) for F
2
ax
. Also, we need to consider the effect of the ionic radii of
the ions in the structure for these tetragonal centers, so a relation
to understand the strength of the tetragonal distortion can be
obtained between the size of Li
+
ion (0.068 nm [39]) in Mg–Li
center and that of the replaced Mg
2+
ion (0.066 nm [39]), by
comparing the value of the distortion for Mg vacancy and Mg–Li
substitution case. Thus, the distortion along the ligand distances
in Mg-vacancy case is expected to be smaller than that in Mg–Li
case. Applying Macfarlane’s perturbation method, Zhou et.al
calculated the distortions
D
R = 0.0107 nm for Cr
3+
–V
B
and
0.0099 nm for Cr
3+
-Li
+
center [14]. For all ligands, this makes R
become 0.2087 nm for Cr
3+
-V
B
and 0.2079 nm for Cr
3+
-Li
+
case with
respect to R
0
= 0.1980 nm. These are comparable distortion values
with respect to those determined here by DFT but with an elonga-
tion character.
In order to calculate the ZFSP Dfor each center, we apply SPM
using the structural parameters obtained from DFT calculations.
The results are given in Table 2 for the tetragonal Cr
3+
centers using
several SPM parameter sets. The experimental ZFSPs in [10
4
cm
1
]
were obtained at room temperature as follows: D=b
0
2
= –683 for
the Mg vacancy case and D=b
0
2
=627 for Mg–Li substitution case
[7]. As can be seen in this Table, using the SPM parameters as in the
ranges given in [38], we can get the experimental ZFSP Din Step-IV
for Mg vacancy case and Step-V for the Mg–Li substitution case.
Thus, it indicates that Step-IV and Step-V are the most probable
structural models for these cases. However, when we consider the
minimum energy argument in DFT calculations we see that
Step-IV is the most likely model for both Mg vacancy case and
Mg–Li substitution case.The dependencies of ZFSP Don the intrinsic
parameters (t
2
and 
b
2
) in the ranges given in [38] are presented in
Figs. 2 and 3 for both Mg Vacancy case and Mg–Li substitution case
to see the trends of ZFSP Dfor all 5 steps followed in SPM calcula-
tions. Experimental values are also indicated in the figures as hori-
zontal lines. Fig. 2 shows that the Dchanges with t
2
linearly for all
steps and for both structural cases, while Dis almost insensible to

