Ultralow Thermal Conductivity and High-Temperature Thermoelectric Performance in n-Type K2.5Bi8.5Se14

Article abstract of DOI:10.1021/acs.chemmater.9b02327

We studied the narrow band-gap (0.55 eV) semiconductor K_2.5Bi_8.5Se₁₄ as a potential thermoelectric material for power generation. Samples of polycrystalline K_2.5Bi_8.5Se₁₄ prepared by spark plasma sintering exhibit exceptionally low lattice thermal conductivities (κ_lat) of 0.57-0.33 W m^-1 K^-1 in the temperature range of 300-873 K. The physical origin of such low κ_lat in K_2.5Bi_8.5Se₁₄ is related to the strong anharmonicity and low phonon velocity caused by its complex low symmetry, large unit cell crystal structure, and mixed occupancy of Bi and K atoms in the lattice. High-resolution scanning transmission electron microscopy studies and microanalysis indicate that the K_2.5Bi_8.5Se₁₄ sample is a single phase without intergrowth of the structurally related K₂Bi₈Se₁₃ phase. The undoped material exhibits an n-type character and a figure-of-merit (ZT) value of 0.67 at 873 K. Electronic band structure calculations indicate that K_2.5Bi_8.5Se₁₄ is an indirect band-gap semiconductor with multiple conduction bands close to the Fermi level. Phonon dispersion calculations suggest that K_2.5Bi_8.5Se₁₄ has low phonon velocities and large Grüneisen parameters that can account for the observed ultralow κ_lat. The degree of n-type doping can be controlled by introducing Se deficiencies in the structure, providing a simple route to increase the ZT to ～1 at 873 K.

Full text of DOI:10.1021/acs.chemmater.9b02327

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Article
Ultralow Thermal Conductivity and High Temperature
Thermoelectric Performance in n-Type K2.5Bi8.5Se14
Zhong-Zhen Luo, Songting Cai, Shiqiang Hao, Trevor P. Bailey, Xiaobing Hu, Riley
Hanus, Runchu Ma, Gangjian Tan, Daniel G. Chica, G. Jeffrey Snyder, Ctirad Uher,
Christopher Wolverton, Vinayak P. Dravid, Qingyu Yan, and Mercouri G. Kanatzidis
Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.9b02327 • Publication Date (Web): 11 Jul 2019
Downloaded from pubs.acs.org on July 12, 2019
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Ultralow Thermal Conductivity and High
Temperature Thermoelectric Performance in
n-Type K Bi Se
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.5 8.5
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Zhong-Zhen Luo, Songting Cai, Shiqiang Hao, Trevor P. Bailey, Xiaobing Hu,
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Riley Hanus, Runchu Ma, Gangjian Tan, Daniel G. Chica, G. Jeffrey Snyder,
Ctirad Uher, Christopher Wolverton, Vinayak P. Dravid, Qingyu Yan, * Mercouri
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1,
2
,
G. Kanatzidis *
1School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang
Avenue 639798, Singapore
2Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
3Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois
6
0208, United States
4Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
5Department of Materials Science and Engineering, NUANCE Center, Northwestern University,
Evanston, Illinois 60208, United States
6State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan
University of Technology, Wuhan, 430070, China
ABSTRACT
We studied the narrow bandgap (0.55 eV) semiconductor K Bi Se , as a potential
2
.5 8.5
14
thermoelectric material for power generation. Samples of polycrystalline K Bi Se
14
2
.5 8.5
prepared by spark plasma sintering exhibit exceptionally low lattice thermal
−
1
−1
conductivities (κ ) of 0.57 − 0.33 Wm K in the temperature range of 300 − 873 K.
lat
The physical origin of such low κlat in K Bi Se is related to the strong
2.5
8.5
14
anharmonicity and low phonon velocity caused by its complex low-symmetry, large
unit cell crystal structure and mixed-occupancy of Bi and K atoms in the lattice.
High-resolution scanning transmission electron microscopy (HRSTEM) studies and
micro-analysis indicates that the K Bi Se sample is a single phase without
2.5 8.5
14
intergrowth of the structurally related K Bi Se phase. The undoped material exhibits
2
8
13
n-type character and a figure of merit (ZT) value of 0.67 at 873 K. Electronic band
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structure calculations indicate that K Bi Se is an indirect bandgap semiconductor
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with multiple conduction bands close to the Fermi level. Phonon dispersion
calculations suggest K Bi Se has low phonon velocities and large Grüneisen
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.5 8.5
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parameters that can account for the observed ultralow κ . The degree of n-type
lat
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doping can be controlled by introducing Se deficiencies in the structure providing a
simple route to increase the ZT to ~1 at 873 K.
