Design Strategy for High Performance Thermoelectric Materials: the

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Design Strategy for High Performance Thermoelectric Materials: the Prediction of Electron Doped KZrCuSe3 Shiqiang Hao, Logan Ward, Zhongzhen Luo, Vidvuds Ozolins, Vinayak P. Dravid, Mercouri G. Kanatzidis, and Christopher Wolverton Chem. Mater., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on March 25, 2019

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Chemistry of Materials

Design Strategy for High Performance Thermoelectric Materials: the Prediction of Electron Doped KZrCuSe3 Shiqiang Hao,1 Logan Ward,1 Zhongzhen Luo,2 Vidvuds Ozolins,3 Vinayak P. Dravid,1 Mercouri G. Kanatzidis,2 and Christopher Wolverton1* 1 Department

of Materials Science and Engineering, Northwestern University, Evanston IL 60208

2 Department 3 Department

of Chemistry, Northwestern University, Evanston IL 60201

of Applied Physics, Yale University, New Haven, Connecticut 06511, and Energy Sciences Institute, Yale University, West Haven, Connecticut 06516 Abstract

Thermoelectric materials enable direct conversion of heat into electrical energy, providing a promising route for power generation and waste heat recovery. A very active research effort is ongoing to search for high performance thermoelectric systems including bulk materials and nano-composites. In this paper, we propose an efficient strategy for identifying thermoelectric materials with high figures of merit among the tens of thousands of known compounds from the Inorganic Crystal Structure Database (ICSD). The search strategy integrates several steps to find materials with very low lattice thermal conductivity and high power factor by the virtue of the coexistence of rattling atomic vibrations with favorable electronic band structures. Using our approach, we predict a very high figure of merit (ZT) in electron-doped KZrCuSe3 crystals along the crystallographic a-axis, with an estimated average over temperature ZTave of about 1.9 from 300 K to 1000 K. The overall ZTave performance of electron-doped KZrCuSe3 is better than most current state-of-the-art thermoelectric materials. Our work supplies not only a current urgent theoretical material prediction suggesting experimental confirmation but also a practical materials design strategy that is widely applicable in the search for improved thermoelectrics.

Introduction There has been extensive research interest in the thermoelectric field, driven by the current requirements for more efficient systems for energy conversion and power generation.1-4 The most important physical quantity that characterizes the thermoelectric conversion efficiency is the figure of *Corresponding

author: [email protected]

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merit ZT which is defined as 𝑍𝑇 = 𝜎𝑆2𝑇 𝜅, where

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σ is electrical conductivity, S See beck coefficient, 

thermal conductivity, and T temperature.5 According to the formula, we can consider either by maximizing the power factor (S2) or by minimizing the thermal conductivity to improve the figure of merit of the interested systems. Ideally, one would like to find a material that can be engineered to simultaneously possess and high power factor (σS2) and low thermal conductivity. The current research progress of nanostructured thermoelectrics has combined several cutting-edge approaches to improve ZT.6 The integrated approach incorporates important aspects to: 1) enhance Seebeck coefficients by electronic band structure convergence,7,8 2) keep carrier mobility high through minimizing the band energy offset between host materials and second phase precipitates,9-11 and 3) reduce lattice thermal conductivity through two phase nanostructuring to form atomic or nanoscale lattice disorder. On the other hand, the searching of pure bulk materials without nano-precipitates has been also very active. A recent outstanding example, SnSe, exhibits a super high ZT value (ZTmax=2.6) in the undoped case at a temperature range of ~723-973K in the b-crystal axis.12 Correspondingly,

the

hole-doped SnSe shows a significant ZT boost along the b axis from 0.1 to 0.7 at room temperature while keeping a large high temperature ZT maximum (ZTmax) of 2.0.13 Similarly, the analogous materials GeSe 14

and SnPbS215 are both computationally predicted to exhibit high average ZT performance of about 1.0

