Journal of Science: Advanced Materials and Devices (2018) 254e261 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Ab initio study of fundamental properties of XAlO3 (X ¼ Cs, Rb and K) compounds Saadi Berri a, b, * a b Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria Faculty of Science, University of M'sila, Algeria a r t i c l e i n f o a b s t r a c t Article history: Received 18 January 2018 Received in revised form 10 March 2018 Accepted 22 March 2018 Available online 29 March 2018 The structural, electronic, magnetic and optical properties of suggested XAlO3 (X ¼ Cs, Rb and K) perovskites under pressure effects are investigated by means of the first-principles calculations with the technique of the Full Potential Linearly Augmented Plane Wave (FP-LAPW) implemented within Wien2k computer package The electronic exchange correlation energy is determined by using Generalized Gradient Approximation together with SpineOrbit Interaction (GGA ỵ SOI) The lattice constant, bulk modulus and its pressure derivative are calculated Half-metallicity was preserved at ranges of 4.03 e4.19 Å, 4.03e4.18 Å and 3.74e4.09 Å for the CsAlO3, RbAlO3 and KAlO3 compounds, respectively The largest spin-flip gaps are found in the spin up channel, corresponding to a magnetic moment of mB/f.u Optical properties are also studied Dielectric function, refractive index, and loss energy are calculated and discussed The present work presents the first theoretical study of the perovskites of interest and still awaits experimental confirmations © 2018 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/) Keywords: Half-metallic Optical properties Electronic properties Magnetic properties Ferromagnetic materials Introduction Numerous investigations have been extensively done regarding the perovskite structure with different compositions and structures, motivated by their possible applications in numerous industrial and engineering domains [1] These compounds have many interesting properties such as mixed-conducting oxides for gas separation (e.g., SrFeCo0.5Ox) [2], electro-ceramic material (e.g., SrRuO3) [3], cathode (e.g., LaMnO3) [4], photoelectrode and photocatalytic (e.g., BiFeO3) [5], photodetector (e.g., CsPbX3 (X ¼ Cl, Br, I)) [6], photovoltaic (e.g., (Br,I)PbX3) [7], solid electrolyte (e.g., (La,Sr)(Ga,Mg)O3-z) [8], hydrogen sensor (e.g., BaCeO3) [9], piezoelectric transducer (e.g., BaTiO3, Pb(Zr,Ti)O3) [10], thermistor actuator (e.g., Pb(Mg,Nb)O3) [11], Dielectric resonator (e.g., BaTiO3) [12], magnetic memory and ferromagnetism (e.g., GdFeO3, LaMnO3) [13e15], electrooptical modulator (e.g., (Pb, La)(Zr, Ti)O3) [16], laser (e.g., YAlO3) [17], superconductor (e.g., Ba(Pb, Bi)O3) [18], semi-conductivity (e.g., SrTiO3) [19], ferro-electricity (e.g., BaxSr1ÀxTiO3) [20] and half-metallic ferromagnet [21] In the present paper, the magnetic, electronic and optical properties of KAlO3, RbAlO3 and CsAlO3 are reported As far as the electronic structure, magnetic and optical properties of materials are concerned; these features play a crucial role in determining their magneto-optic properties for devices Therefore, accurate knowledge of these properties is very important for the application The aim of this work is to examine the electronic band structure of a wide range of perovskites KAlO3, RbAlO3 and CsAlO3, with emphasis on their derived properties The calculations are performed using ab initio a full relativistic version of the full-potential augmented plane-wave scheme within a generalized gradient approximation plus spineorbit interaction The rest of the paper is organized as follows: The theoretical background is presented in Section Results and discussions are presented in Section A summary of the results is given in Section Method of calculations * Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria E-mail address: berrisaadi12@yahoo.fr Peer review under responsibility of Vietnam National University, Hanoi Ab-initio calculations are executed using DFT as implemented within WIEN2K computer package [22] We have used the fullpotential linearized augmented plane wave (FP-LAPW) plus local https://doi.org/10.1016/j.jsamd.2018.03.001 2468-2179/© 2018 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/) S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 orbitals method through a density functional theory approach [22,23] The linearized augmented plane waves (LAPW) will be: fk;i xị ẳ > > < iGi þkÞx UÀ2e /outsid 255 ! where l is the polarization vector of light 〈Ojnecnjs〉 is the optical transition matrix from valence to conduction states and P is the …esphere /inside XÂ Ã > aalm ual ðEl ; ị ỵ balm u_ al El ; ị Ylm xa > : …sphere (1) lm K ¼ vector in Brillouin zone; Gi ¼ reciprocal lattice vector; Ula ðEl ; dinger equation for atom a, azimuthal ị ẳ solution of radial Schro a ðE ; Þ ¼ energy derivative of quantum number l, and energy El; U l l Ula ; aalm and balm determined by requiring basis functions to be continuous and smooth at sphere boundaries Here, the KohneSham equations are solved by expanding the wave functions in the spherical harmonics form inside the atom spheres Plane wave expansion is used in the interstitial regions of atoms inside the unit cell We have used lmax ¼ 10 for angular momentum expansion and RMTKmax ¼ as a plane wave cut-off with 4000 k points to achieve self-consistency Here RMT is the average muffintin (MT) radius and Kmax is the wave function cut-off The radii RMT of the muffin tins (MT) are chosen to be approximately proportional to the corresponding ionic radii The energy between successive iterations is converged to 0.0001 Ry and forces are minimized to mRy BohrÀ1 The MonkhorstePack (MP) technique is used for Brillouin zone integrations Exchange-correlation effects are treated using generalized gradient approximation (GGA) as parameterized by Perdew et al [24] To treat the interactions of heavier elements like Cs, Rb and K one needs to consider spineorbit interaction (SOI) during the calculations A dense k-mesh with 8000 k-points was used in the first Brillouin zone to calculate the linear optical properties Anyway, the optical prosperities such as dielectric functions, extinction coefficients, and refractive indices and energy loss as functions of photon energy are presented without spin-polarized “spin-up” and “spin-down”, because usually one gives unified results for these experimental observables We present the structural, electronic, Half-metallic and optical properties of cubic (Pm-3m) KAlO3, RbAlO3 and CsAlO3 at zero and elevated pressures The perovskite alkali metal aluminum oxygen (K, Rb and Cs)AlO3 usually crystallize in the cubic ABO3 perovskite structure (space group pm-3m) The atomic positions in XAlO3 are as follows: X atom at (0, 0, 0), Al atom at (0.5, 0.5, 0.5), and O atoms at (0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0) Optical properties of a solid are usually described in terms of the complex dielectric function ε(w) ẳ 1(w) ỵ i2(w) The imaginary part 2(w) was calculated from the momentum matrix elements between the occupied and unoccupied wave functions within the selection rules The real part ε1(w) of the dielectric function was calculated by the Kramers-Kronig transformation [25] of the imaginary part ε2(w) Other optical constants were computed from the values of ε(w) The frequency dependent complex dielectric tensor ε2(w) components are calculated by using the following mathematical expressions [26,27]: uị ẳ 2 16pe2 X! 