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First principle study of electronic, mechanical, optical and thermoelectric properties of CsMO3 (M = Ta, Nb) compounds for optoelectronic devices
Accepted Manuscript First principle study of electronic, mechanical, optical and thermoelectric properties of CsMO3 (M = Ta, Nb) compounds for optoelectronic devices B. Sabir, G. Murtaza, R.M. Arif Khalil, Qasim Mahmood PII:
S1093-3263(18)30483-2
DOI:
10.1016/j.jmgm.2018.09.011
Reference:
JMG 7235
To appear in:
Journal of Molecular Graphics and Modelling
Received Date: 4 July 2018 Revised Date:
18 September 2018
Accepted Date: 19 September 2018
Please cite this article as: B. Sabir, G. Murtaza, R.M. Arif Khalil, Q. Mahmood, First principle study of electronic, mechanical, optical and thermoelectric properties of CsMO3 (M = Ta, Nb) compounds for optoelectronic devices, Journal of Molecular Graphics and Modelling (2018), doi: https://doi.org/10.1016/ j.jmgm.2018.09.011. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Fig. 2: Calculated electronic band structures at ground state lattice constant by using PBEsol-mBJ potential for (a) CsNbO3 (b) CsTaO3.
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First principle study of electronic, mechanical, optical and thermoelectric properties of CsMO3 (M = Ta, Nb) compounds for optoelectronic devices B. Sabira, G. Murtazaa*, R.M.Arif Khalilb, Qasim Mahmooda a
Centre for Advanced Studies in Physics, GC University, Lahore-54000, Pakistan Materials Research Simulation Laboratory (MRSL), Department of Physics, Bahauddin Zakariya University,Multan,60800,Pakistan. * Corresponding author detail: Tel.: +92-4299211589, Ext.105, E-mail.: [email protected] (G. Murtaza)
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Abstract
The electronic, mechanical, optical and thermoelectric properties of Cesium based perovskites
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CsMO3 (M = Nb, Ta) in the cubic phase has been performed through PBEsol-mBJ scheme in the framework of DFT. The electronic band structures and density of states show the studied materials having a direct band gap in the visible range. The mechanical stability and ductile behavior have been analyzed from elastic constants. Moreover, the optical behavior of the studied materials has been analyzed in terms of dielectric functions, refractive index, extinction coefficient, absorption coefficient, optical conductivity, reflectivity and energy loss factor.
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Finally, the material response with temperature has been elaborated by electrical conductivity, thermal conductivity, Seebeck coefficient, power factor, heat capacity, Hall coefficient, susceptibility and electron density by using BoltzTraP code. This first principle calculation of optical and thermoelectric properties of the novel compounds provides a new route to the
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Key Words:
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experimentalist for the potential application in energy renewable devices.
DFT; Direct bandgap semiconductors; Mechanical stability; Thermoelectric and thermodynamic behavior; Optical emerging materials
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1. Introduction The cubic perovskites oxides with general formula ABO3 have attracted much attention, because of their simple synthesis and various physical properties that result from highly correlated d-band
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electrons and strong electron-lattice couplings [1]. These materials have been extensively used in optoelectronics, thermoelectric, laser frequency doubling waveguide and are very favorable for advanced technological application [2-5]. The waste of thermal energy and increasing its demand in the advanced scientific world inspired the researchers to fabricate the thermoelectric devices
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that convert the waste heat energy into electrical energy. For this purpose, the cesium based perovskites oxide type semiconductors are always in great attention because of high electrical conductivity, specific heat capacity and low value of thermal conductivity that increases their
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thermal efficiency. Moreover, along with thermal properties, these materials are also beneficial for optoelectronic device applications because their band gap falls in the visible region of the electromagnetic spectrum. Therefore, alkaline transition metal oxides are considered for excessive scientific and industrial applications like refrigerators generators, thermal sensors, since they have outstanding mechanical, thermal and electronic properties. These oxides have high dielectric constant, high breakdown strength, wide band gap, low current leakage density
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and under phase transition at different pressure [6, 7]. From a theoretical point of view, among all oxides, electronic character and optical response of BaTiO3 has been widely explored and compare by experimentally and theoretically by a rich variety of techniques [8]. Similar electronic, thermoelectric and optical trend with phase transition study has been explored by the
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researchers for SrZrO3[9]. This compound has much application in hydrogen sensors, stream electrolysis and high voltage capacitor high k-gate dielectrics. Tantalum Oxide among all the
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transition metal oxide has a high refractive index, low thermal stress and high dielectric constant therefore have potential applications in photoelectronics. Moreover, it is also used in solar cells and has better thermochromic properties. Alkali metal tantalates have to gain interest in their applications in high temperature resistance or capacitor dielectric materials and in photocatalysis [10]. Alkali metal Tantalates and Niobate show luminescence with high Stokes shifts [11-12] especially lanthanide Tantalates are gaining importance as x-ray phosphors. The luminescence of KNbO3 and KTaO3 are also studied and compared [13]. Environmental concerns are looking for such new material which is lead-free piezoelectric and K0.5Na0.5NbO3 (KNN)-based oxides are a likely lead-free alternative [14].
From the family of alkali earth metals, KTaO3 show soft 2
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ferroelectric behavior in a pure state and stabilizes at a lower temperature [15]. Among them, LiNbO3 is also metallic with instable ferroelectric nature at room temperature [16, 17]. Moving down to this family RbNbO3 and RbTaO3 have been also reported ferroelectric nature with large band gap. However, they are difficult to use in practical applications at room temperature [18].
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Phase stability of NaNbO3 and KNbO3 are also investigated at different temperatures [19]. Moreover, mixed alkali oxides like KxLi1-xTaO3, KTaxNb1-xO3, KNaxTa1-xO3 are favorable to use semiconductor in electro-optics and photo-optical devices [20-24]. On the other hand, Cesium is becoming prominent part used to enhance the stability of solar cells. Interfaces between electron
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–selective layer and perovskites layers are modified by Cs compounds, make them more efficient and low cost [25]. This available experimental and theoretical background of alkali earth-
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transition metal oxides demand computational approach of CsMO3(M= Nb,Ta) to identify their role to suggest high efficient materials in optoelectronic and thermoelectric applications. In the present work, we have presented in detail electronic, optical and thermoelectric analysis of CsNbO3 and CsTaO3 from first principle calculations. To the best of our knowledge, the experimental and theoretical literature is limited in this area. On the behalf of the expected trends of the similar type perovskites oxides, the cesium based compounds have been analyzed.
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Therefore, the reported theoretical data provides deep insight into the experimental researchers. 2. Method of calculations
In the present article, the first principle calculations of CsNbO3 and CsTaO3 compounds have
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been analyzed by full potential linearized augmented plane wave method (FP-LAPW) method developed in Wien2k code [26]. The PBEsol approximation [27] has been used to optimize the
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cubic structures of the studied materials through Murnaghan’s equation of states [28]. The Charpit’s method to solve the nonlinear first order differential equation for compatible solution by tensor analysis has been used to find the elastic constants that give the complete information about the mechanical behavior of the studied compounds. Further, electronic and optical properties have been calculated by using the modified Becke and Johnson potential scheme of Trans and Balaha (TB-mBJ) [28] has been applied that improve the electronic band gap up to experimental limits. The advancement of this modification is the adjustment of self consistently converged value c in the equation given below,
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BR VxmBJ ,σ ( r ) = cVx ,σ ( r ) + (3c − 2)
1
π
5 2tσ ( r ) 12 ρσ ( r )
(1)
Where ‘c’ depends upon free parameters (constant values to adjust the potential) α and β. Basis
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functions inside non-overlapping spheres around the muffin-tin sphere are expended as a combination of spherical harmonic function whereas in the interstitial region as plane wave type in the reciprocal lattice. To avoid electron leakage semi-core states are included and are express with local orbitals. The product of muffin-tin radius and the maximum value of plane wave
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cutoff are adjusted as RMT x Kmax =8 and Gaussian parameter Gmax = 14. For the best convergence, we make a k-mesh of 10×10×10 by taking 1000 k point selection. In the end, the
3. Results and discussion 3.1 Electronic Properties
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thermoelectric and thermodynamic properties are calculated by BoltzTraP code [29].
