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First principles study of structural, electronic and thermoelectric properties of skutterudite GdFe4As12 compounds
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First Principles Study of Structural, Electronic and Thermoelectric Properties of Skutterudite GdFe4 As12 compounds M. Boucharef , L. Djoudi , M. Merabet , S. Benalia , R. Belghit , N. Bettahar , D. Rached PII: DOI: Reference:
S0577-9073(19)30993-1 https://doi.org/10.1016/j.cjph.2019.11.021 CJPH 1015
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Chinese Journal of Physics
Received date: Revised date: Accepted date:
16 May 2019 11 October 2019 14 November 2019
Please cite this article as: M. Boucharef , L. Djoudi , M. Merabet , S. Benalia , R. Belghit , N. Bettahar , D. Rached , First Principles Study of Structural, Electronic and Thermoelectric Properties of Skutterudite GdFe4 As12 compounds, Chinese Journal of Physics (2019), doi: https://doi.org/10.1016/j.cjph.2019.11.021
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Highlights Investigate the structural and electronic and magnetic properties of GdFe4As12 material. The semi-metallic nature of this compound. GdFe4As12 compound is of great interest for thermoelectric devices.
First Principles Study of Structural, Electronic and Thermoelectric Properties of Skutterudite GdFe4As12 compounds
M. Boucharef
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, L. Djoudi , M. Merabet , S. Benalia , R. Belghit , N. Bettahar , D. Rached
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Laboratory of Magnetic Materials, Faculty of Sciences, University of Djillali Liabes, Sidi- Bel- Abbes, 22000, Algeria. 2
Department of Technology, Faculty of Technology, University of Yahia Fares, Medea, 26000, Algeria Centre Universitaire de Tissemsilt, Institut des Sciences et de la Technologie, Tissemsilt, Algérie 4 Laboratory Studies of Surface and Interfaces of Solid Materials (LESIMS), Department of Physics, Faculty of Sciences, University Badji Mokhtar, P.O. Box 12, Annaba 23000, Algeria 3
Abstract The full potential linearized augmented plane wave (FP-LAPW) method has been used to investigate structural, electronic and thermoelectric properties of Skutterudite GdFe4As12 compounds in the framework of the density functional theory (DFT) within the generalized gradient approximation (GGA) and (GGA+U). The ground-state properties are determined in the cubic structure (Im-3, space group 204). It is found that the most stable phase structure of GdFe4As12 compounds is the ferromagnetic phase and it shows a semi-metallic behavior with narrow gap. The calculation of the density of states near the Fermi level shows the compound to be suitable for the effective thermoelectric application. In addition, the high Seebeck coefficient value is obtained in the n-type region than p-type, indicating the prominence of n-type doping in filled skutterudite GdFe4As12.
Keywords: DFT; FP-LAPW; Skutterudites compound; Ferromagnetic; Semi-metallic; Thermoelectric.
1. Introduction The chemical formula of filled skutterudite is (RM4X12, R = rare earth; M = Fe, Ru, Os; X = P, As, Sb), It has attracted much attention recently because of its interesting physical properties in low temperatures. Several of the interesting properties of these compounds are associated with the R ion that dominates the atomic ‘cage’ in the binary (unfilled) type skutterudite structure. Among these properties are: Magnetic [1], superconducting [2-4], semiconducting [5], intermediate valence [6, 7], metal-insulator transition [8, 9], heavy fermions [10], and non-Fermi liquid behavior [11] have been noted in these materials. Further, skutterudite compounds exhibit remarkable thermoelectric properties [12, 13], The good thermoelectric properties appear to arise from the cage structure; the R atoms ‘rattle’ in their cage, which reduces the lattice thermal conductivity [14]. Many of these facts depend on strong hybridization between the localized f-electron states of R rare earth ions with the conduction electron states. GdFe4As12 compound is among the ternary filled skutterudite, he is synthesizing for the first time in 2011by Sekine et al [15] using the high-pressure synthesis technique. They are found that is characterized by its magnetic behavior. In 2013, Keiko Takeda and co-workers have investigated the effect of pressure on cell volume [16], in the present work we have done the complete analysis of magnetic and electronic structure, and we have reported the semimetallic nature of this compound using the FP-LAPW method. And we have ameliorated the thermoelectric calculations in order to provide reference data for the experimentalist on this compound. The structure of the recent work is as follows: In Section 2, the description of the FP-LAPW computational method is presented, in section 3; we display the results and discussion for structural, electronic, magnetic, and thermoelectric properties. Finally, in Section 4 we sum up the conclusions of our work.
2. Calculation Methodology
In the field of condensed matter theory and computational materials, density functional theory (DFT) is a powerful tool widely for the calculation of electronic and structural properties of solids [17], it is a universal quantum mechanical approach for many body problems. In this approach, the quantum many-body problems of an interacting electron gas are mapped exactly onto a set of single particles moving in an effective local potential with the same density as is real, and the obtained one electron equations are called Kohn–Sham equations [2, 18]. In this work, we have used the full potential linearized augmented plane wave (FP-LAPW) method [19] implemented in the WIEN2k code [20], to investigate the structural properties of the considered compounds, the exchange and correlation (XC) potential were treated by PBEsol [21] version of the generalized gradient approximation (GGA) for both ferromagnetic (FM), and paramagnetic (PM) states. To calculate the electronic, magnetic and thermoelectric properties, the local spin density approximation + Coulomb repulsion (U) is used to modulate the (GGA) approximation, the adopted on-site Coulomb repulsion term (U) for the present calculations is 0.441 Ry [22] and 0.286 Ry [23] for Gd-f and Fe-d respectively, In order to ensure convergence of the computed structures and energetic we use the value of plane wave cut-off Rmt×Kmax=14, The RMT (muffin-tin radii) were selected to be 2.50, 2.18 and 2.08 (a.u.) for Gd, Fe and As, respectively. The maximum radial expansion lmax = 10 and 2000 k-points (12×12×12 mesh size) are the values used for performing present self-consist calculations, but the second part of these studies, are improved in order to elucidate thermoelectric properties for the present compound. The code used for these computations is BoltzTraP code [24] which is based on constant scattering time approximation (CSTA) and rigid band approximation (RBA) [25, 26]. To achieve more appropriate results for thermoelectric properties, we used here a very high k-mesh (40,000) case in the Irreducible Brillouin zone (IBZ).
3. Results and discussions 3.1. Structural properties The GdFe4As12 compound crystallizes in the cubic space group (N°204, Im-3) [17, 26]. Gd, Fe and As atoms occupying the position listed in Table 1. The geometry structure of GdFe4As12 is shown in Fig. 1. We notice that the skutterudite structure has two non-equivalent characteristics atomic positions y and z, which are not fixed by symmetry, For our compound, the value of parameter y and z are 0.3442 [16], 0.1535 [16] respectively.
In order to determine the equilibrium structural properties of our compound, a set of different volumes around the experimental value are chosen and for each volume, the total energies are calculated for both paramagnetic (PM), and ferromagnetic (FM) states with GGA approximation. In principle, the internal coordinates y and z should be also relaxed and the best value that minimizes the total energy. The obtained total energies versus volume data are fitted by the non-linear Murnaghan equation of state [27] to determine the ground state properties such as the equilibrium lattice parameters (a), the bulk modulus and its pressure derivative (B and B’, and internal parameters ). The result is presented in Fig. 2. The quantities a, B and B’, for both states are summarized together in Table 2 with the available experimental data. As can be seen that the most stable state for our compound is the ferromagnetic state, the obtained lattice constants are in reasonable agreement with the experimental data; which is 1.0% smaller to the corresponding experimental value, this is due to the use of GGA approximation to calculate the exchange and correlation potential, which is known to underestimate this quantity in comparison to experiment values. However, to the best of our knowledge, there are no experimental or theoretical results for B and its pressure derivative available to be compared with our theoretical result.