b
2
(Fig. 3). It is also clearly seen from both figures that, in accor-
dance with the experimental values, the most probable steps are
Step-IV and Step-V for Mg Vacancy case and Mg–Li substitution
case, respectively. The configurations of the atoms around Cr
3+
cen-
ters in these steps are depicted in Fig. 4 for the two tetragonal cases
to visualize them better.
3.2. Trigonal Cr
3+
centers
The structural mechanisms to have charge compensation for
the trigonal Cr
3+
center in KMgF
3
crystal can be associated with a
cation (K) vacancy along the trigonal axis [1 1 1]. Typically, dis-
placements of the neighboring F- ligands away from the vacancy
center can be expected due to the increase in the negativity of
the effective charge for this vacancy center. In spite of the fact that
the charge compensation is not possible and there is no info in lit-
erature, we have also considered a K–Li substitution case for the
trigonal Cr
3+
center. If there are Li
+
ions in the structure of KMgF
3
,
thus it is reasonable to consider the possibility for the Li substitu-
tion for K vacancy site. For the trigonal Cr
3+
centers we have carried
out both the DFT and SPM calculations based on the following
three steps: Step-I: only Cr is free to move; Step-II: all ions are free
to move; Step-III: Cr is frozen, the rest are free to move. The results
of DFT calculations are tabulated in Table 3.
From Table 3, it is clear that K-vacancy and K–Li substitution
cases reveals different structural characteristics, i.e. though yield-
ing very similar direction angles (K–Cr–F
2
and K–Cr–F
1
angles in
Table 3) for the upper F
1
(nearer to K vacancy) and the lower F
2
ligands in Step-II and Step-III, quite different ligand distances in
all three steps with respect to R
0
= 0.1993 nm [19] and
h
0
= 54.7356 degree. Taking into account the electrostatic interac-
tions between the K-vacancy and F ligands it is expected that the
F
1
ligands should move away from K-vacancy by displacing away
from [111]-axis resulting a shorter ligand distance for F
1
and
Table 2
Calculated values of the ZFSP D(in 10
4
cm
1
) for the tetragonal Cr
3+
centers in the
presence of Mg vacancy case and Li substitution into Mg vacancy case. The values best
matched with the experimental Dare given in bold.
SPM parameters Step-I Step-II Step-
III
Step-IV Step-V
Mg vacancy case
t
2
=0.24; R
0
= 0.2113 nm 1817.7 1079.0 2089.9 650.5 299.7
t
2
=0.27; R
0
= 0.2113 nm 2040.2 1212.3 2348.2 729.1 335.1
t
2
=0.21; R
0
= 0.2113 nm 1594.2 945.4 1830.9 571.3 263.8
t
2
=0.2525;
R
0
= 0.2113 nm
1910.6 1134.6 2197.6 683.3
*
314.5
t
2
=0.24; R
0
= 0.1993 nm 1843.4 1094.3 2119.4 659.7 303.9
Mg–Li substitution case
t
2
=0.24; R
0
= 0.2113 nm 1736.0 1115.4 2139.7 159.0 556.9
t
2
=0.27; R
0
= 0.2113 nm 1948.7 1253.1 2404.1 178.1 624.4
t
2
=0.21; R
0
= 0.2113 nm 1522.3 977.3 1874.6 139.7 489.0
t
2
=0.2712;
R
0
= 0.2113 nm
1958.7 1259.6 2416.4 178.9 627.1
⁄
t
2
=0.24; R
0
= 0.1993 nm 1760.5 1131.2 2169.9 161.2 564.8
*
Giving the best results.
-0,27 -0,26 -0,25 -0,24 -0,23 -0,22 -0,21
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
ZFSP D (x10
-4
cm
-1
)
t
2
Step-I
Step-II
Step-III
Step-IV
Step-V
Mg Vacancy case
(a)
Expt. D
-0,27 -0,26 -0,25 -0,24 -0,23 -0,22 -0,21
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Expt. D
(b)
ZFSP D (x10
-4
cm
-1
)
t
2
Step-I
Step-II
Step-III
Step-IV
Step-V
Mg - Li substitution case
Fig. 2. Dependence of the ZFSP Don the intrinsic parameters t
2
in Eqs. (2)–(4) for
(a) Mg vacancy case and (b) Mg–Li substitution case in Cr
3+
doped KMgF
3
.
Y. Emül et al. / Chemical Physics 444 (2014) 52–60 55