The geometries of cubic Perovskites CsNbO3, and CsTaO3 and their ground state properties are studied by using Birch Murnaghan’s equation of state as given below.
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B′ BoV Vo VO ETot (V ) = Eo (V ) + B 1 − + − 1 B′ ( B′ − 1) V V
(2)
Here Vo is volume at static equilibrium, B is bulk modulus and Eo describe the total energy per
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primitive cell in the ground state. The calculated values of the ground state parameters like lattice constant and Bulk modulus have been presented in Table 1. The lattice constant for CsNbO3 is
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smaller than CsTaO3 because atomic radii and atomic number of Ta (4.26, 73) is larger than Nb (4.003, 41). To explain the electronic behavior of the studied compounds, the band structures (BS) and density of states (DOS) are presented in Fig. 2 (a, b) and Fig. 3 (a, b). From the band structures, direct band gap at Γ symmetry point having values 1.95eV for CsNbO3 and 2.90 eV for CsTaO3 has been noted. Therefore, the studied materials are wide band gap semiconductors with band gap lies in the visible region of the electromagnetic spectrum that makes the studied materials potential candidate for optoelectronic applications. The increased value of band gap from Nb to Ta is dependent on hybridization between the conduction band and s character of transition metals. It is clear from the Fig.3, the individual 4d states of Nb and 5d 4
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states of Ta have major contribution with the minor contribution of 2p states of O in conduction band while in the valence band major contributor is 2p states of O with a minor contribution of 4d states of Nb and 5d states of Ta. Therefore, the opposite trends of pd-hybridizations in the
nonmagnetic behavior as explained in the earlier work [7]. 3.2 Mechanical Properties
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valence and conduction bands may cancel the effects of the spin orientation of electrons to show
Elastic properties of solids provide information on interatomic potentials reaction to external force and many fundamental solid state phenomena related to materials such as stability,
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strength, ductile or brittleness of the material, Young's modulus (Y), bulk modulus (B), shear modulus (G), anisotropy factor and other elastic parameters [30]. For cubic materials, three basic
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independent elastic constants C11, C12, and C44 are enough to calculate all the above mentioned properties. Calculated values of these parameters for CsNbO3 and CsTaO3 compounds are listed in Table 1 that satisfy the mechanical stability criteria C11-C12 >0 , C11+2C12>0, and C12< B < C11 [31-32]. Hardness and stiffness of the materials are measured by the bulk modulus (B), share modulus (G) and Young's modulus (Y). In solids, an isotropic material can be completely described by Bulk and share modulus estimated through Voigte-Reusse Hill (VRH)
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approximation [33-35]. From our calculated values presented in Table 1, it is clear that the value of bulk modulus and share modulus is lower for CsNbO3 as compare to CsTaO3, so in comparison, CsTaO3 is a hard material. Young’s modulus is the ratio of stress and strain and in computed materials CsTaO3 has a greater value of Young's modulus as compared to CsNbO3
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which means CsTaO3 undergoes less strain and is stiff material. Materials with a greater value of Young's modulus have covalent bond nature [36]. For cubic materials, Cauchy pressure (C12-C44)
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also explains the nature of bond in the system. According to it, those materials which have a positive value of Cauchy pressure have metallic nature. On the other hand, the negative value of Cauchy pressure means angular bond nature. To check the brittle and ductile nature of the material Pugh’s ratio (B/G) is calculated. Materials having B/G ratio greater than 1.75 has ductile nature and for a value, lower than this number is brittle in nature [37]. Both materials under study have a ratio greater than this critical value indicate their ductile nature. Moreover, the ductile nature of studied materials also noted from the possion ratio (ѵ). Its value is greater than 0.25 for ductile materials. Hence passions ratio confirm the ductile behavior. Another important factor of elastic constants is an anisotropic factor (A) and its value should be unity for 5
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isotropic materials. In our case, its value for CsNbO3 and CsTaO3 is lesser than unity which shows that these under study compounds are not anisotropic. 3.2 Optical properties
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In this section, material response to applied external electromagnetic field is measured in terms of complex dielectric constant ε(ω) =ε1(ω)+iε2(ω), Where real part of dielectric constant ε1(ω) represents the polarization of light and imaginary part of dielectric constant ε2(ω) represent the absorption of light by the material, refractive index n (ω), extinction coefficient k (ω), optical
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conductivity σ(ω), absorption coefficient α(ω), reflectivity R(ω) and optical loss energy L(ω) parameter. The calculated values of above mentioned parameters for CsMO3 (M = Nb, Ta) in the
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energy range 0-30 eV are presented in Fig. 4(a-d) and Fig. 5 (a-d). The peaks of ε1 (ω) increase from critical values and reach to maximum polarization at 3 eV and 4 eV for CsNbO3 and CsTaO3. Its value drops to a minimum value when frequencies slightly shift from resonance value as shown in Fig.4a. This indicates the plasmonic effect is maximum at a resonance frequency that disperses the light falling on the material. After 5 eV, the values of ε1 (ω) starts fluctuating in the high energy region due to a different rate of transition. The values of ε1 (ω) at
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18 eV become negative that show the reflection of light falling on the material surface and materials become metallic [38]. Moreover, it is evident from Table 1, the zero frequency value of ε1 (0) and band gap Eg of the studied materials satisfy Penn’s model whose mathematical form can be written as ε1 (0) ≈1+ (ħωp/Eg) 2[39]. The real and imaginary part of the dielectric constants
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is interlinked through Kramers-Kronig relation [40]. The imaginary part of the dielectric constant ε2 (ω) tells us about the absorption of light as shown in Fig.4b. The critical value of absorption
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coefficient that represent the optical band gap of the studied materials 1.95 eV for CsNbO3 and 2.9 eV for CsTaO3 are present in Table 1. The values of the band gap calculated from Fig. 4b and band structures presented in Fig. 2 (a, b) are consistent that shows the reliability of our computed results. Moreover, the optical band gap values lie in the visible region of the electromagnetic spectrum that makes the studied materials suitable for optoelectronic applications as explained above. It is also clear from Fig. 4b, the absorption of light is maximum in the periphery of 5 eV where the dispersion of light is minimum. In the higher energy region, the fluctuation in peaks of absorption represent the different rate of inter-band transition and finally drops to zero because of the metallic behavior of the studied materials at high energy region. The shifting of peaks of 6
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maximum absorption to higher energy from Nb to Ta represents the redshift that may be due to different hybridization between 4d Nb, 5d Ta and 2p O. The refractive index n (ω) and extinction coefficient k (ω) measures the transparency and
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absorption of light of the studied materials are depicted in Fig. 4c and Fig. 4d. The measured values of refractive index n (ω) and extinction coefficient k (ω) have similar trends as real and 2 2 imaginary part of the dielectric constants and linked through the relations n − k = ε1 (ω ) and
2nk = . The value of rethe fractive index lies in the range from 2 to 3 for optoelectronic devices,
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operate able in the visible region. Furthermore, the static values of refractive index n (0) and rethe al part of dielectric constant ε1 (0) are connected with each other through the relation =
0 as shown in Table 1. The extinction coefficient k (ω) has the same behavior as ε2
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(ω).