3.2. Electronic and magnetic properties As exposed in Fig. 2. and table 2. The equilibrium lattice constant calculates with GGA approximation in the ferromagnetic state is the most less equilibrium energy for our compound. For this reason, and to understand the electronic and magnetic properties of filled skutterudite GdFe4As12, we calculate these properties with spin-polarized at its equilibrium lattice constant for this state using GGA and GGA+U approximations. The energy band structures calculated in spin-up and spin-down configurations along the high symmetry directions of the Brillouin zone are presented in Fig. 3 using GGA and GGA+U approximations. The calculated energy bands show similar profile to the previously calculated plots for EuRu4P12 [28] EuFe4Sb12 [29]. We can observe that the energy bands are greatly populated just near the Fermi level of minority and majority spin, which gives great mobility of charge carriers, which increased the electrical conductivity as compared to other compounds. This observation allowed us to study the thermoelectric properties.
In order to check the precision of our band structures results, we present the calculated density of states, the total density of states (DOS) and partial DOS are shown in Fig. 4 using GGA and GGA+U approximations. The densities of states found by the calculation are comparatively similar to
previously reported plots [30, 31]. For both figures, we can see that there are three distinct regions separated from each other by small energy gaps. The core region (below -12.0 eV) is primarily dominated by s state electrons of the arsenic atom for both spin channels. The valence region is essentially contributed by the d state of Fe atoms. The conduction region is mainly contributed by the d state of Gd atoms. Around Fermi level EF, The most important feature of the DOS plot is the presence a narrow gap due a very low density of states but it is different to zero for both spin channels, it has the same character to previously calculated plots for [28, 29, 32] filled Skutterudites, the narrow gap promotes the superconducting behavior with highly effective masses, this gives a substantial rise to the great value of thermoelectric Seebeck coefficients [33], and it indicates that this compound has a semi-metallic behavior and it is relatively similar to the previous reports of analogous compounds EuRu4P12 [28] and EuFe4P12 [32]. The calculated partial magnetic moment within the muffin-tin spheres of the respective Gd, Fe and As atoms, and the total magnetic moments with GGA and GGA+U approximations are given in Table 3 to gather with an available value of experimental total spin magnetic moments. In comparison with the experimental data, we find that our values are underestimated, the main contribution to the total magnetic moment is due to Gadolinium with small contribution from Fe-3d state, and this agree with the results of the refs [34-36]. Also, we calculate the spin polarization factor at Fermi level with GGA+U approximation. The simplest definition of spin polarization [37] is:
P = (N↑- N↓) / (N↑+ N↓)
Where N is the density of states of minority (N↓), and majority (N↑) spin at the Fermi level. As shown in Fig. 5, the calculate value of polarization at the Fermi level is 0.96, this value is due to the presence of high relatively concentrated density of states at EF (in minority spin N↓) and negligible contribution (in majority spin N↑), The value of spin polarization which we obtain is close to that obtained for iso structural KFe4Sb12 and NaFe4Sb12 [38]. The density of states on the Fermi level is relatively high in these types of compounds possessing superconducting behavior, which forms a larger electronic specific heat [39, 40]. This explains the importance of this compound in thermoelectric applications.
1.1. Thermoelectric properties During the last two decades, an intensive effort has been made by the researchers around the globe to find high-performance thermoelectric materials. Thermoelectricity refers to the direct energy conversion between heat and electricity, and its technology can be applied to the thermocouples, power generator, and refrigerator [41]. The efficiency of a thermoelectric device is evaluated by thermoelectric figure of merit
ZT S 2T , where is the electric conductivity, is the electrical part of the thermal conductivity and S is the Seebeck coefficient, which represents the ability of a system of charged particles to generate an electromotive force when a temperature gradient is applied across the system [30]. We determine these parameters using BoltzTrap code [24] which is based on the Boltzmann theory [42-44]. The BoltzTraP code is a calculating tool based on the smooth Fourier interpolations of the band energies. The code uses the interpolated band structure by WIEN2k to compute the derivatives necessary to evaluate the transport properties. The transport coefficients necessary to find ZT can be obtained directly. Using scalar coefficients [24, 29, 45]:
1 f (T , ) i ,k 0 d
1 2 K B2T i ,k e K BT S
2
f 0 (T , ) d
f 0 (T , ) eK B i , k d K BT
Where:
is the volume of a unit cell. f 0 is a Fermi-Dirac distribution function.
e is the electron charge.
is the chemical potential.
is the energy. T is the temperature absolute. K B is the Boltzmann constant [46]. The transport distribution i ,k is written as [47].
i ,k e2 i ,k k Where:
v and v are the group velocities.
k is the relaxation time.
We note that the chemical potential defines the doping level or carrier concentration in a material [48], It has negative values when Fermi level shifts down towards the valence band indicating the ability of p-type doping, and are positive values when the Fermi level shifts upward to the conduction band indicating the ability of n-type doping.
1.1.1. Seebeck Coefficient Mathematically, Seebeck Coefficient is S V T [49], for p-doped has positive values and has negative values for n-doped systems, we have calculated this parameter for chemical potentials ranging from -1.36 at 1.36 in spin-up and (spin-dn) configurations at T=300K, 600K and 900K, and it’s plotted in Fig. 6. The absolute value (magnitude) of the Seebeck coefficient S increases with the decreasing absolute value (magnitude) of the chemical potential for both spin up and spin down, that means these materials will exhibit good thermoelectric properties for lower doping (lower chemical potential). And he increases with an increasing temperature, this is due to an increasing charge-carrier concentration [50] for both configurations spin up and spin dn.
At room temperature, the higher value of the Seebeck coefficient is found for a positive range of chemical potential with spin-dn configurations. That’s means to get a high value of Seebeck coefficient; our compound supported the n-type doping This value equal to 99.30(µV/K) is close to the experimental value for iso structural compounds 81.5(µV/K) for PrFe4Sb12, 83.7 (µV/K) for NdFe4Sb12 and 79.4 (µV/K) for CeFe4Sb12 [51]. The high value of S in our calculation can be related to the calculated flat band structures due to Fe-3d states near the EF with highly effective mass [29, 52].
1.1.2. Electrical Conductivity Electrical conductivity measures the ability of a material of the flow of electric current either due to negative electrons or positive holes, on gaining kinetic energy and move in the material thus producing an electric current. For a good thermoelectric device, materials should have high electrical conductivity to reduce Joule heating effect [49]. The electrical conductivity against chemical potential at 300 K, 600 K and 900 K temperature for spinup and spin-down configurations are plotted in Fig. 7. It is clear from the figure that for different temperatures, the magnitude of the electrical conductivity increases with the increase of absolute values of the chemical potential; and the high value of electrical conductivity is observed in the positive range of chemical potential with spin-dn configuration, that means our compound supported the n-type doping similar to Seebeck coefficient observation.
1.1.3. Thermal conductivity The thermal conductivity , of the compound, indicates its ability to conduct heat for both; electronic and lattice vibrations. The thermal conductivity is usually dominated by the lattice vibrations in semiconductors, while in metals free electrons are a good source of thermal conductivity [53]. The thermal conductivity should be small with that temperature gradient for a good thermoelectric device. Present electronic part of thermal conductivity as a function of chemical potential for 300 K, 600 K and 900 K temperature at spin-up and spin-down configurations are exposed in Fig. 8. Similar to electrical conductivity, the magnitude of The Thermal conductivity also increases with increasing temperature, this is because as the temperature increases, more electrons get excited, and he also increases when one moves away from µ=0 for both configurations. We see that thermal conductivity has lower values in p-type (negative value of chemical potential) for spin-dn configuration at a different temperature, which helps to improve a good value of the figure of merit and then improve a good thermoelectric property.
At room temperature with the chemical potential of -1.5 eV, the value of the electronic thermal conductivity in units (1014 W/m Ks) is 11.41 for spin-up and 12.70 for spin-dn compared with same chemical structure for CaCo4Sb12, SrCo4Sb12, BaCo4Sb12 the value is 8.6, 7.99, 6.74 respectively [54]; The difference in value is due to the difference of the approximation used; Khan [54] uses the PBEsol08 GGA approximation [21] without adding the Hubbard factor, which we added to our calculation.
