Electronic and thermoelectric properties of RbYSn half-Heusler compound with 8 valence electrons: Spin-orbit coupling effect

Chemical Physics 528 (2020) 110510

Contents lists available at ScienceDirect

Chemical Physics journal homepage: www.elsevier.com/locate/chemphys

Electronic and thermoelectric properties of RbYSn half-Heusler compound with 8 valence electrons: Spin-orbit coupling effect

T

D.M. Hoata,b, , Mosayeb Naseric ⁎

a

Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam c Department of Physics, Kermanshah Branch, Islamic Azad University, P.O. Box 6718997551, Kermanshah, Iran b

ARTICLE INFO

ABSTRACT

Keywords: FP-LAPW Half-Heusler compounds with 8 valence electrons Electronic properties Thermoelectric properties Spin-orbit coupling effect

In this paper, we present the systematical investigation on the phase stability, electronic structure and thermoelectric properties of new half-Heusler compound RbYSn. The structural and dynamical stabilities of RbYSn are proven. Our calculations show that the studied compound is direct semiconductor with band gap of 0.892 eV. The spin-orbit coupling (SOC) has strong influence on the valence band of RbYSn compound with a split of 0.135 eV at the highest point. Our obtained results show that RbYSn has high thermopower resulting from the favorable features of its band structure. The SOC effect on the thermoelectric properties of RbYSn compound, including Seebeck coefficient, electrical conductivity, electronic thermal conductivity and power factor, also is analyzed and discussed in details. The power factor increases with increasing temperature and its maximum value at 800 K is found between 5.9 × 1011 (W/mK2 s) and 6.3 × 1011 (W/mK2 s).

1. Introduction Searching for new efficient renewable energy resources and optimizing the existing ones have become into one of the most extensively investigated fields in science and technology. Between them, there is found the production of electricity directly from the waste thermal energy during human activity [1]. Usually, the dimensionless figure of merit is used to measure the performance of materials used in thermoelectric generators [2,3]. This important thermoelectric parameter is calculated using the following fomula:

ZT =

S2 T

(1)

here S is Seebeck coefficient, is electrical conductivity and is thermal conductivity including the contributions from lattice vibrations and electron movements. High Seebeck coefficient, high electrical conductivity and low thermal conductivity, which lead to high values of ZT, are desirable factors to have efficient thermoelectric materials. However, these properties are coupled and optimizing them is a true challenge [4]. So far, some very efficient materials have been used, for example, Bi2 Te3 [5,6], Mg 2 Si [7–9], Sb2Te3 [10,11], PbTe [12,13], and so on. On the other hand, great effort of the scientific community has been focused on the Heusler intermetallic compounds due to their

⁎

intringuing properties. In general, they are divided in three subgroups: (1) Full-Heusler (FH) alloys with the stoichiometry 2:1:1 X2YZ; (2) HalfHeusler (HH) alloys with the stoichiometry 1:1:1 XYZ and (3) Equiatomic Quaternary Heusler (EQH) alloys with the stoichiometry 1:1:1:1 X1X2YZ, where X, Y, X1 and X2 are magnetic elements, which Z is an element belonging to the main groups [14–18]. So far, more than 1000 Heusler compounds have been investigated, and most of them have been found to be promising candidates for spintronic applications because of their extremely interesting electronic nature including spingapless semiconductor (SGS), half-metallic (HM), and the zero-gap HM as well as exceptional magnetic properties such as Giant Magnetoresistance, Tunnelling Magnetoresistance and Magnetocaloric effect [19–23]. Additionally, the good thermoelectric performance has been found for some HH compounds such as IVB group-based p-type MCoSb [24] and n-type MNiSn (M = Ti, Zr and Hf) [25]. Recently, the Boltzmann transport theory has been widely employed to calculate and predict the thermoelectric properties which can provide valuable informations [26]. For example, some theoretical works have been dedicated to the prediction of thermoelectric properties of half-Heusler compounds with 8 valence electrons. Direct band gap semiconductors of 0.19 and 0.41 eV were predicted by Yasemin O. Ciftci et al. [27] for KScC and KScGe, respectively, and high thermopower at room temperature as well as larger thermopower for p-doping resulting from the presence of one more valence band also were

Corresponding author at: Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail addresses: [email protected] (D.M. Hoat), [email protected] (M. Naseri).

https://doi.org/10.1016/j.chemphys.2019.110510 Received 30 May 2019; Received in revised form 18 August 2019; Accepted 24 August 2019 Available online 26 August 2019 0301-0104/ © 2019 Elsevier B.V. All rights reserved.

