C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
735–743
ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL
OXIDES MgxZn1-xAl2O4 BY FIRST-PRINCIPLES CALCULATIONS
ELEKTRONSKE IN OPTI^NE LASTNOSTI SPINELNIH OKSIDOV
MgxZn1-xAl2O4, IZPELJANE IZ TEORETI^NIH OSNOV
Chao Xiang1, Jianxiong Zhang1, Yun Lu2, Dong Tian3, Cheng Peng1
1Yangtze Normai University, School of Mechanical and Engineering, Fuling 408000, China
2Chiba University, Institute of Material Science and Engineering, Chiba 2790000, Japan
3Kunming University of Science and Technology, Faculty of Science, Kunming 650093, China
1254618608@qq.com
Prejem rokopisa – received: 2016-10-07; sprejem za objavo – accepted for publication: 2017-02-10
doi:10.17222/mit.2016.296
The structural, electronic and optical properties of perfect MgxZn1-xAl2O4 oxides have been studied by first-principles
calculations within the generalized gradient approximation of the density functional theory. It is interesting to note that a linear
increase of cell volume (V) with increasing doping amount (x) occurs. The band gap increases in the series from 3.851 eV to
5.079 eV, which is in agreement with theoretical and experimental values. In addition, a blue shift of the absorption shoulder is
observed in the UV region with the increase of x, as predicted by the imaginary part 2() of the dielectric function at zero
frequency as well as bandgap. This can be explained by the threshold of the electronic transition from O-2p to the empty Mg-3p
electron states due to the substitution of Zn with Mg. The real part 1() of the dielectric function located at zero frequency has
a square fit relationship with refractive index n(0), which is 1.71–1.77 from x=0 to x=1. The energy-loss function shows that the
replacement of Zn by Mg is responsible for a decrease in the intensity of the sharp peaks. The reflectivity shows that a higher
coefficient of reflectivity (R(0)) at zero frequency corresponds to a smaller bandgap.
Keywords: electronic transitions, dielectric function, refractive index, adsorption shoulder
Preiskovali smo strukturne, elektronske in opti~ne lastnosti idealnih MgxZn1-xAl2O4 oksidov, izpeljane iz teoreti~nih osnov
znotraj posplo{ene gradientne aproksimacije funkcionalne teorije gostote. Opazili smo linearno pove~anje celi~nega volumna
(V) z nara{~ajo~o koncentracijo Mg (x). [irina prepovedanega pasu nara{~a od 3.851 eV to 5.079 eV v skladu s teoreti~nimi in
eksperimentalnimi vrednostmi. Poleg tega ob nara{~anju dele`a Mg opazimo modri premik dodatnega absorpcijskega vrha v UV
obmo~ju, kakor napovedujeta vrednosti imaginarnega dela 2() dielektri~ne funkcije pri frekvenci 0 in prepovedanega pasu. To
je mogo~e pojasniti s pragom elektronskega prehoda elektronov iz O-2p v prazen Mg-3p zaradi nadomestitve Zn z Mg. Kvadrat
realnega dela 1() dielektri~ne funkcije pri frekvenci 0 se ujema z lomnim koli~nikom n(0), ki je 1.71–1.77 za x=0 do x=1.
Funkcija izgube energije, ka`e, da zamenjava Zn z Mg povzro~a zmanj{anje intenzitete ostrih vrhov. Reflektivnost ka`e, da vi{ji
koeficient refleksije (R(0)) pri frekvenci 0 odgovarja manj{i {irini prepovedanega pasu.
Klju~ne besede: prehodi elektronov, dielektri~na funkcija, lomni koli~nik, dodatni absorpcijski vrh
1 INTRODUCTION
Spinal oxides with the general chemical formula
AB2O4 have a close-packed, face-centered-cubic struc-
ture (space group Fd3m) characterized by two
symmetrically distinct polyhedra: a tetrahedron and an
octahedron. They are widely used in various fields such
as catalysis, gas sensor, semiconductor, biomedical,
catalyst carrier, as well as electroluminescent displays
owing to their catalytic, physical, structural, electronic
and optical properties.1,2 Among them, MgAl2O4 and
ZnAl2O4 have high-temperature resistance,3,4 and they
are highly reflective for wavelengths in the ultraviolet
(UV) region, which make them candidate materials for
reflective optical coating in aerospace applications.5 In
particular, MgAl2O4 is one of the potential candidates for
the full wave band transparent window materials with
high transmittance in IR- and visible-wavelength even
extending to microwave ranges,6,7 and it also can be used
as lamps and lasers,8 transparent ceramic material for
high-temperature,9 transparent armor and glass.10
Similarly, ZnAl2O4 can be used as a ceramic material
similar to MgAl2O4. It can be used as a transparent
conductor, optical material and dielectric material,11,12
and it is suitable for UV photoelectronic applications.13
Simultaneously, much work has been done on the
structural, electronic and optical properties of MgAl2O4
and ZnAl2O4 over the past few years.14–27 The effect of
point vacancies on the spectral properties of MgAl2O4
has been studied by S. L. Jiang et al.14 They revealed that
the absorption peak at 5.3 eV is attributed to the neutral
oxygen vacancy Vo
0 , while two peaks at 3.2 eV and 4.75
eV are attributed to the 1+ charged oxygen vacancy Vo
1 + .
A related mechanism of transparency in MgAl2O4 nano-
ceramics prepared by sintering under high pressure and
low temperature has been studied by J. Zhang et al.15,
who suggested that the decrease in the transparency with
increasing temperature (>700 °C) is therefore a result of
the light scattering at large pores. The low-temperature,
high-pressure preparation of transparent nanocrystalline
MgAl2O4 ceramics has been investigated by T. C. Lu et
Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743 735
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
UDK 67.017:621.3.011.5:535.327 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 51(5)735(2017)
al.,16 indicating that the nanoceramics are highly
transparent even though their relative densities are all
less than 99 %, owing to the low or negligible light
scattering from the nanosized grains and pores. The
optical properties of ZnAl2O4 nanomaterials obtained by
the hydrothermal method have been investigated by
Miron and co-workers,17 demonstrating that the band gap
is determined from the absorbance spectra, and it de-
pends strongly on the temperature used for further
heating the samples. A first-principles study on struc-
tural, electronic and optical properties of spinel oxides
ZnAl2O4, ZnGa2O4 and ZnIn2O4 has been carried out by
F. Zerarga and co-workers,18 implying that the peaks and
structures in the optical spectra are assigned to interband
transitions. The fabrication of transparent polycrystalline
ZnAl2O4 – a new optical bulk ceramic – has been inve-
stigated by Goldstein and co-workers19, who suggested
that specimens have a high transparency (ILT78\%;
 = 800 nm; t = 2 mm). Plus, the differences in struc-
tural, electronic and optical performance between alumi-
num spinel MgAl2O4 and ZnAl2O4 have been
presented.28–30 To the best of our knowledge, the struc-
ture, electronic and optical properties of MgxZn1-xAl2O4
(0<x<1), expressed quantitatively, which is that Zn2+ of
ZnAl2O4 is replaced by Mg2+, has not been investigated.
The main aim of this investigation is to study the effect
of the replacement of Zn by Mg on the structural,
electronic and optical properties of ZnAl2O4.
2 MODEL AND COMPUTATIONAL DETAILS
In our calculations a 56-atom unit cell was modeled
for the investigation of spinel MgxZn1-xAl2O4 in Figure 1.
All the calculations were performed using the Cam-
bridge Serial Total Energy Package (CASTEP) prog-
ram,31 based on density functional theory (DFT).
Electron-ion interaction for cations and anions was