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INTRODUCTION
Thermoelectric materials can achieve direct conversion of heat to electrical power and
can play an important role in increasing energy utilization efficiency, harvesting waste
heat and producing power in places where neither solar cells not windmills can. The
conversion efficiency of a thermoelectric material depends on the dimensionless
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figure of merit, ZT = S σT/(κ + κ ), where S, σ, T, κ and κ are the Seebeck
lat
ele
lat
ele
coefficient, electrical conductivity, absolute temperature, lattice and charge carrier
thermal conductivity, respectively.1-2 The most fundamental challenge of obtaining a
2
high ZT is attaining the simultaneous enhancement in power factor (PF, S σ) and
reduction in total thermal conductivity (κ = κ + κ ).
tot
lat
ele
Research efforts in developing good thermoelectric materials include enhancing
power factor and reducing κ . The power factor can be enhanced via the electronic
lat
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band structure engineering (eg. band convergence, resonant states, gap states, Fermi
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level pinning, multiple bands, and band alignment using secondary phases ). The
hierarchical architectures on all length scales (eg. solid-solution alloying,9-11
nanostructures,1, 12 grain boundaries, off-center atoms,
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14-15
and defect engineering16)
can reduce κ . Another strategy is to discover entirely new materials with
lat
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intrinsically low κ and favorable electronic structures.
lat
In general, materials with very low κlat are those that exhibit intrinsic bond
anharmonicity, anisotropic structures,17, 19-21 complex crystal structures, relatively
low-symmetry and large unit cells,23-24 heavy constituent elements,25-26 atomic
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disorder, metals with stereochemically active lone-pairs of electrons,
“rattler”
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vibrations, etc. Thus, studying materials with such attributes is a promising strategy
to identify new advanced thermoelectrics.
The Bi-/Sn-based chalcogenide semiconductors with stereochemically active
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34-42
34, 43
BiSe,44
lone-pair of electrons, such as CsBi Te , K Bi Se ,
K Bi Se ,
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AgBi S , AgBiS2,46 SnSe,47-48 etc., have emerged as a promising family of
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thermoelectric materials, owing to their ultralow κ . Recently, high ZT ~1.3 at 873 K
lat
for the monoclinic β-K Bi Se based material has been attained by Cl doping.
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However, its synthetic process is tedious, including long reaction time (~21 days),
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high energy-consuming, and complex multi-step reactions. Moreover, the second
phase (~20-30% K Bi Se ) often co-exist in the β-K Bi Se sample, which makes
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it complicated for the study of the intrinsic thermoelectric properties of pure
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β-K Bi Se . Like β-K Bi Se , the second phase, K Bi Se , also has a
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low-symmetry complex monoclinic crystal structure and a large unit cell with two
+
different interconnected types of Bi/Se building blocks and K atoms in tunnels,
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showing low κ at T < 300 K.
lat
In this work, we focus of pure single phase samples of n-type K Bi Se and
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.5 8.5
14
Se deficient samples, and assessed the charge transport, thermal transport and
thermoelectric properties as a function of temperature.34 We find that undoped
−1 −1
polycrystalline n-type K Bi Se samples show an ultralow κ of 0.35 Wm K
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.5 8.5
14
lat
and a ZT value of ~0.67 at 873 K. We report elastic measurements which reveal low
−
1
average phonon velocities, v (1610 ms ), small Young’s modulus, E (35.8 GPa),
a
large Grüneisen parameter, γ (1.96) and low Debye temperature, Θ (126 K), in
D
agreement with the phonon dispersion calculations and consistent with the ultralow
κlat. Furthermore, we demonstrate controlled electron doping by introducing Se
deficiencies, of the type K Bi Se14-x, which improves the power factor and yields a
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.5 8.5
ZT value of ~1 at 873 K.
EXPERIMENTAL SECTION
Raw materials. The starting materials used were Bi shot (99.999%, American
Elements, USA), Se pieces (99.99%, American Elements, USA), K chunks (99.99%,
Aldrich Chemical Co., USA). K Se was synthesized by a stoichiometric reaction of K
2
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1, 49
and Se (with Se excess of 0.5%) in liquid NH as described elsewhere.