Chemical Physics 528 (2020) 110510

D.M. Hoat and M. Naseri

Fig. 1. Crystal structure and calculated energy in function of volume of RbYSn half-Heusler compound.

observed in these compounds. LiMgN was proven to be promising candidate for applications in thermoelectric devices at high temperatures by Anuradha et al. [28] due to its power factor as high as 2.31 × 1012 (Wm−1 s−1 K−2). Potential applicability in thermoelectric applications of KScX (X = Sn and Pb) and KYX (X = Si and Ge) also was demonstrated by D. Shrivastava et al. [29,30], the p-doping was found favorable for these materials due to high power factor. Vikram et al. [31] studied the I-III-IV half-Heusler compounds and found high ZT values of 0.83 for n-type conduction and 0.81 for p-type conduction in case of LiAlGe, which is comparable with other promising thermoelectric materials. In principles, the half-Heusler compound with 8 valence electrons family could be formed by a lot of members as varying the constituent atoms. Aforementioned works demonstrated that those with s-block elements occupying the X-site show good thermoelectric properties. However, despite their chemical similarity, the transport properties may vary as changing the chemical composition. In this work, we investigate the structural, dynamical, electronic and thermoelectric properties of new compound RbYSn belonging to type I-II-IV subgroup. Our calculations asserted that this material can be experimentally realized. Its structural and dynamical also are demonstrated. High calculated power factor suggests that RbYSn compound can be promising candidate for applications in thermoelectric generators. We hope that the results presented herein will motivate the experimental works devoted to the synthesis and characterization of thermoelectric properties of RbYSn and other HH compounds.

1 i (k + G ) r e V k G (r )

=

l, m

(Alm, k + G ul

interstitial (r , E0) +

Blm, k + G

inside

region muffin

tin

ul (r , E0 )) Yml (r ) (2) In this work, we set the expansion of spherical harmonics up to lmax = 10 and the plane waves are limited by RMT Kmax = 7 . Upper limit for the expansion of the potential and charge is set to Gmax = 12 (a.u−1). The energy cut-off −6 Ryd is used to separate the core and valence states. The convergence criterium of self-consistent iterations is set to be 0.0001 Ryd for energy and 0.001 e for charge. We use a k-mesh of 10 × 10 × 10 for the intergraion in Brillouin zone. In the materials containing heavy elements as constituent, the spinorbit coupling (SOC) effect should be important. Therefore, we also include the SOC in calculations by means of the second variational method [40] and the total Hamiltonian can be expressed as:

H=

2m

2

+ Veff + HSO

(3)

where the spin-orbit Hamiltonian HSO :

HSO =

1 1 dVMT 2Mc 2 r 2 dr

.l 0

0 0

(4)

here, is the Pauli spin matrix. The thermoelectric properties of RbYSn HH compound are obtained by solving the Boltzmann transport equations. For such goal, the rigid band [41] and constant relaxation time approximations as implemented BoltzTraP code [42] are used. It is worth to mention that very dense kmesh of 30 × 30 × 30 is employed for thermoelectric calculations.

2. Methodology and computational parameters We have carried out the first principles calculations within the framework of the density functional theory (DFT) [32] to study the structural and electronic properties of RbYSn HH compound. For the structural optimization, the exchange-correlation potentials are described within the generalized gradient approximation with revised Perdew-Burke-Ernzerhof scheme (GGA-PBESol) [33], while for the electronic calculations, the Tran-Blaha modified Becke-Johnson exchange potential [34–36] with improvement by Koller [37] (mBJ) is adopted to obtain more accurate electronic structure of the studied material. The self-consistent Kohn-Sham equations are solved using the full-potential linearized augmented plan-wave (FP-LAPW) method [38] as implemented in WIEN2k package [39]. In this method, the expansion of wave functions is written as follows:

