Elucidating DFT study on structural, electronic, thermal and elastic properties of SrTcO3 by using GGA and mBJ approach

Elucidating DFT study on structural, electronic, thermal and elastic properties of SrTcO3 by using GGA and mBJ approach

Accepted Manuscript Elucidating DFT study on structural, electronic, thermal and elastic properties of SrTcO3 by using GGA and mBJ approach S.M. Soha...

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Accepted Manuscript

Elucidating DFT study on structural, electronic, thermal and elastic properties of SrTcO3 by using GGA and mBJ approach S.M. Sohail Gilani , Saad Tariq , M. Imran Jamil , Bashir Tahir , M.A. Faridi PII: DOI: Reference:

S0577-9073(17)31572-1 10.1016/j.cjph.2018.01.002 CJPH 429

To appear in:

Chinese Journal of Physics

Received date: Revised date: Accepted date:

1 December 2017 28 December 2017 2 January 2018

Please cite this article as: S.M. Sohail Gilani , Saad Tariq , M. Imran Jamil , Bashir Tahir , M.A. Faridi , Elucidating DFT study on structural, electronic, thermal and elastic properties of SrTcO3 by using GGA and mBJ approach, Chinese Journal of Physics (2018), doi: 10.1016/j.cjph.2018.01.002

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Highlights Study provides plausible temperature range for electron-phonon couplings.



Elastic and thermal properties are the first study of compound.



By using PBE-GGA, STO exhibits anti-ferromagnetic structure.



mBJ-GGA study shows ferromagnetic attributes.



Ferromagnetic frustration arises due to Sr-p and O-s electronic states.

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Elucidating DFT study on structural, electronic, thermal and elastic properties of SrTcO3 by using GGA and mBJ approach S. M. Sohail Gilani1, Saad Tariq2*[email protected], M. Imran Jamil3, Bashir Tahir4, M. A. Faridi1 1

Centre for High Energy Physics, University of Punjab, Lahore, 54590, Pakistan Centre of Excellence in Solid State Physics, University of Punjab, Lahore, 54590, Pakistan 3 Department of Physics, School of Science, University of Management and Technology, Lahore, 54770, Pakistan

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Department of Electrical and Computer Engineering, McMaster University, Ontario, Canada.

*Corresponding author.

Abstract

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Generalized gradient approximation and Modified Becke and Johnson (mBJ) potential scheme, within density functional theory, has been implemented to evaluate the structural, electronic and thermo-elastic attributes of SrTcO3. The structural stability of the very compound has been probed from tolerance factor, elastic stability criterion and ground state optimizations. In the study of electronic properties, formation of band-gap has been resolved by using density of states

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and from electron spin density contour plots. It is for the first time that mechanical and thermodynamical properties have been studied in terms of elastic constants, melting temperature,

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enthalpy of formation and Debye temperature. Our results have shown that SrTcO3 exhibit a stable ductile nature that makes it a convincing candidate for high temperature electronic Keywords

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applications.

1.

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Density Functional Theory; Modified Becke and Johnson potential; Strontium Technate technate.

Introductions

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Technetium is the lightest radioactive element extracted artificially from fission reactions. Technetium (Tc) based perovskites have been seldom investigated due to their natural rare occurrence and radioactive risks. The physical and chemical properties of such compounds have largely been neglected; presumably because of the absence of any stable isotopes of Tc. Light radioactive compounds are important in the synthesis of radio pharmaceuticals [1] and in the management of nuclear wastes [2]. In 2011, Rodriguez et. al. [3] successfully fabricated Tcbased perovskite SrTcO3 (STO) for the first time and observed

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that it has a high Neel

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temperature (TN) of 1000 K. The high value of TN, change in magnetic order and structural phase transitions of STO have triggered intensive studies among the various researchers. For example, Gordon et. al. [4] studied STO experimentally

by using x-rays and neutron diffraction

techniques. In their study, they found the change in magnetic ordering and structural phase transitions when it goes from orthorhombic (Pnma) phase at room temperature to cubic (Pm-3m)