The absorption coefficient of light tells us about the decay of light intensity per unit length is presented in Fig.5a. Its value increases from zero frequency limits and reaches to a maximum value at 18 eV after different rare of transition. The peak of maximum intensity at 18 eV is consistent with the imaginary part of the dielectric constant and extinction coefficient. The small
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difference in peak intensity may be due to approximations involved in the calculations of these parameters. Moreover, the extinction coefficient and absorption coefficient are proportional each through the relation ɑ = 4
⁄ [41]. The optical conductivity as show in Fig. 5b, tells us about
bond breaking in the material when electromagnetic waves of high energy falls on them and
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electronic current. This is a clue about the conversion of light energy into electrical energy and this effect satisfied the Maxwell equations of electromagnetism in optics. Basically, the three
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process, absorption, transmission and reflections are taking place with surplus energy when high photon energy light falls on the material surface. The reflection of light R (ω) explores the surface behavior of the studied materials. Its value increases from zero limit R (0) and reaches to peak value in a region where absorption in minimum as show in Fig. 5c. The peaks of different intensity shows the photons are reflected at different incident angles from the material surface. In the end, the optical loss factor represents the loss of energy either by dispersion, scattering or heating which is depicted in Fig. 5d. Its value is minimum in the visible region and then starts increasing at high energy. Therefore, the overall analysis of the optical behavior of the studied
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compounds shows, the studied materials has minimum energy loss, maximum absorption in the visible region make the them potential materials for optoelectronic devices. 3.2 Thermoelectric and thermodynamic properties
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The electrons transport properties depend upon the band structure are calculated by semi classical Boltzmann transport theory and rigid band theory as implemented in BoltzTraP code. Thermoelectric materials have significant importance for energy renewable device applications because heat energy lost in many energy generating and consuming devices. The best
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thermoelectric has small electrical to thermal conductivity ratio to enhance the efficiency of the devices. We have investigated the thermoelectric behavior of cesium based perovskites CsMO3 (M = Nb, Ta) in the temperature range 0-800K in terms of electrical conductivity (σ/τ), thermal
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conductivity(k/τ), Seebeck coefficient (S), and power factor (S2σ/τ) as presented in Fig 6 (a-d) respectively. The electrical conductivity tells us how much electrons are available for conduction with increasing temperature. It is clear from the Fig. 6a, the electrical conductivity of both studied compounds CsMO3 (M = Nb, Ta) increases with temperature. The slope of the graph is high for CsTaO3 than CsNbO3 because of greater atomic number of Ta (73) than Nb (41). The
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increasing atomic number makes the weak grip of the nucleus on valence electrons with increasing temperature that easily pushed the more electrons toward the conduction band which increase the electrical conductivity of both compounds [29]. The thermal conductivity of both the studied compounds also increases with a rise in temperature
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as shown in Fig. 6c. In semiconductor materials, thermal conductivity (k) depends on electronic (ke) as well as phononic (kp) contribution [42-43]. When temperature increases in
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semiconductors, lattice vibrations of the atoms are also increased. These lattice vibrations allow materials to conduct heat from one point to another through convection but this part is very small as compared to electronic contribution. The major contribution of thermal conductivity may be due to lattice vibration in cesium (Cs) based compound because they are found to be a category of large band gap semiconductors in nature. The phonon calculations were performed using density functional perturbation theory approach [52] to understand the behaviour of thermal conductivity. The values of frequency were found to be free from imaginary frequencies which show the lattice stability of these compounds. The highest optical flat modes of vibration ɷ were calculated at the values of 889 cm-1 and 980 cm-1 for CsNbO3 and CsTaO3 at Γ-point symmetry 8
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as shown in Figure 7 (a-b). These modes of vibrations possibly can play a crucial role in thermal conductivity. Moreover, the Seebeck effect defines the potential induced in the material due to the difference in temperature across the material due to the movement of available electrons. Fig. 6(b) represents the Seebeck coefficient calculated from the relation S=∆V/∆T. Since in wide
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bandgap semiconductors, there are only a few free electrons available at low temperature. It can be seen that at 0k the observed value of Seebeck coefficient is about 100(µV/K) and a very sharp increase in S has been identified when temperature increases for both the compounds and achieve its maximum rate at 200K up to 210 (µV/K) for CsNbO3 and 170 (µV/K) for CsTaO3.
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Our calculated results show that after 200k further increase in temperature does not create more potential across CsNbO3 and CsTaO3. Beyond 200K, temperature graph of S remains constant
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with minor decreasing drift till 800K.
Another most important parameter is the power factor (PF) that describes the efficiency of the studied materials. It is predicted that materials with a high value of power factor are more desirable for a thermoelectric application that should be unity or greater than unity [44, 45]. Our calculated graphs at different temperature of PF for both the studied compounds are presented in Fig. 6d that shows the increasing trend with increasing temperature at reaches to maximum value
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1.7×1012 (W/mK2s) at 800k. The efficiency from PF gives only the electrons contribution as shown in Fig. 6d without thermal effect. Furthermore, we have tried to calculate the thermoelectric efficiency by the dividing the PF from electronic thermal conductivity at room temperature from the figure of merit ZT = σS2/κT in which the ratio of electrical to thermal
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conductivity should me minimum. Its value is 0.73 for CsNbO3 and 0.68 for CsTaO3 at room temperature that suggests the studied materials for thermoelectric applications.
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In addition to above, the response of thermodynamic properties such as specific heat capacity at constant volume Cv, Thermal expansion coefficient (susceptibility) χ, Hall coefficient RH and charge carrier density n of CsMO3 (M=Nb, Ta) compounds versus temperature up to 800K have also been studied as shown in Fig. 8(a-d). The specific heat capacity at constant volume for harmonic approximation shows the material capacity to absorb the heat. Total heat capacity is generally combined effect of phonon and electron heat capacity in semiconductor materials. Its value increases linearly with increasing temperature up to 6.8 (Jmol-1k-1) at 800K (see Fig. 8(a)). The linear trend of specific heat capacity follows the Dulong and Petit law that tells us the Cv does not expand with the classical limit ͠~3R, where R is the gas constant. Therefore, a linearly 9
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increasing trend shows that molar heat capacity follows the Debye temperature rule at a lower temperature as Cv α T3[46]. Fig. 8 (b) represents the susceptibility of our materials and is plotted against temperature in the range of 0-800K. Results reveal that CsNbO3 has susceptibility 0.6 × 10-9 m3mol-1 at 0K and it attains a maximum value of 1.8x10-9 m3mol-1 at 800K, whereas for
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CsTaO3 susceptibility is1x10-9 m3mol-1 at 0K and it reaches the value above at 1.4 x 10-9 m3mol-1 at 800K. It is clear from the graphs that our materials under study have nonmagnetic nature in spite of doping from transition metals since the value of susceptibility is very low for both compounds. This factor is in agreement with the electrical response of material where in spite of
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hybridization no magnetic moment has been observed [47]. Fig. 8c is a detailed description of Hall effect response at different temperature and according to calculations, the value of RH is
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maximum and decreases exponentially with increasing temperature and finally reaches at zero for both the studied compounds. Since Hall Effect describes the stable electric field due to the accommodation of opposite charge density at both ends of semiconductor, this can be explained on the basis of the fact that by increasing temperature phonon vibrations are also increased and in the result, more scattering is observed in the material. The maximum values of hall coefficients for CsNbO3 and CsTaO3 are 2.5x10-8m3/C and 1x10-8m3/C at 50K respectively. Therefore, in
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semiconductor materials the inverse relation between temperature and Hall coefficient has been noted may be due to the negative temperature coefficient effect. The trend of thermally generated charge concentration is increasing with an increase in temperature due to the movement of an electron from the valence band to the conduction band by generating electron-hole pair [48].