3. Results and discussion 3.1. Phase stability and lattice dynamical properties RbYSn half-Heusler (HH) compound can crystallize in face-centered cubic (FCC) structure with F4 3 m space group (No. 216) in which the Wyckoff atomic position of Rb, Y and Sn is 4b(0.5; 0.5; 0.5), 4a(0; 0; 0) and 4c(0.25; 0.25; 0.25) [29], respectively. The crystal structure of considered compound is display in Fig. 1. The unit cell contains four formula units, and it can be seen as the zinc-blende sublattice formed by Y and Sn atoms (Y4Sn4) being filled by four Rb atoms in the side

2

Chemical Physics 528 (2020) 110510

D.M. Hoat and M. Naseri

middles. The geometry of RbYSn HH compound is optimized following the minimum energy approach, which corresponds to the ground state of the material. For such purpose, we calculate the total energy at 11 volumes and the obtained results are plotted as in Fig. 1. The volumedependence of total system energy is represented using the Birch-Munarghan equation of state [43]:

E (V ) = E0 +

9V0 B 16

V0 V

2 3

3

1 B +

V0 V

2 3

2

1

6

4

V0 V

Table 1 Total energy (meV) of RbYSn compound with different magnetization directions (that in [001]-direction is chosen to be reference). Magnetization direction

RbYSn

2 3

(5)

Et

[Eb (Rb) + Eb (Y ) + Eb (Sn)] 3

(6)

Et

[Ea (Rb) + Ea (Y ) + Ea (Sn)] 3

[100]

[110]

[101]

[011]

[111]

0

−4.562

2.572

−2.335

−1.072

−5.914

−3.842

3.2. Electronic properties

where Et is the total energy of primitive cell, Eb is the energy per atom of constituent atoms in bulk. Our calculated Hf of RbYSn HH compound is −2.311 (eV/atom). The negative value of Hf indicates that the synthesis of this material is energetically favorable and it can be experimentally fabricated without major difficulty. While the cohesive energy Ec is used to examine the structural stability of the material after its experimental formation and it is estimated using the following expression [46,47]:

Ec =

[010]

that there are no imaginary modes, this result indicates that RbYSn HH compound is dynamically stable. In the primitive cell, there are 3 atoms which generate 9 vibrational modes: 3 acoustic and 6 optical modes. At point, the frequencies of optical modes are 94.625 cm−1 (degenerated), 101.062 cm−1, 115.335 cm−1 (degenerated) and 128.542 cm−1. The maximum frequency of acoustic modes is 79.586 cm−1 (in L – X direction) and the minimum frequency of optical modes is 74.620 cm−1 (in X – K direction). This results indicates clearly that there is no phonon band gap in considered compound. This feature is favorable for thermoelectric performance of RbYSn HH compound with low thermal conductivity resulting from the phonon scattering [50].

where, V0 is the experimental volume, B and B are bulk modulus and its derivative, respectively. After minimizing the energy in Eq. (5) in function of volume, the calculated optimal lattice constant, bulk modulus, its derivative and total energy of primitive cell at equilibrium are 7.768 (Å), 28.911 GPa, 3.899 and −25079, 504556 (Ryd), respectively. Now we examine the phase stability of RbYSn HH compound estimating its formation energy and cohesive energy. The formation energy Hf is used to predict the possible experimental formation of material under investigation and it is calculated with the following formula [44,45]:

Hf =

[001]

The electronic properties of RbYSn compound are investigated using the mBJ potential without (mBJ) and with SOC (mBJ + SOC). The SOC is included in the calculations by setting the magnetization in [0 1 1] direction due to its lowest energy (see Table 1). The electronic band structure of RbYSn compound has been calculated in high symmetry directions of first Brillouin zone W – L – – X – W – K. The obtained band structures are displayed in Fig. 3. Our calculations show that RbYSn compound is a direct semiconductor as both valence band maximum and conduction band minimum are located at the high symmetry point X. These results agree well with previous theoretical ones for I-III-IV half-Heusler compounds [29]. Using mBJ potential, the calculated band gap is 0.892 eV, whereas including the SOC in calculations, the band gap is decreased 0.067 eV giving a value of 0.825 eV. From the detailed analysis of band structure, we observe that: in that calculated with mBJ potential, there is found the twofold degeneracy in L – – X direction for upper part of valence band and in L – direction for lowest part of conduction band, these degeneracies generate the flatness which is favorable for Seebeck coefficient. However, when the SOC is taken into account, the degeneracy is destroyed in valence band, while it is maintained in conduction band. Clearly, the valence band is more influenced by the SOC than the conduction band. To show the SOC effect on valence band of considered material, we also calculate the spin-orbit splitting around Fermi level (X point). The value of this important parameter is 0.135 eV, which demonstrates the significant effect of SOC on valence band. In Fig. 4, we show the calculated density of states of RbYSn compound including the total (TDOS) and partial (PDOS) ones. From the figure, we can see that the upper part of valence band from −1.8 eV to 0 eV is formed mainly from the strong hybridization between Y-d and Sn-p states. It is noted clearly that the SOC splits this hybridized state from −0.9 eV to 0 eV. The lowest partition from the calculated band gap up to 3 eV of conduction band is dominated mainly by Y-d state, wheareas the hybridization between Rb-d and Y-d states shows main contribution to the band structure at higher energies.