larger angle than h
0
since the negativity of the effective charge of
K-vacancy increases, which is consistent with the results of our
DFT calculations as seen in Table III. On the other hand, for the
K–Li substitution case, with no change in the negativity of the
effective charge for this K cation site, it is also reasonable to
see an increase in both ligand distances F
1
and F
2
due to the quite
difference in the ionic radii of K
+
(0.133 nm) and Li
+
(0.068 nm).
Next, using these structural parameters obtained from DFT, we
have carried out SPM calculations for both cases. The results of
the calculated ZFSP Dare presented in Table 4. As can be seen in
this table, the obtained Dvalues are different from the experimen-
tal D(D
exp
) value, which is smaller by about 30% than D
exp
even for
the K-vacancycase. We have only one D
exp
(1528(4) 10
4
cm
1
)
value for the trigonal Cr
3+
center at room temperature, as a result
of EPR investigations [3]. It is seen in SPM calculations that the
small changes in K–Cr–F
2
and K–Cr–F
1
angles affect much more
the values of D. For K-vacancy case in both Step-II and Step-III, it
is possible to get D
exp
with very small angular changes. For exam-
ple, only increasing the angles by 0.08°(less than 0.15%) becomes
sufficient to get D
exp
in Step-II. It should be noted that the results of
perturbation calculations [15] for the local distortion parameters
around the trigonal Cr
3+
center yielded very large distortions,
namely R
1
= 0.194082 nm, R
2
= 0.205092 nm, h
1
= 57.4935, and
h
2
= 52.5452 degree, which correspond to
D
R
1
=0.005218 nm,
D
R
2
= 0.005792 nm,
D
h
1
=2.1904, and
D
h
2
= 2.7579 degree. We
can also see from Table 4 that the intrinsic parameter t
2
has almost
no effect on Dand using a different reference distance R
0
(0.1993 nm) does not affect D values much, only a 1% change.
Furthermore, from the results of SPM calculations, we can clearly
see that K–Li substitution case, for which no charge compensation
occurs, is not reasonable for the trigonal Cr
3+
center in KMgF
3
.It
appears from SPM that both Step-II (with an off-center displace-
ment for Cr
3+
) and Step-III yield rather similar and reasonable
results, while DFT results reveal that Step-II is more plausible
due to having minimum energy state.
Moreover, the dependencies of ZFSP Don the distortion param-
eters
D
hare presented in Fig. 5 for both trigonal Cr
3+
center cases.
As seen the change in
D
hhas a clear linear effect on D. The config-
urations of the atoms around Cr
3+
centers in these steps are shown
in Fig. 6 for both trigonal cases. This figure depicts the optimized
structure around trigonal Cr
3+
central cases, which obtained from
DFT calculations.
3.3. The Cr
3+
–O
2-
pair in KMgF
3
The presence of the CrF
5
O
4-
center, known as tetragonal charge
compensation CrF
5
O defect center, was suggested [7] experimen-
tally and then investigated by employing some semi-empirical
[17] calculations. This center is based on the replacement of an
O
2
ion instead of one of the axial F
-
ions. In this case, there is
no need to consider any vacancy since the presence of impurity
O
2
ion for the axial F- provides the charge compensation along