and 1.5 across the 300 to 800 K temperature range. In all these systems, one important reason for the high ZT is the enhancement of the power factor through multiband effects, which is achieved through the successful doping in single crystals. Additionally, these compounds possess intrinsically low lattice thermal conductivity due to unusual strong lattice anharmonicity and associated phonon scattering in their anisotropic crystal structures known as two-dimensional material with van der Waals gap.12 The search for materials with even lower lattice thermal conductivity and higher ZT is still very active.16-19 For example, CsAg5Te3 has recently been found to have super low total thermal conductivity ranging from 0.18 Wm–1K–1 to 0.20 Wm–1K–1 from 296 K to 727 K.20 On the one hand, the ultralow lattice thermal conductivity originated from the very strong lattice anharmonicity characterized by the large Gruneisen parameters, as described in the case of SnSe.12 On the other hand, a new type of “concerted rattling” vibrational modes plays a key role in lowering the lattice thermal conductivity of CsAg5Te3. These rattling vibrations can suppress the group velocity at multiple anti-crossing points in the phonon dispersion and simultaneously enhance the intensity of Umklapp processes, therefore strongly reducing the phonon contribution to the heat transport.28, 29 The localized rattling modes arise from one or more weakly bonded atom types, which can “rattle” in oversized cages within the crystal structure framework. A hallmark of these rattling atoms is their large atomic displacements.


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Drawing upon the lessons offered by the discovery of outstanding thermoelectric performance in p-type SnSe and CsAg5Te3, we formulate a design strategy to screen known compounds from crystallographic databases (such as ICSD) for prospective thermoelectrics with high power factors combining low lattice thermal conductivity. Several research groups have used high throughput calculations to predict thermoelectric performance of a large number of systems and then identify promising candidates for thermoelectrics.21,22 However, due to complex properties and associated computational expense required for these searches, some properties e.g. lattice thermal conductivity have to be calculated using simplified models. Moreover, the electron and hole mobilities and Seebeck coefficients are calculated using highly approximate methods (i.e., constant relaxation time approximation). In this work, we propose a strategy for predicting high thermoelectric performance on the basis of the physical origins of previous very successful materials. Particularly, we stress on the discovery of a set of attributes of crystal structures, phonon dispersions and electronic band structures, from which we can identify good thermoelectrics. We use this set of attributes (“descriptors”) to theoretically identify KZrCuSe3 as a compound with highly promising thermoelectric performance; the validity of our predictive framework is verified by detailed calculations of the transport properties including power factors and thermal conductivities. Our set of attributes can be used to quickly screen materials based on the data available in material databases and, thereby, accelerate the progress of rational materials discovery.

Screening Strategy Our screening strategy is designed to identify, without performing any new experimental measurements or DFT calculations, materials that possess electronic and vibrational properties similar to known thermoelectrics. In particular, we focused on finding materials with characteristics similar to SnSe and CsAg5Te3 using three distinct criteria, which are described below. Band Gap Energy: To find materials likely to exhibit suitable band gap energies, we queried the Open Quantum Materials Database (OQMD) to find materials with band gap greater than 0 and less than 1 eV. According to the OQMD, CsAg5Te3 has a band gap energy of 0.2 eV. In order to refine this search to only materials that have been observed experimentally, we limited this search to materials listed in the Inorganic Crystal Structure Database (ICSD). This screen limited our search from the 34795 structures in both the ICSD and OQMD down to only 2781 materials. Vibrational Properties: Our next step was to refine this list of small band gap materials to those likely to have low thermal conductivity. While it is certainly possible to accurately predict thermal conductivity from first-principles,16,23-26 evaluating the thermal conductivity of the 2781 materials



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identified based on our band gap screen is beyond what is practical currently (the largest high-throughput screen22 is smaller by an order of magnitude). Rather than attempting to compute thermal conductivity, we focused on three heuristics: the presence of rattling atoms, mass contrast, and unit cell complexity. The initial screening step aimed to detect the presence of rattling atoms using data from the ICSD. Rattling atoms in a structure have much larger vibrational amplitude than their neighboring atoms, which reduces phonon lifetimes by the Umklapp scattering and thus reduces the mean free path and thermal conductivity.20 In order to identify materials with rattling atoms, we computed the ratio between the largest (Bmax) and the smallest thermal displacement factors (Bmin) of each atom in the structure. Since these factors describe the effect of the atomic vibrations on the measured x-ray diffraction pattern,27 they are often determined during structure solution and are available in the ICSD for many of our candidate materials. Because too large an asymmetry in vibrations can interfere with electrical conductivity (as in skutterudites), we sought to find materials with a

𝐵𝑚𝑎𝑥 𝐵𝑚𝑖𝑛

close to that of CsAg5Te3 (2.46).