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phase near 800 K. A study of Mravlje et. al. [5] portrayed an electronic band-gap of 1.0 eV and a magnetic moment of 2.5µB in cubic phase. While, Borisov et. al. [6] estimated a band-gap of 0.15 eV by using generalized gradient approximation (GGA) and 0.4 eV by using Hubbard parameter (U) in GGA+U with U = 0.5 eV. In another work, Chun-lan et. al. [7] studied magneto-structural coupling of STO in orthorhombic phase by using GGA functional and there

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they found a G-type antiferromagnetic nature of it. Franchini et. al. [8] studied electronic properties from Heyd, Scuseria and Ernzerhof (HSE) calculations and they obtained a band-gap of 1.48 eV. Wang et. al. [9] made a use of the value U = 3.0 eV in the ultra-soft pseudopotential plane wave method and they obtained a band-gap of about 1.7 eV in the orthorhombic phase. Whereas, Middey et. al. [10] applied GGA+U (U = 2 eV) to obtain a band-gap of 1.1 eV in the

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orthorohmbic phase. It is worth to notice that GGA calculations, for related ABO3 perovskites, underestimate the band-gap value. While the hybrid B3PW and B3LYP functionals allow to

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achieve a much better agreement of the band gap values with the experiment [11, 12]. These aforementioned variations in electronic band-gap are evident because of the presence of dorbitals in the correlation effects. Such attributes have also been demonstrated in a similar type

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of Sr based perovskite like SrZrO3 [13].

In the past, main focus of the researchers has been confined in understanding the structural

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behavior of STO. Only few theoretical studies on electrical properties of STO in orthorhombic and cubic phases have been reported. The uniqueness of STO as compared to other ABO3 type

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perovskites is its high Neel temperature. But experimental as well as theoretical investigations have not explored the elastic and thermal properties in the cubic phase of STO to date. Moreover, there were no reports on electronic properties by using mBJ potential. Therefore to interpret its other unique attributes we have investigated all the above-mentioned properties in detail for the first time.

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2. Computational methodology The structural properties of STO have been analyzed by using Wien2k code [14] in spin polarized configurations within the frame work of density functional theory (DFT). The Perdew, Burke and Ernzerhof Generalized Gradient Approximation (PBE-GGA) [15] along with Modified Becke and Johnson (mBJ-GGA) potential [16] have been used to investigate electronic

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and magnetic properties. Cubic structure of STO has been obtained by positioning Sr, Tc, O1, O2 and O3 atoms at (0, 0, 0), (0.5, 0.5, 0.5), (0, 0.5, 0.5), (0.5, 0, 0.5) and (0.5, 0.5, 0) respectively. To investigate magnetic effects of STO, calculations of spin-polarized wave function expansion are performed by considering lmax= 12. For total energy convergence we have chosen RMT*Kmax = 8, where RMT values of Sr, Tc, and O atoms are taken as 2.5, 1.74, 1.82 a. u. respectively. For the

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best convergence, the k-points are selected through script method by the k-mesh of 20× 20× 20 and convergence is set by iteration process up to 0.1× 10-4 Ryd.

3.

Results and discussions

In section 3.1, structural properties elucidate stability of the structure along with various aspects of ground state energy and bond lengths. . The information provided above in the computational

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methodology section tells how to obtain optimized results of electronic properties. The results obtained are on the basis of successful convergence of Self Consistent Field (SCF). A

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comparison of these results with available literature has been given in Table 1. In electronic properties section, Electronic Density of States (EDOS) represents the bonding probability per

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state in respective band regions. Electron spin density contour plots, shown in Figs. 6 and 7, are used to elucidate covalent and ionic character of STO along [110] direction. Band nature of STO

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has also been discussed in detail in this section . Thermal and elastic properties have been discussed in sections 3.3 and 3.4 respectively.