3
Synthesis of K Bi Se14−x. Ingots were synthesized according to the nominal
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.5 8.5
compositions of K Bi Se (x = 0, 0.007, 0.021, 0.042, 0.063, 0.07, and 0.105)
14−x
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.5 8.5
mixing the K Se, Bi and Se in 13 mm diameter carbon-coated quartz tubes under an
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N -filled glove box. The tubes were evacuated to ~2 × 10 Torr and flame-sealed.
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Then, the sealed quartz tubes were slowly heated to 1023 K over 15 h and soaked at
this temperature for one day, then quenched in water. For a typical experiment, the
following amounts were used: K Se (0.7 g, 4.45 mmol), Bi (6.3297 g, 30.29 mmol),
2
and Se (3.5814 g, 45.36 mmol) to prepare a ~10.6 g ingot of K Bi Se13.979.
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Band gap measurement. To probe the band gap of K Bi Se , the optical diffuse
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reflectance measurement was performed on finely ground powder by using a Nicolet
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700 FT-IR spectrometer. The spectra were collected in the mid-IR region of 6000 −
−1
00 cm at room temperature. The optical band gap was calculated from reflectance
data using Kubelka-Munk function.41
Scanning Electron Microscopy (SEM) and Transmission electron microscopy
TEM. Scanning/transmission electron microscopy ((S/TEM) and STEM energy
dispersive spectroscopy (EDS) experiments investigations were carried out using an
aberration-corrected JEOL ARM200F microscope operated at 200 kV. The thin TEM
specimens were prepared by conventional methods, including cutting, grinding,
dimpling, tripod, with minimal duration of Ar-ion milling (2.8 kV for ~2 hours until a
hole is formed in the specimen, followed by ion cleaning with 0.3 kV) with a liquid
N cooling stage.
2
Spark plasma sintering (SPS). The obtained ingots of K Bi Se were
14−x
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.5 8.5
hand-ground to a fine powder using agate mortar and pestle. Then, the fine powders
were filled into a 12.7 mm diameter graphite die and densified by using the SPS
technique (SPS-211LX, Fuji Electronic Industrial Co. Ltd.) at 773 K with an axial
compressive stress of 40 MPa for 10 min under vacuum. The resulting
cylindrical-shaped pellets had high theoretical density (> 97%).
Electrical transport properties measurements. The electrical conductivity and
Seebeck coefficient were simultaneously determined by an Ulvac Riko ZEM-3 system
under a low-pressure helium atmosphere from 300 K to 873 K. For intrinsic
K Bi Se , two different directions: one along the primary surface of the pellets and
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.5 8.5
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perpendicular to the SPS pressing direction (K Bi Se -), and the other along the
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.5 8.5
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SPS pressing direction and perpendicular to the primary surface of the pellets
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(
K Bi Se -) were tested. For K Bi Se
samples, the only direction of along
14-x
2.5 8.5
14
2.5 8.5
the primary surface of the pellets and perpendicular to SPS process direction was
tested. All samples have the dimensions of approximately 11 mm × 3 mm × 3 mm.
Before the ZEM-3 measurement, a thin layer (0.1 – 0.2 mm) of boron nitride was
spray coated on the surface of the bars to avoid evaporation of Se and to protect the
instruments. The estimated uncertainties of the Seebeck coefficient and electrical
conductivity measurements are ~3% and 5%, respectively.50
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Hall measurements. The temperature-dependent Hall effect measurement was
completed with an AC 4-probe method in a homemade system with excitation fields
of ± 0.5 Tesla. The specimens were polished with the size of ~1 mm × 3 mm × 8 mm.
The homemade system uses an air-bore, helium-cooled superconducting magnet to
generate the field within a high temperature oven that surrounds the Ar-filled sample
probe. The estimated error is based on the standard deviation of several data points at
a single temperature. The carrier concentration (n) was calculated from the Hall
coefficient assuming a single carrier, i.e. n = 1/(e|R |), where e is the electron charge
H
and R is the Hall coefficient, with the error propagated from the Hall coefficient. The
H
Hall mobility (µ ) was determined as µ = σR .