〈Oj l n ec n js〉 d u U u uị ẳ þ (2) s 2P p Z∞ X u ε2 ðu0 Þ u0 À u2 du0 (3) principal value of the integral and the integral is over irreducible Brillouin zone The optical constants such as a refractive index n(w), are calculated in terms of the real and the imaginary parts of the complex dielectric function as follows [28] 1 uị ỵ 21 uị ỵ 22 uị2 p nuị ẳ 1 (4) The energy loss function L(w) solid at normal incidence can be derived by the following equation uị ẳ Luị ẳ Im uị uị2 ỵ uị2 (5) The following equation define the formation energy (Ef) for the XAlO3(X ¼ K, Rb and Cs) and determine the thermal stability of a compounds i h f Tot bulk bulk Ef ẳ EXAlO E ỵ E ỵ 3E X Al O (6) tot tot tot where EKAlO , ERbAlO and ECsAlO are the equilibrium total energies 3 calculated by first principles of the KAlO3, RbAlO3 and CsAlO3 bulk , E bulk and Ebulk correspond compounds per formula unit EKbulk , ERb Cs Al to the total energy per atom of solid for the K, Rb, Cs and Al atoms, respectively During calculation, Cs and Rb are taken as bodycentered cubic structure (space group Im-3m) and K and Al are taken as cubic close-packed (space group Fm-3m) The vacancy formation energy is about 3.02 eV [29] Results and discussion The main objective in this work is to calculate the total energy as a function of the unit-cell volume in both ferromagnetic (FM) and paramagnetic (PM) states As presented in Fig 1, the structural optimization curves are obtained in the FM and PM configurations The calculated total energies are fitted to the Murnaghan equation of state (EOS) EeV [30], so as to determine the ground state properties, such as equilibrium lattice constant a(Å), bulk modulus B(GPa) and its pressure derivative B' The calculated structural parameters of KAlO3, RbAlO3 and CsAlO3 are summarized in Table It can also be observed that the lattice constant ao for the PM and FM states has an increasing trend: a(CsAlO3) > a(RbAlO3) > a(KAlO3) The lattice constant increase with increasing atomic radii of alkali metal R(Cs ¼ 1.88 Å) > R(Rb ¼ 1.72 Å) > R(K ¼ 1.64 Å) [31] The crystal rigidity can be measured by the bulk modulus B, so a large B represents high crystal rigidity The bulk modulus was found to be increased in the following order: B(KAlO3) > B(RbAlO3) > B(CsAlO3) This increasing trend reveals that the compressibility as well as the hardness of the material increases in the same sequence On the other hand, for the FM phase the bulk modulus of KAlO3 is larger than those of RbAlO3 and CsAlO3 This means that KAlO3 is a harder 256 S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 -16517,74 RbAlO3 -6900,22 FM -16517,75 PM -16517,76 Energy (Ry) Energy (Ry) -6900,21 -6900,23 -6900,24 -6900,25 -6900,26 340 CsAlO3 FM PM -16517,77 -16517,78 -16517,79 -16517,80 360 380 400 420 440 460 480 -16517,81 340 360 380 400 420 440 460 480 500 500 V (u a.)3 V (u a.)3 -2141,55 Energy (Ry) FM KAlO3 -2141,56 PM -2141,57 -2141,58 -2141,59 -2141,60 340 360 380 400 420 440 460 V (u a.)3 Fig Calculated total energy as a function of volume for XAlO3 (X ¼ Cs, Rb and K) compounds Table Lattice constant a (Å), bulk modulus B (in GPa), and pressure derivative of bulk modulus B0 , total, partial magnetic moment (in mB) and formation energy for XAlO3 (X ¼ Cs, Rb and K) compounds a (Å) B (GPa) B0 Etot (Ry) Formation energy Ef (Ry) FM PM FM PM FM PM 3.87 3.86 3.95 3.86 4.02 4.00 118.32 119.62 110.20 111.74 97.20 96.95 4.53 4.35 4.38 4.29 4.13 3.65 À2141.59125 À2141.59861 À6900.26075 À6900.25000 À16517.8100 À16517.8015 À1.93064 À1.89126 À1.40094 À1.33248 À1.40094 À1.34259 mX mAl mO minterstitial mTotal e 0.002 0.022 0.172 À0.021 À0.023 À0.018 0.626 0.624 0.586 0.118 0.099 0.083 2.00 2.00 2.00 e e e Compounds KAlO3 RbAlO3 CsAlO3 KAlO3 RbAlO3 CsAlO3 material than RbAlO3 and CsAlO3 Until now, experimental or theoretical lattice parameters, the bulk modulus and its pressure derivative value have not been reported At an equilibrium lattice