1.1.4. Figure of merit The performance of a thermoelectric material can be predicted by its figure of merit (ZT), which is directly proportional to the high Seebeck coefficient and electrical conductivity, while inversely proportional to the thermal conductivity. Fig. 9 show the graph of ZT against the chemical potential at T= 300 K, 600 K and 900 K in spin-up and spin-down configurations. It is clear from the figure that at room temperature ZT sharply rises as chemical potential increases from zero, and the peak value is observed at 0.17 µ(eV) chemical potentials in n-type region for spin down configuration; This is because the Seebeck coefficient gives maximum values and thermal conductivity stays a minimum value in this chemical potential; but when the temperature increases the peak get a maximum for 0.19 µ(eV) chemical potentials in n-type region for spin up configuration at T=900K. On the other hand, one can notice that when the chemical potential is 0 the value of the ZT in 300 K is bigger than the other values of 600 K and 900 k, for both spin state. At room temperature the maximum value of ZT calculated with GGA+U is 0.28 which is higher than the previous experimental values of some of the analogous compounds CeFe4Sb12 (ZT=0.1) [55], RFe4Sb12 (R=Ca, La, Sr, Ce, Ba, Pr, Yb, Eu, and Nd) ZT is (0.1 0.2) [51]; This finding allows us to claim that the filled skutterudite GdFe4As12 are potential candidates for thermoelectric applications if one can further reduce their thermal conductivities via some techniques, such as alloying, nano-structuring, or super-lattice growth.
2. Conclusion In summary, the structural, electronic and magnetic properties are performed within the density functional theory using the full potential linearized augmented plane waves (FPLAPW) method, employing GGA and GGA+U as embodied in the WIEN2k code, while the thermoelectric properties calculations are carried out applying the semiclassical Boltzmann transport theory and it’s obtained from the calculated band structures by performing additional post-processing applying the BoltzTraP package. Our main results are as follows:
The most stable state for our compound is the ferromagnetic state. The analysis density of state diagrams, and after determining the magnetic moment and calculate the polarization factor reveals that our compound is a semi-metal behavior. The calculations of the thermoelectric properties reveal that the investigated compounds have good properties for lower doping, and it is supported the n-type doping and might also be enhanced by some techniques, such as nano-structuring, superlattice growth or alloying which attributes further reduction of lattice thermal conductivity. Several approaches can be used for this purpose which includes partial substitution of Fe by Co, Ni etc. which have more valence electrons than Fe. This could reduce the high holes concentration in the material and raise the Seebeck coefficient to enhance ZT.
The effectiveness of inclusion the Coulomb repulsion (U) in calculating the electronic, magnetic and thermoelectric properties are verified.
References 1.
2. 3. 4.
5.
6.
Danebrock, M.E., C.B.H. Evers, and W. Jeitschko, Magnetic properties of alkaline earth and lanthanoid iron antimonides AFe4Sb12 (A = Ca, Sr, Ba, La-Nd, Sm, Eu) with the LaFe4P12 structure. Journal of Physics and Chemistry of Solids, 1996. 57(4): p. 381-387. Meisner, G.P., Superconductivity and magnetic order in ternary rare earth transition metal phosphides. Physica B+C, 1981. 108(1): p. 763-764. Shirotani, I., et al., Superconductivity of filled skutterudites LaRu4As12 and PrRu4As12. Physical Review B, 1997. 56(13): p. 7866-7869. Takeda, N. and M. Ishikawa, Superconducting and Magnetic Properties of Filled Skutterudite Compounds RERu4Sb 12 (RE=La, Ce, Pr, Nd and Eu). Journal of the Physical Society of Japan, 2000. 69(3): p. 868-873. Shirotani, I., et al., Electrical and Magnetic Properties of La1−xCexRu4P12and CeOs4P12with the Skutterudite Structure. Journal of Solid State Chemistry, 1999. 142(1): p. 146-151. Dilley, N.R., et al., Intermediate valence in the filled skutterudite compound YbFe4Sb12. Physical Review B, 1998. 58(10): p. 6287-6290.
7.
8. 9.
10. 11.
12. 13.
14. 15.
16.
17. 18. 19. 20. 21. 22.
23. 24. 25. 26. 27.
Shirotani, I., et al., X-ray study with synchrotron radiation for filled skutterudite YbFe4P12 at ambient and high pressures. Physica B: Condensed Matter, 2006. 382(1): p. 8-13. Sekine, C., et al., Metal-Insulator Transition in PrRu4P12 with Skutterudite Structure. Physical review letters, 1997. 79(17): p. 3218-3221. Matsuhira, K., et al., Specific Heat Study on Sm-based Filled Skutterudite Phosphides SmT4P12 (T=Fe, Ru and Os). Journal of the Physical Society of Japan, 2005. 74(3): p. 1030-1035. Bauer, E.D., et al., Kondo insulating behaviour in the filled skutterudite compound CeOs4Sb12. Journal of Physics: Condensed Matter, 2001. 13(20): p. 4495. Takeda, N. and M. Ishikawa, The effect of La substitution and magnetic field on nonFermi-liquid behaviour in CeRu 4 Sb 12. Journal of Physics: Condensed Matter, 2001. 13(26): p. 5971. Sales, B., D. Mandrus, and R.K. Williams, Filled skutterudite antimonides: a new class of thermoelectric materials. Science, 1996. 272(5266): p. 1325-1328. Chihiro Sekine, et al., Thermoelectric Properties of CeRu4P12 and CeOs4P12 with Filled Skutterudite-Type Structure. Japanese Journal of Applied Physics, 2001. 40(5R): p. 3326. Mahan, G. and B. Sales, Thermoelectric materials: New approaches to an old problem. Physics Today, 1997. 50(3): p. 42-47. Sekine, C., et al., Magnetic properties of new filled skutterudite compounds GdFe4As12 and TbFe4As12. Journal of Physics: Conference Series, 2011. 273(1): p. 012120. Takeda, K., et al., X-ray Study with Synchrotron Radiation for New Filled Skutterudite GdFe4As12 at Ambient Pressure and High Pressures, in Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013). 2014, Journal of the Physical Society of Japan. Grandjean, F., et al., Some physical properties of LaFe4P12 type compounds. Journal of Physics and Chemistry of Solids, 1984. 45(8): p. 877-886. Oftedal, I., Roentgenographische Untersuchungen von SnS2, TiS2, TiSe2, TiTe2. Zeitschrift für Physikalische Chemie, 1928. 134(1): p. 301-310. Petersen, M., et al., Improving the efficiency of FP-LAPW calculations. Computer Physics Communications, 2000. 126(3): p. 294-309. Blaha, P., et al., wien2k. An augmented plane wave+ local orbitals program for calculating crystal properties, 2001. Perdew, J.P., et al., Restoring the density-gradient expansion for exchange in solids and surfaces. Physical review letters, 2008. 100(13): p. 136406. Feng, J., et al., Electronic structure, mechanical properties and thermal conductivity of Ln2Zr2O7 (Ln= La, Pr, Nd, Sm, Eu and Gd) pyrochlore. Acta Materialia, 2011. 59(4): p. 1742-1760. Rai, D., et al., Calculation of coulomb repulsion (U) for 3d transition elements in Co2YAl type Heusler alloys. Armenian Journal of Physics, 2012. 5(3): p. 105-110. Madsen, G.K.H. and D.J. Singh, BoltzTraP. A code for calculating band-structure dependent quantities. Computer Physics Communications, 2006. 175(1): p. 67-71. Merabet, M., et al., Elastic and electronic properties calculations of the filled skutterudite CeOs4P12. Journal of Physics: Conference Series, 2016. 758: p. 012010. Takegahara, K., H. Harima, and A. Yanase, Crystal Electric Fields for Cubic Point Groups. Journal of the Physical Society of Japan, 2001. 70(5): p. 1190-1193. Murnaghan, F.D., Proc. Natl. Acad. Sci. USA 30, 1944(5390).