(7)

where Ea is the energy of isolated atom. Our computed Ec of RbYSn HH compound is −3.310 (eV/atom). Negative signature of Ec implies that the considered material is structurally stable, that is, the chemical bondings existing in the material can be stabilized after its formation without major difficulty. Additionally, the phonon band structure of RbYSn HH compound has been calculated using the density functional perturbation theory (DFPT) [48] implemented in CASTEP package [49]. In Fig. 2, the obtained phonon dispersion curve along direction – X – K – Γ – L – X – W in the Brilloun zone is displayed. From the figure, it can be seen clearly

3.3. Thermoelectric properties In the framework of the Boltzmannn transport theory and rigid band approximation, the tensors of thermoelectric properties including Seebeck coefficient, electrical conductivity and electronic thermal conductivity, respectively, are calculated as follow:

Fig. 2. Calculated phonon dispersion curve of RbYSn half-Heusler compound. 3

Chemical Physics 528 (2020) 110510

D.M. Hoat and M. Naseri

Fig. 3. Self-consistent band structure of RbYSn compound: (a) without and (b) with SOC.

Fig. 5. Seebeck coefficient of RbYSn compound without and with SOC as function of (a) doping concentration and (b) chemical potential at temperatures 300 K and 800 K.

Fig. 4. Total and partial density of states of RbYSn compound without (black lines) and with (red lines) SOC.

S

T, µ =

T, µ =

0

(T ;µ ) =

1 eT

( )

(T , µ )

1

( )

1 e 2T

( )(

f0 (T , , µ )

µ

f0 (T , , µ )

d f0 (T , , µ)

µ )2

d

here N, i and k represent the number of k-points, band index and wave vector, respectively. i, k is relaxation time and the group velocity (i, k ) is the group velocity. The dependence of Seebeck coefficient S on carrier concentration and chemical potential is depicted in Fig. 5. The negative feature of S indicates n-type conduction, and it is related to conduction band with electrons as main charge carrier. While the positive sign of S implies the p-type conduction with holes as majority carriers, and it is connected to the valence band. As seen in Fig. 5a, the S shows very similar charge concentration dependence in both electron and hole dopings. It has high values at low doping and decreases according to increasing the doping level. Whereas, the increase of temperature can be favorable factor to reach higher thermopower of RbYSn compound. It seems that the SOC do not influence importantly on this thermoelectric parameter. The maximum absolute Seebeck coefficient is 1400.3 (µ V/K) and 1454.9 (µ V/K) at 300 K for n- and p-doping, respectively. From Fig. 5b,

(8)

(9)

d

(10)

where and are tensor indices, is cell volume, f0 (T , , µ ) is the ( ) represents the transport tensor Fermi distribution function and which is calculated from the band structure as follows:

( )=

e2 N

i, k i, k

i, k

i, k

(

i, k )

(11) 4

Chemical Physics 528 (2020) 110510

D.M. Hoat and M. Naseri

Fig. 6. Electrical conductivity of RbYSn compound without and with SOC as function of (a) doping concentration and (b) chemical potential at temperatures 300 K and 800 K.