described by the ultra-soft pseudo-potential. The Mg-3s
and -3p, Zn-3d and -4s, Al-3s and -3p, as well as O-2s
and -2p states were treated as valence electrons. The
exchange-correlation potential was calculated by the
generalized gradient approximation (GGA) developed by
the Perdew, Burke, and Ernzerhof functional (PBE).32
The Engel-Vosko scheme (GGA+U) was applied to
electronic properties calculations.33 The on-site Coulomb
Hubbard interaction U = 1 eV is used to treat correctly
the localized 3d electrons in the MgxZn1-xAl2O4. The unit
cell was optimized using the Broyden, Fletcher, Gold-
farb, Shanno (BFGS) method,34 and convergence tole-
rance of energy charge, maximum force and stress were
1×10–5 eV, 0.03 eV/nm, and 0.05 GPa, respectively.18,35
The plane-wave basis set cutoff energy was set to
340 eV.18,35,36 The Brillouin-zone integration was imple-
mented within Monkhorst-Pack scheme using a 4×4×4
mesh to optimize structures and calculate the electronic
and optical properties.
3 RESULTS AND DISCUSSION
3.1 Structure and electronic properties
To obtain the stable structure of MgxZn1-xAl2O4
spinel, the internal coordinates and lattice parameters of
crystals were relaxed during geometry optimization.
Structure parameters such as average bond lengths, cell
volumes and lattice constants are presented, in compari-
son with the experimental data and values available from
other calculations. As can be seen from Tables 1 and 2,
the calculated equilibrium lattice constants a0 of both
ZnAl2O4 and MgAl2O4 are larger than the experimental
values with less than 2 % deviation. Plus, substitution of
Zn with Mg causes a slight increase in the lattice con-
stant of ZnAl2O4. This is in agreement with the previous
report.28 In addition, one can see that the substitution of
Zn with Mg is responsible for the formation of the
pseudo-cubic, spinel-type structure. The average bond
lengths of dAl-O increases with increasing doping con-
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
736 Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 2: Calculated average bond length (nm) of MgxZn1-xAl2O4
Figure 1: MgxZn1-xAl2O4 crystal structure. The gray, pink, green and
red represent Zn, Al, Mg and O atoms, respectively.
centration (from x=0 to x=1) in Figure 2. In contrast,
both dZn-O and dMg-O are nearly unchanged. This suggests
that the increase of lattice constants is mostly due to an
increase of dAl-O. The minimum dAl-O in MgAl2O4 is
0.1938 nm, which indicates that the strength of the
chemical bond (Al-O) of MgAl2O4 is stronger than that
of MgxZn1-xAl2O4. The cell volume (V) is listed in Table
2. The volume-x curve is plotted, where x is the concen-
tration of Mg. It is interesting to note that the unit-cell
volume (V) changes linearly with the doping amount x
(Figure 3).
Table 1: Calculated structure parameters for MgxZn1-xAl2O4 (x=0,
x=1), experimental measurement and other available theoretical values
ZnAl2O4 MgAl2O4
Present Expt. Calc. Present Expt. Calc.
a0
(nm) 0.8194
0.8091137 0.803218
0.8208
0.8083643 0.802728
0.808638
0.799528 0.8084444 0.8107425
0.819339
0.80645
0.814627
m
0.8021540 0.8093414
0.801841
0.8246
0.80242
The calculated band gaps are presented in Figure 4.
From the figure it is easy to see that the bottom of the
conduction band and the top of the valence band for
MgxZn1-xAl2O4 occurs at  point with a direct band gap.
Among them, ZnAl2O4 (x=0) has a band gap value of
3.851 eV, which is very close to the experimental value.48
The MgAl2O4 (x=1) has a band gap value of 5.079 eV,
which is underestimated with respect to the experimental
value of 7.8 eV.49 A similar issue has been addressed in
previous theoretical calculations for MgAl2O4 such as
5.30 eV14, 5.1 eV27 and 5.36 eV.28 This is mostly due to
the fact that the calculated band gaps are related to DFT
limitations, not considering the discontinuity in the
exchange-correlation potential,50 as mentioned in 35. The
calculations also show that the band-gap value increases
due to changing the cation Zn with Mg. The band gap is
4.078 for x=0.25, 4.349 for x=0.50 and 4.638 eV for
x=0.75.
As discussed above, the band gap of optimized
MgxZn1-xAl2O4 is different (from x=0 to x=1). This is
attributed to the difference in the density of states
(DOS). To further elucidate the nature of the electronic
band structure, we calculated the total density of states
(DOS) and partial density of states (PDOS) of O, Zn, Mg
and Al for the spinel oxides. As can be seen from Fig-
ure 5, the Fermi level is set to zero. It is mostly created
by Zn-3d and O-2p states for x=0, with small con-
tributions coming from Al-3p, and it is mostly created by
Mg-3p and O-2p states for x=1, with small contributions
of Al-3p. The character of the upper valence band is
localized between -6.2 eV and 0 eV, which is mainly due
to hybridization between the Zn-3d and O-2p states and
due less to hybridization of O-2p with Zn-3p, Zn-4s,
Mg-3s, Mg-3p, Al-3s and Al-3p as well. The lower
valence band in the energy range -18.8 eV to -16.3 eV is
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743 737
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 3: Calculated the unit cell volume V (nm3) as a function of
composition x
Table 2: Calculated structure parameters for MgxZn1-xAl2O4
0.000 0.250 0.500 0.750 1000 Al2O3
a(nm) 0.8194 0.8198 0.8202 0.8205 0.8208
b(nm) 0.8194 0.8197 0.8202 0.8205 0.8208
c(nm) 0.8194 0.8197 0.8199 0.8203 0.8208
dZn-O(nm) 0.1980 0.201918 0.1979 0.1978 0.1979 0.203218
dAl-O(nm) 0.1938 0.196318 0.188b 0.1939 0.1940 0.1942 0.1943 0.1941925 0.19247
dMg-O(nm) 0.1980 0.1980 0.1978 0.1978 0.1956925
Volume (nm3) 550.25 0.55092 0.55164 0.55237 0.55312
Figure 4: Calculated electronic band structure of MgxZn1-xAl2O4
(x=0, x=0.25, x=0.5, x=0.75, x=1)
al.,16 indicating that the nanoceramics are highly
transparent even though their relative densities are all
less than 99 %, owing to the low or negligible light
scattering from the nanosized grains and pores. The
optical properties of ZnAl2O4 nanomaterials obtained by
the hydrothermal method have been investigated by
Miron and co-workers,17 demonstrating that the band gap
is determined from the absorbance spectra, and it de-
pends strongly on the temperature used for further
heating the samples. A first-principles study on struc-
tural, electronic and optical properties of spinel oxides
ZnAl2O4, ZnGa2O4 and ZnIn2O4 has been carried out by
F. Zerarga and co-workers,18 implying that the peaks and
structures in the optical spectra are assigned to interband
transitions. The fabrication of transparent polycrystalline
ZnAl2O4 – a new optical bulk ceramic – has been inve-
stigated by Goldstein and co-workers19, who suggested
that specimens have a high transparency (ILT78\%;
 = 800 nm; t = 2 mm). Plus, the differences in struc-
tural, electronic and optical performance between alumi-
num spinel MgAl2O4 and ZnAl2O4 have been
presented.28–30 To the best of our knowledge, the struc-
ture, electronic and optical properties of MgxZn1-xAl2O4
(0<x<1), expressed quantitatively, which is that Zn2+ of
ZnAl2O4 is replaced by Mg2+, has not been investigated.
The main aim of this investigation is to study the effect
of the replacement of Zn by Mg on the structural,
electronic and optical properties of ZnAl2O4.
2 MODEL AND COMPUTATIONAL DETAILS
In our calculations a 56-atom unit cell was modeled
for the investigation of spinel MgxZn1-xAl2O4 in Figure 1.
All the calculations were performed using the Cam-
