Specific thermoelectric features of novel CaPd3B4O12 (B = Ti, V) perovskites following DFT calculations

Accepted Manuscript Specific thermoelectric features of novel CaPd3B4O12 (B = Ti, V) perovskites following DFT calculations Muhammad Umer, Ali Irfan, Mamoona Mahboob, Sobia Ali, Malika Rani, Sikander Azam, Salman Khan, Muhammad Irfan, I.V. Kityk PII:

S0921-4526(18)30442-3

DOI:

10.1016/j.physb.2018.06.042

Reference:

PHYSB 310950

To appear in:

Physica B: Physics of Condensed Matter

Received Date: 12 June 2018 Revised Date:

28 June 2018

Accepted Date: 29 June 2018

Please cite this article as: M. Umer, A. Irfan, M. Mahboob, S. Ali, M. Rani, S. Azam, S. Khan, M. Irfan, I.V. Kityk, Specific thermoelectric features of novel CaPd3B4O12 (B = Ti, V) perovskites following DFT calculations, Physica B: Physics of Condensed Matter (2018), doi: 10.1016/j.physb.2018.06.042. 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.

ACCEPTED MANUSCRIPT Specific Thermoelectric Features of novel CaPd3B4O12 (B = Ti, V) perovskites following DFT Calculations

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Muhammad Umer1, Ali Irfan1, Mamoona Mahboob2, Sobia Ali2, Malika Rani2, Sikander Azam3*, Salman Khan4, Muhammad Irfan5, I.V.Kityk6

Department of Chemistry, The University of Lahore, Sargodha campus, 40100 Sargodha, Pakistan 2 3

Department of Physics, The University of Lahore, Sargodha campus, 40100 Sargodha, Pakistan

Department of Physics, COMSATS Institute of Information Technology,Park Road, TarlaiKalan, Islamabad 45550, Pakistan. 5 Department of Physics, The University of Sargodha, 40100 Sargodha, Pakistan 6

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Department of Physics, Women University Multan, Multan, Pakistan

Institute of Optoelectronics and Measuring Systems, Faculty of Electrical Engineering ,

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Częstochowa University Technology, PL-42201, Armii Krajowej 17, Czestochowa, Poland

Abstract

Perovskite materials demonstrate excellent elastic and thermoelectric properties. We report for the first time theoretical investigation of CaPd3B4O12 (B = Ti, V) perovskite and

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perform the electronic calculations using full potential linear augmented plane wave (FPLAPW) method within a framework of DFT approach. The transport properties were

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calculated using semi-local Boltzmann transport theory. As the Pd2+ occupied at A′-sites in perovskite their orbitals are very close to Fermi level and cause drastic changes in electronic

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band structure and transport properties of CaPd3B4O12 (B = Ti, V) perovskite. Both materials exhibit good elastic properties. The thermoelectric figure of merit for CaPd3Ti4O12 is (ZT = 0.8) so this material is good for cooling devices and thermoelectric applications. Our investigated results are in good agreement with experimental reported results. Key words: Perovskite; Transport Theory; Thermoelectric Properties; Elastic Properties; Fermi Energy. DFT calculations.

*Corresponding author:

SikanderAzam ([email protected])

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1.

Introduction Perovskite are important class of compounds due to remarkable flexibility in their

structures, which may be used in the different optoelecornic devices [1]. Different types of

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perovskite such as hydrides ABH3 [2], halides ABX3 [3] and oxides ABO3 [4] have been recently studied and generally the oxide perovskites have a chemical formula ABO3, where A is a monovalent or divalent cation and B is a penta- or tetravalent metal and perfect perovskite have cubic symmetry. Perovskite oxides gained much attention because of their diverse applications in catalysis [5], fuel cells [6], electrochemical sensing/photovoltaic [7]

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and in thermoelectric devices [8]. Research activities are still in progress to identify new materials with improved structural strength and in progress in order to identify new materials

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with structural strength and desired fictionalization [9]. Structural phase transitions are very common features of perovskites [10]. Materials at low temperatures are often characterized in terms of crystal chemical concepts, because descriptions of their high temperature properties are usually based on defect chemistry [11].