28. 29.
30.
31. 32.
33. 34. 35.
36. 37. 38.
39.
40. 41. 42. 43. 44. 45. 46.
47. 48.
Shankar, A., et al., Ground state properties of filled skutterudite EuRu4P12: A first principles study. Journal of Alloys and Compounds, 2013. 578: p. 559-564. Shankar, A., et al., Study of 5f electron based filled skutterudite compound EuFe4Sb12, a thermoelectric (TE) material: FP-LAPW method. Journal of Alloys and Compounds, 2015. 619: p. 621-626. Nouneh, K., et al., Band energy and thermoelectricity of filled skutterudites LaFe4Sb12 and CeFe4Sb12. Journal of Alloys and Compounds, 2007. 437(1): p. 3946. Fornari, M. and D.J. Singh, Electronic structure and thermoelectric prospects of phosphide skutterudites. Physical Review B, 1999. 59(15): p. 9722-9724. Shankar, A. and R.K. Thapa, Electronic, magnetic and structural properties of the filled skutterudite EuFe4P12: LSDA and LSDA+U calculation. Physica B: Condensed Matter, 2013. 427: p. 31-36. Sekine, C., et al., Magnetic and electrical properties of the filled skutterudite-type compound EuRu4P12. Physica B: Condensed Matter, 2000. 281-282: p. 308-310. Berri, S., First-principles study on half-metallic properties of the Sr2GdReO6 double perovskite. Journal of Magnetism and Magnetic Materials, 2015. 385: p. 124-128. Berri, S., The electronic structure and spin polarization of Co2Mn0.75(Gd, Eu)0.25Z (Z=Si, Ge, Ga, Al) quaternary Heusler alloys. Journal of Magnetism and Magnetic Materials, 2016. 401: p. 667-672. Shankar, A., et al., An ab initio study of filled skutterudites ROs4P12 (R= Sm, Eu and Gd). Phase Transitions, 2015. 88(11): p. 1062-1073. Coey, J.M.D. and S. Sanvito, Magnetic semiconductors and half-metals. Journal of Physics D: Applied Physics, 2004. 37(7): p. 988. Leithe-Jasper, A., et al., Weak itinerant ferromagnetism and electronic and crystal structures of alkali-metal iron antimonides: NaFe4Sb12 and KFe4Sb12. Physical Review B, 2004. 70(21): p. 214418. Viennois, R., et al., Spin fluctuations in the skutterudite compound LaFe 4 Sb 12. The European Physical Journal B-Condensed Matter and Complex Systems, 2005. 46(2): p. 257-267. Bauer, E., et al., Crystal structure and physical properties of Eu0.83Fe4Sb12. Physical Review B, 2001. 63(22): p. 224414. Zaitsev, V., et al., Thermoelectrics handbook: macro to nano. CRC Press, Taylor & Francis, Boca Raton, 2006. Allen, P., Boltzmann theory and resistivity of metals. KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE, 1996: p. 219-250. Hurd, C., The Hall effect in metals and alloys. 2012: Springer Science & Business Media. Ziman, J., Electrons & phonons Oxford. London (i960). a rZ, 2001. 1. Scheidemantel, T.J., et al., Transport coefficients from first-principles calculations. Physical Review B, 2003. 68(12): p. 125210. Takeuchi, T., Conditions of electronic structure to obtain large dimensionless figure of merit for developing practical thermoelectric materials. Materials transactions, 2009. 50(10): p. 2359-2365. Mahan, G.D. and J.O. Sofo, The best thermoelectric. Proceedings of the National Academy of Sciences, 1996. 93(15): p. 7436-7439. Khan, B., et al., Effects of chemical potential on the thermoelectric performance of alkaline-earth based skutterudites (AFe4Sb12, A=Ca, Sr and Ba). Journal of Alloys and Compounds, 2017. 694: p. 253-260.
49.
50.
51.
52.
53.
54.
55.
Aliabad, H.R., et al., Ab initio calculations of structural, optical and thermoelectric properties for CoSb3 and ACo4Sb12 (A= La, Tl and Y) compounds. Computational Materials Science, 2012. 65: p. 509-519. Guechi, N., et al., Elastic, Optoelectronic and Thermoelectric Properties of the LeadFree Halide Semiconductors Cs2AgBiX 6 (X = Cl, Br): Ab Initio Investigation. Journal of Electronic Materials, 2018. 47(2): p. 1533-1545. Qiu, P., et al., High-temperature electrical and thermal transport properties of fully filled skutterudites RFe4Sb12 (R= Ca, Sr, Ba, La, Ce, Pr, Nd, Eu, and Yb). Journal of applied physics, 2011. 109(6): p. 063713. Carlini, R., et al., Skutterudites for Thermoelectric Applications: Properties, Synthesis and Modelling, in Alloys and Intermetallic Compounds: From Modeling to Engineering, A. Cristina, Editor. 2017, CRC press Taylor&Francis. Rabina, O., Y.-M. Lin, and M.S. Dresselhaus, Anomalously high thermoelectric figure of merit in Bi1−xSbx nanowires by carrier pocket alignment. Applied Physics Letters, 2001. 79(1): p. 81-83. Khan, B., et al., Comparative study of thermoelectric properties of Co based filled antimonide skutterudites with and without SOC effect. Computational Materials Science, 2017. 131: p. 308-314. Morelli, D.T. and G.P. Meisner, Low temperature properties of the filled skutterudite CeFe4Sb12. Journal of applied physics, 1995. 77(8): p. 3777-3781.
Fig. 1. Crystal structure of the filled skutterudite GdFe4As12 generated by XCrySDen[30]
Fig. 2. Total energy versus volume curve of GdFe4As12, with GGA approximation.
Fig. 3. The energy band structures of GdFe4As12 in spin-up and spin-down configurations with: (A) GGA and (B) GGA+U approximations.
Fig. 4. Total and partial DOS of GdFe4As12 in spin-up and spin-down configurations with : (A) GGA and (B) GGA+U approximations.
Fig. 5.The density of states of minority (N↓) and majority (N↑) spin at the Fermi level.
Fig. 6. Seebeck coefficient of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation.
Fig. 7. Electrical conductivity of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation
Fig. 8. Electrical part of thermal conductivity of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation.
Fig. 9. Figure of merit of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation.
Table 1. The atomic position for GdFe4 As12 skutterudite compound Atom
Wyckoff Position
Atomic position
Gd
(2a)
(0, 0, 0)
Fe
(8c)
(-1/4, 1/4, 14) (1/4, -1/4, 1/4)
As
(24g)
(0, y, z) (0, y,-z) (y, 0, z) (-y, 0, z) (y, z , 0) (y, -z ,0)
(1/4, 1/4, -1/4)
(1/4, 1/4, 1/4)
(0, -y, -z) (0, -y, z) (-z, 0, -y) (z, 0, -y) (-y, -z, 0) (-y, z, 0)
Table 2. Lattice constant a0, bulk modulus B, its pressure derivative B’ and minimum energy at equilibrium E0 (in Ry) for paramagnetic (PM), and ferromagnetic (FM) states with GGA approximation.