bridge Serial Total Energy Package (CASTEP) prog-
ram,31 based on density functional theory (DFT).
Electron-ion interaction for cations and anions was
described by the ultra-soft pseudo-potential. The Mg-3s
and -3p, Zn-3d and -4s, Al-3s and -3p, as well as O-2s
and -2p states were treated as valence electrons. The
exchange-correlation potential was calculated by the
generalized gradient approximation (GGA) developed by
the Perdew, Burke, and Ernzerhof functional (PBE).32
The Engel-Vosko scheme (GGA+U) was applied to
electronic properties calculations.33 The on-site Coulomb
Hubbard interaction U = 1 eV is used to treat correctly
the localized 3d electrons in the MgxZn1-xAl2O4. The unit
cell was optimized using the Broyden, Fletcher, Gold-
farb, Shanno (BFGS) method,34 and convergence tole-
rance of energy charge, maximum force and stress were
1×10–5 eV, 0.03 eV/nm, and 0.05 GPa, respectively.18,35
The plane-wave basis set cutoff energy was set to
340 eV.18,35,36 The Brillouin-zone integration was imple-
mented within Monkhorst-Pack scheme using a 4×4×4
mesh to optimize structures and calculate the electronic
and optical properties.
3 RESULTS AND DISCUSSION
3.1 Structure and electronic properties
To obtain the stable structure of MgxZn1-xAl2O4
spinel, the internal coordinates and lattice parameters of
crystals were relaxed during geometry optimization.
Structure parameters such as average bond lengths, cell
volumes and lattice constants are presented, in compari-
son with the experimental data and values available from
other calculations. As can be seen from Tables 1 and 2,
the calculated equilibrium lattice constants a0 of both
ZnAl2O4 and MgAl2O4 are larger than the experimental
values with less than 2 % deviation. Plus, substitution of
Zn with Mg causes a slight increase in the lattice con-
stant of ZnAl2O4. This is in agreement with the previous
report.28 In addition, one can see that the substitution of
Zn with Mg is responsible for the formation of the
pseudo-cubic, spinel-type structure. The average bond
lengths of dAl-O increases with increasing doping con-
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
736 Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 2: Calculated average bond length (nm) of MgxZn1-xAl2O4
Figure 1: MgxZn1-xAl2O4 crystal structure. The gray, pink, green and
red represent Zn, Al, Mg and O atoms, respectively.
centration (from x=0 to x=1) in Figure 2. In contrast,
both dZn-O and dMg-O are nearly unchanged. This suggests
that the increase of lattice constants is mostly due to an
increase of dAl-O. The minimum dAl-O in MgAl2O4 is
0.1938 nm, which indicates that the strength of the
chemical bond (Al-O) of MgAl2O4 is stronger than that
of MgxZn1-xAl2O4. The cell volume (V) is listed in Table
2. The volume-x curve is plotted, where x is the concen-
tration of Mg. It is interesting to note that the unit-cell
volume (V) changes linearly with the doping amount x
(Figure 3).
Table 1: Calculated structure parameters for MgxZn1-xAl2O4 (x=0,
x=1), experimental measurement and other available theoretical values
ZnAl2O4 MgAl2O4
Present Expt. Calc. Present Expt. Calc.
a0
(nm) 0.8194
0.8091137 0.803218
0.8208
0.8083643 0.802728
0.808638
0.799528 0.8084444 0.8107425
0.819339
0.80645
0.814627
m
0.8021540 0.8093414
0.801841
0.8246
0.80242
The calculated band gaps are presented in Figure 4.
From the figure it is easy to see that the bottom of the
conduction band and the top of the valence band for
MgxZn1-xAl2O4 occurs at  point with a direct band gap.
Among them, ZnAl2O4 (x=0) has a band gap value of
3.851 eV, which is very close to the experimental value.48
The MgAl2O4 (x=1) has a band gap value of 5.079 eV,
which is underestimated with respect to the experimental
value of 7.8 eV.49 A similar issue has been addressed in
previous theoretical calculations for MgAl2O4 such as
5.30 eV14, 5.1 eV27 and 5.36 eV.28 This is mostly due to
the fact that the calculated band gaps are related to DFT
limitations, not considering the discontinuity in the
exchange-correlation potential,50 as mentioned in 35. The
calculations also show that the band-gap value increases
due to changing the cation Zn with Mg. The band gap is
4.078 for x=0.25, 4.349 for x=0.50 and 4.638 eV for
x=0.75.
As discussed above, the band gap of optimized
MgxZn1-xAl2O4 is different (from x=0 to x=1). This is
attributed to the difference in the density of states
(DOS). To further elucidate the nature of the electronic
band structure, we calculated the total density of states
(DOS) and partial density of states (PDOS) of O, Zn, Mg
and Al for the spinel oxides. As can be seen from Fig-
ure 5, the Fermi level is set to zero. It is mostly created
by Zn-3d and O-2p states for x=0, with small con-
tributions coming from Al-3p, and it is mostly created by
Mg-3p and O-2p states for x=1, with small contributions
of Al-3p. The character of the upper valence band is
localized between -6.2 eV and 0 eV, which is mainly due
to hybridization between the Zn-3d and O-2p states and
due less to hybridization of O-2p with Zn-3p, Zn-4s,
Mg-3s, Mg-3p, Al-3s and Al-3p as well. The lower
valence band in the energy range -18.8 eV to -16.3 eV is
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743 737
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 3: Calculated the unit cell volume V (nm3) as a function of
composition x
Table 2: Calculated structure parameters for MgxZn1-xAl2O4
0.000 0.250 0.500 0.750 1000 Al2O3
a(nm) 0.8194 0.8198 0.8202 0.8205 0.8208
b(nm) 0.8194 0.8197 0.8202 0.8205 0.8208
c(nm) 0.8194 0.8197 0.8199 0.8203 0.8208
dZn-O(nm) 0.1980 0.201918 0.1979 0.1978 0.1979 0.203218
dAl-O(nm) 0.1938 0.196318 0.188b 0.1939 0.1940 0.1942 0.1943 0.1941925 0.19247
dMg-O(nm) 0.1980 0.1980 0.1978 0.1978 0.1956925
Volume (nm3) 550.25 0.55092 0.55164 0.55237 0.55312
Figure 4: Calculated electronic band structure of MgxZn1-xAl2O4
(x=0, x=0.25, x=0.5, x=0.75, x=1)
mostly attributed to the O 2s states which split into two:
a sharp peak at -17.8 eV and a lower part 2.3 eV wide
with double peaks for x=0. A similar issue appears for
x=1, from which we can see that the lower valence band
located at approximately -15.4 eV – -18.1 eV is mostly
due to the O 2s states, which split into two: a sharp peak
at -16.1 eV and a lower double peak with a width of 2.1
eV. This is in agreement with other theoretical calcula-
tions.14,25 Moreover, we note that Zn-4s and Al-3p states
play the main role in the conduction band above the
Fermi level (between 3.8 eV and 8.2 eV) for x=0, while
conduction band is mainly created by Mg-3p states for
x=1.
3.2 Optical properties
The common response from both electronic and ionic
polarization are taken into account in the condition of a
low-frequency electric field, although only electronic
polarization is considered as the dielectric function, and
phonon contributions to the optical is not taken into
account, when calculating optical properties in CASTEP
package. It is well known that the optical properties are
determined considering only direct interband transitions.
One of the main optical characteristics of a solid is its
dielectric function, which can express other optical pro-
perties and describe the optical response of the medium.
The dielectric function, (), is given in Equation (1):
() = 	() + 
() (1)
Here 	() and 
() are the real and imaginary parts
of the dielectric function, respectively. The complex
2() is defined as Equation (2):39