H
H
H
Thermal conductivity measurements. The thermal diffusivity (D) was measured in
the temperature range 300 K to 873 K using a Netzsch Laser Flash Analysis (LFA)
4
57 instrument under a continuous N flow. The Cowan model with pulse correction
2
3
was used for data analysis. The samples with dimensions of ~10 × 10 × 1.5 mm were
measured in the same directions as the electrical transport properties measurement.
The rectangular samples were coated with a thin layer of graphite to prevent the
emissivity of the material during the measurement. The total thermal conductivity was
calculated with the relationship κ = D·C ·ρ, where specific heat capacity is determined
p
according to the Dulong-Petit approximation, C = 3R/푀 (R is the ideal gas constant,
p
and 푀 is the average molar mass of each element) and ρ is the density (calculated
using the sample’s geometry and mass). Considering the estimated uncertainty of
measurements from D (5%) and ρ (5%), the combined uncertainty associated with the
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measurements for the determination of ZT is about 20%.
Speed of sound measurements. The speeds of sound were measured by the
pulse-echo method where a piezoelectric transducer coupled to the sample first sends
the initial stress-wave pulse, and then acts as receiver measuring the echoed
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ultrasound reflection.51 The delay time, t , between subsequent reflections was
d
determined by maximizing the cross-correlation of the two reflections as follows. If
σ (t) is the amplitude of reflection N, then ∑ 휎 (푡)휎
(푡 ― 푡 ) is maximized by
푑
N
푁
푁 + 1
푡
varying t . The corresponding value of t along with the sample thickness, h, were
d
d
used to calculate the speed of sound, 푣퐿,푇 = 2ℎ/푡 . A longitudinal transducer
푑
(measuring v ) with a principle frequency of 5 MHz (Olympus V1091) and a
L
transverse transducer (measuring v ) at 5 MHz (Olympus V157-RM) were used with a
T
Panametrics 5072PR pulser/receiver. A Tektronix TBS 1072B-EDU oscilloscope was
used to record the waveforms. A typical waveform contained around four reflections
(3 delay time measurements), and the measurements from a minimum of three
waveforms (corresponding to 9 individual speed of sound measurements) were
averaged. A single crystal of yttrium aluminum garnet (YAG) with known properties
was used to determine that measurements of the speed of sound on this home-built
system have an accuracy of better than 0.6%. The values for the average speed of
sound v , Young’s modulus E, Poisson’s ratio v , Grüneisen parameter γ, and Debye
a
p
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temperature Θ were computed using the equations given by Pei et al.
D
Band structure calculations. Density functional theory (DFT) calculations of
pristine K Bi Se were carried out. The calculations were performed using the
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.5 8.5
14
generalized gradient approximation with PBE52 functional for the
exchange-correlation functional and projector-augmented wave potentials as
53
implemented in Vienna Ab initio Simulation Package (VASP). All structures are
fully relaxed with respect to cell vectors and cell-internal positions. The total energies
were numerically converged to approximately 3 meV/cation using a basis set energy
cutoff of 450 eV and dense k-meshes corresponding to 4000 k-points per reciprocal
atom in the Brillouin zone.
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RESULTS AND DISCUSSION
Crystal structure. K Bi Se crystallizes in the low-symmetry monoclinic space
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group P2 /m (No. 11) with a = 17.534(4) Å, b = 4.206(1) Å, c = 21.387(5) Å, β =
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09.65(2)°. K Bi Se has a complex three-dimensional (3D) anionic framework
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made up of two different types of Bi/Se polyhedral building blocks, NaCl- and
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Bi Te -type fragments, which are highlighted by the blue squares, Figure 1. The
2
3
Bi Te -type rods are arranged one by one to form layers parallel to the a-axis. Then,
2
3
the NaCl-type rod-like fragments connect the layers to build a 3D framework with K+
in the channel, Figure 1. The widths of the NaCl- and Bi Te -type blocks are three
2
3
and five Bi polyhedra, respectively. In the asymmetric unit, there are 3 K sites, 10 Bi
sites, and 14 Se sites that are crystallographically unique. The K(1) and K(3) sites are
disordered with Bi(5) and Bi(7) at a ratio of 76%/24% and 72%/28%, respectively.
The K(1) and Bi(5) have the same site, and the distances between the K(3) and Bi(7)
site is 0.54 Å.