GdFe4As12 Present
Exp
a(A°)
y(As)
z(As)
B(GPa)
B’(GPa)
E0 (Ry)
PM
8.2092
0.3407
0.1512
138.9411
4.2053
-86954.712841
FM
8.2243
0.3427
0.1559
139.2525
4.7423
-86955.249765
8.3024[17]
0.3442[16]
0.1535[16]
Table 3. Total and partial magnetic moments of GdFe4As12 using GGA and GGA+U approximations Magnetic moment (µB)
Present
Exp[17]
Gd
Fe
As
GGA
6.86111
-0.17852
-0.00216
6.18
GGA+U
6.88923
0.58777
-0.05028
8.00
-
-
-
-
Total
8.09
First Principles Study of Structural, Electronic and Thermoelectric Properties of Skutterudite GdFe4 As12 compounds M. Boucharef , L. Djoudi , M. Merabet , S. Benalia , R. Belghit , N. Bettahar , D. Rached PII: DOI: Reference:
S0577-9073(19)30993-1 https://doi.org/10.1016/j.cjph.2019.11.021 CJPH 1015
To appear in:
Chinese Journal of Physics
Received date: Revised date: Accepted date:
16 May 2019 11 October 2019 14 November 2019
Please cite this article as: M. Boucharef , L. Djoudi , M. Merabet , S. Benalia , R. Belghit , N. Bettahar , D. Rached , First Principles Study of Structural, Electronic and Thermoelectric Properties of Skutterudite GdFe4 As12 compounds, Chinese Journal of Physics (2019), doi: https://doi.org/10.1016/j.cjph.2019.11.021
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Highlights Investigate the structural and electronic and magnetic properties of GdFe4As12 material. The semi-metallic nature of this compound. GdFe4As12 compound is of great interest for thermoelectric devices.
First Principles Study of Structural, Electronic and Thermoelectric Properties of Skutterudite GdFe4As12 compounds
M. Boucharef
1,2
1,3
1,3
1,3
4
1
, L. Djoudi , M. Merabet , S. Benalia , R. Belghit , N. Bettahar , D. Rached
1
1
Laboratory of Magnetic Materials, Faculty of Sciences, University of Djillali Liabes, Sidi- Bel- Abbes, 22000, Algeria. 2
Department of Technology, Faculty of Technology, University of Yahia Fares, Medea, 26000, Algeria Centre Universitaire de Tissemsilt, Institut des Sciences et de la Technologie, Tissemsilt, Algérie 4 Laboratory Studies of Surface and Interfaces of Solid Materials (LESIMS), Department of Physics, Faculty of Sciences, University Badji Mokhtar, P.O. Box 12, Annaba 23000, Algeria 3
Abstract The full potential linearized augmented plane wave (FP-LAPW) method has been used to investigate structural, electronic and thermoelectric properties of Skutterudite GdFe4As12 compounds in the framework of the density functional theory (DFT) within the generalized gradient approximation (GGA) and (GGA+U). The ground-state properties are determined in the cubic structure (Im-3, space group 204). It is found that the most stable phase structure of GdFe4As12 compounds is the ferromagnetic phase and it shows a semi-metallic behavior with narrow gap. The calculation of the density of states near the Fermi level shows the compound to be suitable for the effective thermoelectric application. In addition, the high Seebeck coefficient value is obtained in the n-type region than p-type, indicating the prominence of n-type doping in filled skutterudite GdFe4As12.
Keywords: DFT; FP-LAPW; Skutterudites compound; Ferromagnetic; Semi-metallic; Thermoelectric.
1. Introduction The chemical formula of filled skutterudite is (RM4X12, R = rare earth; M = Fe, Ru, Os; X = P, As, Sb), It has attracted much attention recently because of its interesting physical properties in low temperatures. Several of the interesting properties of these compounds are associated with the R ion that dominates the atomic ‘cage’ in the binary (unfilled) type skutterudite structure. Among these properties are: Magnetic [1], superconducting [2-4], semiconducting [5], intermediate valence [6, 7], metal-insulator transition [8, 9], heavy fermions [10], and non-Fermi liquid behavior [11] have been noted in these materials. Further, skutterudite compounds exhibit remarkable thermoelectric properties [12, 13], The good thermoelectric properties appear to arise from the cage structure; the R atoms ‘rattle’ in their cage, which reduces the lattice thermal conductivity [14]. Many of these facts depend on strong hybridization between the localized f-electron states of R rare earth ions with the conduction electron states. GdFe4As12 compound is among the ternary filled skutterudite, he is synthesizing for the first time in 2011by Sekine et al [15] using the high-pressure synthesis technique. They are found that is characterized by its magnetic behavior. In 2013, Keiko Takeda and co-workers have investigated the effect of pressure on cell volume [16], in the present work we have done the complete analysis of magnetic and electronic structure, and we have reported the semimetallic nature of this compound using the FP-LAPW method. And we have ameliorated the thermoelectric calculations in order to provide reference data for the experimentalist on this compound. The structure of the recent work is as follows: In Section 2, the description of the FP-LAPW computational method is presented, in section 3; we display the results and discussion for structural, electronic, magnetic, and thermoelectric properties. Finally, in Section 4 we sum up the conclusions of our work.
2. Calculation Methodology
In the field of condensed matter theory and computational materials, density functional theory (DFT) is a powerful tool widely for the calculation of electronic and structural properties of solids [17], it is a universal quantum mechanical approach for many body problems. In this approach, the quantum many-body problems of an interacting electron gas are mapped exactly onto a set of single particles moving in an effective local potential with the same density as is real, and the obtained one electron equations are called Kohn–Sham equations [2, 18]. In this work, we have used the full potential linearized augmented plane wave (FP-LAPW) method [19] implemented in the WIEN2k code [20], to investigate the structural properties of the considered compounds, the exchange and correlation (XC) potential were treated by PBEsol [21] version of the generalized gradient approximation (GGA) for both ferromagnetic (FM), and paramagnetic (PM) states. To calculate the electronic, magnetic and thermoelectric properties, the local spin density approximation + Coulomb repulsion (U) is used to modulate the (GGA) approximation, the adopted on-site Coulomb repulsion term (U) for the present calculations is 0.441 Ry [22] and 0.286 Ry [23] for Gd-f and Fe-d respectively, In order to ensure convergence of the computed structures and energetic we use the value of plane wave cut-off Rmt×Kmax=14, The RMT (muffin-tin radii) were selected to be 2.50, 2.18 and 2.08 (a.u.) for Gd, Fe and As, respectively. The maximum radial expansion lmax = 10 and 2000 k-points (12×12×12 mesh size) are the values used for performing present self-consist calculations, but the second part of these studies, are improved in order to elucidate thermoelectric properties for the present compound. The code used for these computations is BoltzTraP code [24] which is based on constant scattering time approximation (CSTA) and rigid band approximation (RBA) [25, 26]. To achieve more appropriate results for thermoelectric properties, we used here a very high k-mesh (40,000) case in the Irreducible Brillouin zone (IBZ).
3. Results and discussions 3.1. Structural properties The GdFe4As12 compound crystallizes in the cubic space group (N°204, Im-3) [17, 26]. Gd, Fe and As atoms occupying the position listed in Table 1. The geometry structure of GdFe4As12 is shown in Fig. 1. We notice that the skutterudite structure has two non-equivalent characteristics atomic positions y and z, which are not fixed by symmetry, For our compound, the value of parameter y and z are 0.3442 [16], 0.1535 [16] respectively.
In order to determine the equilibrium structural properties of our compound, a set of different volumes around the experimental value are chosen and for each volume, the total energies are calculated for both paramagnetic (PM), and ferromagnetic (FM) states with GGA approximation. In principle, the internal coordinates y and z should be also relaxed and the best value that minimizes the total energy. The obtained total energies versus volume data are fitted by the non-linear Murnaghan equation of state [27] to determine the ground state properties such as the equilibrium lattice parameters (a), the bulk modulus and its pressure derivative (B and B’, and internal parameters ). The result is presented in Fig. 2. The quantities a, B and B’, for both states are summarized together in Table 2 with the available experimental data. As can be seen that the most stable state for our compound is the ferromagnetic state, the obtained lattice constants are in reasonable agreement with the experimental data; which is 1.0% smaller to the corresponding experimental value, this is due to the use of GGA approximation to calculate the exchange and correlation potential, which is known to underestimate this quantity in comparison to experiment values. However, to the best of our knowledge, there are no experimental or theoretical results for B and its pressure derivative available to be compared with our theoretical result.
