In conclusion, first-principle calculations have been performed using WIEN2K with GGA and GGA þ U exchange correlation to investigate the structural, electronic and half-metallic properti[r]
Trang 1Original Article
First-principles calculations to investigate structural, electronic,
Saadi Berria,b,*
a Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria
b Department of Physics, Faculty of Science, University of M'sila, Algeria
a r t i c l e i n f o
Article history:
Received 12 April 2019
Received in revised form
18 May 2019
Accepted 26 May 2019
Available online 3 June 2019
Keywords:
UX 2 O 6 (X¼Cr,V)
Half-metallic
Magnetic semiconductor
Electronic structure
Thermal properties
a b s t r a c t
Full potential linearized augmented plane wave plus local orbital's (FP-LAPWþ LO) method within density functional theory (DFT) is used to investigate the structural, electronic and half-metallic prop-erties of hexagonal UX2O6(X¼ Cr,V) Features such as the lattice constant (a and c), bulk modulus and its pressure derivative are reported The calculated lattice parameters are in good agreement with available experimental results Band structure and overall densities of states have proved UV2O6as an indirect half-metallic material with a band gap of 2.88 eV and UCr2O6as a magnetic semiconductor The results obtained, make the hexagonal UX2O6a candidate material for future spintronic applications Based on the quasi-harmonic Debye model, the thermodynamic properties of the material in question have been predicted taking into account of the lattice vibrations The variation of the lattice constant, bulk modulus and heat capacity as a function of pressure in the range 0e40 GPa and temperatures of 0e1500 K is computed Ourfindings show that external effects are highly effective in tuning some of the macroscopic properties of the compounds under study
© 2019 The Author Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
1 Introduction
Oxide ceramics materials of general formula AB2O6attracted a
great deal of attention followed by the discovery of exotic
proper-ties such as microwave dielectric properproper-ties of AB2O6(e.g., A¼ Ca,
Mg, Mn, Co, Ni, Zn, and B]Nb, Ta) [1], superconductivity (e.g.,
KOs2O6)[2], antiferromagnet (e.g., CuTa2O6)[3], an ionic solid at
high temperatures (573 K) (e.g., KTaWO6)[4], semiconductor with
a narrow band gap (2.70e2.85 eV) (e.g., Bi2WO6)[5], catalyst for
selective oxidation of methanol to methylal (e.g., SbRe2O6)[6], the
possible vibration modes (e.g., ThTi2O6) [7], ferromagnetic (e.g.,
ScRe2O6) [8], electrode material in lithium ion batteries (e.g.,
CdV2O6) [9], magnetic (e.g., PdAs2O6) [10], high-performance
supercapacitors (e.g., MnNb2O6)[11], suitable hosts for
redemit-ting phosphors (e.g., Te R2O6(R¼ La, Gd))[12e14], superior
elec-trochemical performances (e.g., ZnSb2O6)[15]
Half-metallic ferromagnets represent a new class of materials which absorbed a lot of attention considering their possible ap-plications in spintronics[16] This material has a complete (100%) spin polarization at the Fermi level because one spin channel is metallic while the other channel is semiconducting Various half-metallic ferromagnetisms have been predicted by the first-principles calculations or experimentally synthesized, such as double perovskites (for example, Sr2GdReO6[17,18]and Ba2NiUO6
[19]); zinc blende (ZB) CaC and CaN compounds[20]; Suzuki-type compounds Li6TMCl8 [21]; perovskite XAlO3(X ¼ Cs, Rb and K)
[22]; quaternary Heusler compounds (for example, PtZrTiAl, PdZrTiAl, CoMnCrSb, and Ti2RhSn1-xSix)[23e25]; CrO2[26]andg -U3O8 [27] Z Ali et al.[28] studied the electronic and magnetic properties of BaUO3using GGAþ U from which they found that it is
a half-metal with a ferromagnetic behavior Meantime, theoretical studies based on density functional theory have been conducted to predict the properties including phase stability, electronic structure and Half-Metallic properties[29e35]
In this paper, we investigated the structural, electronic, half-metallic and thermodynamic properties of UV2O6 and UCr2O6 compound using thefirst principle methods The remaining of the paper is organized as follows: The theoretical background is
* Laboratory for Developing New Materials and Their Characterizations,
Univer-sity of Setif 1, Algeria.