Ikuya Yamada et al. [12] have successfully substituted the Pd2+ in CaCu3B4O12 (B = Ti, V)

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perovskites, by applying special conditions under high temperature and pressure in which the A′-sites are entirely occupied by Pd2+ ions. They have reported electric, magnetic and structural properties versus temperature, and they have found that CaPd3Ti4O12 possess paramagnetic and revealed insulating properties, while CaPd3V4O12 exhibits metallic nature

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and have paramagnetic behavior. A′-sites near the Fermi level are very sensitive and hence the Pd2+ occupancy drastically varies the electronic properties for these fabricated perovskites

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(CaPd3Ti4O12 and CaPd3V4O12).

Many of the principal properties of solid compounds depend on the nature and

degree of orbital hybridization at or near the valence level in the respective atoms (the so-called “frontier” orbitals). These properties include electrical and thermal conductivity, magnetic susceptibility, crystal structure, phase transitions, and thermodynamic stability. [1315]. One of the principal goal of this work is to achieve a deeper understanding of these orbital interactions and their effects on the above mentioned properties. We have applied the full potential linear augmented plane wave (FP-LAPW) method which is proved to be one of the most accurate and reproducible method for the electronic structure calculations within the framework of the density functional theory (DFT). Additionally semi-classic Boltzmann 2

ACCEPTED MANUSCRIPT transport theory is used for thermoelectric studies. The computational details of electronic band structure, elastic and thermoelectric properties for the investigated perovskites and our calculated results are consistent with the experimental results. 2.

Computational Methodology We have carried out our calculations within a framework of density functional theory applying full-potential linearized augmented plane-wave (FP-LAPW) method as

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(DFT)

employed in WIEN2K code [16].The modified Becke Johnson (mBJ) [17, 18] inter-change potential was applied to assess the exchange-correlation energy. For the CaPd3Ti4O12 (CaPd3V4O12) compounds the LAPW spheres radii were chosen as the follows: for Ca 2.34

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(2.30), for Ti (V) 184 (1.82) Bohr, for Pd 1.98 (1.97) Bohr and 1.67 (1.64) Bohr for O atom. To determine the basis set for the basic wave functions, the cutoff RMT×Kmax (RMT is the

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muffin-tin sphere radius and Kmaxis the maximum modulus for reciprocal Kvectors) was taken to be equl to 8.0, for energy convergence we used 3000 K points. The calculations were performed

using the full-lattice optimization in the irreducible Brillouin zone. The self-

consistency was applied to validate the electronic structure, thermoelectric properties in the self-reliable field and it was thought to be converged once the entire energy is stabilized within accuracy of 0.1mRy.

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Thermoelectric transport properties were studied from the electronic structure applying Boltzmann transport theory. The perovskite CaPd3B4O12 (B = Ti, V) crystals have a cubic symmetry, and their unit cell crystal configuration is depicted in Fig.1. It possesses the space (No.204);

lattice constants are equl to

a/Å 7.49777(14) 7.40317(8) for

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group :

CaPd3Ti4O12 and CaPd3V4O12. The atomic site positions are equl to : Ca 2a (0, 0, 0), Pd 6b

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(0, 1/2, 1/2), Ti/V 8c (1/4, 1/4, 1/4), O 24g (x, y, 0); where the value of x (O) = 0.2961(4) and y (O) = 0.1859(3) for CaPd3Ti4O12; x (O) = 0.2947(3) and y (O)= 0.1856(3)for CaPd3V4O12.

3. 3.1

Results and Discussion

Structural Properties The ground state properties of the titled compounds have been calculated for CaPd3Ti4O12

and CaPd3V4O12.The perovskite structures were optimized to acquire their ground state properties by minimization of total energy.

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ACCEPTED MANUSCRIPT The Fig.2 shows dependence of total energy versus volume curve. The energy in terms of volume (EV) curve was fitted by the Birch-Murnaghan’s equation of state(1). B′  BVo BV  (Vo / V ) E (V ) = Eo + + 1 −  B′  B′  B′ − 1

(1)

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The Eo and B represent the stable energy and bulk modulus respectively, while B′ is the first derivative of the bulk modules with respect to pressure. We calculated the theoretical lattice constants using experimental data and decreasing the ratio of total energy to the crystal volume. The results of our optimized structural parameters are presented in Table 1.The

Elastic Properties

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decrease in bulk is invdrse to the bulk lattice.