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Finally, it is clear from the Fig. 8d the concentration of charge carriers for CsTaO3 is higher than CsNbO3 because of less ionization energy of Ta as compared to Nb. From the above described
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thermoelectric and thermodynamic behavior of the studied materials, it is clear the high value of thermal efficiency, specific heat capacity and a minimum value of electrical to thermal conductivity ratio make the studies compounds potential candidates for thermoelectric generator and refrigerator applications. 4. Conclusion
In the present study, electronic, mechanical, thermodynamic, optical and thermoelectric properties of CsMO3 (M = Nb,Ta) compounds have been explored by using FP-LAPW method implemented in the DFT based Wien2k code. The electronic band structures calculated at equilibrium lattice constant shows the studied materials are wide bandgap semiconductors 10
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having a band gap in the visible region. The mechanical analysis demonstrates the CsNbO3 and CsTaO3 are ductile, anisotropic and mechanically stable in the cubic phase. The optical analysis shows the optical band gap of CsNbO3 lies in the lower portion and of CsTaO3 in the upper portion of the visible region. The maximum absorption, minimum reflectivity and optical loss in
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the visible region make them suitable materials for optoelectronic devices applications. The static value of the real part of dielectric constant and optical band gap of these materials are exactly according to Penn’s model. Moreover, the reflectivity peaks graph show that they are transparent towards higher frequencies and are suitable shielding material for high energy
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radiation. In the end, the increasing values of electrical conductivity and power factor with temperature show the studied materials are also best suited for thermoelectric applications. The
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increasing value of the specific heat capacity and the decreasing value of hall coefficient show the studied materials are thermodynamically stable. Acknowledgement
We are thankful to the ORIC, GC University, Lahore Pakistan for providing us PhD research grants to establish simulation facilities. Author Bushra Sabir is also thankful to
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HEC for providing IRSIP Scholarship.
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J. Wang, S. Yip, S.R. Phillpot, D. Wolf, Phys. Rev. Lett. 71 (1993) 4182 M. Gasperin, Acta. Cryst. 11 (1958) 739. R. Hill, Proc. Phys. Soc. Lond. A 65 (1952) 349. W. Voigt, Ann. Phys. 38 (1889) 573. A. Reuss, Z. Angew, Math. Phys. 9 (1929) 49. C. Jenkins, S. Khanna, A Modern Integration of Mechanics and Materials in Structural Design, Academic Press (2005) [36]. S.F. Pugh, Philos. Mag. 45 (1954) 823. [37]. Q. Mahmood, M. Hassan J. Alloys and Compounds 704 (2017) 659. [38]. M.J. Mehl, B.M. Barry, D.A. Papaconstantopoulos, in: J.H. Westbrook, R.L. Fleischeir (Eds.), Intermetallic Compounds: Principle and Practice, Volume 1: Principles, John Wiley and Sons, London, (1995)pp.195-210 (chapter9) [39]. O.L. Anderson, J. Phys. Chem. Solids 24 (1963) 909. [40]. K. Xiong, J. Robertson, and S. J. Clark, Appl. Phys. Lett. 89, 022907 (2006). [41]. O. Rabin, L .Yu-Ming, M.S. Dreaaelhaus, Appl. Phys. Lett. 79 (2001) 81-83. [42]. T. Zhu, K. S. Gopalan, K. Stephani, E. Ertekin, arXiv preprint arXiv:1710.03375 (2017). [43]. Boffito C, Toia L, Cattaneo L, Cesium mixtures and use thereof. United States patent application US 10/842,352. (2004) [44]. H.A. Rahnsmaye Aliabad, M. Ghazanfar, I. Ahmad, M.A. Saeed, Comput. Mater. Sci.65(2012)509.
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J.E. Saal, S. Kirklin, M. Aykol, B.Meredig, C. Wolverton, Materials design and
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[51].
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[45]. C. Kittel, Introduction to Solid State Physics, 8th ed. John Wiley & Sons, New York, (2005), 124. [46]. Z. Ali, I. Ahmad, I. Khan, B. Amin ,Intermetallics 31(2012) 287. [47]. D. Wolpert and P. Ampadu, Managing temperature effects in Nanoscale Adaptive Systems, Springer, New York, NY, (2012)1-13 [48]. C. Kim, G. Pilania, R. Ramprasad, J.Phys. Chem. C,120 (2016) 14575. [49]. I. E. Castelli, J. M. García-Lastra, F. Hüser, K. S. Thygesen, K. W. Jacobsen, New Journal of Phy. 15 (2013) 105026 [50]. A. Jain, I. E. Castelli, G. Hautier, D. H. Bailey , K. W. Jacobsen, J. of Material Sci. (2013)
discovery with high-throughput density functional theory: the open quantum
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S.Baroni,S.de Gironcoli, A.dal Corso, P.Giannozzi, Rev.Mod.Phys. 73 (2001)
515. [53].
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materials database (OQMD), JOM 65 (11) (2013) 1501-1509.
I. E. Castelli, K. W. Jacobsen, K.S. Thygesen, (2013). Computational Screening
of Materials for Water Splitting Applications. Kgs. Lyngby: Technical University of
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Denmark (DTU).
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Fig. 1: Calculated energy verses volume optimizations in cubic phase using PBE-sol for (a) CsNbO3 (b) CsTaO3 perovskites.
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Fig. 2: Calculated electronic band structures at ground state lattice constant by using PBEsolmBJ potential for (a) CsNbO3 (b) CsTaO3.
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Fig. 3: Calculated total and partial density of states (DOS) corresponding to ground state lattice constant by using PBEsol-mBJ for (a) CsNbO3 (b) CsTaO3.
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Fig. 4: Calculated plots of (a) real part of dielectric constant (b) imaginary part of dielectric constant(c) refractive index, (d) extinction coefficient for CsNbO3 and CsTaO3 by using PBEsol+mBJ in the energy range 0-30 eV
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Fig. 5: Calculated plots of (a) Absorption coefficient (b) Optical conductivity (c) Reflectivity (d) energy loss function for CsNbO3 and CsTaO3 by using PBEsol+mBJ in the energy range 0-30 eV
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Fig. 6: The calculated (a) electrical conductivity (σ/τ), (b) thermal conductivity (k/τ), (c) Seebeck coefficient (S), and (d) power factor (S2σ/τ) as a function of temperature range 0-800K.
