Energetic Stability and Thermoelectric Property of Alkali-Metal-Encapsulated Type-I Silicon-Clathrate from First-Principles Calculation
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Materials Transactions, Vol. 54, No. 3 (2013) pp. 276 to 285 ©2013 The Japan Institute of Metals Energetic Stability and Thermoelectric Property of Alkali-Metal-Encapsulated Type-I Silicon-Clathrate from First-Principles Calculation Kaoru Nakamura+, Susumu Yamada and Toshiharu Ohnuma Central Research Institute of Electric Power Industry, Yokosuka 240-0196, Japan Possible combinations of alkali metal guest atoms and substitutional group-13 atoms in type-I Si clathrate and their thermoelectric properties were investigated using first-principles calculations. All alkali metals could be encapsulated as the guest element into a Si46 cage, and either Al or Ga was suitable for a substitutional atom. From the formation energy, possible clathrate compositions were selected as K8Al8Si38, K8Ga8Si38,Rb8Al8Si38,Rb8Ga8Si38,Cs8Al8Si38 and Cs8Ga8Si38. The thermoelectric properties of these compositions were calculated as functions of temperature and carrier density, using the Boltzmann transport equation and the calculated band energy. The obtained dependences of the Seebeck coefficient and electrical conductivity on the carrier density were discussed from the viewpoint of band structure. The thermoelectric properties were optimized to maximize ZT for each composition by controlling the carrier density. ZT µ 0.75 was predicted as the highest ZT value for hole-doped Cs8Ga8Si38. [doi:10.2320/matertrans.MBW201204] (Received November 8, 2012; Accepted December 7, 2012; Published January 25, 2013) Keywords: thermoelectric, first-principles calculation, clathrate 1. Introduction extensively investigated for application as thermoelectric materials. In order to achieve high Seebeck coefficient, a low In recent years, reusable and clean energy generation carrier density is desirable because the Seebeck coefficient is technologies have been attracting much attention. Thermo- determined from the transport of entropy per carrier. On the electric conversion is one of the promising clean energy contrary to the Seebeck coefficient, high electrical conduc- sources because it enables the conversion of wasted heat into tivity can be achieved with high carrier density. Thus, there electric power. is a tradeoff relation between the Seebeck coefficient and In 1994, Slack proposed the concept of Phonon Glass electric conductivity, and the optimal carrier density must be Electron Crystal (PGEC).1) This hypothetical material can found to maximize ZT.10) simultaneously behave as glass for phonons and as crystal for Carrier density is frequently optimized in semiconductor carriers. Filled skutterudite and clathrate compounds are nice materials by adding a dopant. Clathrate compounds are examples of Slack’s PGEC concept. Such compounds are thought to be one of the intermetallic compounds that exhibit composed of a characteristic atomic structure. “Host atoms” a Zintl phase11) in which a guest atom supplies an electron form a cage network, and good electrical conductivity is while the substitution of an aliovalent element into a cage site exhibited because of the covalent bonding of the cage can compensate for the supplied electron. If the number of network. Cages are usually formed to encapsulate the guest and substitutional atoms is properly controlled, charge additional element, which is frequently referred to as a neutrality of the system is preserved. The carrier density of “guest atom”. The guest atom is weakly bound in the cage such an intrinsic semiconductor can thus be controlled and vibrates like an Einstein oscillator. The characteristic through adjusting the composition of guest and substitutional vibration of the guest atom can scatter the lattice vibration of atoms. Among the clathrate compounds, Ge-based clathrate the cage. This concept is referred to as “rattling”. Therefore, has been widely investigated59) because its localized d- cage-networked materials such as glassy materials generally electrons give it favorable thermoelectric properties. Si-based exhibit quite low thermal conductivities.19) clathrate, on the other hand, has not been investigated as Thermoelectric materials can generate electric power compared with the Ge-based one for use in thermoelectric through the Seebeck effect. Its conversion efficiency is applications. determined from the dimensionless figure of merit (ZT), For example, reports on the ZT of Si clathrate are quite defined as follows: limited. Kuznetsov et al. estimated the ZT of Ba8Ga16Si30 to 13) 2 be 0.87 at 870 K, and C. Candofi et al. reported that a ZT of ZT ¼ s ·T=ðke þ klÞ; ð1Þ approximately 0.2 had been achieved at 600 K for Ba8Aux- 14) where s is the Seebeck coefficient, · is electrical conductivity Si46¹x, where