Jingyu
Li‡
a,
Wenya
Zhai‡
a,
Chi
Zhang
b,
Yuli
Yan
*a,
Peng-Fei
Liu
*cd and
Gui
Yang
e
aInstitute for Computational Materials Science, School of Physics and Electronics, International Joint Research Laboratory of New Energy Materials and Devices of Henan Province, Henan University, Kaifeng 475004, China. E-mail: yanyl@henu.edu.cn
bCollege of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China
cInstitute of High Energy Physics, Chinese Academy of Sciences (CAS), Beijing 100049, China. E-mail: pfliu@ihep.ac.cn
dSpallation Neutron Source Science Center, Dongguan 523803, China
eSchool of Physics and Electrical Engineering, Anyang Normal University, Anyang 455000, China
First published on 14th June 2021
Understanding the lattice dynamics and low thermal conductivities of oxychalcogenide materials is critical to the development of a new generation of better thermoelectric oxide materials. Here we systematically investigate the lattice vibrational modes as well as phonon thermal conductivity of experimentally synthesized layered oxychalcogenides BiAgOCh (Ch = S, Se, and Te). First-principles calculations indicate that BiAgOSe and BiAgOTe are dynamically stable and low-thermal-conductivity materials. The room-temperature lattice thermal conductivity for BiAgOTe is calculated to be 0.53 W m−1 K−1, which is smaller than that (0.88 W m−1 K−1) of the promising thermoelectric material BiCuOSe. The strong anharmonicity in BiAgOTe causes short lifetime and low group velocity, which accordingly gives rise to ultralow thermal conductivity in BiAgOTe compounds. Our work of the insights into the lattice dynamics and low thermal conductivity will help the development of high-performance thermoelectric oxide materials.
Recently, BiCuOSe oxyselenides have acquired ever-increasing attention as very promising thermoelectric materials due to their high value of ZT (1.5 at 900 K).7–12 The outstanding TE properties could be mainly ascribed to the intrinsically low thermal conductivity of BiCuOSe and its alloys.13–18 In previous studies, much attention has been paid to the lattice dynamics of BiCuOSe with first-principles calculations. The data on Ag-based compounds are still scarce in the literature. As the isomorphic crystals of BiCuOSe, Ag atoms have larger atomic radius and heavier atomic mass than Cu atoms, which enable BiAgOCh to exhibit large unit cell volumes and low thermal conductivity. The dual effects of lone pairs in Bi atoms and rattling vibrations in Ag atoms give BiAgOCh compounds weakly bonded [Bi2O2] and [Ag2Ch2] layers, which could lead to distinct interlayer interactions and further decrease the lattice thermal conductivity. To discriminate differences and understand the origin of the intrinsically low thermal conductivity for both BiAgOCh and BiCuOCh compounds, the study of the lattice dynamics in BiAgOCh compounds is of fundamental interest.
In this work, we investigate the phonon transport of BiAgOCh through solving the linearized phonon Boltzmann transport equation. The lattice thermal conductivity for BiAgOTe is calculated to be 0.53 W m−1 K−1 at room temperature, which is smaller than that for BiCuOSe (0.88 W m−1 K−1). The large Grüneisen parameters in the wide frequency range indicate strong anharmonicity in BiAgOTe. Besides, the compounds have low group velocities and short phonon lifetimes. The low-frequency optical modes contribute observably to the total thermal conductivity, while high-frequency optical phonons cannot be neglected. These features synergistically dominate the ultralow thermal conductivity of BiAgOTe.
The phonon dispersions and density of states (DOS) are calculated using density functional perturbation theory (DFPT) implemented in Phonopy code.22,23 In this process, the 3 × 3 × 2 supercell containing 144 atoms with a 3 × 3 × 2 k-mesh for the Brillouin zone sampling is used for second- and third-order force constant calculations. The lattice thermal conductivity using a single-mode relaxation-time (SMRT) method is obtained from the following formulae:24
(1) |
(2) |
(3) |
In this study, the phonon relaxation time is given by
τλSMRT τλ | (4) |
(5) |
In addition, the phonon mode contributions to the anisotropic κ are discussed using cumulative lattice thermal conductivity defined by
(6) |
This method above with the simulation package Phono3py code23 has been successfully applied to predicting the thermal conductivities of many other materials, such as ZrNiPb,25 BiTeBr,26 and TaCoSn27et al.