[001]-direction. Our calculations have been carried out based on
the following modeling steps for both DFT and SPM calculations:
Step-I: One axial ligand is replaced by O, all the ligands are frozen;
Step-II: Only O is allowed to move, the rest are frozen; Step-III:
Second axial F ligand is also allowed to move; Step-IV: Equatorial
ligands are also allowed to move; Step-V: Cr is also allowed to
move i.e. an off-center displacement for Cr is possible; Step-VI:
All ions in the supercell are free to move. The results of the DFT cal-
culations are tabulated in Table 5 for all steps. As expected, the
results yield that the O
2
ion move towards the central Cr
3+
ion
due to the increase in electrostatic attraction. The last two steps,
Fig. 4. Optimized structure around Cr
3+
ion in KMgF
3
crystal for (a) the Mg vacancy
case and (b) the Mg–Li substitution case.
4,60 4,62 4,64 4,66 4,68 4,70 4,72 4,74 4,76
-2000
-1600
-1200
-800
-400
0
400
800
1200
1600
2000
Expt. D
(a)
Mg Vacancy case
ZFSP D (x10
-4
cm
-1
)
b
2
(cm
-1
)
Step-I
Step-II
Step-III
Step-IV
Step-V
4,60 4,62 4,64 4,66 4,68 4,70 4,72 4,74 4,76
-2000
-1600
-1200
-800
-400
0
400
800
1200
1600
2000
Expt. D
(b)
Mg - Li substitution case
b
2
(cm
-1
)
ZFSP D (x10
-4
cm
-1
)
Step-I
Step-II
Step-III
Step-IV
Step-V
Fig. 3. Dependence of the ZFSP Don the intrinsic parameters 
b
2
in Eqs. (2)–(4) for
(a) Mg vacancy case and (b) Mg–Li substitution case in Cr
3+
doped KMgF
3
.
56 Y. Emül et al. / Chemical Physics 444 (2014) 52–60

Step-V and Step VI, consist of the displacement of the central Cr
3+
ion as well. Since the reduction in O–Cr distance in these steps are
more than those in other steps Cr
3+
also move towards to O
2-
ion
along [001]||z-axis, thus the angle of equatorial F ligands, F
eq
-z-
axis angel, are found to be greater than 90°. Namely, our DFT cal-
culations yield
D
R(O
2
) between 0.02785 nm (min.) and
0.031533 nm (max.) for the steps IV and V, while they yield
D
R
ðF

eq
Þaround 0.009 nm for the steps IV, V and VI. It is clearly seen
that the distortion of the F
eq
ligands are much higher than that
of F
ax
ligand. Also, an inward relaxation of F
eq
ligands is another
common point for all steps.
Using these results of DFT calculations for the structural param-
eters in SPM calculations, we obtained the ZFSPs for each step. The
results are given in Table 6 for different combinations of t
2
and R
0
values. As can be seen in this table, the results of Step III are very
consistent with the experimental ZFSPs, 2167 10
4
cm
1
[3,7]
and 2400 10
4
cm
1
[5]. Thus, the structural model in Step III
can be ascribed for this center, where the axial ligands move only,
i.e. the equatorial F ligands are frozen. Yang [17] suggested a struc-
tural model with the displacements of all ligands for the CrF
5
O
4
center in terms of the change in O ligand length
D
R
1
and other F
ligand lengths
D
R
2
. This model corresponds to our Step-V. How-
ever, the calculated ZFSPs for this step are quite different in both
magnitude and sign than the D
exp
.
The distortion parameters assigned for the displacements for the
equatorial and axial ligands were found in [17] as:
D
R(O
2
)=
0.172R
0
=0.0342 nm and
D
R(F