E-mail address: berrisaadi12@yahoo.fr
Peer review under responsibility of Vietnam National University, Hanoi.
Contents lists available atScienceDirect Journal of Science: Advanced Materials and Devices
j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d
https://doi.org/10.1016/j.jsamd.2019.05.002
2468-2179/© 2019 The Author Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license
Trang 2described in Section 2 Results are presented and discussed in
Section3 A summary of the results is given in
2 Method of calculations
As mentioned already, we have considered the experimental
crystal parameters as reported by Kovba[36], Hoekstra and Siegel
[37] UX2O6 (X¼ V, Cr) compounds crystallize in the hexagonal
space group P-31m (No.162), Z¼ 1 The crystal structures of UX2O6
(X¼ V, Cr) compounds is shown inFig 1 The present computations
are performed through the FP-LAPWþ LO method using DFT as
implemented in WIEN2K code [38] In the study of structural
properties, the exchange correlation energy is treated within the
GGA as parameterized by Perdew, Burk and Emzerhop Perdew
(PBE)-GGA method [39] The threshold energy between valence
and core states is set to be6.0 Ry Here, the KohneSham equations
are solved by expanding the wave functions in the spherical
har-monics form inside the atom spheres A plane wave expansion has
been used in the interstitial regions of atoms inside the unit cell We
have used lmax ¼ 10 for angular momentum expansion and
RMTKmax¼ 8 as a plane wave cut-off with 1400 k points for
hex-agonal phase Here RMTis the average muffin-tin (MT) radius and
Kmaxis the wave function cut-off The radii RMTof the muffin tins
(MT) are chosen to be approximately proportional to the
corre-sponding ionic radii The energy between successive iterations is
converged to 0.0001 Ry and forces are minimized to 1 mRy Bohr1
The 5f(U) and 3d (V and Cr) was treated using the GGA þ U
approach[40] The GGAþ U calculations used an effective
param-eter Ueff¼ U þ J, where U is the Hubbard parameter and J is the
exchange parameter As a matter of fact, the use of the Hubbard parameter (GGA þ U) approaches so as to treat the exchange-correlation potential is very efficient for studying strongly corre-lated electrons where the energy band gap of the material of in-terest can be evaluated more accurately In these cases, the core electrons are taken to be relativistic whereas the valence electrons are considered to be as semi-relativistic This is probably best suited for our system and for a full potential method The Ueffis taken to be 5.01 eV and 4.97 eV for U(5f) and X(3d) atoms similarly to Refs
[41,42], respectively
To investigate the thermodynamic properties of hexagonal UX2O6(X¼ V, Cr) compounds we apply the quasi-harmonic Debye model [43] In this model, the non-equilibrium Gibbs function
G*(V;P,T) is expressed as follows,
GðV; P; TÞ ¼ EðVÞ þ PV þ AVib½qðVÞ; T (1) where E(V) is the total energy per unit cell, PV corresponds to the constant hydrostatic pressure condition,qðVÞ is the Debye
tem-perature, and Avib is a vibrational term that can be written using the Debye model of the phonon density of states as[44],
Avibðq; TÞ ¼ nkT
9q
8Tþ 3 ln1 eq=T
Dðq=TÞ
(2)
where n is the number of atoms per formula unit and Dðq=TÞ is the
Debye integral For an isotropic solid,qis given as[45],
qD¼ Zh6p2V1=2ni1=3
fðrÞ
ffiffiffiffiffiffiffiffiffiffi
BS
Mk2B
s
(3)
where M is the molecular mass per unit cell and BSis the adiabatic bulk modulus The latter is approximated by the static compress-ibility as,