() =
2 2
0
2e
V
u r E Ek
c
k v c
k
v
k
c
k
vπ

  
 ⋅ − −∑
, ,
) (2)
where V is the unit cell volume, u is the vector defining
the polarization of the incident electric field, c and v are
the valence band and conduction band, respectively, r is
the momentum operator, and both Ek
c and Ek
v are eigen-
states. This expression is similar to Fermi’s golden rule
for time-dependent perturbations. The 
() can be
thought of as detailing the real transitions between the
unoccupied and occupied electronic states. The ima-
ginary and real parts of the dielectric function are linked
by a Kramers-Kronig transform because the dielectric
function describes a causal response. Furthermore, the
Kramers-Kronig transform is also used to obtain the
	(), which is:18
 
  
 



1 2 2
0
1
2
( )
' ( ' )
( ' ) ( )
'= +
−
∞
∫π P d (3)
Both imaginary parts and the real of the dielectric
function can also be used to calculate important optical
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
738 Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 5: Calculated total (DOS) and partial densities (PDOS) of states for MgxZn1-xAl2O4 (x=0, x=0.25, x=0.5, x=0.75, x=1)
functions, such as the refractive index n() and the
reflectivity R():18
n( )
( ) ( )





   


	






= +
+⎡
⎣
⎢
⎤
⎦
⎥
2
(4)
R( )