Previous studies have clearly demonstrated that there is a correlation between mass contrast and lattice thermal conductivity.28,29 Generally speaking, higher mass contrast often coincides with lower thermal conductivity. The reasons are that the maximum frequency of the acoustic branches is suppressed by the heavier masses and the dispersion of the optical branches is flattened by reduced coupling due to mass contrast; both effects decrease the phonon group velocities and thus lower the lattice thermal conductivity. To characterize materials by their mass contrast, we simply computed the ratio between the atomic mass of the heaviest and lightest elements in the chemical formula. Even though the mass contrast of CsAg5Te3 is relatively small (MCs/MAg=1.23) in comparison with PbTe (MPb/MTe=1.63), in conjunction with other factors it appears to be sufficiently high to produce low thermal conductivity. Just like high mass contrast, complex crystal structures with

large atom numbers

in the unit cell

also tend to have low thermal conductivities. This effect is attributed to the size of the Brillouin zone decrease

and the associated suppression of the acoustic frequencies and flattening of the optical

branches due to the prevalence of zero group velocities at the zone boundaries. The atomic numbers of the primitive cell of a material can be trivially computed using the crystal structure analysis tools and data available in the OQMD. For comparison, CsAg5Te3 contains 36 atoms in the primitive cell. Multiband effects: Inspired by the high Seebeck coefficients of doped SnSe induced by multiband effects,13 we also screened materials by examining the computed electronic density-of-states (eDOS) near the valence band maximum (VBM) and conduction band minimum (CBM). High eDOS suggests the possibility of high degeneracy of electronic bands and thus large Seebeck coefficients. In addition,


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multiband contributions with different effective masses do not decrease electronic conductivity since the lighter carriers still form the major contribution to conductivity. In order to measure this parameter, we assess the eDOS from the OQMD and screen for materials with a large eDOS close to the edges of the valence and conduction bands.

Results Results of Screening Steps Considering all of the criteria discussed in the previous section, we identify KZrCuSe3 as one of interesting candidate thermoelectric materials.30 It has an exceptionally large mass contrast of 2.33 and a somewhat complex unit cell (12 atoms) in the Cmcm space group, which are both favorable for a low thermal conductivity. Additionally, the ratio between the maximum and minimum thermal factors for the atoms in the unit cell of KZrCuSe3 is 1.94, which is similar to that of CsAg5Te3 and suggests the possibility of anharmonic rattling modes. Finally, this material also has a rapidly varying electronic density of states near the band edges. Because of this exciting combination of attributes in KZrCuSe3, we validate the feasibility of this material as a thermoelectric using detailed DFT calculations. Phonon dispersion and lattice thermal conductivity of KZrCuSe3 We utilize the compressive sensing methods25 to evaluate vibrational contributions to the lattice thermal conductivity of KZrCuSe3. The Grüneisen parameter is a very good type of quantity to reflect the dependence of the change of vibrational frequency upon the crystal structure volume variation. It is useed to evaluate the lattice anharmonicity and thus useful to understand the physical nature of the lattice thermal conductivity behavior. We use first-principles based calculations within the quasi-harmonic approximation to calculated the phonon and Grüneisen dispersions. Generally speaking, the compressive sensing lattice dynamics (CSLD) methods for lattice thermal conductivities are much more comprehensive than the simpler Debye-Callaway model. Due to inclusion of all vibration models in lattice thermal conductivity calculations, the compressive sensing results are relative more accurate than the Debye-Callaway results but also very expensive.