The elastic constants and mechanical properties of CaPd3B4O12(B = Ti, V) compound have been calculated. As the investigated perovskite have a cubic symmetry, so their independent elastic stiffness constants are C11, C12and C44. The values of bulk modulus (B), shear modulus (G), Young’s modulus (Y), Poisson’s ratio (ν) and Zener anisotropic factor (A) using Morteza Jamal code and their results are

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for these materials have been calculated

shown in Table 1.As stated by Voigt and Reuss, the shear moduli,GV and GR , respectively for the cubic structures are given as:

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(2)

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(3)

G = (Gv+GR) / 2

(4) (5)

(6)

(7)

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ACCEPTED MANUSCRIPT The Young modulus(Y) and Poisson’s ratio (ν) have been calculated using equation (6) and (7), respectively, and the bulk modulus(B) is closely related to them. The shear modulus (G) is calculated using equation (4) and it defines the stiffness of the material.

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Table: 1. Calculated elastic parameters for CaPd3B4O12 (B = Ti, V) perovskite. C11

C12

C44

G

B

A

CaPd3Ti4O12

367.10

158.37

50.03

67.45

4.46

0.47

33.50

0.365

317. 07

CaPd3V4O12

360.16

178.70

68.14

76.47

4.78

0.75

35.83

0 .553

292.02

Y

C11-C44

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Elastic Parameters

It is obvious from the results that both CaPd3Ti4O12 as well as CaPd3V4O12 are elastically stable, because

.C11is 71.0% higher than C44 for CaPd3Ti4O12 and

CaPd3V4O12. This one shows the weaker resistance of CaPd3Ti4O12 and CaPd3V4O12 with respect to to the pure shear deformation compared to the resistance of the unidirectional

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compression. Smaller C44 value means lower shear modulus. The calculated value of C44 for CaPd3V4O12 is greater and hence it is stiffer than CaPd3Ti4O12. From the elastic constants we have calculated Zener anisotropic factor (A) using relation

, so according to

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material becomes completely isotropic when it is equal to unity i.e.

. The

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the results the compound CaPd3Ti4O12 is more anisotropic thanCaPd3V4O12.

Band structure and density of states (BS-DOS)

Band structures (BS) for the cubic symmetry perovskite CaPd3B4O12 (B = Ti, V)

compound is calculated within modified Becke-Johnson (mBJ) approximation. The CaPd3V4O12 compound shows the metallic nature but when V is replaced by Ti, the nature of the material’s changes from the metallic to semiconductor. The energy band gaps (Eg) are found to be varied between the top of valance and bottom of conduction. The BS along with highly symmetric points of the Brillouin zone (BZ) for the CaPd3B4O12 (B = Ti, V) compound has been calculated within the mBJ approximation

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ACCEPTED MANUSCRIPT and the curves dislocation for the electronic band structure along with the higher regularity directions of Brillouin zone (BZ) are shown in Fig.3. Our ab-initio computed results show that the investigated compound have the direct band gap of 1.967 eV and it is obvious from the intended energy band structure dispersions. Because the minimal energy of conduction band and the maximal energy of valence band are situated at

. The conduction and

carrier mobility, particularly in the vicinity of the

point.

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valence bands exhibit strong dispersion in k space, which demonstrates the high electron-hole

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The calculated total density of states (TDOS) and partial density of states (PDOS) spectra for CaPd3B4O12 (B = Ti, V) compound are presented in Fig.4. The Fermi energy level (Ef) is

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located at 0.0 eV. It is found that the lower position of valence band for CaPd3Ti4O12 and CaPd3V4O12 bands are provokingly caused by