constant of 3.87 Å for KAlO3, 3.95 Å for RbAlO3 and 4.02 Å for CsAlO3, the total energy of the magnetic phase is 0.10, 0.15 and 0.12 eV f.uÀ1 for KAlO3, RbAlO3 and CsAlO3, which is lower than that of the paramagnetic one In Table 1, we have given the values of formation energy per formula unit of the KAlO3, RbAlO3 and CsAlO3 compounds The negative values of formation energy indicate that the KAlO3, RbAlO3 and CsAlO3 compounds are energetically stable and may be fabricated experimentally The self-consistent scalar relativistic band structures as well as density of states for KAlO3, RbAlO3 and CsAlO3 compounds, along the various symmetry lines within the GGA method, are given in Fig Note that, there is an overall topological resemblance for both compounds For these compounds, the minority spin band is metallic, while the majority spin band shows a semiconducting gap around the Fermi level of 6.62, 6.14, and 4.98 eV, respectively From the above mentioned findings, it can be concluded that these compounds exhibit a half-metallic character The half-metallic gap, which is the minimum between the absolute values of the valence band maximum (VBM) and the conduction band minimum (CBM), represents the same variation law, that is to say, the half-metallic gap also decreases for CsAlO3 (0.29 eV), KAlO3 (0.38 eV) and RbAlO3 (0.50 eV), successively The absence of the transition-metal atoms makes these compounds important model systems for the study of the origin and properties of half metallic ferromagnetism in sep electron systems Normally, exchange interactions are very short-ranged, confined to electrons in orbitals on the same atom or nearest neighbor atoms but longerranged interactions can occur via intermediary atoms and this is termed “super-exchange” The double-exchange mechanism is a type of a magnetic exchange that may arise between ions in S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 8 6 4 2 0 -2 -2 -2 -4 -4 -4 Energy (eV) a) CsAlO3 -6 Total density of States ( St/eV f,u) -8 b) R Γ -6 M X -8 Γ X Γ R M -8 6 4 2 0 -2 -2 -2 CsAlO3 KAlO3 -4 -6 -8 -6 -4 -2 M X -4 -6 -8 -6 -4 -2 Energy (eV) Γ R Γ -4 RbAlO3 -6 KAlO3 257 Γ RbAlO3 -6 -8 -6 -4 -2 Energy (eV) Energy (eV) Fig Spin-polarized a) band structure and b) total densities of states (TDOS) Density of States (St/eV spin f.u) RbAlO3 0,4 1,65 1,10 0,55 1,0 Rb-p 0,2 Rb-s 0,00 0,5 Al-p O-p O-s 0,0 0,0 -0,55 O-s Rb-d -1,10 -1,65 -0,5 -0,2 -1,0 -2,20 Energy (eV) Energy (eV) Density of States (St/eV spin f.u) -24 -18 -12 -6 -0,4 12 -24 -18 -12 -6 12 -24 -18 -12 -6 Energy (eV) 2,0 1,5 1,0 0,4 Cs-p Cs-s In the next stage, we presented the partial densities of states of RbAlO3, KAlO3 and CsAlO3 compounds as illustrated in Fig The Fermi level was set as eV Basically, for these compounds, the DOS can be divided into four parts, at lower energy core states where we find the contribution of X-s states in the core states; the second part Density of States (St/eV spin f.u) different oxidation states First proposed by Clarence Zener [32] and later developed by Anderson and Hasegawa [33], is generally agreed to provide a description of the FM ground state, but this theory predicts the relative ease with which an electron may be exchanged between two species 2,0 1,5 K-s 1,0 K-p 0,2 1,0 Al-p 0,0 0,0 O-s K-d -0,5 -0,5 -0,2 -1,0 -1,0 12 -0,4 -24 -18 -12 -6 CsAlO3 0,5 Al-p O-p O-s 0,0 0,0 0,0 -0,5 O-s Cs-d -0,5 -0,2 -1,5 -2,0 -1,0 -2,5 -0,4 -24 -18 -12 -6 Energy (eV) 12 -24 -18 -12 -6 Energy (eV) 12 -24 -18 -12 -6 Energy (eV) Fig Spin-polarized partial densities of states (DOS) Energy (eV) Energy (eV) 0,2 -1,0 O-p O-s 0,0 1,0 0,5 0,5 0,5 -1,5 -24 -18 -12 -6 KAlO3 0,4 6 12 -24 -18 -12 -6 Energy (eV) 258 S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 a=3.92Å a=3.87Å a=3.84Å a=4.00Å a=3.95Å 4 4 2 2 2 0 0 0 -2 -2 -2 -2 -2 -2 -4 -4 R Γ X M Γ -4 R Γ X M -4 R Γ Γ X Γ M -4 R X Γ M Γ 4 2 2 0 0 -2 -2 -2 -2 -4 -4 X M Γ Energy (eV) Γ -4 R Γ X M Γ X Γ M Γ M Γ R Γ X M Γ a=4.15Å R -4 R a=4.11Å a=4.07Å a=4.03Å Energy (eV) Energy (eV) Energy (eV) Energy (eV) a=3.8Å -4 R Γ X M Γ R Γ X Fig The calculated band structure of RbAlO3 as a function of the lattice constant is from À12 to À5 eV that is mainly derived from X-p states, the third part which is beyond the Fermi level, which represents the contribution of the s and p orbitals of O atoms hybridized with Al p states For unoccupied states above the Fermi level, which represents the contribution of the p orbitals of Al atoms hybridized with X-d electrons is principally for the highest conduction bands (CB) In a practical application, the external stress is one of the important factors to destroy half-metallicity The energy values of the conduction band minimums (CBM) and the valence band maximums (VBM) are used to characterize the half-metallicity under different lattice distortions for CsAlO3, KAlO3 and RbAlO3 compounds, as given in Fig In order to examine the effect of external stress on the half-metallicity, the band structures of RbAlO3 compound at different lattice constants were calculated, as shown in Fig In both spin channels, with lattice expanding, a clear change of the Fermi level position is observed The band structures at different lattice constants were presented only for RbAlO3 because it is similar to that of KAlO3 and CsAlO3 compounds with a small difference From Figs and 5, the half-metallicity can be kept in the range of 4.03e4.18 Å for RbAlO3 and in the range of 3.74e4.09 Å for KAlO3 and in the range of 4.03e4.19 Å for CsAlO3, respectively On the other hand, for the HM ferromagnets RbAlO3, KAlO3 and CsAlO3 studied in this paper, the effect of correlations might be expected to be less important since the magnetic Fig Conduction band minimum (CBM), valence band maximum (VBM), spin-up band gap Eg[ and total magnetic moment as a function of the lattice constant S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 With-SO -4 Without-SO -4 -4 CsAlO3 RbAlO3 -5 -5 -6 -6 -7 -7 259 KAlO3 -5 -6 Energy (eV) -7 -8 -9 -10 -8 -8 -16 -16 -17 -17 -18 -18 -19 -19 -20 -20 R Γ X M Γ -11 -16 -17 -18 -19 R Γ X M Γ -20 R Γ X M Γ Fig The calculated band structures of the perovskites using GGA and GGA ỵ SOC methods properties are governed by p electrons which experience fewer correlations than d electrons Meanwhile, one can see that the values of the total magnetic moments for RbAlO3, KAlO3 and CsAlO3 compounds are still z2 mB in the range of 3.75e4.09 Å, 3.69e5.37 Å and 3.75e4.09 Å, respectively Furthermore, it can be seen that for both compounds, in both spin directions, the band structure shows a semiconducting nature in the stress range of À14% to 3%, À14% to À7% and À14% to 3% for RbAlO3, KAlO3 and CsAlO3 compounds, respectively Next, in Fig we depict the band structures for RbAlO3, KAlO3 and CsAlO3 compounds with and without spineorbit interaction in a PM state at the equilibrium lattice constants In WIEN2k, spineorbit effects are included via a second variational procedure to calculate the eigenvalues and eigenvectors using the scalar relativistic wave functions The similar features of band structure are found for KAlO3 and CsAlO3 compounds In the case of CsAlO3 compound, the results show considerable differences in the energy levels both in the valence band (in the À19 eV to À17 eV and À7 eV to À5 eV regions) The calculated total and atom-resolved magnetic moments for RbAlO3, KAlO3 and CsAlO3 compounds are summarized in Table The present study shows that the total magnetic moments of ~2 mB/ fu for both compounds are close to an integer, which agrees with the half metallicity of these materials Here, the main source of Fig The