Figure 1. Calculated phonon and Grüneisen dispersions, phonon density of states, and lattice thermal conductivity. (a) Phonon dispersions of KZrCuSe3 at equilibrium volume V0 (solid lines) and at isotropically compressed volume 0.98 V0 (dashed lines). The transverse acoustic phonon modes are plotted in red and green color and the longitudinal acoustic phonon branches are labeled in blue lines. (b) Projected phonon density of states at equilibrium volume V0 (c) Grüneisen parameters. (d) Projected phonon density of states at compressed volume 0.98 V0. The first Brillouin zone high symmetry points can be found in Figure 2(f). (e) Lattice thermal conductivity. (f) Atomic structure of KZrCuSe3.

Based on our design criteria, we can evaluate the phonon dispersion of KZrCuSe3 and the phonon density of states (DOS). The phonon and Grüneisen dispersions are plotted in Figs. 1(a) and (c). Based on the phonon dispersion plots, we can evaluate the longitudinal Debye temperature by Θ = 𝜔𝐷 𝑘𝐵 (𝜔𝐷 and 𝑘𝐵 are respectively

the largest acoustic frequency and Boltzmann constant). For the phonon

velocity, we calculate the slope of the acoustic phonon branches around the Γ point. Generally speaking, a lower phonon velocity and longitudinal Debye temperature are indicatives of lower lattice thermal conductivities. For KZrCuSe3, the average phonon velocities along Γ-X, Γ-Z and Γ-Y are relatively low, calculated to be 1533, 1892, and 1611 m/s, respectively. The phonon DOS shows several peaks at low


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frequencies, which can be attributed to vibrations of predominantly Zr (32cm-1), K (65 cm-1) and Se (32cm-1). It can be seen from Figs.1 (b) and (d) that the K and Zr peaks shift strongly with increasing volume, suggesting that the K and Zr atoms are very sensitive to volume change and signaling the possibility that both K and Zr are rattling atoms. In contrast to the traditional rattling compounds, where only one kind of

rattling atom undergoes large vibrations in an oversized cage, the rattling modes in

KZrCuSe3 involve both the K and Zr atoms, and we thus call these modes “double rattling”. Besides the double rattling vibrations, another interesting feature of KZrCuSe3 phonon dispersion is the strong variation of the TA’ and low-lying optical modes upon volume change, as shown in Fig.1(a) by solid and dashed lines. This strong variation of the TA’ frequency with volume indicates extremely large Grüneisen parameters in both the Γ-X direction and Γ-Y direction with average values of about 9.1 and 12.3, respectively. Thus, we have indications of strong anharmonicity and rattling modes, both suggestive of low lattice thermal conductivity. Hence we use CSLD further explore the properties of KZrCuSe3

25

to calculate anharmonic force constants and Boltzmann transport theory to calculate lattice

thermal conductivity.26 By automatically constructing high-order anharmonic lattice Hamiltonians from DFT calculations, CSLD is more general and straight-forward than the other first-principles methods for treating anharmonicity, while requiring modest computational resources. As shown in Fig.1(e), the lattice thermal conductivity is very low approximately 0.7 W m-1 K-1 at 300 K, and decreasing to 0.3 W m-1 K-1 at 700 K. This very low frequency of optical modes are thus important in lattice thermal conductivity calculations as mentioned in previous literatures.31,32 The very low lattice thermal conductivities have been confirmed by experimental observations as shown in the Supporting Information Fig.S2. Electronic Thermoelectric Properties of KZrCuSe3 Having established the favorable low lattice thermal conductivity, we now turn our attention to the calculated electronic transport properties including electrical conductivity, electronic contribution to the thermal conductivity and Seebeck coefficient, which are shown in Figs. 2(a)-(c). For a given value of carrier concentration and relaxation time, the electrical conductivity and Seebeck coefficient can be evaluated by the Boltzmann transport theory as illustrated in the Supporting Information section. Fig. 2(a) shows the a axis KZrCuSe3 Seebeck coefficients for four levels of the carrier concentrations. The Seebeck coefficients of KZrCuSe3 at different doping levels are plotted in Fig. 2(a) as a function of temperature. It is clear that for relatively low carrier concentrations (e.g. 51018 and 11019 cm-3), the Seebeck coefficient decreases with increasing temperature. While for relative high carrier concentrations (e.g. 51019 and 11020 cm-3) the decreasing trend is much slower. The conduction band at Γ-Y exhibits hole-like behavior (negative curvature), which significantly reduces electron transport especially at high temperature and low electron concentrations. For high electron concentrations, this part of hole like contribution becomes