O-p (Ca-p and O-s) states with small

admixture of Pd-s/p, Ti-s/p, Ca-s/p and O-s (V-s/p and Pd-p) orbitals within the energy range of -8.0 to -6.5 (-21.0 to -19.5) eV, in an energy range of -1.5 to 0.0 (-7.5 to -3.0) eV, Ti-d Pdd and O-p) orbital shows higher contribution with a small admixture of O-s/p, Ti-p and Pd-d (Pd-s/p and V-s/p) orbitals. For the CaPd3V4O12 compound the Fermi level is determined by a

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contribution of Pd-d, V-d and O-p orbitals with a small admixture of Pd-d states. The conduction bands for CaPd3Ti4O12 and CaPd3V4O12 are mainly formed by the d-state of Pd and V atoms which are located within 3.0 to 13.0 (11.5) eV energy range. The orbitals overlap between Pd-s and Ti-p, O-s and Pd-p, Pd-s and Pd-p, O-s and Ti-p, Ti-p and Pd-p, O-

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s and Pd-p, V-s and Pd-p, Pd-p and Ca-s, Ti-s and Ti-p in valance and conduction band region reflect a strong orbital mixing or interaction between them, which may

cause the

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broadening of the energy bands in this range. Following the Fig.4 one can see that the valence band is just situated below the Fermi energy (-3.5 to 0.0 eV) for CaPd3Ti4O12 and CaPd3V4O12 and it is mainly originated from

the Ti-d, Pd-d , O-p and Pd-d, V-d and O-p

orbitals. At the same time one can say that the conduction band just above the Fermi level (2.0-5.0 eV) is caused mainly due to d-state of Pd and V atoms. Rest of the band structure shows the weak hybridizations of orbital and hence the wider band gap energy gap. For CaPd3V4O12, the calculated values of total density of states (TDOS) at Fermi level N(EF) is 10.671 states/eV unit cell. The electronic specific heat coefficient ( γ ) is calculated by using an expression (8), where K β is the Boltzmann constant. The calculated value of specific heat coefficients ( γ ) is equal to about 1.87 mJ/mol-K2, 6

ACCEPTED MANUSCRIPT γ = π 2 N (EF )K β2 1 3

3.4

(8)

Fermi surface (FS) The Fermi surfaces for CaPd3V4O12 were calculated due to their interesting features

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and clear metallic origin. For metallic compounds the Fermi surface (FS) structure is formed as a result of electronic states jump over Fermi level. The energy distribution curves (ECD) for k-points of the Brillioun zone are used to determine the FS (i.e. the bands crossing the Fermi energy).Electrons near the Fermi levels contribute more towards to the conductivity of

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a material. Therefore, following the FS we can easily comprehend the electronic structure (ES) of particular metallic composite. We have computed the FS in 2D and 3D model (shown

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inFig.5) using FP-LAPW method for the perovskite CaPd3V4O12. The investigated compounds have seven bands that cross the Fermi level and we studied the merged band structures in more details. The empty area comprises holes while the shaded region corresponds to the electrons. The FS contain different colors and they are related to electronic mobility in that region. The Violet color defines slow moving of electrons while the red color considered for electrons with higher velocity, the rest of colors show a

Thermoelectric properties

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transitional velocity range.

Using the standard Boltzmann kinetic transport theory and the rigid band

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approximation we have calculated the thermoelectric properties of perovskite CaPd3B4O12 (B = Ti, V). Thermoelectric properties can be evaluated from Seebeck coefficient (S), electrical conductivity (σ), figure of merit (ZT) and thermal conductivity (K). All these quantities are dependent on temperature and have been investigated within 50-800 K using BoltzTrap program that is based on Boltzmann kinetic transport theory. It is impossible to calculate electron relaxation time from band structure. So it is assumed to be constant. The good thermoelectric materials exhibit high Seebeck coefficient (S) value with low resistivity and thermal conductivity. 4.1

Electrical conductivity (σ σ)

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ACCEPTED MANUSCRIPT Following the calculated electronic band structure, the electrical conductivity (σ) has been evaluated. The investigated compounds (CaPd3V4O12 and CaPd3Ti4O12) show different behavior due to the particular valence shell electronic configuration for the V and Ti atoms. The Fig.6 (a) shows the electrical conductivity plots for CaPd3B4O12 (B = Ti, V) under constant relaxation time vs temperature (T).The compound CaPd3V4O12 shows decrease in

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electrical conductivity during an increase of temperature due to its metallic nature and small carrier concentration up to 800 K, while the CaPd3Ti4O12 shows linear relationship with temperature. It is a consequence of excitation of carriers from the occupied states to

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unoccupied levels with increasing temperature.