real part ε1(u) and imaginary part ε2(u) of dielectric constant ε(u) for the perovskites XAlO3 (X ¼ Cs, Rb and K) in the PM state at the equilibrium lattice constants 260 S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 Table Position of the principal peaks of the imaginary part of the dielectric function for XAlO3 (X ¼ Cs, Rb and K) compounds GPa 15 GPa GPa 15 GPa GPa 15 GPa KAlO3 RbAlO3 CsAlO3 A1 A2 A3 1.47 1.63 0.97 1.33 1.15 1.59 1.89 2.05 1.28 1.71 1.70 1.99 2.20 2.35 1.90 2.02 2.30 2.79 magnetization in these compounds is thus two contributions one each from the oxygen atoms and the interstitial region, whereas the moments of the alkali metal and aluminum are small The nature of attraction in this system can be described by the sep exchange splitting Mainly, the first microscopic dielectric function describes the behavior of linear response of a material to the electromagnetic radiation field applied which displays the absorptive character of that material The real part of the dielectric function describes how much material polarized as a result of induced electric dipole creation when an electric field is applied while the imaginary part indicates how much material absorbs photon energy There are two contributions to ε2(u), namely, the intraband and interband transitions The contribution from intraband transitions is important only for metals The interband transitions can further be split in to direct and indirect transitions We neglect the indirect interband transitions, which involve scattering of phonons and are expected to give only a small contribution to ε2(u) In Fig we present the dielectric function of RbAlO3, KAlO3 and CsAlO3 compounds as calculated by FP-LAPW method at two different pressures (0.0 and 15.0 GPa) The real parts ε1(u) of these three alloys sharply increase in the photo energy range of 0e3 eV and disappear around eV (see Fig 7a) For ε1(u) > 0, photons propagate through the materials, for ε1(u) < 0, the electromagnetic wave is damped and for ε1(u) ¼ 0, only longitudinally polarized waves are possible For energies up to eV, based on our calculated band structure it would be worthwhile to identify the interband transitions that are responsible for the structure in ε2(u) We remark that the material possesses a high dielectric function within Near infrared NIR region and decreases at higher energy in the Near ultraviolet (NUV) Our analysis of the ε2(u) (See Fig 7b) spectra shows that the threshold energy (the first critical point) of the dielectric function (see Table 2) occurs at about A1, A2 and A3 eV, respectively These points are mainly coming from the electron transition from the O-p (VB), O-s (VB) and X-p (VB) to X-d (CB) orbitals The refractive index is a quantity that describes how much light is refracted after entering a material [34] The calculated refractive index n(u) and the loss energy at zero and elevated pressures using the GGA approach are displayed in Fig 8a Our results of n(u) show that XAlO3 has strong extinction effects at Near infrared NIR regions and then decreases with photon energy The energy loss function of XAlO3 as a function of photon energy is shown in Fig 8b, which describes the energy loss of a fast electron traversing the material It is observed that the prominent peaks are found at 2.66(3.31) eV, 2.88(3.51) eV and 2.74(3.25) eV at 0.0(15.0) GPa for KAlO3, CsAlO3 and RbAlO3, respectively The peaks in the energy loss spectra represent the characteristic associated with the plasma resonance and the corresponding frequency is the so-called plasma frequency up It is defined by the bulk plasma frequency up which occurs at ε1(u) ¼ and ε2(u) < [35] This indicates rapid reduction in the reflectance Hence this material becomes transparent when the incident photon energy is higher than 2.66 (3.31) eV, 