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Fig. 7: Calculated dispersion curves of (a) CsNbO3 (b) CsTaO3 along symmetry direction.
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Fig. 8: Calculated plots of (a) specific heat capacity at constant volume (b) Susceptibility (c) Hall coefficient (d) charge carrier density for CsNbO3 and CsTaO3 by using BoltzTraP code in temperature range 0-800k.
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Table 1
4.104 180.12 4.665 1.95
ε1 (0) n (0) R (0) C11 C12 C44 B G Y B/G υ A ɷ(cm-1)
5.87 2.42 0.173 324.84 110.92 96.41 180.22 100.50 254.68 1.813 0.267 0.901 889
2.1b,2.8b d ,2.12
CsTaO3
Exp.
4.100 4.09a 195.72 5.000 2.90 3.15c,3.70a, 3.51d 4.69 2.16 0.135 396.80 89.93 98.43 195.22 117.67 293.18 1.764 0.258 0.642 980
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ao (Å) Bo (GPa) Bc Eg (eV)
Exp
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CsNbO3
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Parameters
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The calculated parameters of CsMO3 (M= Ta, Nb) in cubic phase by using PBEsol and PBEsolmBJ potential.
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Ref [49]a, Ref [50]b, Ref [51]c , Ref [53]d
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Highlights
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First principle study of cesium based perovskites CsMO3 (M = Nb, Ta) in cubic phase The electronic band structures reveals the studied materials are wide bandgap semiconductors having a band gap in the visible region. The mechanical analysis demonstrates the CsNbO3 and CsTaO3 are ductile, anisotropic and mechanically stable in cubic phase. The optical analysis shows the optical band gap of CsNbO3 lies in the lower portion and of CsTaO3 in the upper portion of the visible region. The increasing values of electrical conductivity and power factor with temperature show the studied materials are also best suited for thermoelectric applications.
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S1093-3263(18)30483-2
DOI:
10.1016/j.jmgm.2018.09.011
Reference:
JMG 7235
To appear in:
Journal of Molecular Graphics and Modelling
Received Date: 4 July 2018 Revised Date:
18 September 2018
Accepted Date: 19 September 2018
Please cite this article as: B. Sabir, G. Murtaza, R.M. Arif Khalil, Q. Mahmood, First principle study of electronic, mechanical, optical and thermoelectric properties of CsMO3 (M = Ta, Nb) compounds for optoelectronic devices, Journal of Molecular Graphics and Modelling (2018), doi: https://doi.org/10.1016/ j.jmgm.2018.09.011. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Fig. 2: Calculated electronic band structures at ground state lattice constant by using PBEsol-mBJ potential for (a) CsNbO3 (b) CsTaO3.
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First principle study of electronic, mechanical, optical and thermoelectric properties of CsMO3 (M = Ta, Nb) compounds for optoelectronic devices B. Sabira, G. Murtazaa*, R.M.Arif Khalilb, Qasim Mahmooda a
Centre for Advanced Studies in Physics, GC University, Lahore-54000, Pakistan Materials Research Simulation Laboratory (MRSL), Department of Physics, Bahauddin Zakariya University,Multan,60800,Pakistan. * Corresponding author detail: Tel.: +92-4299211589, Ext.105, E-mail.: [email protected] (G. Murtaza)
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b
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Abstract
The electronic, mechanical, optical and thermoelectric properties of Cesium based perovskites
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CsMO3 (M = Nb, Ta) in the cubic phase has been performed through PBEsol-mBJ scheme in the framework of DFT. The electronic band structures and density of states show the studied materials having a direct band gap in the visible range. The mechanical stability and ductile behavior have been analyzed from elastic constants. Moreover, the optical behavior of the studied materials has been analyzed in terms of dielectric functions, refractive index, extinction coefficient, absorption coefficient, optical conductivity, reflectivity and energy loss factor.
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Finally, the material response with temperature has been elaborated by electrical conductivity, thermal conductivity, Seebeck coefficient, power factor, heat capacity, Hall coefficient, susceptibility and electron density by using BoltzTraP code. This first principle calculation of optical and thermoelectric properties of the novel compounds provides a new route to the
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Key Words:
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experimentalist for the potential application in energy renewable devices.
DFT; Direct bandgap semiconductors; Mechanical stability; Thermoelectric and thermodynamic behavior; Optical emerging materials
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1. Introduction The cubic perovskites oxides with general formula ABO3 have attracted much attention, because of their simple synthesis and various physical properties that result from highly correlated d-band
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electrons and strong electron-lattice couplings [1]. These materials have been extensively used in optoelectronics, thermoelectric, laser frequency doubling waveguide and are very favorable for advanced technological application [2-5]. The waste of thermal energy and increasing its demand in the advanced scientific world inspired the researchers to fabricate the thermoelectric devices
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that convert the waste heat energy into electrical energy. For this purpose, the cesium based perovskites oxide type semiconductors are always in great attention because of high electrical conductivity, specific heat capacity and low value of thermal conductivity that increases their
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thermal efficiency. Moreover, along with thermal properties, these materials are also beneficial for optoelectronic device applications because their band gap falls in the visible region of the electromagnetic spectrum. Therefore, alkaline transition metal oxides are considered for excessive scientific and industrial applications like refrigerators generators, thermal sensors, since they have outstanding mechanical, thermal and electronic properties. These oxides have high dielectric constant, high breakdown strength, wide band gap, low current leakage density
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and under phase transition at different pressure [6, 7]. From a theoretical point of view, among all oxides, electronic character and optical response of BaTiO3 has been widely explored and compare by experimentally and theoretically by a rich variety of techniques [8]. Similar electronic, thermoelectric and optical trend with phase transition study has been explored by the
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researchers for SrZrO3[9]. This compound has much application in hydrogen sensors, stream electrolysis and high voltage capacitor high k-gate dielectrics. Tantalum Oxide among all the
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transition metal oxide has a high refractive index, low thermal stress and high dielectric constant therefore have potential applications in photoelectronics. Moreover, it is also used in solar cells and has better thermochromic properties. Alkali metal tantalates have to gain interest in their applications in high temperature resistance or capacitor dielectric materials and in photocatalysis [10]. Alkali metal Tantalates and Niobate show luminescence with high Stokes shifts [11-12] especially lanthanide Tantalates are gaining importance as x-ray phosphors. The luminescence of KNbO3 and KTaO3 are also studied and compared [13]. Environmental concerns are looking for such new material which is lead-free piezoelectric and K0.5Na0.5NbO3 (KNN)-based oxides are a likely lead-free alternative [14].
From the family of alkali earth metals, KTaO3 show soft 2
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ferroelectric behavior in a pure state and stabilizes at a lower temperature [15]. Among them, LiNbO3 is also metallic with instable ferroelectric nature at room temperature [16, 17]. Moving down to this family RbNbO3 and RbTaO3 have been also reported ferroelectric nature with large band gap. However, they are difficult to use in practical applications at room temperature [18].