3.2. Electronic and magnetic properties As exposed in Fig. 2. and table 2. The equilibrium lattice constant calculates with GGA approximation in the ferromagnetic state is the most less equilibrium energy for our compound. For this reason, and to understand the electronic and magnetic properties of filled skutterudite GdFe4As12, we calculate these properties with spin-polarized at its equilibrium lattice constant for this state using GGA and GGA+U approximations. The energy band structures calculated in spin-up and spin-down configurations along the high symmetry directions of the Brillouin zone are presented in Fig. 3 using GGA and GGA+U approximations. The calculated energy bands show similar profile to the previously calculated plots for EuRu4P12 [28] EuFe4Sb12 [29]. We can observe that the energy bands are greatly populated just near the Fermi level of minority and majority spin, which gives great mobility of charge carriers, which increased the electrical conductivity as compared to other compounds. This observation allowed us to study the thermoelectric properties.
In order to check the precision of our band structures results, we present the calculated density of states, the total density of states (DOS) and partial DOS are shown in Fig. 4 using GGA and GGA+U approximations. The densities of states found by the calculation are comparatively similar to
previously reported plots [30, 31]. For both figures, we can see that there are three distinct regions separated from each other by small energy gaps. The core region (below -12.0 eV) is primarily dominated by s state electrons of the arsenic atom for both spin channels. The valence region is essentially contributed by the d state of Fe atoms. The conduction region is mainly contributed by the d state of Gd atoms. Around Fermi level EF, The most important feature of the DOS plot is the presence a narrow gap due a very low density of states but it is different to zero for both spin channels, it has the same character to previously calculated plots for [28, 29, 32] filled Skutterudites, the narrow gap promotes the superconducting behavior with highly effective masses, this gives a substantial rise to the great value of thermoelectric Seebeck coefficients [33], and it indicates that this compound has a semi-metallic behavior and it is relatively similar to the previous reports of analogous compounds EuRu4P12 [28] and EuFe4P12 [32]. The calculated partial magnetic moment within the muffin-tin spheres of the respective Gd, Fe and As atoms, and the total magnetic moments with GGA and GGA+U approximations are given in Table 3 to gather with an available value of experimental total spin magnetic moments. In comparison with the experimental data, we find that our values are underestimated, the main contribution to the total magnetic moment is due to Gadolinium with small contribution from Fe-3d state, and this agree with the results of the refs [34-36]. Also, we calculate the spin polarization factor at Fermi level with GGA+U approximation. The simplest definition of spin polarization [37] is:
P = (N↑- N↓) / (N↑+ N↓)
Where N is the density of states of minority (N↓), and majority (N↑) spin at the Fermi level. As shown in Fig. 5, the calculate value of polarization at the Fermi level is 0.96, this value is due to the presence of high relatively concentrated density of states at EF (in minority spin N↓) and negligible contribution (in majority spin N↑), The value of spin polarization which we obtain is close to that obtained for iso structural KFe4Sb12 and NaFe4Sb12 [38]. The density of states on the Fermi level is relatively high in these types of compounds possessing superconducting behavior, which forms a larger electronic specific heat [39, 40]. This explains the importance of this compound in thermoelectric applications.
1.1. Thermoelectric properties During the last two decades, an intensive effort has been made by the researchers around the globe to find high-performance thermoelectric materials. Thermoelectricity refers to the direct energy conversion between heat and electricity, and its technology can be applied to the thermocouples, power generator, and refrigerator [41]. The efficiency of a thermoelectric device is evaluated by thermoelectric figure of merit
ZT S 2T , where is the electric conductivity, is the electrical part of the thermal conductivity and S is the Seebeck coefficient, which represents the ability of a system of charged particles to generate an electromotive force when a temperature gradient is applied across the system [30]. We determine these parameters using BoltzTrap code [24] which is based on the Boltzmann theory [42-44]. The BoltzTraP code is a calculating tool based on the smooth Fourier interpolations of the band energies. The code uses the interpolated band structure by WIEN2k to compute the derivatives necessary to evaluate the transport properties. The transport coefficients necessary to find ZT can be obtained directly. Using scalar coefficients [24, 29, 45]:
1 f (T , ) i ,k 0 d
1 2 K B2T i ,k e K BT S
2
f 0 (T , ) d
f 0 (T , ) eK B i , k d K BT
Where:
is the volume of a unit cell. f 0 is a Fermi-Dirac distribution function.
e is the electron charge.
is the chemical potential.
is the energy. T is the temperature absolute. K B is the Boltzmann constant [46]. The transport distribution i ,k is written as [47].
i ,k e2 i ,k k Where:
v and v are the group velocities.
k is the relaxation time.
We note that the chemical potential defines the doping level or carrier concentration in a material [48], It has negative values when Fermi level shifts down towards the valence band indicating the ability of p-type doping, and are positive values when the Fermi level shifts upward to the conduction band indicating the ability of n-type doping.
1.1.1. Seebeck Coefficient Mathematically, Seebeck Coefficient is S V T [49], for p-doped has positive values and has negative values for n-doped systems, we have calculated this parameter for chemical potentials ranging from -1.36 at 1.36 in spin-up and (spin-dn) configurations at T=300K, 600K and 900K, and it’s plotted in Fig. 6. The absolute value (magnitude) of the Seebeck coefficient S increases with the decreasing absolute value (magnitude) of the chemical potential for both spin up and spin down, that means these materials will exhibit good thermoelectric properties for lower doping (lower chemical potential). And he increases with an increasing temperature, this is due to an increasing charge-carrier concentration [50] for both configurations spin up and spin dn.
At room temperature, the higher value of the Seebeck coefficient is found for a positive range of chemical potential with spin-dn configurations. That’s means to get a high value of Seebeck coefficient; our compound supported the n-type doping This value equal to 99.30(µV/K) is close to the experimental value for iso structural compounds 81.5(µV/K) for PrFe4Sb12, 83.7 (µV/K) for NdFe4Sb12 and 79.4 (µV/K) for CeFe4Sb12 [51]. The high value of S in our calculation can be related to the calculated flat band structures due to Fe-3d states near the EF with highly effective mass [29, 52].
1.1.2. Electrical Conductivity Electrical conductivity measures the ability of a material of the flow of electric current either due to negative electrons or positive holes, on gaining kinetic energy and move in the material thus producing an electric current. For a good thermoelectric device, materials should have high electrical conductivity to reduce Joule heating effect [49]. The electrical conductivity against chemical potential at 300 K, 600 K and 900 K temperature for spinup and spin-down configurations are plotted in Fig. 7. It is clear from the figure that for different temperatures, the magnitude of the electrical conductivity increases with the increase of absolute values of the chemical potential; and the high value of electrical conductivity is observed in the positive range of chemical potential with spin-dn configuration, that means our compound supported the n-type doping similar to Seebeck coefficient observation.
1.1.3. Thermal conductivity The thermal conductivity , of the compound, indicates its ability to conduct heat for both; electronic and lattice vibrations. The thermal conductivity is usually dominated by the lattice vibrations in semiconductors, while in metals free electrons are a good source of thermal conductivity [53]. The thermal conductivity should be small with that temperature gradient for a good thermoelectric device. Present electronic part of thermal conductivity as a function of chemical potential for 300 K, 600 K and 900 K temperature at spin-up and spin-down configurations are exposed in Fig. 8. Similar to electrical conductivity, the magnitude of The Thermal conductivity also increases with increasing temperature, this is because as the temperature increases, more electrons get excited, and he also increases when one moves away from µ=0 for both configurations. We see that thermal conductivity has lower values in p-type (negative value of chemical potential) for spin-dn configuration at a different temperature, which helps to improve a good value of the figure of merit and then improve a good thermoelectric property.
At room temperature with the chemical potential of -1.5 eV, the value of the electronic thermal conductivity in units (1014 W/m Ks) is 11.41 for spin-up and 12.70 for spin-dn compared with same chemical structure for CaCo4Sb12, SrCo4Sb12, BaCo4Sb12 the value is 8.6, 7.99, 6.74 respectively [54]; The difference in value is due to the difference of the approximation used; Khan [54] uses the PBEsol08 GGA approximation [21] without adding the Hubbard factor, which we added to our calculation.