Powder X-ray diffraction (PXRD). As shown in Figure 2a, the PXRD patterns of
the SPSed K Bi Se samples were measured along two directions: (1) the
2
.5 8.5
14
5
4
scattering vector of the X-ray is perpendicular to the primary surface of the pellets
(K Bi Se -, parallel to the direction of applied pressure, blue pattern) and (2) the
2
.5 8.5
14
scattering vector of the X-ray is parallel to the primary surface of the pellets
K Bi Se -; perpendicular to the applied pressure, black pattern). For
(
2.5 8.5
14
K Bi Se samples, the only direction tested was the scattering vector of the X-ray
2
.5 8.5
14-x
parallel to the primary surface of the pellets. All Bragg peaks can be indexed to the
K Bi Se phase (ICSD 84269), Figure 2a. Moreover, the PXRD patterns as shown
2
.5 8.5
14
in Figure 2a indicate the anisotropic structure of K Bi Se , which is consistent
2
.5 8.5
14
with the needle shaped K Bi Se crystals with their long axis along the monoclinic
2
.5 8.5
14
b-axis, Figure S1 (Supporting information). The needle shaped samples also show the
orientation and alignment features after the SPS process as shown in Figure S2
(Supporting information).
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Thermal analysis and electronic energy band gap. The differential thermal analysis
(
DTA) of K Bi Se is shown in Figure S3 (Supporting Information). There is an
2.5 8.5 14
endothermic peak at 974 K corresponding to the melting during the heating cycle and
an exothermic peak at 949 K of recrystallization. PXRD patterns show that the DTA
product is K Bi Se after heating to 1073 K for two consecutive heating-cooling
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.5 8.5
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cycles, Figure S4 (Supporting Information), indicating congruent melting. The optical
absorption spectrum in Figure 2c reveals that the electronic energy band gap of
34
K Bi Se is about 0.55 eV, in agreement with previous reports.
2
.5 8.5
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TEM results analysis. K Bi Se and K Bi Se have the same space group
2
.5 8.5
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2
8
13
(
P2 /m), similar unit cells (a = 17.534(4) Å, b = 4.206(1) Å, c = 21.387(5) Å, β =
1
1
9
09.65(2)° for K Bi Se and a = 17.492(3) Å, b = 4.205(1) Å, c = 18.461(4) Å, β =
2.5 8.5 14
34
0.49(2) for K Bi Se ), and share the same Bi Te and NaCl type blocks. Therefore,
2
8
13
2
3
the possibility of intergrowth between the two structures is high. It was confirmed by
the previous study of K Bi Se sample via PXRD and TEM measurements.40
2
8
13
Although there is no observable diffraction peaks from K Bi Se in the PXRD
2
8
13
pattern, it is necessary to verify the purity by high-resolution transmission electron
microscopy.
The highly anisotropic nature of the synthesized ingot as well as SPS sample was
characterized by scanning electron microscopy (SEM), as shown in Figure S1
(Supporting Information). Typically, the ingot consists of grains and crystals of
needle-like morphology, where the width of the needles is around 10 microns. Similar
results are also observed in the sample after SPS, where the preferred growth
orientation during crystallization is observed, Figure S2 (Supporting Information). As
shown in Figure S2a (Supporting Information), the needle-like grains tend to orient in
layers along the plane normal to SPS pressure (in-plane). The preferred growth
direction, b-axis, is labeled with red arrows in the figure, indicating that b-axis is
randomly oriented within the plane. On the contrary, along the plane parallel to SPS
pressure, many voids are observed between stacked layers. The differences between
these two directions account for the fact that the electrical and thermal transport
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properties along SPS pressure (K Bi Se -) are lower than that along perpendicular
2.5 8.5
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to SPS pressure (K Bi Se -) since electron/heat flow needs to occur through
2.5 8.5 14
stacked layers as well as many pores.
We also performed atomic-resolution micro-analysis with an aberration (probe)
corrected scanning/transmission electron microscope under 200 kV. Figure 3a is
typical high angle annular dark field STEM (HAADF-STEM) image of K Bi Se
0
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.5 8.5
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specimen, showing mainly z-contrast. The selected area electron diffraction pattern
SAED) in the inset matches with monoclinic K Bi Se (space group: P2 /m)
(
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.5 8.5
14
1
along [010] direction. No extra spots, spot splitting, streaking are observed, indicating
that the K Bi Se sample is a single phase, and with no K Bi Se second phase
2
.5 8.5
14
2
8
13
intergrown. The magnified image in Figure 3b indicates the good agreement with the
superimposed model of the crystal structure.