Fig. 7. Electronic thermal conductivity of RbYSn compound without and with SOC as function of (a) doping concentration and (b) chemical potential at temperatures 300 K and 800 K.

we can see that beyond chemical potential range [−0.3 eV to 1.05 eV], the S value is negligible. At fixed temperature, there two pronounced peaks, one in n-region and one in p-region. It seems that these peaks shift to lower chemical potential levels and their value decreases slightly when the SOC is considered. For example, at 300 K and, the maximum absolute value of thermopower is 1446.9 (µ V/K) and 1400.5 (µ V/K) for n-type in case of without and with SOC effect, respectively. While this parameter for p-type is 1454.9 (µ V/K) and 1335.4 (µ V/K), respectively. It is also seen clearly that the maximum absolute value of S decreases considerably with rising temperature from 300 K to 800 K. Specifically, at temperature 800 K, these maximums are 526.5(537.7) (µ V/K) and 521.7(509.5) (µ V/K) for n(p)-type in case of calculations without and with SOC, respectively. Fig. 6 shows the variation of the electrical conductivity ( ) in function of carrier concentration and chemical potential. We found that ( ) increases linearly with the increase of electron concentration up to −0.6 (e/uc) and hole concentration up to 0.7 (e/uc) (See Fig. 6a). And with higher doping levels, the increase becomes considerably lower. It is obvious that ( ) decreases with rising temperature, this result is due to the high charge carrier concentration and dispersion effect at high temperatures. It seems that the SOC is not significant for n-doping, but in case of p-doping, the inclusion of SOC decreases the electrical conductivity of RbYSn HH compound, in special, at high doping levels. Undoubtedly, this reduction corresponds to the significant effect of SOC on the valence band, specifically, the increase of effective mass of holes. From Fig. 6b, we can see that the mBJ potential predicts higher electrical conductivity for n-region. However, when the SOC is included, this property decreases considerably and its values are comparable with those in p-region. For calculations without SOC, the maximum electrical conductivity in n-region is 14.7 × 1019 ( ms) 1 and 13.1 × 1019 ( ms) 1 at temperature of 300 K and 800 K, respectively. For good thermoelectric performance, the materials must have low thermal conductivity. The thermal conductivity has two contribution: (1) the phonons contribution ph and (2) electronic contribution el . In this work, we calculate the electronic part of thermal conductivity of RbYSn HH compound. The plots of calculated electronic thermal

conductivity el/ in function of carrier concentration and chemical potential are displayed in Fig. 7. It can be seen that el/ shows very similar behavior to electrical conductivity / obeying the proportional relationship as established by the Wiedemann-Franz law: = LT [51], here L and T are Lorenz number and temperature, respectively. We also can observe in Fig. 7a that el/ increases rapidly with increasing both the doping concentration and the temperature. The SOC inclusion decreases this parameter in case of holes doping, whereas there is not significant change for electrons doping. In function of chemical potential (Fig. 7b), we can see clearly that at given temperature, the SOC decreases the el/ in n-region, while the opposite trend is seen in pregion. In the considered range of chemical potential, there are found two maximum in n-region when the SOC is not included, which are 10.0 × 1014 (W/mK s) and 19.1 × 1014 (W/mK s) at temperature of 300 K and 800 K, respectively. Now, we discuss the power factor PF of RbYSn HH compound. PF is a key thermoelectric parameter and it is defined as: PF = S 2 . In general, this parameter is used to determine the optimal contribution from Seebeck coefficient and electrical conductivity (as seen above, these two properties always shows opposite behavior). Fig. 8 shows the calculated PF in function of carrier concentration and chemical potential. It is seen that PF of the studied material increases fastly with rising temperature from 300 K to 800 K. From Fig. 8a, we can see that PF is negligible when the doping level is very small and higher than −0.8(1.2) (e/uc) for n(p)-doping. Whereas, as seen in Fig. 8b, the thermoelectric performance of the considered HH compound will be very poor in chemical potentials beyond the ranges [−0.3 eV to 1.5 eV] in n-region and [0.75 eV–1.05 eV] in p-region, in which the PF takes very small values. At given temperature, there are two peaks, one for ntype and the other for p-type. In Table 2, the value of these peaks are listed. It is seen that without the SOC effect, the maximum value of PF is 7.3 × 1011 (W / mK 2 s ) for p-doping with hole concentration of 0.186 (e/ uc) or chemical potential of −0.02 eV. However, when the SOC is taken into account, the maximum is found to be 6.3 × 1011 (W / mK 2 s ) in ndoping with electron concentration is 0.15 (e/uc) and chemical potential of 0.84 eV. 5