Seebeck coefficient(S)

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Seebeck coefficient plays a crucial role to illustrate the thermocouple effectiveness and thermoelectric response of materials. The electrons carry both heat and charges of the diffusion of electrons in the material depending on temperature gradient which generates reverse electric field and voltage called Seebeck voltage. Space asymmetric electronic distribution around Fermi level is closely related to the sign and magnitude of Seebeck voltage. The decrease of Joule heating causes a decrease in electrical conductivity.Seebeck

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coefficient of CaPd3B4O12 (B = Ti, V) is depicted in Fig. 6 (b). The CaPd3V4O12 compound shows positive Seebeck sign up to 200 K, and becomes negative afterward. Further increase in temperature causes the higher carrier concentration and hence the Seebeck coefficient becomes more negative. So the CaPd3V4O12 behaves as p-type at lower temperatures and

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becomes n-type at thigher temperature.The CaPd3Ti4O12 compound demontrates a p-type performance with the conductivity predominantly arising from hole carriers. The Seebeck

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coefficient having maximum value at 350 K approximately and beyond this temperature it decreases. This fluctuation may be due to the phase transition. Both compounds have the dispersive nature at 800 K, as -

and

Seebeck coefficient

for CaPd3Ti4O12 and CaPd3V4O12, respectively.

4.3

Thermal conductivity(K)) The investigated materials (CaPd3V4O12 and CaPd3Ti04O12) show prinicpipally

different conductive features

versus

temperature. Fig.6 (c) shows the temperature

dependence of CaPd3B4O12 (B = Ti, V) and both compound exhibit linear change in thermal 8

ACCEPTED MANUSCRIPT conductivity with increasing temperature. Temperature directly influences on the structural properties including electron-phonon scattering, vacancies or other fixed defects that practically participate in overall thermal response of the materials. At temperature 800 K the CaPd3V4O12 shows greater electronic thermal conductivity (

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.

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respect to CaPd3Ti4O12

) with

Resistivity (ρ ρ)

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Due to the metallic nature of CaPd3V4O12 compound, the linear trend in resistivity with increasing temperature is observed up to 300 K, as shown in Fig.6 (d). For an

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elevated temperature, the molecular and lattice phonons contribute more to the resistivity. Electronic band structure shows the semiconducting behavior of CaPd3Ti4O12 as described earlier. So the resistivity of CaPd3Ti4O12 decreases with increasing temperature. The observed trend in conductive behavior of CaPd3B4O12 (B = Ti, V) is inconsistent with the experimental results.

Figure of merit (ZT)

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4.5

Thermoelectric figure of merit (ZT) is a dimensionless quantity used to assess the thermoelectric response of materials. It is related with Seebeck coefficient (S), temperature

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equation(9).

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(T), electrical conductivity (σ) and thermal conductivity (K) by the relation given by

S 2σ eT ZT = ke + k p

where the thermal Conductivities Ke and Kp are

(9)

attributed to electrons and phonons,

respectively. At lower temperatures the carrier concentration is relatively low, so the thermal conductivity is mainly caused by

contribution of thermal lattice phonons. The BoltzTraP

code evaluates thermal response only due to the contribution of electronic part and in our calculations we neglect the thermal lattice vibrations contribution. The calculated figure of merit is shown in Fig.6 (e). The ZT plot reflects that both materials show quite different behaviors versus temperature. CaPd3V4O12, has a decrease in ZT value and dramatically increases after 250 K temperature reaching a maximum (ZT = 0.04) at 800 K. On the other 9

ACCEPTED MANUSCRIPT hand, the CaPd3Ti4O12shows a remarkable increase in ZT value at lower temperature (100 K), and a linear trend is observed with a slight variation (± 0.01). At 800K the maximum value of ZT achieved for CaPd3Ti4O12 is equal to about 0.80. So according to figure of Merit (ZT), the CaPd3Ti4O12 exhibits good thermoelectric properties and best material for cooling and thermoelectric devices.