2.88 (3.51) eV and 2.74 (3.25) eV at 0.0 (15.0) GPa for KAlO3, CsAlO3 and RbAlO3, respectively GPa 15 GPa 12 a) b) 4 KAlO3 24 Intensity (arb u.) Refractive index n (arb u.) KAlO3 20 16 12 CsAlO3 8 CsAlO3 4 RbAlO3 0 Energy (eV) RbAlO3 Energy Loss (eV) Fig The reflective index n(u) and energy loss function L(u) for the perovskite compounds XAlO3 (X ¼ Cs, Rb and K) in the PM state at the equilibrium lattice constants S Berri / Journal of Science: Advanced Materials and Devices (2018) 254e261 Conclusion For the XAlO3 (X ¼ Cs, Rb and K) compounds, the structural, electronic, magnetic and optical properties under various pressures have been reported using the full potential augmented plane wave method (FP-LAPW), implemented in the Wien2k within GGA ỵ SOC The lattice constant, bulk modulus and its pressure derivative of these perovskites are calculated Half-metallically is found in all the three compounds, with the largest spin-flip gaps in the spin up channel with a magnetic moment of mB/fu The halfmetallicity characteristic exists in the relatively wide ranges of 4.03e4.19 Å, 4.03e4.18 Å and 3.74e4.09 Å for the CsAlO3, RbAlO3 and 4.03e4.18 compounds, respectively Optical properties are also calculated and analyzed The dielectric function, refractive index, and loss energy are calculated and discussed References [1] Wen-Hong Kao, Sandra L Haberichter, Kathryn R Bullock, Corrosion resistant coating for a positive lead/acid battery electrode, J Electrochem Soc 139 (11) (1992) L105eL107, https://doi.org/10.1149/1.2069084 [2] U Balachandran, B Ma, P.S Maiya, R.L Mievillea, J.T Duseka, J.J Piccioloa, J Guana, S.E Dorrisa, M Liub, Development of mixed-conducting oxides for gas separation, Solid State Ionics 108 (1998) 363e370 [3] Thi Tuyet Mai Phan, Ngoc Chau Chu, Van Boi Luu, Hoan Nguyen Xuan, Duc re, Enhancement of polarization Thang Pham, Isabelle Martin, Pascal Carrie property of silane-modified BaTiO3 nanoparticles and its effect in increasing dielectric property of epoxy/BaTiO3 nanocomposites, J Sci Adv Mater Devices (1) (2016) 90e97 [4] N.Q Minh, Ceramic fuel-cells, J Am Ceram Soc 76 (1993) 563e588 [5] Upendra A Joshi, Jum Suk Jang, Pramod H Borse, Jae Sung Lee, Microwave synthesis of single-crystalline perovskite BiFeO3 nanocubes for photoelectrode and photocatalytic applications, Appl Phys Lett 92 (2008) 242106 [6] Parthiban Ramasamy, Da-Hye Lim, Bumjin Kim, Seung-Ho Lee, Min-Sang Lee, Jong-Soo Lee, All-inorganic cesium lead halide perovskite nanocrystals for photodetector applications, Chem Commun 52 (2016) 2067e2070 [7] Adam H Slavney, Te Hu, Aaron M Lindenberg, Hemamala I Karunadasa, A Bismuth-Halide double perovskite with long carrier recombination lifetime for photovoltaic applications, J Am Chem Soc 138 (7) (2016) 2138e2141 [8] M Feng, J.B Goodenough, A superior oxide-ion electrolyte, Eur J Solid State Inorg Chem 31 (8e9) (1994) 663e672 [9] H Iwahara, H Uchida, K Ono, K Ogaki, Proton conduction in sintered oxides based on BaCeO3, J Electrochem Soc 135 (2) (1988) 529e533 [10] D Dimos, C Mueller, Perovskite thin films for high-frequency capacitor applications, Annu Rev Mater Res 28 (1998) 397e419 [11] T Shaw, S Trolier-McKinstry, P McIntyre, The properties of ferroelectric films at small dimensions, Annu Rev Mater Sci 30 (2000) 263e298 [12] H Kishi, Y Mizuno, H Chazono, Base-metal electrode-multilayer ceramic capacitors: past, present and future perspectives, Japan J Appl Phys Part 42 (1) (2003) 1e15 [13] G.H Jonker, Magnetic compounds with perovskite structure Conducting and non-conducting compounds, Physica 22 (8) (1956) 707e722 261 [14] J DeTeresa, M Ibarra, P Algarabel, C Ritter, C Marquina, J Blasco, et al., Evidence for magnetic polarons in the magnetoresistive perovskites, Nature 386 (6622) (1997) 256e259 [15] Y Moritomo, A Asamitsu, H