3.1

Structural properties

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The ground state parameters, of cubic STO, have been calculated by using PBE-GGA functional to investigate the structural stability. The parameters namely the lattice constant (a0), the bulk modulus (Bo), pressure derived bulk modulus (B/), and ground state energy (E0) are found to match closely with the results in available literature. For the values of these parameters see Table 1. By using interatomic distances in Goldschmidt's [17] tolerance factor

√ (

, phase

)

transformations of perovskites can be estimated. Tolerance factor can also be calculated as a

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function of bond length which is equal to sum of ionic radii. These lengths are obtained by making a unit cell from our calculated lattice parameters of SrTcO3. The obtained values for SrTc, Sr-O and Tc-O distances are 3.42, 2.79 and 1.97 respectively in atomic units. Sum of rSr and rO radii corresponding to Sr-O bond length and sum of rTc and rO radii corresponding to Tc-O bond length are used in the above given equation for Goldschmidt's tolerance factor. The value =1 elucidates stable cubic phase and in our study it has found to be 0.99. The volume

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of

optimization of STO by using PBE-GGA has provided lattice constant being 3.99Ǻ that matches closely with the experimental lattice constant 3.97 Ǻ [3] and 3.96 Ǻ [4]. In the DOS graphs (see Figure 3) we have observed that by considering mBJ-GGA functional, the large number of Sr-p states correspond to frustration which can be easily seen there that is not present in PBE-GGA

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DOS graphs (Figure 2). This is because of the fact that available states in core energy level in valance band, by using PBE-GGA, have energy range that ends up for O-p states near -8.30 eV. While, by using mBJ-GGA, sensitive small energy ranges can be estimated for core energy levels. Thus O-s and Sr-p states have been found to fall in core lower energy range near -17.16 eV in which probability of Sr-p states (14 States/ eV) is much higher than that of O-s states.

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Therefore filled energy states (Sr-p = 2p6, 3p6, 4p6) correspond to slight frustration, that falls between transitions, from ferromagnetic to anti-ferromagnetic. Our calculations do not negate

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experimental facts but in fact we are discussing the role of functional in observing small frustration. Such materials have the property to exhibit fluctuating magnetic nature between antiferromagnetic and ferromagnetic. This is purely a quantum mechanical effect that requires very

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sensitive magnetic instruments to measure experimentally. Analysis of electronic properties of STO by using PBE-GGA and mBJ-GGA has been discussed in detail in the next section.

Electronic properties

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3.2

There have been few reports [6-10] on electronic properties of STO in orthorhombic phase but

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no detailed studies

are found in cubic phase. We have discussed electronic properties

systematically by using PBE-GGA and mBJ-GGA functional in cubic phase. By using PBEGGA we have found that STO exhibit antiferromagnetic nature. Electronic density of states (EDOS) plot for spin up configuration shown in Fig. 2 has been used to explain this phenomenon. For spin down EDOS we obtained similar results to spin up states as they should be for anti-ferromagnetism. In conduction band (CB), O-p states and Tc-d-t2g states are p-d hybridized near Fermi level and Sr-d states reside next to hybridization. Whereas conduction

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band minimum (CBMi) has been located near Fermi level that portrays n-type semiconducting attribute. In valence band (VB), O-p states ranges from -8.30 eV to -2.78 eV with number of available states are being 2.4 states/ eV. Here maximum contribution of available states are because of Tc-d-t2g states i.e. 1.5 states/ eV and then by O-p states i.e. 1 state/eV. Over all available states for conduction are 3.5 states/ eV. The p-d hybridization between O-p states and

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Tc-d-t2g states start to occur in the range of -2.27 eV to 1.11 eV. Then O-p states take hybridization with Tc-d-eg states ranging from 1.11 eV to 3.07 eV. O-p states then make hybridization with Sr-d states ranging from 3.07 eV to 8.66 eV.

By using mBJ-GGA functional, the obtained EDOS has been explained in Fig. 3. The major difference observed between PBE-GGA and mBJ-GGA calculations is that the PBE-GGA has

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underestimated core electronic correlation effects. Due to which Sr-p states and O-s states have been neglected in convergence. By using mBJ-GGA functional corrections, frustrated magnetic effect has been observed in STO. In spin up configuration, conduction band contribution falls off in the range 1.034 eV to 7.29 eV due to Tc-d-eg states near Fermi level. There are also exhibition of Sr-d states in upper conduction states as in PBE-GGA. In Valence band maxima (VBM); Tc-

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d-t2g and O-p states are ranging from -0.153 to -7.25 eV. Here occurs p-d hybridization between O-p and Tc-d-t2g states. In spin down configuration conduction band (CB) is composed of Tc-d-

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t2g states in the range from 0.2633 to 7.23 eV. Only few states are available for Sr-d states. VBM composed of O-p states lies only in the range -1.62 to -7.25 eV. Core valance states are Sr-20.23 eV.