1.1.4. Figure of merit The performance of a thermoelectric material can be predicted by its figure of merit (ZT), which is directly proportional to the high Seebeck coefficient and electrical conductivity, while inversely proportional to the thermal conductivity. Fig. 9 show the graph of ZT against the chemical potential at T= 300 K, 600 K and 900 K in spin-up and spin-down configurations. It is clear from the figure that at room temperature ZT sharply rises as chemical potential increases from zero, and the peak value is observed at 0.17 µ(eV) chemical potentials in n-type region for spin down configuration; This is because the Seebeck coefficient gives maximum values and thermal conductivity stays a minimum value in this chemical potential; but when the temperature increases the peak get a maximum for 0.19 µ(eV) chemical potentials in n-type region for spin up configuration at T=900K. On the other hand, one can notice that when the chemical potential is 0 the value of the ZT in 300 K is bigger than the other values of 600 K and 900 k, for both spin state. At room temperature the maximum value of ZT calculated with GGA+U is 0.28 which is higher than the previous experimental values of some of the analogous compounds CeFe4Sb12 (ZT=0.1) [55], RFe4Sb12 (R=Ca, La, Sr, Ce, Ba, Pr, Yb, Eu, and Nd) ZT is (0.1 0.2) [51]; This finding allows us to claim that the filled skutterudite GdFe4As12 are potential candidates for thermoelectric applications if one can further reduce their thermal conductivities via some techniques, such as alloying, nano-structuring, or super-lattice growth.
2. Conclusion In summary, the structural, electronic and magnetic properties are performed within the density functional theory using the full potential linearized augmented plane waves (FPLAPW) method, employing GGA and GGA+U as embodied in the WIEN2k code, while the thermoelectric properties calculations are carried out applying the semiclassical Boltzmann transport theory and it’s obtained from the calculated band structures by performing additional post-processing applying the BoltzTraP package. Our main results are as follows:
The most stable state for our compound is the ferromagnetic state. The analysis density of state diagrams, and after determining the magnetic moment and calculate the polarization factor reveals that our compound is a semi-metal behavior. The calculations of the thermoelectric properties reveal that the investigated compounds have good properties for lower doping, and it is supported the n-type doping and might also be enhanced by some techniques, such as nano-structuring, superlattice growth or alloying which attributes further reduction of lattice thermal conductivity. Several approaches can be used for this purpose which includes partial substitution of Fe by Co, Ni etc. which have more valence electrons than Fe. This could reduce the high holes concentration in the material and raise the Seebeck coefficient to enhance ZT.
The effectiveness of inclusion the Coulomb repulsion (U) in calculating the electronic, magnetic and thermoelectric properties are verified.
References 1.
2. 3. 4.
5.
6.
Danebrock, M.E., C.B.H. Evers, and W. Jeitschko, Magnetic properties of alkaline earth and lanthanoid iron antimonides AFe4Sb12 (A = Ca, Sr, Ba, La-Nd, Sm, Eu) with the LaFe4P12 structure. Journal of Physics and Chemistry of Solids, 1996. 57(4): p. 381-387. Meisner, G.P., Superconductivity and magnetic order in ternary rare earth transition metal phosphides. Physica B+C, 1981. 108(1): p. 763-764. Shirotani, I., et al., Superconductivity of filled skutterudites LaRu4As12 and PrRu4As12. Physical Review B, 1997. 56(13): p. 7866-7869. Takeda, N. and M. Ishikawa, Superconducting and Magnetic Properties of Filled Skutterudite Compounds RERu4Sb 12 (RE=La, Ce, Pr, Nd and Eu). Journal of the Physical Society of Japan, 2000. 69(3): p. 868-873. Shirotani, I., et al., Electrical and Magnetic Properties of La1−xCexRu4P12and CeOs4P12with the Skutterudite Structure. Journal of Solid State Chemistry, 1999. 142(1): p. 146-151. Dilley, N.R., et al., Intermediate valence in the filled skutterudite compound YbFe4Sb12. Physical Review B, 1998. 58(10): p. 6287-6290.
7.
8. 9.
10. 11.
12. 13.
14. 15.
16.
17. 18. 19. 20. 21. 22.
23. 24. 25. 26. 27.
Shirotani, I., et al., X-ray study with synchrotron radiation for filled skutterudite YbFe4P12 at ambient and high pressures. Physica B: Condensed Matter, 2006. 382(1): p. 8-13. Sekine, C., et al., Metal-Insulator Transition in PrRu4P12 with Skutterudite Structure. Physical review letters, 1997. 79(17): p. 3218-3221. Matsuhira, K., et al., Specific Heat Study on Sm-based Filled Skutterudite Phosphides SmT4P12 (T=Fe, Ru and Os). Journal of the Physical Society of Japan, 2005. 74(3): p. 1030-1035. Bauer, E.D., et al., Kondo insulating behaviour in the filled skutterudite compound CeOs4Sb12. Journal of Physics: Condensed Matter, 2001. 13(20): p. 4495. Takeda, N. and M. Ishikawa, The effect of La substitution and magnetic field on nonFermi-liquid behaviour in CeRu 4 Sb 12. Journal of Physics: Condensed Matter, 2001. 13(26): p. 5971. Sales, B., D. Mandrus, and R.K. Williams, Filled skutterudite antimonides: a new class of thermoelectric materials. Science, 1996. 272(5266): p. 1325-1328. Chihiro Sekine, et al., Thermoelectric Properties of CeRu4P12 and CeOs4P12 with Filled Skutterudite-Type Structure. Japanese Journal of Applied Physics, 2001. 40(5R): p. 3326. Mahan, G. and B. Sales, Thermoelectric materials: New approaches to an old problem. Physics Today, 1997. 50(3): p. 42-47. Sekine, C., et al., Magnetic properties of new filled skutterudite compounds GdFe4As12 and TbFe4As12. Journal of Physics: Conference Series, 2011. 273(1): p. 012120. Takeda, K., et al., X-ray Study with Synchrotron Radiation for New Filled Skutterudite GdFe4As12 at Ambient Pressure and High Pressures, in Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013). 2014, Journal of the Physical Society of Japan. Grandjean, F., et al., Some physical properties of LaFe4P12 type compounds. Journal of Physics and Chemistry of Solids, 1984. 45(8): p. 877-886. Oftedal, I., Roentgenographische Untersuchungen von SnS2, TiS2, TiSe2, TiTe2. Zeitschrift für Physikalische Chemie, 1928. 134(1): p. 301-310. Petersen, M., et al., Improving the efficiency of FP-LAPW calculations. Computer Physics Communications, 2000. 126(3): p. 294-309. Blaha, P., et al., wien2k. An augmented plane wave+ local orbitals program for calculating crystal properties, 2001. Perdew, J.P., et al., Restoring the density-gradient expansion for exchange in solids and surfaces. Physical review letters, 2008. 100(13): p. 136406. Feng, J., et al., Electronic structure, mechanical properties and thermal conductivity of Ln2Zr2O7 (Ln= La, Pr, Nd, Sm, Eu and Gd) pyrochlore. Acta Materialia, 2011. 59(4): p. 1742-1760. Rai, D., et al., Calculation of coulomb repulsion (U) for 3d transition elements in Co2YAl type Heusler alloys. Armenian Journal of Physics, 2012. 5(3): p. 105-110. Madsen, G.K.H. and D.J. Singh, BoltzTraP. A code for calculating band-structure dependent quantities. Computer Physics Communications, 2006. 175(1): p. 67-71. Merabet, M., et al., Elastic and electronic properties calculations of the filled skutterudite CeOs4P12. Journal of Physics: Conference Series, 2016. 758: p. 012010. Takegahara, K., H. Harima, and A. Yanase, Crystal Electric Fields for Cubic Point Groups. Journal of the Physical Society of Japan, 2001. 70(5): p. 1190-1193. Murnaghan, F.D., Proc. Natl. Acad. Sci. USA 30, 1944(5390).