BSy BðVÞ ¼ Vd2EðVÞ
fðrÞ in Eq.(3)is reported in Refs.[46] The Poisson rationis taken to
be 0.25 [47] Thus, the non-equilibrium Gibbs function G*(V;P,T) versus (V; P, T) is minimized with respect to the volume V as,
vG* ðV; P; TÞ vV
Fig 1 Crystal structure for UX 2 O 6
S Berri / Journal of Science: Advanced Materials and Devices 4 (2019) 319e326 320
Trang 3By solving Eq.(5), one can obtain the thermal equation-of state (EOS) V(P,T) The heat capacity CVand the thermal expansion
co-efficientaare given by[48],
CV¼ 3nk
4Dq
T
3q=T
eq=T 1
(6)
S¼ nkh4Dq
T
3 ln1 eq=Ti
(7)
a¼gCV
wheregis the Gr}uneisen parameter, which is defined as,
g¼ d lnqðVÞ
Through the quasi-harmonic Debye model, one could calculate the thermodynamic quantities at any given temperatures and pressures of UX2O6(X¼ V, Cr) compounds from the obtained EeV data at T¼ 0 and P ¼ 0
3 Results and discussion The main objective in this work is to calculate the total en-ergy as a function of the unit-cell volume around the equilib-rium cell volume V0 for UX2O6 (X ¼ V, Cr) compounds in the spin-polarization (FM state) Fig 2shows the total energy as a function of the unit-cell volume The equilibrium lattice con-stant (a and c), bulk modulus B and its first-order pressure derivative B0have been computed using Murnaghan's equation
of state (EOS)[49] The equilibrium lattice parameters (a and c),
Table 1
Lattice constant a (Å), c (Å), bulk modulus B (in GPa), and first-pressure derivative of bulk modulus B 0 for UX 2 O 6 compounds.
Fig 3 The band structure of the UCr 2 O 6 and UV 2 O 6 for the spin-up and spin-down
electrons.
-10 -8 -6 -4 -2 0 2 4 6 8 10
Total
U
Cr
O
Energy(eV)
-10 -8 -6 -4 -2 0 2 4 6 8
10
Energy(eV)
Total
U
V
O
Trang 4-8 -6 -4 -2 0 2 4 6 8 -0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
U-DX2Y U-DZ2
-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8
Cr-DX2Y
O-p
Energy (eV)
Energy (eV)
-1,2
-0,8
-0,4
0,0
0,4
0,8
1,2
Cr-DZ2
U-f
(a)
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
U-DX2Y U-DZ2
(b)
-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8
V-DX2Y
O-p
Energy (eV)
Energy (eV)
-0,8
-0,4
0,0
0,4
0,8
V-DZ2
U-f
Fig 5 Spin-polarized partial densities of states (DOS) for (a) UCr 2 O 6 and (b) UCr 2 O 6
S Berri / Journal of Science: Advanced Materials and Devices 4 (2019) 319e326 322
Trang 5the bulk moduli B and their corresponding pressure derivatives
B0, along with the experimental results where available[36,37],
are listed in Table 1 The predicted values of the optimized
structural parameters and their equivalent experimental ones
yields excellent agreement as listed in Table 1 To our
knowl-edge, there are no experimental or theoretical data reported for
the bulk modulus and its pressure derivative for the material of
interest, and hence our results are predictions We have also
included in Table 1 the bulk modulus for CaTa2O6 [50] for
comparison purpose
Figs 3 and 4show respectively the self-consistent scalar
rela-tivistic spin-polarized band structures and total density of states of
U(V, Cr)2O6in its Hexagonal phase The partial densities of states, in
which the spin-up and spin-down sub-bands, are shown inFig 5
The Fermi level set as 0 eV The band structure and density of states
computed via the GGA approach are shown as a prototype given the
fact that the band profiles obtained from GGA approach are quite
similar to those calculated via GGAþ U method with a negligible
difference in details Based on the lattice symmetry, the integration