=
−
+
⎡
⎣⎢
⎤
⎦⎥
1
1
2
(5)
The peak of the imaginary part of the dielectric
function corresponds to electronic transitions from the
valence to conduction bands, depending on the electronic
transition energy of the conduction and valence band,
i.e., the band-gap energies. The instrumental smearing of
0.3 eV is used to simulate the broadening effects. The
dielectric functions for various x are displayed in Figure
6. It can be seen that the first critical point starts at (3.49,
3.61, 3.90, 4.22 and 4.63) eV from x=0 to x=1. These are
known as the edge of the optical absorption. Further-
more, the different widths of the non-zero part of 
()
are related with different widths of the adsorption
spectra, as shown in Figure 6, suggesting that absorption
region for MgxZn1-xAl2O4(x=0) is wider than that of
MgxZn1-xAl2O4}(x=1). Other peak locates at (7.38, 10.87,
14.63 and 15.54) eV for x=0, (7.49, 7.37, 11.65, 12.83
and 14.22) eV for x=0.25, (6.83, 7.84, 10.31, 12.81 and
15.36) eV for x=0.5, (5.81, 10.16, 12.85 and 15.85) eV
for x=0.75 and (6.25, 7.69, 10.01, 12.91 and 16.16) eV
for x=1, in comparison with other theoretical values
listed in Table 3. These peaks of origins and features on
the basis of decomposing each spectrum to its individual
pair contribution from each pair of valence and conduc-
tion bands are obtained by the analysis of 
().18 The
calculated real part of 	() in infinite wavelength (i.e.,
the limit of zero energy) for x=0 is 3.15 and for x=1 is
2.93, which are in agreement with previous theoretical
values such as 2.6691 for ZnAl2O418 and 3.112 for
MgAl2O4.25 In addition, the 	() in infinite wavelength
is 3.09 for x=0.25, 3.03 for x=0.5, and 2.98 for x=0.75,
signaling a negative trend with the increase of the doping
amount x. These can also indicate that the real part 	()
of the limit of zero energy has a square fit relationship
with the refractive index n localized zero energy. The
	() reaches a maximum value of 4.22 at about 6.15 eV
for x=0, 4.28 at 8.88 eV for x=0.25, 4.30 at 8.82 eV for
x=0.5, 4.29 at 8.84 eV for x=0.75 and 4.39 at 8.73 for
x=1.
Table 3: The imaginary part (2()) of dielectric function for
MgxZn1-xAl2O4 (x=0, x=1).
ZnAl2O4 MgAl2O4
Present Calc.18 Calc.40 Present Calc.23 Calc.25
Threshol
d Peak
position
3.49 4.31 ~4.25 4.63 7.4
7.38 7.82 ~8.01 6.25 6.27
10.87 10.98 7.69 7.44
14.63 14.08 10.01 9.42
15.54 12.91 10.19
The refractive index and the extinction coefficient are
shown in Figure 7. One can see that the static refractive
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743 739
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 7: Refractive index of Mg doped ions at various doping con-
centration
Figure 6: Dielectric function of Mg doped ions at different doping
concentration
mostly attributed to the O 2s states which split into two:
a sharp peak at -17.8 eV and a lower part 2.3 eV wide
with double peaks for x=0. A similar issue appears for
x=1, from which we can see that the lower valence band
located at approximately -15.4 eV – -18.1 eV is mostly
due to the O 2s states, which split into two: a sharp peak
at -16.1 eV and a lower double peak with a width of 2.1
eV. This is in agreement with other theoretical calcula-
tions.14,25 Moreover, we note that Zn-4s and Al-3p states
play the main role in the conduction band above the
Fermi level (between 3.8 eV and 8.2 eV) for x=0, while
conduction band is mainly created by Mg-3p states for
x=1.
3.2 Optical properties
The common response from both electronic and ionic
polarization are taken into account in the condition of a
low-frequency electric field, although only electronic
polarization is considered as the dielectric function, and
phonon contributions to the optical is not taken into
account, when calculating optical properties in CASTEP
package. It is well known that the optical properties are
determined considering only direct interband transitions.
One of the main optical characteristics of a solid is its
dielectric function, which can express other optical pro-
perties and describe the optical response of the medium.
The dielectric function, (), is given in Equation (1):
() = 	() + 
() (1)
Here 	() and 
() are the real and imaginary parts
of the dielectric function, respectively. The complex
2() is defined as Equation (2):39

() =
2 2
0
2e
V
u r E Ek
c
k v c
k
v
k
c
k
vπ

  
 ⋅ − −∑
, ,
) (2)
where V is the unit cell volume, u is the vector defining
the polarization of the incident electric field, c and v are
the valence band and conduction band, respectively, r is
the momentum operator, and both Ek
c and Ek
v are eigen-
states. This expression is similar to Fermi’s golden rule
for time-dependent perturbations. The 
() can be
thought of as detailing the real transitions between the
unoccupied and occupied electronic states. The ima-
ginary and real parts of the dielectric function are linked
by a Kramers-Kronig transform because the dielectric
function describes a causal response. Furthermore, the
Kramers-Kronig transform is also used to obtain the
	(), which is:18
 
  
 



1 2 2
0
1
2
( )
' ( ' )
( ' ) ( )
'= +
−
∞
∫π P d (3)
Both imaginary parts and the real of the dielectric
function can also be used to calculate important optical
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
738 Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 5: Calculated total (DOS) and partial densities (PDOS) of states for MgxZn1-xAl2O4 (x=0, x=0.25, x=0.5, x=0.75, x=1)
functions, such as the refractive index n() and the
reflectivity R():18
n( )
( ) ( )





   


	






= +
+⎡
⎣
⎢
⎤
⎦
⎥
2
(4)
R( )