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Phase stability of NaNbO3 and KNbO3 are also investigated at different temperatures [19]. Moreover, mixed alkali oxides like KxLi1-xTaO3, KTaxNb1-xO3, KNaxTa1-xO3 are favorable to use semiconductor in electro-optics and photo-optical devices [20-24]. On the other hand, Cesium is becoming prominent part used to enhance the stability of solar cells. Interfaces between electron
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–selective layer and perovskites layers are modified by Cs compounds, make them more efficient and low cost [25]. This available experimental and theoretical background of alkali earth-
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transition metal oxides demand computational approach of CsMO3(M= Nb,Ta) to identify their role to suggest high efficient materials in optoelectronic and thermoelectric applications. In the present work, we have presented in detail electronic, optical and thermoelectric analysis of CsNbO3 and CsTaO3 from first principle calculations. To the best of our knowledge, the experimental and theoretical literature is limited in this area. On the behalf of the expected trends of the similar type perovskites oxides, the cesium based compounds have been analyzed.
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Therefore, the reported theoretical data provides deep insight into the experimental researchers. 2. Method of calculations
In the present article, the first principle calculations of CsNbO3 and CsTaO3 compounds have
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been analyzed by full potential linearized augmented plane wave method (FP-LAPW) method developed in Wien2k code [26]. The PBEsol approximation [27] has been used to optimize the
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cubic structures of the studied materials through Murnaghan’s equation of states [28]. The Charpit’s method to solve the nonlinear first order differential equation for compatible solution by tensor analysis has been used to find the elastic constants that give the complete information about the mechanical behavior of the studied compounds. Further, electronic and optical properties have been calculated by using the modified Becke and Johnson potential scheme of Trans and Balaha (TB-mBJ) [28] has been applied that improve the electronic band gap up to experimental limits. The advancement of this modification is the adjustment of self consistently converged value c in the equation given below,
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BR VxmBJ ,σ ( r ) = cVx ,σ ( r ) + (3c − 2)
1
π
5 2tσ ( r ) 12 ρσ ( r )
(1)
Where ‘c’ depends upon free parameters (constant values to adjust the potential) α and β. Basis
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functions inside non-overlapping spheres around the muffin-tin sphere are expended as a combination of spherical harmonic function whereas in the interstitial region as plane wave type in the reciprocal lattice. To avoid electron leakage semi-core states are included and are express with local orbitals. The product of muffin-tin radius and the maximum value of plane wave
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cutoff are adjusted as RMT x Kmax =8 and Gaussian parameter Gmax = 14. For the best convergence, we make a k-mesh of 10×10×10 by taking 1000 k point selection. In the end, the
3. Results and discussion 3.1 Electronic Properties
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thermoelectric and thermodynamic properties are calculated by BoltzTraP code [29].
The geometries of cubic Perovskites CsNbO3, and CsTaO3 and their ground state properties are studied by using Birch Murnaghan’s equation of state as given below.
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B′ BoV Vo VO ETot (V ) = Eo (V ) + B 1 − + − 1 B′ ( B′ − 1) V V
(2)
Here Vo is volume at static equilibrium, B is bulk modulus and Eo describe the total energy per
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primitive cell in the ground state. The calculated values of the ground state parameters like lattice constant and Bulk modulus have been presented in Table 1. The lattice constant for CsNbO3 is
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smaller than CsTaO3 because atomic radii and atomic number of Ta (4.26, 73) is larger than Nb (4.003, 41). To explain the electronic behavior of the studied compounds, the band structures (BS) and density of states (DOS) are presented in Fig. 2 (a, b) and Fig. 3 (a, b). From the band structures, direct band gap at Γ symmetry point having values 1.95eV for CsNbO3 and 2.90 eV for CsTaO3 has been noted. Therefore, the studied materials are wide band gap semiconductors with band gap lies in the visible region of the electromagnetic spectrum that makes the studied materials potential candidate for optoelectronic applications. The increased value of band gap from Nb to Ta is dependent on hybridization between the conduction band and s character of transition metals. It is clear from the Fig.3, the individual 4d states of Nb and 5d 4
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states of Ta have major contribution with the minor contribution of 2p states of O in conduction band while in the valence band major contributor is 2p states of O with a minor contribution of 4d states of Nb and 5d states of Ta. Therefore, the opposite trends of pd-hybridizations in the
nonmagnetic behavior as explained in the earlier work [7]. 3.2 Mechanical Properties
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valence and conduction bands may cancel the effects of the spin orientation of electrons to show
Elastic properties of solids provide information on interatomic potentials reaction to external force and many fundamental solid state phenomena related to materials such as stability,
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strength, ductile or brittleness of the material, Young's modulus (Y), bulk modulus (B), shear modulus (G), anisotropy factor and other elastic parameters [30]. For cubic materials, three basic
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independent elastic constants C11, C12, and C44 are enough to calculate all the above mentioned properties. Calculated values of these parameters for CsNbO3 and CsTaO3 compounds are listed in Table 1 that satisfy the mechanical stability criteria C11-C12 >0 , C11+2C12>0, and C12< B < C11 [31-32]. Hardness and stiffness of the materials are measured by the bulk modulus (B), share modulus (G) and Young's modulus (Y). In solids, an isotropic material can be completely described by Bulk and share modulus estimated through Voigte-Reusse Hill (VRH)
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approximation [33-35]. From our calculated values presented in Table 1, it is clear that the value of bulk modulus and share modulus is lower for CsNbO3 as compare to CsTaO3, so in comparison, CsTaO3 is a hard material. Young’s modulus is the ratio of stress and strain and in computed materials CsTaO3 has a greater value of Young's modulus as compared to CsNbO3
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which means CsTaO3 undergoes less strain and is stiff material. Materials with a greater value of Young's modulus have covalent bond nature [36]. For cubic materials, Cauchy pressure (C12-C44)
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also explains the nature of bond in the system. According to it, those materials which have a positive value of Cauchy pressure have metallic nature. On the other hand, the negative value of Cauchy pressure means angular bond nature. To check the brittle and ductile nature of the material Pugh’s ratio (B/G) is calculated. Materials having B/G ratio greater than 1.75 has ductile nature and for a value, lower than this number is brittle in nature [37]. Both materials under study have a ratio greater than this critical value indicate their ductile nature. Moreover, the ductile nature of studied materials also noted from the possion ratio (ѵ). Its value is greater than 0.25 for ductile materials. Hence passions ratio confirm the ductile behavior. Another important factor of elastic constants is an anisotropic factor (A) and its value should be unity for 5
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isotropic materials. In our case, its value for CsNbO3 and CsTaO3 is lesser than unity which shows that these under study compounds are not anisotropic. 3.2 Optical properties
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In this section, material response to applied external electromagnetic field is measured in terms of complex dielectric constant ε(ω) =ε1(ω)+iε2(ω), Where real part of dielectric constant ε1(ω) represents the polarization of light and imaginary part of dielectric constant ε2(ω) represent the absorption of light by the material, refractive index n (ω), extinction coefficient k (ω), optical
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conductivity σ(ω), absorption coefficient α(ω), reflectivity R(ω) and optical loss energy L(ω) parameter. The calculated values of above mentioned parameters for CsMO3 (M = Nb, Ta) in the
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energy range 0-30 eV are presented in Fig. 4(a-d) and Fig. 5 (a-d). The peaks of ε1 (ω) increase from critical values and reach to maximum polarization at 3 eV and 4 eV for CsNbO3 and CsTaO3. Its value drops to a minimum value when frequencies slightly shift from resonance value as shown in Fig.4a. This indicates the plasmonic effect is maximum at a resonance frequency that disperses the light falling on the material. After 5 eV, the values of ε1 (ω) starts fluctuating in the high energy region due to a different rate of transition. The values of ε1 (ω) at
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18 eV become negative that show the reflection of light falling on the material surface and materials become metallic [38]. Moreover, it is evident from Table 1, the zero frequency value of ε1 (0) and band gap Eg of the studied materials satisfy Penn’s model whose mathematical form can be written as ε1 (0) ≈1+ (ħωp/Eg) 2[39]. The real and imaginary part of the dielectric constants
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is interlinked through Kramers-Kronig relation [40]. The imaginary part of the dielectric constant ε2 (ω) tells us about the absorption of light as shown in Fig.4b. The critical value of absorption
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coefficient that represent the optical band gap of the studied materials 1.95 eV for CsNbO3 and 2.9 eV for CsTaO3 are present in Table 1. The values of the band gap calculated from Fig. 4b and band structures presented in Fig. 2 (a, b) are consistent that shows the reliability of our computed results. Moreover, the optical band gap values lie in the visible region of the electromagnetic spectrum that makes the studied materials suitable for optoelectronic applications as explained above. It is also clear from Fig. 4b, the absorption of light is maximum in the periphery of 5 eV where the dispersion of light is minimum. In the higher energy region, the fluctuation in peaks of absorption represent the different rate of inter-band transition and finally drops to zero because of the metallic behavior of the studied materials at high energy region. The shifting of peaks of 6
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maximum absorption to higher energy from Nb to Ta represents the redshift that may be due to different hybridization between 4d Nb, 5d Ta and 2p O. The refractive index n (ω) and extinction coefficient k (ω) measures the transparency and
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absorption of light of the studied materials are depicted in Fig. 4c and Fig. 4d. The measured values of refractive index n (ω) and extinction coefficient k (ω) have similar trends as real and 2 2 imaginary part of the dielectric constants and linked through the relations n − k = ε1 (ω ) and
2nk = . The value of rethe fractive index lies in the range from 2 to 3 for optoelectronic devices,
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operate able in the visible region. Furthermore, the static values of refractive index n (0) and rethe al part of dielectric constant ε1 (0) are connected with each other through the relation =
0 as shown in Table 1. The extinction coefficient k (ω) has the same behavior as ε2
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(ω).