pathsG-K-M-G-A are performed so as to treat the band structure
for Hexagonal phase
For the UV2O6compound, one can observe the absence of a gap
at the Fermi level for the majority-spin band, which confirms the
metallic behavior found for the spin-up, while the minority spin
band shows a semiconducting gap around the Fermi level Hence, in
this compound the minority-spin band, the valence band
maximum (VBM) is located at theGpoint and the conduction band
minimum (CBM) is located in the K direction The half-metallic gap
[17], which is determined as the minimum between the lowest
energy of majority (minority) spin conduction bands with respect
to the Fermi level and the absolute values of the highest energy of
the majority (minority) spin valence bands, is 2.88 eV This energy
gap in the minority-spin band gap leads to 100% spin polarization at
the Fermi level, resulting in the half-metallic behavior at
equilib-rium state
For the UCr2O6compound, there is a energy band gap in both
spin channel but the two gaps are not located at the same energy
region and the Fermi Note that, there is a difference in the band
structure plot for the two spin channel For the majority-spin band,
both the valence band maximum (VBM) and the conduction band
minimum (CBM) occur at the high-symmetry point K in the
Bril-louin zone Hence, the material being studied here is a direct
band-gap semiconductor However, as far as the minority-spin channel is
concerned, the VBM occurs atGpoint and the CBM is located at the
K point Therefore, the material in question is an indirect band-gap
semiconductor
Fig 6illustrates the total density of states of UX2O6 in the
hexagonal (P-31m) structure at three different pressures (0.0,
15.0 and 30.0 GPa).Table 2presents our obtained energy band
gap values for UX2O6 compound calculated using PBE-GGA
approache at various pressures, namely 0.0, 15.0 and 30.0 GPa
Accordingly, one can see that the energy band gap increases with
increasing pressure For the UV2O6 compound, one can note a
preserved half-metallic nature in the stress range of 0.0 GPa up to
30.0 GPa
The nature of the electronic band structure has been elucidated
by calculating the total and partial densities of states (DOS) of
UX2O6compound for an energy range ranging from8 to 8 eV (see
Fig 5) At low energies and in particular in the core states the main
contribution is due to O-p state; the second part which is beyond
the Fermi level, where the contribution is due to X DX2Y and X DZ2
states The conduction band is above the Fermi level This bond is
essentially composed of U DX2Y and U DZ2 orbitals hybridization
with U 5f states
Normally, exchange interactions are very short-ranged, confined to electrons in orbitals on the same atom or nearest neighbor atoms but longer-ranged interactions can occur via intermediary atoms and this is termed superexchange The double-exchange mechanism is a type of a magnetic exchange that may arise between ions in different oxidation states First proposed by Clarence Zener[51]and later developed by Anderson
-15 -10 -5 0 5 10 15
UCr2O6
P=30 GPa
P=15 GPa
Energy (eV)
-15 -10 -5 0 5 10 15
UV2O6
P=30 GPa P=15 GPa
Energy (eV)
P=0 GPa (b)
Fig 6 Spin-polarized total densities of states (TDOS) for (a) UCr 2 O 6 and (b) UCr 2 O 6 at various pressures.
Table 2 Calculated static constants and energy band gap for UX 2 O 6 compounds at different pressures.
Table 3 Individual and net magnetic moments (mB ) of UX 2 O 6 (A ¼ Cr, Mo) from GGA and GGA þ U method.