=
−
+
⎡
⎣⎢
⎤
⎦⎥
1
1
2
(5)
The peak of the imaginary part of the dielectric
function corresponds to electronic transitions from the
valence to conduction bands, depending on the electronic
transition energy of the conduction and valence band,
i.e., the band-gap energies. The instrumental smearing of
0.3 eV is used to simulate the broadening effects. The
dielectric functions for various x are displayed in Figure
6. It can be seen that the first critical point starts at (3.49,
3.61, 3.90, 4.22 and 4.63) eV from x=0 to x=1. These are
known as the edge of the optical absorption. Further-
more, the different widths of the non-zero part of 
()
are related with different widths of the adsorption
spectra, as shown in Figure 6, suggesting that absorption
region for MgxZn1-xAl2O4(x=0) is wider than that of
MgxZn1-xAl2O4}(x=1). Other peak locates at (7.38, 10.87,
14.63 and 15.54) eV for x=0, (7.49, 7.37, 11.65, 12.83
and 14.22) eV for x=0.25, (6.83, 7.84, 10.31, 12.81 and
15.36) eV for x=0.5, (5.81, 10.16, 12.85 and 15.85) eV
for x=0.75 and (6.25, 7.69, 10.01, 12.91 and 16.16) eV
for x=1, in comparison with other theoretical values
listed in Table 3. These peaks of origins and features on
the basis of decomposing each spectrum to its individual
pair contribution from each pair of valence and conduc-
tion bands are obtained by the analysis of 
().18 The
calculated real part of 	() in infinite wavelength (i.e.,
the limit of zero energy) for x=0 is 3.15 and for x=1 is
2.93, which are in agreement with previous theoretical
values such as 2.6691 for ZnAl2O418 and 3.112 for
MgAl2O4.25 In addition, the 	() in infinite wavelength
is 3.09 for x=0.25, 3.03 for x=0.5, and 2.98 for x=0.75,
signaling a negative trend with the increase of the doping
amount x. These can also indicate that the real part 	()
of the limit of zero energy has a square fit relationship
with the refractive index n localized zero energy. The
	() reaches a maximum value of 4.22 at about 6.15 eV
for x=0, 4.28 at 8.88 eV for x=0.25, 4.30 at 8.82 eV for
x=0.5, 4.29 at 8.84 eV for x=0.75 and 4.39 at 8.73 for
x=1.
Table 3: The imaginary part (2()) of dielectric function for
MgxZn1-xAl2O4 (x=0, x=1).
ZnAl2O4 MgAl2O4
Present Calc.18 Calc.40 Present Calc.23 Calc.25
Threshol
d Peak
position
3.49 4.31 ~4.25 4.63 7.4
7.38 7.82 ~8.01 6.25 6.27
10.87 10.98 7.69 7.44
14.63 14.08 10.01 9.42
15.54 12.91 10.19
The refractive index and the extinction coefficient are
shown in Figure 7. One can see that the static refractive
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743 739
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 7: Refractive index of Mg doped ions at various doping con-
centration
Figure 6: Dielectric function of Mg doped ions at different doping
concentration
index n(0) at the zero frequency limits is 1.77, 1.76,
1.73, 1.72 and 1.71 from x=0 to x=1, which are con-
sistent with values derived from the real part 	() of the
dielectric function mentioned above. They reach a maxi-
mum value of 2.12 at 10.05 eV for x=0, 2.14 at 9.01 eV
for x=0.25, 2.13 at 8.97 eV for x=0.5, 2.14 at 8.95 ev for
x=0.75 and 2.16 at 8.84 eV for x=1, compared to other
theoretical values listed in Table 4. We note that the
refractive index n(0) decreases with an increase of x. It
indicates that the n(0) likely is decided by the bond
length of Zn-O, Al-O, Mg-O and the volume of
MgxZn1-xAl2O4.
Table 4: Calculated refractive index for MgxZn1-xAl2O4 (x=0, x=1)
n (0)
n
Maximum Energy(eV)
ZnAl2O4
Present 1.77 2.13 10.15
Calc. 1.63 2.16 10.71
Calc. 1.74
MgAl2O4
Present 1.71 2.16 8.84
Calc.53 1.61 2.40 11.35
Calc.25 1.763
Expt.54 1.71
The different band structure is responsible for diffe-
rent structure in the optical spectra because the optical
spectra originates from the transitions from the top va-
lence band to the bottom conduction band. For instance,
a different band gap corresponds to different absorption
edge. The relationship between the absorption edge and
the band gap is described by Equation (6):
hc
d T
A
hc
Eg 
⎛
⎝
⎜ ⎞
⎠
⎟ ⎛
⎝
⎜ ⎞
⎠
⎟ ⎛
⎝
⎜ ⎞
⎠
⎟ = −⎛⎝
⎜ ⎞
⎠
⎟
2 2
21 1ln (6)
where  is the wavelength, T is the transmissivity, A is
the transition coefficients of the direct band gap, d is the
thickness and Eg is the value of the band gap. As shown
in Figure 8a, it is found that MgxZn1-xAl2O4(x=0) shows
an absorption shoulder around 360 nm, which is in
agreement with the experimental value. For instance, the
optical absorbance spectrum of ZnAl2O4 was detected in
the 250–400 nm region at room temperature,17 and its
adsorption shoulder was also observed in the 290–375 nm
wavelength region for the sample calcined at 700 °C.52
MgxZn1-xAl2O4(x=1) shows an absorption shoulder
around 270 nm, meaning that the absorption shoulder
undergoes a small blue shift. This is in agreement with
the imaginary part 
() of the dielectric function, and
also suggests that perfect MgAl2O4 spinel is a
transparent crystal, and its transparency is higher than
that of ZnAl2O4 in the visible region. Meanwhile, the
absorption shoulder is 340 nm for x=0.25, 310 nm for
x=0.50, 290 nm for x=0.75 and 270 nm for x=1.
Moreover, as shown in Figure 8b, where it seems that
the absorption region shifts towards lower energy for
ZnAl2O4 than MgAl2O4 due to the smaller band gap of
the former than the latter, as predicted by the imaginary
part of the dielectric function as well as the data derived
from Equation (6). The absorption edge starts from
about (3.66, 3.95, 4.18, 4.50 and 4.86) eV from x=0 to
x=1. This is mainly attributed to electronic transitions
from the O-2p located at the top of the valence band to
the empty Zn-4s electron states dominating the bottom
of the conduction band for x=0. Since Zn is replaced by
Mg, electronic transitions from O-2p to the empty
Mg-3p electron states, yielding an increase in band gap,
so that absorption edge starts at higher energy (4.86
eV), due to Mg-3p electron states dominating the
bottom of the conduction band for x=1. Other peaks
locates at (7.46, 11.77, 13.80, 16.05 and 17.15) eV for
x=0, (6.75, 7.57, 11.91, 13.63 and 17.30) eV for x=0.25,
(5.61, 13.41 and 17.35) for x=0.5, (5.85, 10.49, 13.21
and 17.58) eV for x=0.75 and (6.28, 7.76, 10.21, 13.33,
15.11 and 17.66) eV for x=1, in comparison with other