not so important, so the Seebeck decreasing trend is much slower. It is also interesting to compare the Seebeck coefficients of electron doped KZrCuSe3 with hole doped SnSe at the same carrier concentration and temperature. Generally speaking, the calculated KZrCuSe3 Seebeck coefficients are much higher than those of SnSe sample at the same range of carrier concentrations. For example, at 51019 cm-3 and 300K, the Seebeck coefficient of KZrCuSe3 is around -285 V/K, which is much larger than that of hole doped SnSe of 160 V/K.13 Even at 700 K, the absolute values of Seebeck coefficients of two systems are almost the same. These large Seebeck coefficients of KZrCuSe3 are another promising of the good thermoelectric properties of this compound. However, for the transport properties, at this time we cannot confirm theoretical predictions experimentally due to desired electron carrier concentrations in KZrCuSe3 are not achievable. It needs to mention that the thermoelectric properties calculated by Boltzmann transport are using an approximation of constant relaxation time. However, the constant relaxation time is generally different and ranging from several to tens seconds for different systems. Moreover, it is very difficult and time consuming to get the exact relaxation time for a specific system. Hence, we consider three examples to present a range of thermoelectric property at certain carrier concentrations and temperatures.


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Figure 2 .Calculated thermoelectric properties of KZrCuSe3 a axis. (a) Seebeck coefficients at four level of electron concentrations. (b) Corresponding normalized electronic conductivities at different electron concentrations. (c) Normalized electrical thermal conductivity at different electron concentrations. (d) Figure of merit ZT at 51019 cm-3 and different relaxation time. (e) Figure of merit ZT at 11020 cm-3 and different relaxation time. (f) Electronic band structure of KZrCuSe3 and Fermi level at four doping levels. The intrinsic Fermi level is shown as dashed line at 0 eV. Other Fermi energy lines located between 0 and 0.5 eV are corresponding to the electron doped concentration of 51018, 51019, and 11020 cm-3, respectively, suggesting that the heavily doping pushes the Fermi energy deeply into the second conduction band. The first Brillouin zone high symmetry points of orthorhombic Cmcm structure are plotted in inset figure.

Band structure and effective mass of KZrCuSe3 To further explore the physics of the KZrCuSe3 thermoelectric behavior, we show the electronic band structure of the Cmcm structure. Firstly, the band gap of KZrCuSe3 is calculated as 0.19 eV, which agrees very well with our experimental measured value of 0.22 eV shown in the Fig.S3. Figure 2(f) shows the DFT band structure of KZrCuSe3. The CBM locates at the Γ point with a second CBM close in energy lied at the Y point. These two CBM energy difference is about 0.04 eV, which is even smaller than the



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corresponding energies for SnSe (about 0.06 eV)13 and in PbTe (0.15 eV).33 With doping, the Fermi level can easily cross this tiny energy difference from Γ to Y. This multiple conduction bands of KZrCuSe3 with similar energy differences to SnSe and GeSe crystals is a distinctive band structure feature, which will induce multi-band effect for high electronic transport properties. In order to further understand the physical origin of the relative high Seebeck coefficients, we compare our calculated effective masses of the top two conduction band minima with the experimental measured effective masses of hole doped PbS, PbSe, PbTe and our previous work on SnSe. For PbS and PbSe, both the transverse effective mass and the longitudinal mass are very small. They are respectively mL*=0.068 m0 (k vector along the Γ-L direction, where m0 is the free electron mass), mT*= 0.064 m0 for PbSe and mL*=0.075 m0, mT*= 0.105 m0 for PbS.34 For PbTe, the values are also as small as mL*=0.31 m0 mT*= 0.22 m0.34 For KZrCuSe3, the effective masses exhibit anisotropic behavior at each local conduction band minimum with a larger value in the kz direction (c-axis) than both in-plane directions of kx and ky (a and b-axes). Interestingly, for the lowest conduction band minimum in the Γ-Z direction, the calculated effective masses are mkz*=0.41 m0, mkx*=0.08 m0, and mky*=0.13 m0, which are much heavier than those of PbS and PbSe. While, for the second minimum at the Y point band structure, the mkz*=0.22 m0, mkx*=0.03 m0, and mky*=0.18 m0 are lighter than those for the first minimum. Due to the effective mass is proportional to Seebeck coefficient, the heaver electrons from the first band