Method m Cr/V m U m o m interstitial m Total
UV 2 O 6 GGA 1.20023 1.16116 0.01953 0.59170 4.00 GGA þ U 1.19956 1.16366 0.02038 0.59209 4.00 UCr 2 O 6 GGA 2.49963 0.37332 0.00794 0.66150 6.00 GGA þ U 2.49884 0.37552 0.00800 0.66269 6.00
Trang 6and Hasegawa[52], is generally agreed to provide a description of
the FM ground state this theory predicts the relative ease with
which an electron may be exchanged between two species
Elec-tronic structures from a full-potential linearized augmented plane
wave method also demonstrated that the half-metallic character is
not caused by direct U-U or X-X interactions but by indirect
OeXeOeU ped and pef couplings, which are simultaneously
responsible for their ferrimagnetic character[53]
The calculated total and atom-resolved magnetic moments of
UCr2O6and UV2O6in the GGA and GGAþ U methods are
summa-rized inTable 3 The total magnetic moments per unit cell of 6.00
and 4.00mBfor UCr2O6and UV2O6compound are close to an integer
which agrees with the half metallicity of these materials The main
source of magnetization in these compounds is thus the unfilled U
(5f), Cr and V (3d) states and small contributions from the
inter-stitial region, whereas the moments of the Oxygen are small Our
results for magnetic moment for uranium atoms which is in
agreement with previous studies[27] The magnetic moments of
the Cr and V atoms are in agreement with theoretical data[54]
In this computational work, to investigate the thermodynamic
properties of UCr2O6and UV2O6compounds under high
tempera-ture and high pressure, we apply the quasi-harmonic Debye
approximation As a first step, a set of total energy calculation
versus primitive cell volume (EeV) was carried out, in the static approximation The results are thenfitted with a numerical EOS in order to determine its structural parameters at P¼ 0 and T ¼ 0, and
to derive the macroscopic properties as a function of pressure and temperatures from standard thermodynamic relations
The diagrams that represent the volume unit cell-temperature
at various pressures and lattice constant-pressure at different temperatures for UCr2O6and UV2O6compounds being studied here are shown inFig 7 Note that for a given pressure, the volume unite cell increases monotonically with raising temperature Neverthe-less, the rate of increase seems to be very moderate On the other hand, for a given temperature, the volumes unite cell decreases with increasing pressure In the present work, our calculated vol-umes for UCr2O6and UV2O6compounds at zero pressure and room temperature is found to be 704.04 and 703.54 (u.a.)3, respectively
InFig 8, the relationships between bulk modulus (B) and tem-peratures (T) are all nearly linear at various pressures from 0 to
40 GPa One can notice that the bulk modulus is an important parameter to define its resistance to volume change under compression The bulk modulus decreases monotonically and very moderately when the temperature increases At room temperature and zero pressure, the bulk modulus for UCr2O6and UV2O6 com-pound is 843.61 GPa and 849.29 GPa, respectively
Fig 7 Temperature dependence of the volume at various pressures.
S Berri / Journal of Science: Advanced Materials and Devices 4 (2019) 319e326 324
Trang 7The evolution of the heat capacity at a constant volume CVas a
function of temperature at various pressures ranging from 0 to
40 GPa is displayed inFig 9 Note that CVincreases with raising
temperature The behavior appears to be rapid at low temperatures
but becomes slow at high temperatures For temperatures less than
1100 K, CV depends on both temperature and pressure At high
temperatures, CV approaches approximately 215.40 and
215.96 J mol1K1for UCr2O6and UV2O6compounds, respectively
The details in this change seem to depend on pressure The
behavior of CVfor all compounds of interest exhibits similar
fea-tures in a wide range of pressures and temperafea-tures At zero
pressure and a temperature of room temperature, our findings
yielded values of CVof about 108.62 and 108.08 J mol1K1for
UCr2O6and UV2O6compounds, respectively
4 Conclusion
In conclusion,first-principle calculations have been performed
using WIEN2K with GGA and GGAþ U exchange correlation to
investigate the structural, electronic and half-metallic properties of
the hexagonal UX2O6(X¼ Cr,V) under different pressures It was
found that the UV2O6is an indirect half-metallic material with a
band gap of 2.88 eV, whereas the UCr2O6 is a magnetic
semi-conductor The half metallicity is attributed by the
double-exchange interaction mechanism via the U(f)eO(p)eX(d)-p
bounding The results obtained, make the hexagonal UX2O6 a
candidate material for future spintronic applications This
com-pound can keep perfect half-metallicity within the wide ranges of
the pressure from 0 to 30 GPa The thermal effects on the
macro-scopic properties of the compounds under study were predicted
using the quasi-harmonic Debye model where the lattice vibrations
were taken into consideration
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