theoretical values listed in Table 5.
Table 5: The adsorption spectra of perfect MgxZn1-xAl2O4 (x=0, x=1).
ZnAl2O4 MgAl2O4
Present Calc.18 Calc.40 Present Calc.14
Threshold
Peak
position
3.66 4.20 ~4.31 4.86 ~5.05
7.46 7.83 ~8.03 6.28 ~6.14
13.80 14.17 7.76 ~7.03
16.05 16.41 10.21 ~10.15
17.15 17.35 13.33 13.75
The energy-loss function has a large effect on usage
of material. For example, the sharper peak of energy
loss, explained narrower scope, the better the optical
storage efficiency. Besides, energy loss function is an
important factor for describing the energy loss of a fast
electron traversing in a material, and the prominent
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
740 Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 8: Absorption spectra of Mg doped ions at various doping
concentration: a) the unit of the vertical axis for absorption spectra is
wavelength (nm), b) the unit of abscissa is energy (eV)
peaks in the energy-loss function representing a charac-
teristic associated with the plasma resonance (a collec-
tive oscillation of the valence electrons).51 The energy-
loss function is displayed in Figure 9. It can be seen that
the primary peak emerges at 22.43 eV for x=0
(ZnAl2O4), which is consistent with the theoretical value
of 20.99 eV.18 Additionally, the energy-loss function for
ZnAl2O4 between 0 eV and 12 eV is in agreement with a
previous report.40 Other peaks are located at 22.19 eV for
x=0.25, 22.00 eV for x=0.5, 21.78 eV for x=0.75 and
21.60 eV for x=1.
There is close relationship between reflectivity and
band gap, i.e., the higher coefficient of reflectivity (R(0))
at zero frequency corresponds to a smaller band gap.
Additionally, the reflection takes an important role in
optical losses. As can be seen from Figure 10 the high
reflectivity localizes between 18.61 eV and 22.32 eV,
which is consistent with the energy-loss function men-
tioned above.
4 CONCLUSIONS
The effect of Mg+2 versus Zn+2 by comparing the
structural, electronic and optical properties of
MgxZn1-xAl2O4 (from x=0 to x=1) has been implemented
using the DFT+U method. The calculations show that the
volume of the unit cell changes linearly with increasing
Mg-doping amount (x). The Al-O bond length of
MgxZn1-xAl2O4 increases with x, suggesting it has a
weaker bond stiffness. On the basis of the imaginary
parts of the dielectric function, it is found that critical
points occur at about 3.49 eV for ZnAl2O4, which is
lower than that for Mg-doped ZnAl2O4, indicating that
absorption shoulder undergoes a blue shift in the UV
region as evidenced by the absorption spectra. The blue
shift is probably due to the electronic transition from
O-2p to the empty Mg-3p electron states. For real parts
of dielectric function, the limit of zero energy has a
square fit relationship with the refractive index (n(0))
localized zero energy, which is verified by the reflec-
tivity spectra. Furthermore, the absorbance spectra,
reflectivity spectra and the refractive index show that
these compounds are suitable for UV reflective coatings.
The peak of the energy-loss function shows that
MgxZn1-xAl2O4 can be a candidate for optical storage ma-
terials.
Acknowledgment
This work is supported by the project from
Chongqing Municipal Education Commission (No.
KJ1601218), Young Foundation of Yangtze Normai
University (No. 2015XJXM29) and Talent Program of
Yangtze Normai University (No. 2015KYQD03).
6 REFERENCES
1 N. Bouropoulos, I. Tsiaoussis, P. Poulopoulos, P. Roditis, S. Bas-
koutas, ZnO controllable sized quantum dots produced by polyol
method: an experimental and theoretical study, Mater. Lett., 62
(2008), 3533–3535, doi:10.1016/j.matlet.2008.03.044
2 W. S. Tzing, W. H. Tuan, The strength of duplex Al2O3-ZnAl2O4
composite, J. Mater. Sci. Lett., 15.16 (1996), 1395–1396,
doi:10.1007/BF00275286
3 S. A.T. Redfen, R. J. Harrison, H. S. C. O’Neill, D. R. R. Wood,
Thermodynamics and kinetics of cation ordering in MgAl2O4 spinel
up to 1600 °C from in situ neutron diffraction, Amer. Mineral., 84.3
(1999), 299–310, doi:10.2138/am-1999-0313
4 H. Cynn, S. K. Sharma, T. F. Cooney, M. Nicol, High-temperature
Raman investigation of order-disorder behavior in the MgAl2O4
spinel, Phys. Rev. B, 45.1 (1992), 500–502, doi:10.1103/PhysRevB.
45.500
5 QivaStar. Inc, Ridgeerest. CA, and Hugest Space and Communi-
cation CO., El. Segundo, CA, U. S. Pat. N0. 5820669, 1998
6 K. P. Surendran, P.V. Bijumon, P. Mohanan, M.T. Sebastian,
(1-x)MgAl2O4-xTiO2 dielectrics for microwave and millimeter wave
applications, Appl. Phys., A 81.4 (2005), 823–826, doi:10.1007/
s00339-005-3282-5
7 P. Fu, W. Z. Lu, W. Lei, Y. Xu, X. H. Wang, J. M. Wu, Transparent
polycrystalline MgAl2O4 ceramic fabricated by spark plasma
sintering: Microwave dielectric and optical properties, Ceram. Int.,
39.3 (2013), 2481–2487, doi:10.1016/j.ceramint.2012.09.006
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743 741
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 10: Calculated reflection of MgxZn1-xAl2O4 obtained from the
CASTEP calculation
Figure 9: Calculated energy loss function of MgxZn1-xAl2O4 obtained
from the CASTEP calculations
index n(0) at the zero frequency limits is 1.77, 1.76,
1.73, 1.72 and 1.71 from x=0 to x=1, which are con-
sistent with values derived from the real part 	() of the
dielectric function mentioned above. They reach a maxi-
mum value of 2.12 at 10.05 eV for x=0, 2.14 at 9.01 eV
for x=0.25, 2.13 at 8.97 eV for x=0.5, 2.14 at 8.95 ev for
x=0.75 and 2.16 at 8.84 eV for x=1, compared to other
theoretical values listed in Table 4. We note that the
refractive index n(0) decreases with an increase of x. It
indicates that the n(0) likely is decided by the bond
length of Zn-O, Al-O, Mg-O and the volume of
MgxZn1-xAl2O4.
Table 4: Calculated refractive index for MgxZn1-xAl2O4 (x=0, x=1)
n (0)
n
Maximum Energy(eV)
ZnAl2O4
Present 1.77 2.13 10.15
Calc. 1.63 2.16 10.71
Calc. 1.74
MgAl2O4
Present 1.71 2.16 8.84
Calc.53 1.61 2.40 11.35
Calc.25 1.763
Expt.54 1.71
The different band structure is responsible for diffe-
rent structure in the optical spectra because the optical
spectra originates from the transitions from the top va-
lence band to the bottom conduction band. For instance,