Fig. 1 (a) Schematic illustration of the layered BiAgOCh (Ch = S, Se, and Te) crystal structures. (b) Electron localization function of BiAgOCh projected on the (100) plane. |
Fig. 2 shows the phonon dispersion and vibrational DOS for BiAgOCh materials. All of the phonon frequencies of BiAgOSe and BiAgOTe are positive in the Brillouin zone, which indicates that the structures of the two materials are dynamically stable. For BiAgOS, these are a few negative modes around Γ, M, and A points. The highest cutoff frequencies are 15.74, 14.41, and 13.42 THz for BiAgOS, BiAgOSe and BiAgOTe, respectively, with the chalcogen atomic number increasing. In all compounds, the vibrations of O decoupled from other atoms and occupy the high-frequency optical region above about 6.73 THz, while the acoustic vibrations and the low-frequency optical branches are mainly from the Bi, Ag, and Ch atoms. Such distributions are primarily ascribed to the large mass difference between O and Bi/Ag/Ch atoms. In BiAgOS, there is no phonon gap in the range from 4 and 8 THz with weak coupling vibrations between O and S atoms. Meanwhile, a complete decoupling optic phonon gap appears in BiAgOSe and BiAgOTe and gradually increases when going from S to Se, and Te with the increasing mass. The mass homology relation can be employed to explain the above mode frequency difference.16 In particular, the mass of the unit cell Muc changes from 729.826 amu for BiOAgS to 920.896 amu for BiOAgTe, by a factor of 1.26. Therefore, the mode frequencies can be decreased by the factor if replacing the mass of S by that of Te. The change in the middle low-frequency region of the phonon dispersion is the reason for the formation of the optical–optical gap.
In order to analyze the origin of low lattice thermal conductivity in BiAgOCh, the phonon lifetime τ and Grüneisen parameters γ are calculated in Fig. 3. The three lowest phonon Grüneisen parameters and lifetime are shown in Fig. S2 (ESI†). The γ is a dimensionless quantity measuring the anharmonic interaction of a crystal, which can be obtained by31,32
(7) |
Fig. 3 Calculated Grüneisen parameters for (a) BiAgOS, (c) BiAgOSe, and (e) BiAgOTe. Phonon lifetime for (b) BiAgOS, (d) BiAgOSe, and (f) BiAgOTe. |
Generally, a system with large |γ| implies that it possesses strong anharmonicity and phonon–phonon scattering, resulting in short phonon relaxation time τ and low κ. Obviously, the BiAgOCh possess obviously large |γ| at low-frequency acoustic phonon modes (Fig. 3). This will generate strong phonon–phonon interaction, and thus lead to the low lattice thermal conductivity in BiAgOCh. Generally speaking, acoustic phonon modes dominate the lattice thermal conductivity. The tiny unstable acoustic phonon modes for BiAgOS and softened phonon modes for BiAgOSe along the Γ–M direction can be seen as the reason for strong anharmonicity in the low-frequency region. From Fig. 3(b), (d) and (f), the phonon lifetime of acoustic branches is higher than their optical modes for all materials. The τ of BiAgOSe at low frequency acoustic branches is apparently smaller than that of BiAgOTe and BiAgOS. In high-frequency optical branches, the phonon lifetime for BiAgOTe in a wide frequency range remains unaffected, which indicates that optical branches do not enhance the scattering channels for BiAgOTe.