Thermoelectric transport properties of undoped sample. The thermoelectric
performance of as made undoped samples along two different directions,
K Bi Se - and K Bi Se -, is shown in Figure 4. As discussed above the
2
.5 8.5
14
2.5 8.5
14
SPSed samples exhibit preferential orientation because of the monoclinic anisotropic
crystal structure and the preferred growth direction along the b-axis. The electrical
conductivities for both K Bi Se - and K Bi Se - increase with rising
2
.5 8.5
14
2.5 8.5
14
temperature, as would be expected from an intrinsic semiconductor, Figure 4a,
although the Seebeck coefficient is characteristic of a heavily doped semiconductor
up to 700K. Because the b-axis is the best transport direction, the electrical
conductivity of K Bi Se - is higher than that of K Bi Se -. Because
2
.5 8.5
14
2.5 8.5
14
K Bi Se has low carrier concertation at 300 K and increased carrier concertation
2
.5 8.5
14
via thermal activation at high temperature, Figure 6c, the electrical conductivity
−
1
−1
gradually increases from ~9.7 and ~6.3 Sꢀcm at 300 K to ~99 and ~76 Sꢀcm at 873
K for K Bi Se - and K Bi Se -, respectively.
2
.5 8.5
14
2.5 8.5 14
The negative Seebeck coefficient as shown in Figure 4b indicates that
K Bi Se is an n-type semiconductor. The absolute values of the Seebeck
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.5 8.5
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coefficient for both K Bi Se - and K Bi Se - increase with the rise of
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2.5 8.5
14
temperature and reach their maximum values at 723 K, suggesting the onset of
intrinsic excitation conduction that is also seen in the enhanced σ values above 723 K.
From the Goldsmid-Sharp rule, the band gap can be estimated as E = 2eSmaxTmax
,
g
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9
0
where e is the electronic charge, yielding a result of ~0.34 eV, in agreement with the
optically measured band gap.55-56 Although the Seebeck coefficient of K Bi Se -
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.5 8.5
14
is superior to that of K Bi Se - in the entire tested temperature range, a higher
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.5 8.5
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power factor was obtained for K Bi Se - above 523 K as shown in Figure 4c,
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.5 8.5
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because of the higher electrical conductivity.
−1 −1
As shown in Figure 4d, the κtot values are lower than 0.6 Wm K for
K Bi Se - and K Bi Se - over the entire temperature range, with
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.5 8.5
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2.5 8.5
14
K Bi Se - possessing comparatively higher values. The κ values for both
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.5 8.5
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tot
samples increase from T > 723 K because of the enhanced minority charge carrier
contribution. For the κ , K Bi Se - has lower values than K Bi Se - in the
lat
2.5 8.5
14
2.5 8.5
14
entire temperature range, Figure 4e. κ drops rapidly with rising temperature and
lat
−
1
−1
reaches the ultralow value of ~0.33 Wm K at 773 K for K Bi Se -. Finally, the
2
.5 8.5
14
two samples have nearly identical ZT values, with K Bi Se - having a slightly
2
.5 8.5
14
larger maximum value of ~0.67 versus ~0.53 for K Bi Se - at 873K, Figure 4f.
2
.5 8.5
14
N-type doping via Se vacancies
Charge transport properties. Because the K Bi Se - sample exhibited better
2.5 8.5
14
performance we focused on optimizing its thermoelectric properties using Se
deficiency as the doping strategy. Se deficiency is expected to introduce additional
electron carriers corresponding to two electrons per Se atom removed.
The electrical conductivities of K Bi Se
samples, K Bi Se14-x, exhibit a
2.5 8.5
2
.5 8.5
14-x
significant enhancement in electrical conductivity compared to K Bi Se -, Figure
2
.5 8.5
14
−
1
5
a. Specifically, the electrical conductivities markedly increase from 9.6 Sꢀcm for
−
1
K Bi Se - to 372.2 Sꢀcm for x = 0.105 sample at 300 K. For samples with x =
2
.5 8.5
14
0
.07, the electrical conductivity has a sigmoidal temperature dependence. It increases
gradually from 300 K to ~500 K, then levels off and decreases slightly from 500 K to
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50 K before increasing again at T > 750 K, an overall semiconducting trend, Figure
a. In contrast, the more heavily Se deficiencies samples (x = 0.07 and 0.105), exhibit
a decreasing electrical conductivity decreases from 300 K to ~800 K indicating a
metal-like (degenerate semiconductor) behavior from 300 K to ~800 K, Figure 5a.