Chemical Physics 528 (2020) 110510

D.M. Hoat and M. Naseri

[2] R. Guo, X. Wang, Y. Kuang, B. Huang, First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS, Phys. Rev. B 92 (11) (2015) 115202 . [3] D. Hoat, Electronic structure and thermoelectric properties of Ta-based half-Heusler compounds with 18 valence electrons, Comput. Mater. Sci. 159 (2019) 470–477. [4] A. Shafique, Y.-H. Shin, Thermoelectric and phonon transport properties of twodimensional IV–VI compounds, Scientific Rep. 7 (1) (2017) 506. [5] J.S. Son, M.K. Choi, M.-K. Han, K. Park, J.-Y. Kim, S.J. Lim, M. Oh, Y. Kuk, C. Park, S.-J. Kim, et al., n-type nanostructured thermoelectric materials prepared from chemically synthesized ultrathin Bi2Te3 nanoplates, Nano Lett. 12 (2) (2012) 640–647. [6] H. Ni, X. Zhao, T. Zhu, X. Ji, J. Tu, Synthesis and thermoelectric properties of Bi2Te3 based nanocomposites, J. Alloys Compd. 397 (1–2) (2005) 317–321. [7] M. Ioannou, G. Polymeris, E. Hatzikraniotis, A. Khan, K. Paraskevopoulos, T. Kyratsi, Solid-state synthesis and thermoelectric properties of Sb-doped Mg2Si materials, J. Electron. Mater. 42 (7) (2013) 1827–1834. [8] S. Fiameni, S. Battiston, S. Boldrini, A. Famengo, F. Agresti, S. Barison, M. Fabrizio, Synthesis and characterization of Bi-doped Mg2Si thermoelectric materials, J. Solid State Chem. 193 (2012) 142–146. [9] S. Battiston, S. Fiameni, M. Saleemi, S. Boldrini, A. Famengo, F. Agresti, M. Stingaciu, M.S. Toprak, M. Fabrizio, S. Barison, Synthesis and characterization of Al-doped Mg2Si thermoelectric materials, J. Electron. Mater. 42 (7) (2013) 1956–1959. [10] G.-H. Dong, Y.-J. Zhu, L.-D. Chen, Microwave-assisted rapid synthesis of Sb2Te3 nanosheets and thermoelectric properties of bulk samples prepared by spark plasma sintering, J. Mater. Chem. 20 (10) (2010) 1976–1981. [11] G.-H. Dong, Y.-J. Zhu, G.-F. Cheng, Y.-J. Ruan, Sb2Te3 nanobelts and nanosheets: hydrothermal synthesis, morphology evolution and thermoelectric properties, J. Alloys Compd. 550 (2013) 164–168. [12] B. Wan, C. Hu, B. Feng, Y. Xi, X. He, Synthesis and thermoelectric properties of PbTe nanorods and microcubes, Mater. Sci. Eng.: B 163 (1) (2009) 57–61. [13] G. Tai, W. Guo, Z. Zhang, Hydrothermal synthesis and thermoelectric transport properties of uniform single-crystalline pearl-necklace-shaped PbTe nanowires, Cryst. Growth Des. 8 (8) (2008) 2906–2911. [14] F. Dahmane, S. Benalia, L. Djoudi, A. Tadjer, R. Khenata, B. Doumi, H. Aourag, First-principles study of structural, electronic, magnetic and half-metallic properties of the heusler alloys Ti2ZAl (Z= Co, Fe, Mn), J. Supercond. Novel Magn. 28 (10) (2015) 3099–3104. [15] M.A. Carpenter, C.J. Howard, Fundamental aspects of symmetry and order parameter coupling for martensitic transition sequences in Heusler alloys, Acta Crystallogr. Sect. B 74 (6) (2018) 560–573. [16] F. Dahmane, B. Doumi, Y. Mogulkoc, A. Tadjer, D. Prakash, K. Verma, D. Varshney, M. Ghebouli, S.B. Omran, R. Khenata, Investigations of the structural, electronic, magnetic, and half-metallic behavior of Co2MnZ (Z= Al, Ge, Si, Ga) Full-Heusler compounds, J. Supercond. Novel Magn. 29 (3) (2016) 809–817. [17] H. Rozale, A. Amar, A. Lakdja, A. Moukadem, A. Chahed, Half-metallicity in the half-heusler RbSrC, RbSrSi and RbSrGe compounds, J. Magn. Magn. Mater. 