The phonon velocities (υ) are closely relevant to the phonon transportation of BiAgOCh. In general, the reduced υ will lower κ. Herein we calculate the υ in Fig. 4. For all compounds, it is clearly seen that the group velocities of optical phonon modes are higher than those of acoustic modes. In BiAgOS and BiAgOTe, the group velocities along the x-direction are different from those along the z-direction, which leads to a strong anisotropy of lattice thermal conductivity. Among the three compounds, BiAgOTe possesses the lowest group velocities along both the x and z-direction. Combined with the above analysis, the slow speed of phonon, large phonon lifetime τ, and strong phonon anharmonicity will give an ultralow κ in BiAgOTe according to Slack's theory.33
Fig. 4 Phonon group velocities as a function of frequency for (a and b) BiAgOS, (c and d) BiAgOSe, and (e and f) BiAgOTe along x (left column) or z-direction (right column). |
The calculated lattice thermal conductivity of BiAgOCh as a function of temperature is shown in Fig. 5. BiAgOTe shows the lowest lattice thermal conductivity among the three compounds. The average lattice thermal conductivity is calculated to be 0.53 W m−1 K−1 at room temperature for BiAgOTe, which is lower than those of 2.35 W m−1 K−1 for PbTe,34 0.62 W m−1 K−1 for SnSe,35 0.88 W m−1 K−1 for BiCuSeO,36 and 0.82 W m−1 K−1 for MgAgSb.37 Meanwhile, its κ exhibits strong anisotropy. There are two reasons for this: (1) the acoustic branches and some optical branches present different dispersions along the Γ–Z and Γ–X directions, which causes an enormous difference in low group velocities along two different directions; (2) the atomic interactions along the z (weak electrostatic interactions) and x directions (strong covalent and ionic bonding interactions) are different. The weak electrostatic interactions along the z direction impede the phonon transport and result in low κ. For BiAgOS and BiAgOTe, the room temperature lattice thermal conductivities along z-directions are 0.20 and 0.11 Wm−1 K−1, which are much lower than the x-direction (2.43 and 0.74 Wm−1 K−1). In the case of BiAgOSe, the in-plane thermal conductivity is initially larger than the cross-plane value, decreases with raising the temperature, and becomes slightly lower than the cross-plane value after 200 K. In order to probe into its origin, we have calculated the band structures and density of states of BiAgOSe. As shown in Fig. S3 (ESI†), BiAgOS, BiAgOSe, and BiAgOTe are all indirect band gap semiconductors since the valence-band maximum (VBM) and conduction band minimum (CBM) locate at different points. The band edges changes and exhibit multi-valley features when going from S, Se, to Te. As for BiAgOSe, the VBM is along the Γ to M direction and the CBM is at the Z point. Although it shows a similar band structure as BiAgOS, the electronic transitions at the points along the Γ to Z direction easily occur with the smaller energy difference in BiAgOSe. From the density of states in Fig. S4 (ESI†), the Se p and Bi p electrons in BiAgOSe are highly delocalized in the VB and CB zones with sharp peaks. Such delocalized p electrons contribute to more orbital overlap along the out-of-plane direction for BiAgOSe, which endow BiAgOSe with 3D charge and accordingly quasi-3D phonon transports. Thus, BiAgOSe has quite different phonon transport among the three compounds.
The cumulative thermal conductivities along different directions first keep increasing quickly as frequency increases, and then gradually approach a plateau. In Fig. 5(b), (e) and (h), the peak of the derivatives drops rapidly at the high-frequency region because the acoustic phonon branches and the low-frequency optical phonon branches strongly coupled with acoustic modes dominate the lattice thermal conductivity of BiAgOCh. In the high-frequency region, it can be seen that the cumulative thermal conductivities of BiAgOS and BiAgOTe along the x-direction still increase further than that of BiAgOSe. This indicates phonons with a high-frequency region for BiCuOS and BiCuOTe along the x-direction have non-negligible contribution to the lattice thermal conductivity, which is different from most semiconductor materials.38–41
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1ma00375e |
‡ These two authors contributed equally. |
This journal is © The Royal Society of Chemistry 2021 |