)=0.022R
0
=0.0044 nm,
for which it was assumed that
D
RðF

ax
Þ=
D
RðF

eq
Þ. DFT calculations
for Step-III yield
D
R(O
2
)=0.01586 nm,
D
RðF

ax
Þ= 0.005811 nm,
and
D
RðF

eq
Þ= 0.01442 nm. As seen, the results in [17] are quite dif-
ferent from those of DFT. It can be easily expected that the distor-
tion
D
RðF

ax
Þshould be different than
D
RðF

eq
Þdue to the role of
O ligand along the axial direction. We believe that taking
D
R
ðF

ax
Þ=
D
RðF

eq
Þresults in this difference. It should also be noted that
the obtained probable model structure (Step-III) reveals that there
is no off-center displacement of the central Cr
3+
ion in this case. The
atomic configurations of the optimized structure around this center
for Step-III in the calculations are depicted in Fig. 7.
This situation is consistent with the argument [14,40] that the
dopant ion is located at an on-center site when the dopant ion
(Cr
3+
(0.063 nm [39])) is comparable or larger in size than the
replaced host ion (Mg
2+
ion (0.066 nm [39])). This is not the case
for the other tetragonal and trigonal centers. In order to have a bet-
ter insight about the displacement of the central Cr
3+
ion, we have
also determined the Cartesian coordinates and the displacement of
the central Cr
3+
ion for the steps where Cr
3+
is allowed to move,
which are gathered in Table 7 with the initial and final coordinates.
As can be seen in this table, the presence of the Mg
2+
or K
+
vacan-
cies forces a displacement of Cr
3+
less than the Li
+
substitution on
those vacancies. The most profound displacement appears for the
Step-V in CrF
5
O center, which corresponds to almost 7% decrement
on the O
ax
–Cr distance and yields a 4.3 degree change F
eq
-z-axis
angle. Furthermore, for the Step-IV in tetragonal Mg-vacancy case,
Table 4
Calculated values of the ZFSP D(in 10
4
cm
1
) for the trigonal Cr
3+
centers in the presence of K vacancy case and Li substitution into K vacancy case.
SPM parameters K-vacancy K–Li substitution
Step-I Step-II Step-III Step-I Step-II Step-III
t
2
=0.24; R
0
= 0.2113 nm 177.5 930.3 952.4 1.29 530.8 499.6
t
2
=0.24; R
0
= 0.2113 nm 1528.0
*
1528.4
*
t
2
=0.27; R
0
= 0.2113 nm 156.6 926.2 949.8 1.22 528.5 499.6
t
2
=0.21; R
0
= 0.2113 nm 198.4 934.5 955.1 1.36 533.0 499.5
t
2
=0.24; R
0
= 0.1993 nm 180.0 943.5 965.9 1.31 538.3 506.6
*
It is obtained by matching with the experimental D
exp
=1528 10
4
cm
1
, which corresponds K–Cr–F
1
angle = 55.8788°and K–Cr–F
2
angle = 54.0504°for Step-II
whereas 55.1374°and 54.7855°for Step-III.
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3
-3000
-2000
-1000
0
1000
2000
Expt. D
ZFSP D (10
-4
cm
-1
)
Δθ (
degree
)
K-Li substitution_step-I
K-Li substitution_step-II
K-Li substitution_step-III
K-vacancy_step-I
K-vacancy_step-II
K-vacancy_step-III
Fig. 5. Variation of the ZFSP Dwith the angular distortions (
D
h) for trigonal Cr
3+
centers in the Cr
3+
doped KMgF
3
crystal.
Table 3
The results of DFT calculations for the trigonal Cr
3+
centers in the presence of K vacancy case and Li substitution into K vacancy case. The Mulliken
charge distribution (electron units) of Cr and F ligands are also given for all steps.
Parameters K-vacancy K–Li substitution
Step-I Step-II Step-III Step-I Step-II Step-III
Energies (eV) +1.9065 0.0 +0.0095 +0.1053 0.0 +0.0107
4s (Cr) tot. e 0.266 0.267 0.267 0.233 0.238 0.238
3d (Cr) tot. e 4.059 4.123 4.123 4.359 4.360 4.360
2p (F
1
) 5.718 5.688 5.686 5.760 5.772 5.770
2p (F
2
) 5.669 5.671 5.670 5.773 5.777 5.777
K–Cr–F
1
angle 57.6975 55.7940 55.0531 54.9027 55.8373 54.8967
K–Cr–F
2
angle 51.9752 53.9663 54.6999 54.5694 53.8052 54.7188
F
1
–Cr dist. 0.205185 0.191582 0.192865 0.211973 0.210157 0.212142
F
2
–Cr dist. 0.220161 0.195065 0.193752 0.212846 0.214770 0.212626
Y. Emül et al. / Chemical Physics 444 (2014) 52–60 57