336 (2013) 83–87. [18] D. Hoat, Investigation on new equiatomic quaternary Heusler compound CoCrIrSi via FP-LAPW calculations, Chem. Phys. 523 (2019) 130–137. [19] D. Hoat, J. Rivas-Silva, A.M. Blas, Investigation on the structural, elastic, electronic, and magnetic properties of half-metallic Co2MnSi and CoMnIrSi via first-principles calculations, J. Comput. Electron. 17 (4) (2018) 1470–1477. [20] F. Casper, T. Graf, S. Chadov, B. Balke, C. Felser, Half-Heusler compounds: novel materials for energy and spintronic applications, Semicond. Sci. Technol. 27 (6) (2012) 063001 . [21] Y. Sakuraba, K. Takanashi, Giant magnetoresistive devices with Half-Metallic Heusler compounds, Heusler Alloys, Springer, 2016, pp. 389–400. [22] J. Jeong, Y. Ferrante, S.V. Faleev, M.G. Samant, C. Felser, S.S. Parkin, Termination layer compensated tunnelling magnetoresistance in ferrimagnetic Heusler compounds with high perpendicular magnetic anisotropy, Nat. Commun. 7 (2016) 10276. [23] A. Planes, L. Mañosa, X. Moya, T. Krenke, M. Acet, E. Wassermann, Magnetocaloric effect in Heusler shape-memory alloys, J. Magn. Magn. Mater. 310 (2) (2007) 2767–2769. [24] T. Sekimoto, K. Kurosaki, H. Muta, S. Yamanaka, Thermoelectric and thermophysical properties of TiCoSb-ZrCoSb-HfCoSb pseudo ternary system prepared by spark plasma sintering, Mater. Trans. 47 (6) (2006) 1445–1448. [25] S. Populoh, M. Aguirre, O. Brunko, K. Galazka, Y. Lu, A. Weidenkaff, High figure of merit in (Ti, Zr, Hf)NiSn half-Heusler alloys, Scr. Mater. 66 (12) (2012) 1073–1076. [26] N. Hamada, T. Imai, H. Funashima, Thermoelectric power calculation by the Boltzmann equation: NaxCoO2, J. Phys.: Condens. Matter 19 (36) (2007) 365221 . [27] Y.O. Ciftci, S.D. Mahanti, Electronic structure and thermoelectric properties of halfheusler compounds with eight electron valence count-KScX (X= C and Ge), J. Appl. Phys. 119 (14) (2016) 145703 . [28] K. Kaur, R. Singh, R. Kumar, et al., Search for thermoelectricity in Li-based halfHeusler alloys: a DFT study, Mater. Res. Express 5 (1) (2018) 014009 . [29] D. Shrivastava, S.P. Sanyal, Theoretical study of structural, electronic, phonon and thermoelectric properties of KScX (X= Sn and Pb) and KYX (X= Si and Ge) halfHeusler compounds with 8 valence electrons count, J. Alloys Compd. 784 (2019) 319–329. [30] D. Shrivastava, N. Acharya, S.P. Sanyal, Investigation of thermoelectricity in KScSn half-Heusler compound, AIP Conference Proceedings, vol. 1953, AIP Publishing, 2018, p. 110036. [31] Vikram, B. Sahni, C.K. Barman, A. Alam, Accelerated discovery of new 8-electron half-Heusler compounds as promising energy and topological quantum materials, J.