The absorption coefficient of light tells us about the decay of light intensity per unit length is presented in Fig.5a. Its value increases from zero frequency limits and reaches to a maximum value at 18 eV after different rare of transition. The peak of maximum intensity at 18 eV is consistent with the imaginary part of the dielectric constant and extinction coefficient. The small
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difference in peak intensity may be due to approximations involved in the calculations of these parameters. Moreover, the extinction coefficient and absorption coefficient are proportional each through the relation ɑ = 4
⁄ [41]. The optical conductivity as show in Fig. 5b, tells us about
bond breaking in the material when electromagnetic waves of high energy falls on them and
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electronic current. This is a clue about the conversion of light energy into electrical energy and this effect satisfied the Maxwell equations of electromagnetism in optics. Basically, the three
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process, absorption, transmission and reflections are taking place with surplus energy when high photon energy light falls on the material surface. The reflection of light R (ω) explores the surface behavior of the studied materials. Its value increases from zero limit R (0) and reaches to peak value in a region where absorption in minimum as show in Fig. 5c. The peaks of different intensity shows the photons are reflected at different incident angles from the material surface. In the end, the optical loss factor represents the loss of energy either by dispersion, scattering or heating which is depicted in Fig. 5d. Its value is minimum in the visible region and then starts increasing at high energy. Therefore, the overall analysis of the optical behavior of the studied
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compounds shows, the studied materials has minimum energy loss, maximum absorption in the visible region make the them potential materials for optoelectronic devices. 3.2 Thermoelectric and thermodynamic properties
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The electrons transport properties depend upon the band structure are calculated by semi classical Boltzmann transport theory and rigid band theory as implemented in BoltzTraP code. Thermoelectric materials have significant importance for energy renewable device applications because heat energy lost in many energy generating and consuming devices. The best
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thermoelectric has small electrical to thermal conductivity ratio to enhance the efficiency of the devices. We have investigated the thermoelectric behavior of cesium based perovskites CsMO3 (M = Nb, Ta) in the temperature range 0-800K in terms of electrical conductivity (σ/τ), thermal
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conductivity(k/τ), Seebeck coefficient (S), and power factor (S2σ/τ) as presented in Fig 6 (a-d) respectively. The electrical conductivity tells us how much electrons are available for conduction with increasing temperature. It is clear from the Fig. 6a, the electrical conductivity of both studied compounds CsMO3 (M = Nb, Ta) increases with temperature. The slope of the graph is high for CsTaO3 than CsNbO3 because of greater atomic number of Ta (73) than Nb (41). The
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increasing atomic number makes the weak grip of the nucleus on valence electrons with increasing temperature that easily pushed the more electrons toward the conduction band which increase the electrical conductivity of both compounds [29]. The thermal conductivity of both the studied compounds also increases with a rise in temperature
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as shown in Fig. 6c. In semiconductor materials, thermal conductivity (k) depends on electronic (ke) as well as phononic (kp) contribution [42-43]. When temperature increases in
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semiconductors, lattice vibrations of the atoms are also increased. These lattice vibrations allow materials to conduct heat from one point to another through convection but this part is very small as compared to electronic contribution. The major contribution of thermal conductivity may be due to lattice vibration in cesium (Cs) based compound because they are found to be a category of large band gap semiconductors in nature. The phonon calculations were performed using density functional perturbation theory approach [52] to understand the behaviour of thermal conductivity. The values of frequency were found to be free from imaginary frequencies which show the lattice stability of these compounds. The highest optical flat modes of vibration ɷ were calculated at the values of 889 cm-1 and 980 cm-1 for CsNbO3 and CsTaO3 at Γ-point symmetry 8
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as shown in Figure 7 (a-b). These modes of vibrations possibly can play a crucial role in thermal conductivity. Moreover, the Seebeck effect defines the potential induced in the material due to the difference in temperature across the material due to the movement of available electrons. Fig. 6(b) represents the Seebeck coefficient calculated from the relation S=∆V/∆T. Since in wide
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bandgap semiconductors, there are only a few free electrons available at low temperature. It can be seen that at 0k the observed value of Seebeck coefficient is about 100(µV/K) and a very sharp increase in S has been identified when temperature increases for both the compounds and achieve its maximum rate at 200K up to 210 (µV/K) for CsNbO3 and 170 (µV/K) for CsTaO3.
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Our calculated results show that after 200k further increase in temperature does not create more potential across CsNbO3 and CsTaO3. Beyond 200K, temperature graph of S remains constant
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with minor decreasing drift till 800K.
Another most important parameter is the power factor (PF) that describes the efficiency of the studied materials. It is predicted that materials with a high value of power factor are more desirable for a thermoelectric application that should be unity or greater than unity [44, 45]. Our calculated graphs at different temperature of PF for both the studied compounds are presented in Fig. 6d that shows the increasing trend with increasing temperature at reaches to maximum value
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1.7×1012 (W/mK2s) at 800k. The efficiency from PF gives only the electrons contribution as shown in Fig. 6d without thermal effect. Furthermore, we have tried to calculate the thermoelectric efficiency by the dividing the PF from electronic thermal conductivity at room temperature from the figure of merit ZT = σS2/κT in which the ratio of electrical to thermal
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conductivity should me minimum. Its value is 0.73 for CsNbO3 and 0.68 for CsTaO3 at room temperature that suggests the studied materials for thermoelectric applications.