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It should be added that the principal role here begin to play intrinsic cationic defects [20, 21] which may significantly change the ZT. And the oxides even in the disordered glasses additioanl role belongs to anaharmonic phonons [22,23]. These factor may significantly change the experimental data and this one should be taken into account during

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their interpreting of the experimental data.

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Conclusions

The electronic band structure, elastic and thermoelectric properties of novel CaPd3B4O12 (B = Ti, V) perovskite material are studied. These properties were computed by full potential linear augmented plane wave (FP-LAPW) method based on DFT within WIEN2k code to acquire their ground state properties by minimization of the total energy to

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the unit cell volume. The calculated band structure properties have shown that insulating characteristics are formed in CaPd3Ti4O12 due to induction of Ti-atom in the crystal lattice. The valence band just below the Fermi energy (-3.5to 0.0 eV) for CaPd3Ti4O12 and CaPd3V4O12 perovskites is prevailingly originated from Ti-d, Pd-d, O-p and Pd-d, V-d, O-p

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terms contributions, respectively, and the conduction band just above the Fermi energy (2.0 to 5.0 eV) is caused by major contribution of Pd and V (d-orbitals). Thermoelectric figure of

verus

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merit, Seebeck coefficient, electrical conductivity, and thermal conductivity were determined by using BoltzTraP program and it is revealed that, the figure of merit for

CaPd3Ti4O12(ZT = 0.8) is comparatively better than CaPd3V4O12 (ZT = 0.04) within a normal temperature range. So at ambient temperature it is a good material for thermoelectric applications. Our calculated results are in good agreement to the experimental results.

Acknowledgments

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ACCEPTED MANUSCRIPT Project CEDAMNF, reg. no.CZ.02.1.01/0.0/0.0/15_003/0000358, co-funded by the ERDF. Computational time has been provided with the MetaCentrum (LM205) and CERITSC (CZ.1.05/3.2.00/08.0144) infrastructures.

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Figures captions Figure 1. Unit Cell Crystal structure of CaPd3B4O12 (B = Ti, V) perovskite. Figure 2. Energy vs volume (CaPd3B4O12(B = Ti, V) dependence using GGA

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approximation) Figure 3. Band structures of CaPd3B4O12 (B = Ti, V) using mBJ approximation. The Fermi energy is normalized to zero.

Figure 4. (a) Total density state (TDOS) for CaPd3B4O12 (B = Ti, V) partial density of states (PDOS) for Ca (s, p), Ti/V (s, p, d), Pd (s, p, d) and O (s, p), CaPd3B4O12 (B = Ti,

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V) using mBJ approximation.

Figure 5. Fermi surface of perovskite (CaPd3V4O12) using mBJ approximation.

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Figure 6. Calculated transport coefficients (a) electrical conductivity (b) thermal conductivity (c) Seebeck coefficient and (d) power factor of CaPd3B4O12 (B = Ti, V)

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perovskite as a function of the temperature under constant relaxation constant.

Fig.1 Unit cell structures, CaPd3B4O12 (B = Ti, V)perovskite.

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Fig.2 Energy vs volume (CaPd3B4O12(B = Ti, V)using GGA approximation)

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Fig.3 Band structures of CaPd3B4O12 (B = Ti, V) using mBJapproximation.

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Fig.4 (a) Total density state (TDOS) for CaPd3B4O12 (B = Ti, V). Partial densities of states

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(PDOS) for Ca (s, p), Ti/V (s, p, d), Pd (s, p, d) and O (s, p), CaPd3B4O12 (B = Ti, V) using BJ approximation.

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Fig.5 Fermi surface of perovskite (CaPd3V4O12)usingmBJapproximation.

Fig.6 (a) Electrical conductivity temperature behaviours (σ).

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Temperture dependence of Seebeck coefficient (S).

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Fig. 6 (b).

Fig. 6 (c).

Thermal conductivity (κ) versus temprature.

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Temperature resistivity (ρ) features.

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Fig. 6 (d).

Fig. 6 (e).

Figure of Merit (ZT) as funcitons of temperature.

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