Fig. 8. Power factor of RbYSn compound without and with SOC as function of (a) doping concentration and (b) chemical potential at temperatures 300 K and 800 K. Table 2 Maximum value of the power factor (1011 W/mK2s) of RbYSn HH compound. Maximum value of PF

300 K 300 K + SOC 800 K 800 K + SOC

n-type

p-type

3.3 3.2 6.3 6.3

3.5 2.3 7.3 5.9

4. Conclusions We have performed the first principles calculations within FP-LAPW method and Boltzmann transport theory to study the structural, dynamical, electronic and thermoelectric properties of RbYSn HH compound. Its feasibility of being experimentally fabricated is demonstrated with the negative formation energy. While its structural and dynamical stabilities are proven by means of the negative cohesive energy and the absence of imaginary phonon modes, respectively. RbYSn is a direct semiconductor with band gap of 0.892 eV predicted by mBJ potential. A band gap reduction of 0.067 eV was obtained when the SOC is included. The SOC also shows strong effect on the valence band of considered compound. The suitable band gap and flatness of the valence band generate the high values of thermopower of RbYSn. The power factor of the material under study increases considerably with rising temperature. mBJ potential predicts highest power factor of 7.3 × 1011 (W/mK2 s) for p-doping with hole concentration of 0.186 (e/ uc) or chemical potential of −0.02 eV. While the maximum power factor is predicted for n-doping by mBJ + SOC, with value of 6.3 × 1011 (W/mK2 s) at electron concentration is 0.15 (e/uc) or chemical potential of 0.84 eV. References [1] S. Twaha, J. Zhu, Y. Yan, B. Li, A comprehensive review of thermoelectric technology: materials, applications, modelling and performance improvement, Renew. Sustain. Energy Rev. 65 (2016) 698–726.

6

Chemical Physics 528 (2020) 110510

D.M. Hoat and M. Naseri Phys. Chem. C 123 (12) (2019) 7074–7080. [32] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (4A) (1965) A1133. [33] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100 (13) (2008) 136406 . [34] A.D. Becke, E.R. Johnson, A simple effective potential for exchange, J. Chem. Phys. 124 (22) (2006) 221101. [35] F. Tran, P. Blaha, K. Schwarz, Band gap calculations with Becke-Johnson exchange potential, J. Phys.: Condens. Matter 19 (19) (2007) 196208 . [36] F. Tran, P. Blaha, Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential, Phys. Rev. Lett. 102 (22) (2009) 226401 . [37] D. Koller, F. Tran, P. Blaha, Improving the modified Becke-Johnson exchange potential, Phys. Rev. B 85 (15) (2012) 155109 . [38] S. Cottenier, Density Functional Theory and the family of (L)APW-methods: a stepby-step introduction. [39] K. Schwarz, P. Blaha, Solid state calculations using WIEN2k, Comput. Mater. Sci. 28 (2) (2003) 259–273. [40] D. Koelling, B. Harmon, A technique for relativistic spin-polarised calculations, J. Phys. C: Solid State Phys. 10 (16) (1977) 3107. [41] L. Chaput, P. Pécheur, J. Tobola, H. Scherrer, Transport in doped skutterudites: Ab initio electronic structure calculations, Phys. Rev. B 72 (8) (2005) 085126 . [42] G.K. Madsen, D.J. Singh, BoltzTraP. A code for calculating band-structure dependent quantities, Comput. Phys. Commun. 175 (1) (2006) 67–71.

[43] F. Birch, Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K, J. Geophys. Res.: Solid Earth 83 (B3) (1978) 1257–1268. [44] D. Hoat, Structural, optoelectronic and thermoelectric properties of antiperovskite compounds Ae3PbS (Ae = Ca, Sr and Ba): a first principles study, Phys. Lett. A 383 (14) (2019) 1648–1654. [45] Investigation on new equiatomic quaternary heusler compound CoCrIrSi via FPLAPW calculations, Chem. Phys. 523 (2019) 130–137. [46] A. Masihi, M. Naseri, N. Fatahi, A first-principles study of the electronic and optical properties of monolayer -PbO, Chem. Phys. Lett. 721 (2019) 27–32. [47] Z. Azarmi, M. Naseri, S. Parsamehr, A new stable BeP2C monolayer with visible light sensitivity: a first principles study, Chem. Phys. Lett. 728 (2019) 14–18. [48] S. Baroni, S. De Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73 (2) (2001) 515. [49] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I. Probert, K. Refson, M.C. Payne, First principles methods using CASTEP, Z. Cristallogr. Mater. 220 (5/6) (2005) 567–570. [50] M. Holland, Analysis of lattice thermal conductivity, Phys. Rev. 132 (6) (1963) 2461. [51] J. Zhang, H. Liu, L. Cheng, J. Wei, J. Liang, D. Fan, J. Shi, X. Tang, Q. Zhang, Phosphorene nanoribbon as a promising candidate for thermoelectric applications, Scientific Rep. 4 (2014) 6452.

7