a different band gap corresponds to different absorption
edge. The relationship between the absorption edge and
the band gap is described by Equation (6):
hc
d T
A
hc
Eg 
⎛
⎝
⎜ ⎞
⎠
⎟ ⎛
⎝
⎜ ⎞
⎠
⎟ ⎛
⎝
⎜ ⎞
⎠
⎟ = −⎛⎝
⎜ ⎞
⎠
⎟
2 2
21 1ln (6)
where  is the wavelength, T is the transmissivity, A is
the transition coefficients of the direct band gap, d is the
thickness and Eg is the value of the band gap. As shown
in Figure 8a, it is found that MgxZn1-xAl2O4(x=0) shows
an absorption shoulder around 360 nm, which is in
agreement with the experimental value. For instance, the
optical absorbance spectrum of ZnAl2O4 was detected in
the 250–400 nm region at room temperature,17 and its
adsorption shoulder was also observed in the 290–375 nm
wavelength region for the sample calcined at 700 °C.52
MgxZn1-xAl2O4(x=1) shows an absorption shoulder
around 270 nm, meaning that the absorption shoulder
undergoes a small blue shift. This is in agreement with
the imaginary part 
() of the dielectric function, and
also suggests that perfect MgAl2O4 spinel is a
transparent crystal, and its transparency is higher than
that of ZnAl2O4 in the visible region. Meanwhile, the
absorption shoulder is 340 nm for x=0.25, 310 nm for
x=0.50, 290 nm for x=0.75 and 270 nm for x=1.
Moreover, as shown in Figure 8b, where it seems that
the absorption region shifts towards lower energy for
ZnAl2O4 than MgAl2O4 due to the smaller band gap of
the former than the latter, as predicted by the imaginary
part of the dielectric function as well as the data derived
from Equation (6). The absorption edge starts from
about (3.66, 3.95, 4.18, 4.50 and 4.86) eV from x=0 to
x=1. This is mainly attributed to electronic transitions
from the O-2p located at the top of the valence band to
the empty Zn-4s electron states dominating the bottom
of the conduction band for x=0. Since Zn is replaced by
Mg, electronic transitions from O-2p to the empty
Mg-3p electron states, yielding an increase in band gap,
so that absorption edge starts at higher energy (4.86
eV), due to Mg-3p electron states dominating the
bottom of the conduction band for x=1. Other peaks
locates at (7.46, 11.77, 13.80, 16.05 and 17.15) eV for
x=0, (6.75, 7.57, 11.91, 13.63 and 17.30) eV for x=0.25,
(5.61, 13.41 and 17.35) for x=0.5, (5.85, 10.49, 13.21
and 17.58) eV for x=0.75 and (6.28, 7.76, 10.21, 13.33,
15.11 and 17.66) eV for x=1, in comparison with other
theoretical values listed in Table 5.
Table 5: The adsorption spectra of perfect MgxZn1-xAl2O4 (x=0, x=1).
ZnAl2O4 MgAl2O4
Present Calc.18 Calc.40 Present Calc.14
Threshold
Peak
position
3.66 4.20 ~4.31 4.86 ~5.05
7.46 7.83 ~8.03 6.28 ~6.14
13.80 14.17 7.76 ~7.03
16.05 16.41 10.21 ~10.15
17.15 17.35 13.33 13.75
The energy-loss function has a large effect on usage
of material. For example, the sharper peak of energy
loss, explained narrower scope, the better the optical
storage efficiency. Besides, energy loss function is an
important factor for describing the energy loss of a fast
electron traversing in a material, and the prominent
C. XIANG et al.: ELECTRONIC AND OPTICAL PROPERTIES OF THE SPINEL OXIDES ...
740 Materiali in tehnologije / Materials and technology 51 (2017) 5, 735–743
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 8: Absorption spectra of Mg doped ions at various doping
concentration: a) the unit of the vertical axis for absorption spectra is
wavelength (nm), b) the unit of abscissa is energy (eV)
peaks in the energy-loss function representing a charac-
teristic associated with the plasma resonance (a collec-
tive oscillation of the valence electrons).51 The energy-
loss function is displayed in Figure 9. It can be seen that
the primary peak emerges at 22.43 eV for x=0
(ZnAl2O4), which is consistent with the theoretical value
of 20.99 eV.18 Additionally, the energy-loss function for
ZnAl2O4 between 0 eV and 12 eV is in agreement with a
previous report.40 Other peaks are located at 22.19 eV for
x=0.25, 22.00 eV for x=0.5, 21.78 eV for x=0.75 and
21.60 eV for x=1.
There is close relationship between reflectivity and
band gap, i.e., the higher coefficient of reflectivity (R(0))
at zero frequency corresponds to a smaller band gap.
Additionally, the reflection takes an important role in
optical losses. As can be seen from Figure 10 the high
reflectivity localizes between 18.61 eV and 22.32 eV,
which is consistent with the energy-loss function men-
tioned above.
4 CONCLUSIONS
The effect of Mg+2 versus Zn+2 by comparing the
structural, electronic and optical properties of
MgxZn1-xAl2O4 (from x=0 to x=1) has been implemented
using the DFT+U method. The calculations show that the
volume of the unit cell changes linearly with increasing
Mg-doping amount (x). The Al-O bond length of
MgxZn1-xAl2O4 increases with x, suggesting it has a
weaker bond stiffness. On the basis of the imaginary
parts of the dielectric function, it is found that critical
points occur at about 3.49 eV for ZnAl2O4, which is
lower than that for Mg-doped ZnAl2O4, indicating that
absorption shoulder undergoes a blue shift in the UV
region as evidenced by the absorption spectra. The blue
shift is probably due to the electronic transition from
O-2p to the empty Mg-3p electron states. For real parts
of dielectric function, the limit of zero energy has a
square fit relationship with the refractive index (n(0))
localized zero energy, which is verified by the reflec-
tivity spectra. Furthermore, the absorbance spectra,
reflectivity spectra and the refractive index show that
these compounds are suitable for UV reflective coatings.
The peak of the energy-loss function shows that
MgxZn1-xAl2O4 can be a candidate for optical storage ma-
terials.
Acknowledgment
This work is supported by the project from
Chongqing Municipal Education Commission (No.
KJ1601218), Young Foundation of Yangtze Normai
University (No. 2015XJXM29) and Talent Program of
Yangtze Normai University (No. 2015KYQD03).
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j.physleta.2005.06.043
29 Y. Y. Jiang, J. W. Zhang, Z. Q. Hu, J. X. Liu, Synthesis and Visible
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30 F. Y. Zhang, Z. Zeng, J. Q. You, The Electronic and Optical
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