a substantially small displacement is encountered away from the
vacancy.
We have also performed the DFT calculations for the MgF
6
octahedral before and after the Cr
3+
ion substitution for Mg
2+
site.
R
0
, initial Mg–F distance for the pure KMgF
3
, has been obtained by
performing the geometry optimizations in DFT calculations to be
0.2030 nm for the all ligands, which indicates the cubic site sym-
metry around Mg
2+
ion. For this, we optimized the positions of all
the ions in the 135-ion supercell. R
0
was previously calculated for
21-ions cluster to be 0.2011 nm and using 87-ions cluster to be
0.1987 nm [26] using the same exchange correlation function
GGA-BP86 (Becke–Perdew) [41,42]. It should be noted that the
calculations were carried out in [41,42] by optimizing the central
Mg
2+
ion and those of nearest neighbors F

ions (six ligands for
MgF
6
octahedral) as well as those of nearest neighbor Mg
2+
and
K
+
ions, i.e. the other ions in the so-called clusters are kept frozen.
The experimental R
0
was reported 0.1987 nm for the pure KMgF
3
[43]. On the other hand, the distances for the Mg
2+
–Mg
2+
and
Mg
2+
–K
+
are found to be 0.4060 nm and 0.3516 nm, respectively,
before the Cr
3+
substitution, whereas those are found 0.3522 nm
and 0.4096 nm after the Cr
3+
substitution. The change of the
above mentioned distances, corresponding to the distortions
D
Rs, due to the Cr
3+
substitution for Mg
2+
have been calculated
as follows:
D
R(F) = 0.00942 nm;
D
R(Mg) = 0.00360 nm;
D
R
(K) = 0.00060 nm. These results indicate that outward relaxations
undergo for all neighboring ions around Mg
2+
site after the Cr
3+
substitution.
In addition to the Mulliken charges on the s, p, and d orbitals for
Cr
3+
and the six F ligands in Tables 1, 3 and 5, we have also calcu-
lated the total Mulliken charge distribution (electron units) of
Cr
3+
and the F-ligands for each center and every step so as to see
the effect of structural changes on charge distributions. The results
are tabulated in Table 8 for the steps with minimum energy states
in each center. For comparison, the total charges of Cr
3+
,F
ax
and F
eq
of the relaxed Cr doped KMgF
3
supercell, i.e. when no distortion is
considered has been given in column-A of Table 8. Total charges
for the steps with minimum energy states in Mg-vacancy and
Mg–Li substitution of the tetragonal symmetry (see Table 5 and
Fig. 4) cases are given in column-B and -C, respectively. The charges
of Cr
3+
,F
1
ax
,F
2
ax
and the F
eq
ligands for Mg vacancy (Mg–Li substitu-
tion) decreases 4.1% (3.6%), 3.3% (1.9%), 1.5% (0.9%) and 1.5% (1.0%),
respectively. Note that F
1
ax
is the F-ligand closest to the Mg-vacancy
(Mg–Li substitution) on the axial axis (see 4). Total charges for the
steps with minimum energy states K–Li substitution and K-vacancy
of the trigonal symmetry (see Table 3 and Fig. 6) cases are given in
column-D and -E, respectively. The charges of Cr
3+
,F
1
(closest triple
F-ligands to the V
K
or Li), and F
2
for K-vacancy (K–Li substitution)
decreases 5.0% (5.0%), 0.0% (1.3%), and increases 0.1% (decreases
1.1%) respectively. On the other hand, total charges of Cr
3+
and
the F ligands for CrF
5
O site (see Table 5 and Fig. 7) given in col-
umn-F
1
and -F
2
for the lowest energy state and the best agreed step
with SPM calculations (see Table 6), respectively. As can be
obtained from the coulumn-F
1
(-F
2
), total charges of Cr
3+
,F
ax
and
the F
eq
ligands decreases 0.3% (0.1%), 0.2% (0.2%) and 0.6% (0.4%),
Fig. 7. Optimized structure around Cr
3+
ion in KMgF
3
crystal for the CrF
5
O
4
center.
Fig. 6. Optimized structure around Cr
3+
ion in KMgF
3
crystal for (a) the K-vacancy case and (b) the K–Li substitution case.
58 Y. Emül et al. / Chemical Physics 444 (2014) 52–60