x = 5.59. It has not been established whether and T is temperature. ke and kl are electrical and lattice the maximum ZT of Si-based clathrate exceeds 1. Si is a thermal conductivities, respectively. Generally, ZT > 1is ubiquitous element that is cheaper than Ge and is nontoxic. regarded as a standard for actual application of thermoelectric Therefore, we believe that if a stable Si-based clathrate conversion. It is crucial to increase both the Seebeck without harmful and rare-earth element will be obtained, its coefficient and the electrical conductivity while suppressing range of applications is significant, even if it only exhibited the thermal conductivity in order to achieve high thermo- a moderate ZT. Experimental optimization of additional electric performance. PGEC materials exhibit both high elements and the carrier density would require an enormous electrical and low thermal conductivities and have been number of research trials, in general. On the other hand, a numerical method of predicting the thermoelectric properties +Corresponding author, E-mail: [email protected] of materials on the basis of theoretical calculations has been Energetic Stability and Thermoelectric Property of Alkali-Metal-Encapsulated Type-I Silicon-Clathrate from First-Principles Calculation 277 developed. If such a simulation is used to optimize the electrostatic potential at the farthest site from the dopant. This composition of the compound and estimate the maximum ZT, treatment can correct distortion of the band structure induced is would help to develop effective thermoelectric materials. by long-range interaction of an ionized dopant. ET(perfect:0) and In this study, several possible combinations of guest and ET(perfect:+1) are the total energy of the perfect cell when the substitutional atoms for the Type-I Si clathrate and their charge is neutralized and when one electron is removed, thermoelectric properties were systematically investigated respectively. The Fermi energy (¾F) in eq. (2) was measured using first-principles calculation. Alkali metals were consid- from the EVBM determined in eq. (3), and it can vary within ered as guest elements because thermoelectric properties in the band gap. Chemical potentials ®i of element i were alkali metal encapsulated Si clathrates have not been revealed calculated as per atom energy in each primitive cell. Si46 unit although their electronic structures were investigated.15) was used for the perfect cell throughout the calculation. It Reducing the number of substitutional elements is expected was confirmed that the difference in the formation energy to reduce the amount of alloy scattering of the carriers more between the unit cell and the 2 © 2 © 2 expanded supercell than using alkali earth elements for the guest elements would. was about 0.1 eV. This difference does not affect our results On the basis of the calculated thermoelectric properties, we and conclusion. will discuss the optimal composition of guest and substitu- After the structural relaxation, the detailed band structure tional atoms that maximizes ZT and whether ZT > 1 can be was further calculated using the all-electron method based on achieved for Si clathrate. the Full potential Linearized Augmented Plane Wave + Local Orbital (FLAPW+lo) approach implemented in the 20) 2. Computational Procedure WIEN2k code. Rkmax, determines the size of the basis set, was set to 7, which assures convergence of total energy to A plane-wave-basis projector augmented-wave (PAW) less than 0.01 meV/atom for Si46.A12© 12 © 12 k-point method implemented in Vienna ab initio simulation package mesh was used to sample the band energy within the (VASP) code16) was used for structural relaxation and precise Brillouin zone. The exchange-correlation functional was determination of the total energy. The exchange-correlation approximated using a GGA of EngelVosko formalism (EV- functional was defined using a generalized gradient approx- GGA),21) which is known to reproduce the bandgap of Si and imation (GGA) of the PerdewBurkeErnzerhof (PBE) is previously used for the first-principles calculation of the form.17,18) The plane-wave cutoff energy was set to 300 eV Seebeck coefficient of the Zn-substituted Ge-clathrate.22) throughout the calculation. The MonkhorstPack scheme19) On the basis of the band energies obtained at each k-point, was used for k-point sampling. The numerical error was the band energy was interpolated using a 6-times denser grid estimated to be 1 meV/atom for a Si46 unit cell on the basis than the original k-point mesh. The thermoelectric properties, of convergence tests of the cutoff energy and k-point mesh. including the Seebeck coefficient, electrical conductivity, A force of <10¹2 eV/¡ and a total change in energy of and electronic thermal conductivity were calculated by 10¹8 eV were selected as the convergence criteria