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In addition to above, the response of thermodynamic properties such as specific heat capacity at constant volume Cv, Thermal expansion coefficient (susceptibility) χ, Hall coefficient RH and charge carrier density n of CsMO3 (M=Nb, Ta) compounds versus temperature up to 800K have also been studied as shown in Fig. 8(a-d). The specific heat capacity at constant volume for harmonic approximation shows the material capacity to absorb the heat. Total heat capacity is generally combined effect of phonon and electron heat capacity in semiconductor materials. Its value increases linearly with increasing temperature up to 6.8 (Jmol-1k-1) at 800K (see Fig. 8(a)). The linear trend of specific heat capacity follows the Dulong and Petit law that tells us the Cv does not expand with the classical limit ͠~3R, where R is the gas constant. Therefore, a linearly 9
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increasing trend shows that molar heat capacity follows the Debye temperature rule at a lower temperature as Cv α T3[46]. Fig. 8 (b) represents the susceptibility of our materials and is plotted against temperature in the range of 0-800K. Results reveal that CsNbO3 has susceptibility 0.6 × 10-9 m3mol-1 at 0K and it attains a maximum value of 1.8x10-9 m3mol-1 at 800K, whereas for
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CsTaO3 susceptibility is1x10-9 m3mol-1 at 0K and it reaches the value above at 1.4 x 10-9 m3mol-1 at 800K. It is clear from the graphs that our materials under study have nonmagnetic nature in spite of doping from transition metals since the value of susceptibility is very low for both compounds. This factor is in agreement with the electrical response of material where in spite of
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hybridization no magnetic moment has been observed [47]. Fig. 8c is a detailed description of Hall effect response at different temperature and according to calculations, the value of RH is
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maximum and decreases exponentially with increasing temperature and finally reaches at zero for both the studied compounds. Since Hall Effect describes the stable electric field due to the accommodation of opposite charge density at both ends of semiconductor, this can be explained on the basis of the fact that by increasing temperature phonon vibrations are also increased and in the result, more scattering is observed in the material. The maximum values of hall coefficients for CsNbO3 and CsTaO3 are 2.5x10-8m3/C and 1x10-8m3/C at 50K respectively. Therefore, in
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semiconductor materials the inverse relation between temperature and Hall coefficient has been noted may be due to the negative temperature coefficient effect. The trend of thermally generated charge concentration is increasing with an increase in temperature due to the movement of an electron from the valence band to the conduction band by generating electron-hole pair [48].
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Finally, it is clear from the Fig. 8d the concentration of charge carriers for CsTaO3 is higher than CsNbO3 because of less ionization energy of Ta as compared to Nb. From the above described
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thermoelectric and thermodynamic behavior of the studied materials, it is clear the high value of thermal efficiency, specific heat capacity and a minimum value of electrical to thermal conductivity ratio make the studies compounds potential candidates for thermoelectric generator and refrigerator applications. 4. Conclusion
In the present study, electronic, mechanical, thermodynamic, optical and thermoelectric properties of CsMO3 (M = Nb,Ta) compounds have been explored by using FP-LAPW method implemented in the DFT based Wien2k code. The electronic band structures calculated at equilibrium lattice constant shows the studied materials are wide bandgap semiconductors 10
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having a band gap in the visible region. The mechanical analysis demonstrates the CsNbO3 and CsTaO3 are ductile, anisotropic and mechanically stable in the cubic phase. The optical analysis shows the optical band gap of CsNbO3 lies in the lower portion and of CsTaO3 in the upper portion of the visible region. The maximum absorption, minimum reflectivity and optical loss in
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the visible region make them suitable materials for optoelectronic devices applications. The static value of the real part of dielectric constant and optical band gap of these materials are exactly according to Penn’s model. Moreover, the reflectivity peaks graph show that they are transparent towards higher frequencies and are suitable shielding material for high energy
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radiation. In the end, the increasing values of electrical conductivity and power factor with temperature show the studied materials are also best suited for thermoelectric applications. The
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increasing value of the specific heat capacity and the decreasing value of hall coefficient show the studied materials are thermodynamically stable. Acknowledgement
We are thankful to the ORIC, GC University, Lahore Pakistan for providing us PhD research grants to establish simulation facilities. Author Bushra Sabir is also thankful to
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HEC for providing IRSIP Scholarship.
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Denmark (DTU).
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Fig. 1: Calculated energy verses volume optimizations in cubic phase using PBE-sol for (a) CsNbO3 (b) CsTaO3 perovskites.
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Fig. 2: Calculated electronic band structures at ground state lattice constant by using PBEsolmBJ potential for (a) CsNbO3 (b) CsTaO3.
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Fig. 3: Calculated total and partial density of states (DOS) corresponding to ground state lattice constant by using PBEsol-mBJ for (a) CsNbO3 (b) CsTaO3.
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Fig. 4: Calculated plots of (a) real part of dielectric constant (b) imaginary part of dielectric constant(c) refractive index, (d) extinction coefficient for CsNbO3 and CsTaO3 by using PBEsol+mBJ in the energy range 0-30 eV
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Fig. 5: Calculated plots of (a) Absorption coefficient (b) Optical conductivity (c) Reflectivity (d) energy loss function for CsNbO3 and CsTaO3 by using PBEsol+mBJ in the energy range 0-30 eV
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Fig. 6: The calculated (a) electrical conductivity (σ/τ), (b) thermal conductivity (k/τ), (c) Seebeck coefficient (S), and (d) power factor (S2σ/τ) as a function of temperature range 0-800K.
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Fig. 7: Calculated dispersion curves of (a) CsNbO3 (b) CsTaO3 along symmetry direction.
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Fig. 8: Calculated plots of (a) specific heat capacity at constant volume (b) Susceptibility (c) Hall coefficient (d) charge carrier density for CsNbO3 and CsTaO3 by using BoltzTraP code in temperature range 0-800k.
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Table 1
4.104 180.12 4.665 1.95
ε1 (0) n (0) R (0) C11 C12 C44 B G Y B/G υ A ɷ(cm-1)
5.87 2.42 0.173 324.84 110.92 96.41 180.22 100.50 254.68 1.813 0.267 0.901 889
2.1b,2.8b d ,2.12
CsTaO3
Exp.
4.100 4.09a 195.72 5.000 2.90 3.15c,3.70a, 3.51d 4.69 2.16 0.135 396.80 89.93 98.43 195.22 117.67 293.18 1.764 0.258 0.642 980
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ao (Å) Bo (GPa) Bc Eg (eV)
Exp
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CsNbO3
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Parameters
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The calculated parameters of CsMO3 (M= Ta, Nb) in cubic phase by using PBEsol and PBEsolmBJ potential.
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Ref [49]a, Ref [50]b, Ref [51]c , Ref [53]d
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Highlights
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First principle study of cesium based perovskites CsMO3 (M = Nb, Ta) in cubic phase The electronic band structures reveals the studied materials are wide bandgap semiconductors having a band gap in the visible region. The mechanical analysis demonstrates the CsNbO3 and CsTaO3 are ductile, anisotropic and mechanically stable in cubic phase. The optical analysis shows the optical band gap of CsNbO3 lies in the lower portion and of CsTaO3 in the upper portion of the visible region. The increasing values of electrical conductivity and power factor with temperature show the studied materials are also best suited for thermoelectric applications.
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