Kuwahara, Y Tokura, Giant magnetoresistance of manganese oxides with a layered perovskite structure, Nature 380 (6570) (1996) 141e144 [16] M Moret, M Devillers, K Worhoff, P Larsen, Optical properties of PbTiO3, PbZrxTi1-xO3, and PbZrO3 films deposited by metalorganic chemical vapor on SrTiO3, J Appl Phys 92 (1) (2002) 468e474 [17] M Weber, M Bass, G Demars, Laser action and spectroscopic properties of Er3ỵ in YAlO3, J Appl Phys 42 (1) (1971) 301 [18] J Ihringer, J Maichle, W Prandl, A Hewat, T Wroblewski, Crystal-structure of the ceramic superconductor BaPb0.75Bi0.25O3, Z Phys B Condens Matter 82 (2) (1991) 171e176 [19] H.P.R Frederikse, W.R Thurber, W.R Hosler, Electronic transport in strontium titanate, Phys Rev 134 (1964) 442 [20] C.B Samantaray, H Sim, H Hwang, Electronic structure and optical properties of barium strontium titanate (BaxSr1ÀxTiO3) using first-principles method, Phys B Condens Matter 351 (1e2) (2004) 158e162 [21] S Berri, D Maouche, M Ibrir, B Bakri, Electronic structure and magnetic properties of the perovskite cerium manganese oxide from ab initio calculations, Mater Sci Semicond Process 26 (2014) 199e204 [22] P Blaha, K Schwarz, G.K.H Madsen, D Kvasnicka, J Luitz, WIEN2K, an Augmented Plane WaveỵLocal Orbitals Program for Calculating Crystal €t, Wien, Austria, 2001, Properties, Karlheinz Schwarz, Technische Universita ISBN 3-9501031-1-2 [23] J.C Slater, Atomic radii in crystals, Adv Quant Chem (1964) 5564 [24] J.P Perdew, S Burke, M Ernzerhof, Generalized gradient approximation made simple, Phys Rev Lett 77 (1996) 3865 [25] M Alouani, J.M Wills, Calculated optical properties of Si, Ge, and GaAs under hydrostatic pressure, Phys Rev B 54 (1996) 2480 [26] A.H Reshak, S Auluck, Electronic and optical properties of the 1T structures of TiS2, TiSe2 and TiTe2, Phys Rev B 68 (2003) 245113 [27] S Berri, D Maouche, N Bouarissa, Y Medkour, First principles study of structural, electronic and optical properties of AgSbS2, Mater Sci Semicond Process 16 (6) (2013) 1439e1446 [28] A Delin, A.O Eriksson, R Ahuja, B Johansson, M.S Brooks, T Gasche, S Auluck, J.M Wills, Optical properties of the group-IVB refractory metal compounds, Phys Rev B 54 (1996) 1673 [29] Piotr M Kowalski, Bernd Meyer, Dominik Marx, Composition, structure, and stability of the Rutile TiO2(110) surface: oxygen depletion, hydroxylation, hydrogen migration, and water adsorption, Phys Rev B 79 (2009) 115410 [30] F.D Murnaghan, The compressibility of media under extreme pressures, Proc Natl Acad Sci USA 30 (1944) 5390 [31] R.L Moreira, A Dias, Comment on “Prediction of lattice constant in cubic perovskites”, J Phys Chem Solid 68 (2007) 1617 [32] C Zener, Interaction between the d-shells in the transition metals II Ferromagnetic compounds of manganese with perovskite, Struct Phys Rev 82 (1951) 403 [33] P.W Anderson, H Hasegawa, Considerations on double exchange, Phys Rev 100 (1955) 675 [34] S Berri, Theoretical analysis of the structural, electronic and optical properties of tetragonal Sr2GaSbO6, Chin J Phys 55 (6) (2017) 2476e2483 [35] R Saniz, Lin-Hui Ye, T Shishidou, A.J Freeman, Structural, electronic, and optical properties of NiAl3: first-principles calculations, Phys Rev B 74 (2006) 014209e014216 ... (Ef) for the XAlO3( X ¼ K, Rb and Cs) and determine the thermal stability of a compounds i h f Tot bulk bulk Ef ẳ EXAlO E ỵ E ỵ 3E X Al O (6) tot tot tot where EKAlO , ERbAlO and ECsAlO are the... principles of the KAlO3, RbAlO3 and CsAlO3 bulk , E bulk and Ebulk correspond compounds per formula unit EKbulk , ERb Cs Al to the total energy per atom of solid for the K, Rb, Cs and Al atoms,... Journal of Science: Advanced Materials and Devices (2018) 254e261 Table Position of the principal peaks of the imaginary part of the dielectric function for XAlO3 (X ¼ Cs, Rb and K) compounds