28. 29.
30.
31. 32.
33. 34. 35.
36. 37. 38.
39.
40. 41. 42. 43. 44. 45. 46.
47. 48.
Shankar, A., et al., Ground state properties of filled skutterudite EuRu4P12: A first principles study. Journal of Alloys and Compounds, 2013. 578: p. 559-564. Shankar, A., et al., Study of 5f electron based filled skutterudite compound EuFe4Sb12, a thermoelectric (TE) material: FP-LAPW method. Journal of Alloys and Compounds, 2015. 619: p. 621-626. Nouneh, K., et al., Band energy and thermoelectricity of filled skutterudites LaFe4Sb12 and CeFe4Sb12. Journal of Alloys and Compounds, 2007. 437(1): p. 3946. Fornari, M. and D.J. Singh, Electronic structure and thermoelectric prospects of phosphide skutterudites. Physical Review B, 1999. 59(15): p. 9722-9724. Shankar, A. and R.K. Thapa, Electronic, magnetic and structural properties of the filled skutterudite EuFe4P12: LSDA and LSDA+U calculation. Physica B: Condensed Matter, 2013. 427: p. 31-36. Sekine, C., et al., Magnetic and electrical properties of the filled skutterudite-type compound EuRu4P12. Physica B: Condensed Matter, 2000. 281-282: p. 308-310. Berri, S., First-principles study on half-metallic properties of the Sr2GdReO6 double perovskite. Journal of Magnetism and Magnetic Materials, 2015. 385: p. 124-128. Berri, S., The electronic structure and spin polarization of Co2Mn0.75(Gd, Eu)0.25Z (Z=Si, Ge, Ga, Al) quaternary Heusler alloys. Journal of Magnetism and Magnetic Materials, 2016. 401: p. 667-672. Shankar, A., et al., An ab initio study of filled skutterudites ROs4P12 (R= Sm, Eu and Gd). Phase Transitions, 2015. 88(11): p. 1062-1073. Coey, J.M.D. and S. Sanvito, Magnetic semiconductors and half-metals. Journal of Physics D: Applied Physics, 2004. 37(7): p. 988. Leithe-Jasper, A., et al., Weak itinerant ferromagnetism and electronic and crystal structures of alkali-metal iron antimonides: NaFe4Sb12 and KFe4Sb12. Physical Review B, 2004. 70(21): p. 214418. Viennois, R., et al., Spin fluctuations in the skutterudite compound LaFe 4 Sb 12. The European Physical Journal B-Condensed Matter and Complex Systems, 2005. 46(2): p. 257-267. Bauer, E., et al., Crystal structure and physical properties of Eu0.83Fe4Sb12. Physical Review B, 2001. 63(22): p. 224414. Zaitsev, V., et al., Thermoelectrics handbook: macro to nano. CRC Press, Taylor & Francis, Boca Raton, 2006. Allen, P., Boltzmann theory and resistivity of metals. KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE, 1996: p. 219-250. Hurd, C., The Hall effect in metals and alloys. 2012: Springer Science & Business Media. Ziman, J., Electrons & phonons Oxford. London (i960). a rZ, 2001. 1. Scheidemantel, T.J., et al., Transport coefficients from first-principles calculations. Physical Review B, 2003. 68(12): p. 125210. Takeuchi, T., Conditions of electronic structure to obtain large dimensionless figure of merit for developing practical thermoelectric materials. Materials transactions, 2009. 50(10): p. 2359-2365. Mahan, G.D. and J.O. Sofo, The best thermoelectric. Proceedings of the National Academy of Sciences, 1996. 93(15): p. 7436-7439. Khan, B., et al., Effects of chemical potential on the thermoelectric performance of alkaline-earth based skutterudites (AFe4Sb12, A=Ca, Sr and Ba). Journal of Alloys and Compounds, 2017. 694: p. 253-260.
49.
50.
51.
52.
53.
54.
55.
Aliabad, H.R., et al., Ab initio calculations of structural, optical and thermoelectric properties for CoSb3 and ACo4Sb12 (A= La, Tl and Y) compounds. Computational Materials Science, 2012. 65: p. 509-519. Guechi, N., et al., Elastic, Optoelectronic and Thermoelectric Properties of the LeadFree Halide Semiconductors Cs2AgBiX 6 (X = Cl, Br): Ab Initio Investigation. Journal of Electronic Materials, 2018. 47(2): p. 1533-1545. Qiu, P., et al., High-temperature electrical and thermal transport properties of fully filled skutterudites RFe4Sb12 (R= Ca, Sr, Ba, La, Ce, Pr, Nd, Eu, and Yb). Journal of applied physics, 2011. 109(6): p. 063713. Carlini, R., et al., Skutterudites for Thermoelectric Applications: Properties, Synthesis and Modelling, in Alloys and Intermetallic Compounds: From Modeling to Engineering, A. Cristina, Editor. 2017, CRC press Taylor&Francis. Rabina, O., Y.-M. Lin, and M.S. Dresselhaus, Anomalously high thermoelectric figure of merit in Bi1−xSbx nanowires by carrier pocket alignment. Applied Physics Letters, 2001. 79(1): p. 81-83. Khan, B., et al., Comparative study of thermoelectric properties of Co based filled antimonide skutterudites with and without SOC effect. Computational Materials Science, 2017. 131: p. 308-314. Morelli, D.T. and G.P. Meisner, Low temperature properties of the filled skutterudite CeFe4Sb12. Journal of applied physics, 1995. 77(8): p. 3777-3781.
Fig. 1. Crystal structure of the filled skutterudite GdFe4As12 generated by XCrySDen[30]
Fig. 2. Total energy versus volume curve of GdFe4As12, with GGA approximation.
Fig. 3. The energy band structures of GdFe4As12 in spin-up and spin-down configurations with: (A) GGA and (B) GGA+U approximations.
Fig. 4. Total and partial DOS of GdFe4As12 in spin-up and spin-down configurations with : (A) GGA and (B) GGA+U approximations.
Fig. 5.The density of states of minority (N↓) and majority (N↑) spin at the Fermi level.
Fig. 6. Seebeck coefficient of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation.
Fig. 7. Electrical conductivity of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation
Fig. 8. Electrical part of thermal conductivity of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation.
Fig. 9. Figure of merit of GdFe4As12 at T= 300 K, 600 K and 900 K against the chemical potential in spin-up and spin-down configurations with GGA+U approximation.
Table 1. The atomic position for GdFe4 As12 skutterudite compound Atom
Wyckoff Position
Atomic position
Gd
(2a)
(0, 0, 0)
Fe
(8c)
(-1/4, 1/4, 14) (1/4, -1/4, 1/4)
As
(24g)
(0, y, z) (0, y,-z) (y, 0, z) (-y, 0, z) (y, z , 0) (y, -z ,0)
(1/4, 1/4, -1/4)
(1/4, 1/4, 1/4)
(0, -y, -z) (0, -y, z) (-z, 0, -y) (z, 0, -y) (-y, -z, 0) (-y, z, 0)
Table 2. Lattice constant a0, bulk modulus B, its pressure derivative B’ and minimum energy at equilibrium E0 (in Ry) for paramagnetic (PM), and ferromagnetic (FM) states with GGA approximation.
GdFe4As12 Present
Exp
a(A°)
y(As)
z(As)
B(GPa)
B’(GPa)
E0 (Ry)
PM
8.2092
0.3407
0.1512
138.9411
4.2053
-86954.712841
FM
8.2243
0.3427
0.1559
139.2525
4.7423
-86955.249765
8.3024[17]
0.3442[16]
0.1535[16]
Table 3. Total and partial magnetic moments of GdFe4As12 using GGA and GGA+U approximations Magnetic moment (µB)
Present
Exp[17]
Gd
Fe
As
GGA
6.86111
-0.17852
-0.00216
6.18
GGA+U
6.88923
0.58777
-0.05028
8.00
-
-
-
-
Total
8.09