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p states and they are in the range -16.63 to -17.16 eV whereas O-s states lie in the range -18.94 to In Fig. 4 we have shown electronic band structure of STO using PBE-GGA functional which

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portrays anti-ferromagnetism in both the spin states as discussed above with Ref. to Fig. 2. The obtained band-gap value is 0.42 eV that matches well with theoretical band-gap of 0.40 eV [6].

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In Fig. 5 we have represented electronic band structure obtained from mBJ-GGA potential. The obtained band-gap value for spin up channel has been found to be smaller than spin down channel. All these values are listed in Table 1. While in Figs. 6 and 7 we have shown three and two dimensional views of electron spin density plots along [110] direction of spin up and spin down configurations respectively. These contour plots explain plausible origin of ferromagnetism due to spin exchange mechanism. In spin up state, Tc-O atoms have shown strong covalent bonding due to concentrated electron charge around Tc atomic-site. This bonding

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has been observed to be weaker in spin down channel. Both the Sr-O and Sr-Tc atoms have shown strong ionic attributes in the two spin states. This peculiar behavior of ferromagnetism in STO arises due to Tc-d states bonding with O-p valence states and ionic bonding of core electronic charge states of Sr-p and O-s states. As we have observed that STO exhibits antiferromagnetic nature by using PBE-GGA that matches with experimental findings. But by

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using mBJ-GGA potential a very small frustration has been observed which causes ferromagnetism in SrTcO3. This behavior of STO can be further studied in both theoretical and experimental grounds. Small frustrations in strongly correlated radioactive materials is hard to be measured therefore it has been observed theoretically for the first time.

3.3

Thermal properties

following relations *

(

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We have calculated Debye temperature [18] (Θ) and melting temperature [19] (TM) by the

)+

(

(1)

)

(2)

The average sound velocity, )]

, used in equation No. 1

( )

is given by the relation

. Where vl and vt are longitudinal and transverse, average wave, velocities

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[ (

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For STO, the Debye temperature and melting temperatures are 306 K and 2359 K, respectively.

respectively and these are defined by Navier’s equation [20]. Directional sound velocities have

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been obtained by using equations in Refs. [21, 22]. For the temperature range Θ< T< TM, the high-frequency mode of phonon oscillations may occur. For T< Θ, phonon oscillations would

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expect to be frozen. While in high temperature range which is estimated between 306-2359 K we can expect high modes of oscillations in STO. This characteristic of STO may have applications

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in appliances that work at high temperatures. Using Cahill criteria[23] minimum thermal conductivity

of STO has been computed by the

relation

Where, nb, k,

( )

and

(

)(

)

(3)

are no. of atoms per unit volume, Boltzmann constant, longitudinal and

transversal sound velocities, respectively. To study the thermal conductivity along

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crystallographic directions, we have used directional values of

and

which are listed in

Table 2. This directional study can be useful for growing crystals along a particular direction to achieve a maximal or minimal thermally conductive device. Enthalpy of formation (Hf) has been obtained by defining

(

)

(

).

Where a, b and c are constants representing composition of elements in a unit cell. For STO it

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has been found to be -11.14 eV/ unit cell. Negative sign in Hf shows a stable cubic phase and reaction mechanism will be exothermic in nature. Optimized energy values of spin polarized Sr, Tc and O atoms have been used within Fm3m structural phase for Sr and Tc atoms. While for O atom Barrett et. al. [24] has suggested C2/m phase.

3.4

Elastic properties

crystal structure. The stability criteria is (

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Three independent elastic constants C11, C12 and C44 have been used in explaining the stability of −

) > 0,

> 0,

> 0 and B > 0 [25]. We have

found that STO has satisfied all these conditions to exhibit stable cubic phase. Elastic anisotropy factor (A) defines ratio of shear modulus along [100] direction to [110] direction. For isotropic materials A= 1 otherwise one should expect anisotropy along [100] direction. For our case A≠ 1

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therefore, noticeable directional properties can be observed along [100] direction. e.g. along this anisotropic direction, we have found that longitudinal mode of oscillation (VL) has maximum

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value. Furthermore we have found that the thermal conductivity has lowest value along this direction.