respectively. Moreover, total charge of O
2-
decreases from 7.023 to
6.956 (1.0% decline) and 6.883 (2.0% decline) for the steps-VI (F
1
)
and -III (F
2
), respectively. It should be noted that the decrease in
charges for both Mg–Li substitution and K–Li substitution cases
are smaller than the corresponding Mg and K- vacancy cases due
to the charge compensation through Li
+
ion. It is also worth to note
that the steps given in Table 8 with minimum energy states are con-
sistent with the results of SPM calculations to determine the most
reasonable structural model around the Cr
3+
centers.
4. Summary and conclusions
By means of several modeling approaches, structural relax-
ations related with all possible types of Cr
3+
centers in KMgF
3
,
namely the tetragonal (Cr
3+
–V
Mg
and Cr
3+
–Li
+
), trigonal (Cr
3+
–V
K
),
and CrF
5
O cluster centers, have been investigated using ab initio
and semi empirical calculations. It has been shown by exploring
through both DFT and SPM calculations that the presence of Cr
3+
in different structural centers induces some structural distortions
on the CrF
6
or CrF
5
O clusters. DFT calculations have been carried
out on supercells involving 135 ions, on the contrary of the previ-
ous DFT studies where the clusters of less number of ions, instead
of supercell, were taken into account. Moreover, the effect of the
structural changes on the charge distribution (electron units) of
Cr impurity and Fligands has been determined using the DFT cal-
culations for all steps followed in DFT and SPM calculations. Best
modeling approach for each type of center has been predicted by
comparing the experimental ZFSPs with those calculated in SPM
using the obtained structural parameters from DFT.
Through this study, we have gained a better insight on both the
roles of Mg
2+
and K
+
vacancies and Li
+
ion located at those vacancy
sites in the local structural properties around Cr
3+
centers in
KMgF
3
. For the tetragonal centers, it is indicated that the most
probable structural model for the Mg vacancy case is the model
for which all ions including central Cr ion displace from their ori-
ginal positions. On the other hand, the model based on only the
displacements of F ligands (i.e. Cr ion is frozen) is found to be
the most probable structural model for the Mg–Li substitution
case. For the trigonal center, it is seen that two different structural
models are reasonable for the K-vacancy case. Both of them yield
inward relaxations of F ligands but one of them also reveals an
off-center displacement for Cr. However, the model based on free
movement of all ions appears more reasonable since it has mini-
mum energy state. On the other hand, for the CrF
5
O
4
center, inter-
estingly the model based on the displacements of axial O and F
Table 6
Calculated values of the ZFSP D(in 10
4
cm
1
) for the CrF
5
O
4
center.
SPM parameters Step-I Step-II Step-III Step-IV Step-V Step-VI
t
2
=0.24; R
0
= 0.2113 0.159 1739.7 2158.2 944.8 1099.8 469.4
t
2
=0.27; R
0
= 0.2113 0.179 1952.8 2423.6 1060.4 1039.8 397.3
t
2
=0.21; R
0
= 0.2113 0.139 1525.6 1891.8 827.6 1160.8 542.3
t
2
=0.24; R
0
= 0.1993 0.161 1764.3 2188.7 958.1 1115.4 476.0
Table 7
Calculated Cartesian coordinates and the displacement of the central Cr
3+
ion for the
steps where Cr
3+
is allowed to move. All the values are given in nm units. The initial
coordinates of Cr
3+
are (x,y,z): (0.6090, 0.6090, 0.6090).
Steps Final coordinates
xyzDisplace
Mg-vac Step-IV 0.6093 0.6090 0.6090 0.0003
Mg–Li Step-IV 0.6138 0.6090 0.6090 0.0048
K–Li Step-I 0.6086 0.6086 0.6086 0.0008
K–Li Step-II 0.6065 0.6065 0.6065 0.0043
K-vac Step-I 0.6015 0.6015 0.6015 0.0130
K-vac Step-II 0.6071 0.6071 0.6071 0.0033
CrF
5
O Step-V 0.6090 0.6090 0.6241 0.0151
CrF
5
O Step-VI 0.6090 0.6090 0.6212 0.0122
Table 5
The results of DFT calculations for the CrF
5
O
4
center. Calculated values of the distances are given in nm and the angles in degree. The Mulliken charge distribution (electron
units) of Cr and F ligands are also given for all steps. The definitions of the other parameters are as follows: O
ax
–Cr: Cr–O distance; F
ax
–Cr: Cr–F (axial) distance; F
eq
–Cr: Cr–F
(equatorial) distance; Z
Cr
: Displacement of the Cr towards to O; Z
O
: Displacement of the O towards to Cr.
Parameters Steps
Step-I Step-II Step-III Step-IV Step-V Step-VI
Energies (eV) +1.3684 +0.631416 +0.603226 +0.308643 +0.132908 0.0
4s (Cr) tot. e 0.274 0.305 0.305 0.312 0.318 0.321
3d (Cr) tot. e 4.188 4.240 4.238 4.239 4.236 4.221
2p (F
ax
) tot. e 5.762 5.770 5.755 5.756 5.755 5.753
2p (F
eq
) tot. e 5.743 5.741 5.745 5.728 5.728 5.727
2p (0
ax
) tot. e 5.094 4.985 4.995 5.034 5.025 5.073
Z
Cr
0.00000 0.00000 0.0000 0.0000 0.015132 0.0122187
Z
O
0.00000 0.30998 0.30255 0.27852 0.016387 0.0192173
F
ax
–Cr dist. 0.212409 0.212409 0.203798 0.204452 0.217709 0.214591
F
eq
–Cr dist. 0.212408 0.212408 0.212408 0.202897 0.203160 0.202619
O
ax
–Cr dist. 0.212410 0.181411 0.182155 0.184558 0.180890 0.180974
F
eq
-z-axis angel 89.9997 89.9997 89.9997 90.3679 94.3476 93.5508
Table 8
Comparison of total charges on Cr
3+
and the F ligands for the steps with minimum energy states.
Structure A B C D E F1 F2
Steps KMgF
3
:Cr
3+
Tetragonal Mg Vac. Tetragonal Mg–Li sub. Trigonal K–Li sub. Trigonal K vac. CrF
5
O center CrF
5
O center
– Step-IV Step-IV Step-II Step-II Step-VI Step-III
(Cr) tot. e 4.767 4.571 4.596 4.531 4.531 4.751 4.763
(F
ax
) tot. e 7.725 F
1
ax
:7.469
F
2
ax
:7.611
F
1
ax
:7.579
F
2
ax
:7.659
F
1
:7.722 F
1
:7.622 7.708 7.705
(F
eq
) tot. e 7.725 7.598 7.636 F
2
:7.730 F
2
:7.641 7.680 7.696
Y. Emül et al. / Chemical Physics 444 (2014) 52–60 59