induce in larger the

Seebeck coefficients. On the other hand, the light electrons from the second conduction band involved in transport and improve electronic conductivity. The coexistence of heavy and light carriers from the first and second conduction band pockets in KZrCuSe3 is qualitatively very similar to the mechanism that is proposed to operate in SnSe, where both the first and second valence band carriers involved in transport have very impressive power factors.13 The higher carrier mobility of n-doped of KZrCuSe3 together with multi-band effects on improved Seebeck coefficient contributed to the very high ZT performance. For the electronic conductivities and electrical thermal conductivities, it is reasonable to assume that Wiedemann-Franz law is obeyed and that the electrical conductivity is proportional to the electrical thermal conductivity , as shown in Figs. 2(b)-(c). It is not straightforward to compare these values with experimental data of SnSe, since the relaxation time information is missing. However, we still can evaluate the ZT values by giving a range of estimated relaxation time, in such a way we avoid to compare electronic conductivities or electrical thermal conductivities individually but summarize all effects together including low lattice thermal conductivity into ZT values. It is known that the relaxation time depends on the carrier concentration and temperature as a simple model of = CT-1n-1/3,35 suggesting that the higher the temperature, the shorter the relaxation time. This trend is also confirmed by fitting the available experimental SnSe data from 27 fs at 300 K to 5fs at 750K.14 As shown in Fig.2(d), we plot ZT


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as a function of temperature for three constant relaxation times 20,10 and 5 fs, for a carrier concentration of 51019 cm-3. We can expect relaxation times roughly range within 20 to 5 fs from 300 to 1000K, and use these values to estimate ZT would. According to this estimation, the average ZTave from 300-1000K would be about 1.8. Similarly, at the carrier concentration of 11020 cm-3, the estimated ZT is very flat with a maximum 2.2 at 650 K as plotted in Fig.2(e) and an average ZTave about 1.9. This ZTave for KZrCuSe3 is higher than SnSe, over a large temperature range, and hence we predict an electron-doped KZrCuSe3 single crystal as an extremely promising candidate for high thermoelectric performance.

Conclusion We present a computational search strategy for thermoelectric materials with high figure of merit (ZT) using existing databases such as ICSD and OQMD. We first screen desired materials by the ratio of thermal displacement factor to find candidate compounds that could host rattling atoms. We then refine the candidates by considering compounds with high mass contrast, complex (i.e., large) primitive cells, and semiconducting band structures with the band gap in the range from 0 to 1 eV. From the electronic point of view, we further screen the compounds for high electronic density-of-states around the Fermi level, which is favorable for creating high power factors and Seebeck coefficients due to multiband effects. On the basis of our screening strategy, we identify KZrCuSe3 as a candidate high-performance thermoelectric with a “double rattler” K and Zr behavior, strong anharmonicity, and optical mode induced suppression of acoustic frequencies, which combine to yield a very low predicted lattice thermal conductivity. Similarly to the well-known SnSe system, multiband effects in the conduction band of KZrCuSe3 play an important role in creating high Seebeck coefficients at elevated temperatures and moderately high n-type carrier concentrations. The low lattice thermal conductivity together with high Seebeck coefficients contributes the high figure of merit of this material.

Supporting Information Calculations methods of phonon dispersion, lattice thermal conductivity and transport properties, experimental methods and experimental lattice thermal conductivities.

Acknowledgement This material is based upon work supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0014520. Thanks for advice and expertise on compressed sensing calculations from Prof. Ozolins. VO was supported by the US Department of Energy, Office of Science, Basic Energy Sciences under grant No. DE-FG02-07ER46433. Access of QUEST, the supercomputer resource facilities at Northwestern University is acknowledged.



Notes The authors declare no competing financial interest.

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Design Strategy for High Performance Thermoelectric Materials: the

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