Klienmen internal strain parameter, ξ, describes the relative ease of bond bending versus the

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bond stretching. It may also be used to explain piezoelectric effect if variations in the value of ξ are observed under pressure. Usually the value, 0≤ ξ≤ 1, stands for stable structures [26] and in

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bond bending ξ→0 while in bond stretching ξ→1. For STO we get ξ= 0.54 which portrays small resistance against bond bending. STO exhibit ductile nature according to Pough’s (B/G) and

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Frantsevich’s (G/B) ratio. Ductile nature of STO can be estimated by (B/G)> 1.75 and (G/B) < 0.57 and brittle nature of compound by (B/G) < 1.75 and (G/B)> 0.571. All the mentioned properties are listed in Table 2. As for authors knowledge there is no experimental or theoretical data available in literature for comparison of the elastic and thermal properties of this compound. So, our results can be used for comparison in future experimental or theoretical investigations.

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Conclusions In summary, by using PBE-GGA and mBJ-GGA functional scheme following conclusions have been drawn on structural, electronic and thermodynamic properties of SrTcO3. 1. The volume energy optimizations, tolerance factor and formation energy shows stable AFM structure.

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2. By using mBJ-GGA potential, electronic band-structure and density of states analysis shows ferromagnetic attributes in STO, which arises due to frustrated Sr-p and O-s core electronic states.

3. Mechanical properties show that the compound exhibits thermodynamically stable cubic phase and it is ductile in nature.

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4. Thermal properties provide a plausible temperature range for electron-phonon couplings. Which can be further studied in order to fabricate high temperature electronic

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applications of SrTcO3.

3. 4.

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5.

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2.

Deutsch, E., et al., Technetium chemistry and technetium radiopharmaceuticals. Progress in inorganic chemistry, 2009. 30: p. 75. Lieser, K., Technetium in the nuclear fuel cycle, in medicine and in the environment. Radiochimica Acta, 1993. 63(s1): p. 5-8. Rodriguez, E.E., et al., High Temperature Magnetic Ordering in the 4 d Perovskite SrTcO 3. Physical review letters, 2011. 106(6): p. 067201. Thorogood, G.J., et al., Structural phase transitions and magnetic order in SrTcO 3. Dalton Transactions, 2011. 40(27): p. 7228-7233. Mravlje, J., M. Aichhorn, and A. Georges, Origin of the High Néel Temperature in SrTcO 3. Physical review letters, 2012. 108(19): p. 197202. Borisov, V., et al., Magnetic exchange interactions and antiferromagnetism of A TcO 3 (A= Ca, Sr, Ba) studied from first principles. Physical Review B, 2012. 85(13): p. 134410. Ma, C.-L., et al., The active role played by nonmagnetic Sr in magnetostructural coupling in SrTcO 3 from first principles. Physics Letters A, 2011. 375(41): p. 3615-3617. Franchini, C., et al., Exceptionally strong magnetism in the 4 d perovskites R TcO 3 (R= Ca, Sr, Ba). Physical Review B, 2011. 83(22): p. 220402. Wang, G., et al., Comparative study of the magnetism of SrTcO 3 and Ca (Sr) MnO 3. Physics Letters A, 2012. 376(45): p. 3313-3316.