ligands seem more reasonable with a quite large inward relaxation
of O ligand. Furthermore, the results from both DFT and SPM calcu-
lations are in good agreement with the experimental data observed
for the local structure of Cr
3+
centers. It shows that using DFT and
SPM together in investigating the local structure around a para-
magnetic ion would be an effective method for correlation of the
related experimental results.
Conflict of interest
There is no conflict of interest.
Acknowledgement
The present work was supported by the Research Fund from
Bahcesehir University.
References
[1] U. Brauch, U. Dürr, Opt. Commun. 49 (1984) 61.
[2] M. Binois, A. Leble, J.J. Rousseau, J.C. Fayet, J. Phys. Colloq. 34 (1973) 285–288.
[3] J.L. Patel, J.J. Davies, B.C. Cavenett, H. Takeuchi, K. Horai, J. Phys. C Solid State
Phys. 9 (1976) 129.
[4] Y. Vaills, J.Y. Buzare, M. Rousseau, J. Phys. Condens. Mater. 2 (1990) 3997–
4003.
[5] B. Villacampa, J.C. Gonzalez, R. Alcala, P.J. Alonso, J. Phys. Condens. Mater. 3
(1991) 8281–8288.
[6] H. Takeuchi, M. Arakawa, J. Phys. Soc. Jpn. 53 (1984) 376.
[7] R.Yu. Abdulsabirov, A.L. Larionov, V.G. Stepanov, S.N. Lukin, I.M. Krygin, in: E.
Kundla, E. Lippamaa, T. Saluvere (Eds.), Magnetic Resonance and Related
Phenomena, Springer, Berlin, 1979, p. 314.
[8] M. Mortier, J.Y. Gesland, B. Piriou, J.Y. Buzaré, M. Rousseau, Opt. Mater. 4
(1994) 115.
[9] R.C.B. Villacampa, R. Cases, R. Alcala, Radiat. Eff. Def. Solids 135 (1995) 655.
[10] D.R. Lee, T.P.J. Han, B. Henderson, Appl. Phys. A 59 (1994) 365.
[11] H. Ebisu, M. Arakawa, H. Takeuchi, J. Phys. Condens. Mat. 17 (2005) 4653–
4663.
[12] H. Ebisu, H. Takeuchi, M. Arakawa, Phys. Status Solidi B 247 (2010) 983.
[13] H. Takeuchi, M. Arakawa, H. Aoki, T. Yosida, K. Horai, J. Phys. Soc. Japan 51
(1982) 3166.
[14] Q. Zhou, H.-Y. Wu, X.-X. Wu, W.-C. Zheng, Spectrochim. Acta A 64 (2006) 945.
[15] Z. Wen-Chen, Z. Qing, W. Xiao-Xuan, M. Yang, Spectrochim. Acta A 63 (2006)
126.
[16] Z. Wen-Chen, Radiat. Eff. Def. Solids 140 (1997) 323.
[17] Y. Zi-Yuan, Phys. B Condens. Mater. 406 (2011) 3975.
[18] R.W.G. Wyckoff, Cryst. Struct. 2 (1964) 392.
[19] J.D.H. Donnay, H.M. Ondik, Crystal Data: Determinative Tables, Vol. II the U.S.
Department of Commerce, National Bureau of Standards and the Joint
Committee on Powder Diffraction Standards, USA, 1973.
[20] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864.
[21] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133.
[22] P. Ordejón, E. Artacho, J.M. Soler, Phys. Rev. B 53 (1996) R10441.
[23] M.S. José, A. Emilio, D.G. Julian, G. Alberto, J. Javier, O. Pablo, S.-P. Daniel, J.
Phys. Condens. Mater. 14 (2002) 2745.
[24] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993.
[25] L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425.
[26] P. García-Fernández, A. Trueba, B. García-Cueto, J.A. Aramburu, M.T. Barriuso,
M. Moreno, Phys. Rev. B 83 (2011) 125123.
[27] J.M. García-Lastra, M.T. Barriuso, J.A. Aramburu, M. Moreno, J. Phys. Condens.
Mater. 22 (2010) 155502.
[28] C. Rudowicz, Magn. Reson. Rev. 13 (1987) 1.
[29] C. Rudowicz, S.K. Misra, Appl. Spectrosc. Rev. 36 (2001) 11.
[30] D.J. Newman, W. Urban, Adv. Phys. 24 (1975) 793.
[31] D.J. Newman, B. Ng, Rep. Prog. Phys. 52 (1989) 699.
[32] E. Erdem, A. Matthes, R. Böttcher, H. Gläsel, E. Hartmann, J. Nanosci. Nanotech.
8 (2008) 702.
[33] E. Erdem, M. Drahus, R. Eichel, A. Ozarowski, T. Johan, L.C. Brunel, J. Ferroelectr.
363 (2008) 39–49.
[34] M. Açıkgöz, P. Gnutek, C. Rudowicz, Solid State Commun. 150 (2010) 1077.
[35] P. Gnutek, M. Açıkgöz, C. Rudowicz, Opt. Mater. 32 (2010) 1161.
[36] C. Rudowicz, J. Phys. C Solid State Phys. 20 (1987) 6033.
[37] M. Açıkgöz, P. Gnutek, C. Rudowicz, Chem. Phys. Lett. 524 (2012) 49.
[38] M. Açıkgöz, Chem. Phys. Lett. 563 (2013) 50.
[39] R.C. Weast, CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL,
1988. p. 187.
[40] M.J.L. Sangster, J. Phys. C: Solid State Phys. 13 (1980) 5279.
[41] J.P. Perdew, Phys. Rev. B 33 (1986) 8822.
[42] A.D. Becke, Phys. Rev. A 38 (1988) 3098.
[43] L. Hozoi, C. Presura, C. de Graaf, R. Broer, Phys. Rev. B 67 (2003) 035117.
60 Y. Emül et al. / Chemical Physics 444 (2014) 52–60