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Middey, S., et al., Route to high Néel temperatures in 4 d and 5 d transition metal oxides. Physical Review B, 2012. 86(10): p. 104406. Eglitis, R.I., Ab initio hybrid DFT calculations of BaTiO 3, PbTiO 3, SrZrO 3 and PbZrO 3 (111) surfaces. Applied Surface Science, 2015. 358: p. 556-562. Eglitis, R. and A. Popov, Systematic trends in (001) surface ab initio calculations of ABO 3 perovskites. Journal of Saudi Chemical Society, 2017. Nazir, G., et al., Putting DFT to the trial: First principles pressure dependent analysis on optical properties of cubic perovskite SrZrO 3. Computational Condensed Matter, 2015. 4: p. 32-39. Blaha, P., et al., wien2k. An augmented plane wave+ local orbitals program for calculating crystal properties, 2001. Perdew, J.P., K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple. Physical review letters, 1996. 77(18): p. 3865. Koller, D., F. Tran, and P. Blaha, Improving the modified Becke-Johnson exchange potential. Physical Review B, 2012. 85(15): p. 155109. Goldschmidt, V.M., Die gesetze der krystallochemie. Naturwissenschaften, 1926. 14(21): p. 477485. Hao, Y.-J., et al., First-principles calculations of elastic constants of c-BN. Physica B: Condensed Matter, 2006. 382(1): p. 118-122. Fine, M., L. Brown, and H. Marcus, Elastic constants versus melting temperature in metals. Scripta metallurgica, 1984. 18(9): p. 951-956. Screiber, E., O. Anderson, and N. Soga, Elastic constants and their measurements. McGrawHill, New York, 1973. Tariq, S., et al., Exploring structural, electronic and thermo-elastic properties of metallic AMoO 3 (A= Pb, Ba, Sr) molybdates. Applied Physics A, 2018. 124(1): p. 44. Nadeem, S., et al., DFT study of structural, electronic, thermo-elastic properties and plausible origin of superconductivity due to quantum degenerate states in LaTiO3. Journal of Theoretical and Computational Chemistry, 2016. 15(05): p. 1650044. Cahill, D.G., S.K. Watson, and R.O. Pohl, Lower limit to the thermal conductivity of disordered crystals. Physical Review B, 1992. 46(10): p. 6131. Barrett, C., L. Meyer, and J. Wasserman, Antiferromagnetic and Crystal Structures of Alpha‐ Oxygen. The Journal of Chemical Physics, 1967. 47(2): p. 592-597. Karki, B., G. Ackland, and J. Crain, Elastic instabilities in crystals from ab initio stress-strain relations. Journal of Physics: Condensed Matter, 1997. 9(41): p. 8579. Tariq, S., et al., Structural, electronic and elastic properties of the cubic CaTiO3 under pressure: A DFT study. AIP Advances, 2015. 5(7): p. 077111.

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Table 1. Structural and electronic properties of SrTcO3 PBE-GGA

mBJ-GGA

Lattice constant ao(Å)

3.99

3.98, 3.97[a], 3.96[b]

Bulk Modulus Bo (GPa)

190

189

Derivative of Bulk Modulus B/

4.78

4.65

Tolerance factor t

0.99

0.99

Band-gap up spin ↑Eg down spin ↓Eg

0.42

0.94

0.42

1.87

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Ref. [3] Ref. [4]

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Table 2: Elastic and thermal properties of SrTcO3 Results

C11(GPa)

305.573

C12(GPa)

123.857

C44(GPa)

28.949

Bulk modulus B (GPa)

184.4

Shear modulus G (GPa)

46.7

Young modulus Y (GPa)

129.3

Pough’s ratio (B/G)

3.94

Frantesvich ratio (G/B)

0.25

Internal strain ξ

0.54

Anisotropy A

0.32

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2.834

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[110]

3.174

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[100]

VL (Km/sec)

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Properties

2.712

[100]

0.977

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VT (Km/sec)

[111]

[110]

2.448

[111]

1.521 1.400

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Vm (Km/sec) TM (K)

2358.94

Enthalpy of Formation H f (eV)

-11.14

Debye Temperature (Θ) K

305.56

Thermal conductivityΛmin

[100]

0.522

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(Wk1m1) 0.786

[111]

0.585

Figure 1: Energy volume optimizations of STO

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[110]

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Figure 2: Total EDOS of anti-ferromagnetic STO using PBE-GGA

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Jhj

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Figure 3: Total DOS of ferromagnetic STO using mBJ-GGA

Figure 3: Total EDOS of ferromagnetic STO by using mBJ-GGA potential

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Figure 4: Electronic band structure of STO by using PBE-GGA functional

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Figure 5: Electronic band structure of STO by using mBJ-GGA potential

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Figure 6: Electron spin density contour plots along (110) directions in spin up state

Figure 7: Electron spin density contour plots along (110) directions in spin down state

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