The sharp increase of electrical conductivity at T > 800 K for all samples is attributed
to the thermal excitation of minority charge carriers (bipolar conduction).
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All samples exhibit negative Seebeck coefficients. Figure 5b displays the
Seebeck coefficients as a function of temperature for K Bi Se - and
2
.5 8.5
14
K Bi Se
samples. The coefficients for K Bi Se
samples decrease with
14-x
2
.5 8.5
14-x
2.5 8.5
increasing Se deficiencies consistent with the electron donor nature of the deficiency.
Similar to the as-made undoped sample, the absolute values of the Seebeck
coefficients for all K Bi Se samples rise with temperature, then reach their peak
14-x
2
.5 8.5
values at ~700 − 800 K, before declining. The peak in the Seebeck coefficient reflects
the onset of hole carrier excitation at high temperature (bipolar conduction), with a
corresponding sharp increase of electrical conductivity. The power factor improves to
−
1
−2
~4.53 μWcm K at 873 K, obtained for x = 0.021 sample, see Figure S5 (Supporting
−
1
−2
Information). Compared with its sister compound K Bi Se (~6 μWcm K at 873
2
8
13
K),40 K Bi Se has a relatively lower value. This is mainly attributed to the
2
.5 8.5
14
decrease of Seebeck coefficient caused by bipolar conduction at T > 750 K.
The carrier concentrations in the samples were estimated from temperature
dependent Hall effect measurements, with the room temperature results shown in
Figure 6a. For all samples, R < 0 is consistent with the n-type conduction observed
H
in the Seebeck coefficient data. A low number of Se vacanices seem to have a minor
impact on the carrier concentration n, showing a slight decrease in n from ~1.2 × 1020
cm−3 for undoped sample to ~1.1 × 1020 cm−3 for x = 0.021 sample at room
temperature, Figure 6a. At higher Se deficiencies (e.g. x = 0.042 and above), however,
2
0
−3
20
−3
the n is enhanced, such as ~1.5 × 10 cm for x = 0.042 sample, ~2.0 × 10 cm for
20
−3
x = 0.07 sample, and ~2.9 × 10 cm for x = 0.105 sample at room temperature.
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Figure 6b displays the Seebeck coefficient as a function of n (based on the
Pisarenko relation) for K Bi Se and K Bi Se samples. The dotted curves are
2
.5 8.5
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2.5 8.5
14-x
the theoretically calculated values based on the single parabolic band (SPB) model at
00 K (black), 573 K (red) and 773 K (blue) with an effective mass of 1.2 m . At 300
3
e
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K, all samples fit the electron effective mass of ~1.2 m . With rising temperature, the
e
effective mass of electrons increases for the K Bi Se , x = 0.021 and 0.07 samples,
2
.5 8.5
14
as indicated by the position of the data points above the theoretical curves.
As a function of temperature, the n of the undoped, x = 0.021 and 0.07 samples,
Figure 6c, is essentially flat until T ~623 K when minority carriers begin to short the
Hall signal at elevated temperatures, Figure S6 (Supporting Information). According
to Figure 6d, the charge carrier mobility is significantly improved with the
2
−1 −1
introduction of Se deficiencies from ~0.50 cm V s in the undoped sample to ~7.73
2
−1 −1
cm V s in the x = 0.07 sample at room temperature. This plays a large part in
enhancing the power factor. Also the mobility is increasing with rising temperature
2
−1 −1
2
−1 −1
for the undoped (from ~0.50 cm V s at room temperature to 3.03 cm V s at 623
2
−1 −1
K) and x = 0.021 samples (from 2.37 cm V s at room temperature to 5.13
2
−1 −1
cm V s at 573 K) indicating that the charge carrier scattering is dominated by grain
5
7
boundaries. For the x= 0.07 sample we observed dµ /dT < 0, which indicate strong
H
acoustic phonon-charge carrier interactions. We can see that, intrinsic and
K Bi Se
2.5 8.5
samples show lower mobilities compared to the Cl-doped K Bi Se
2 8 13
14-x
2
−1 −1
19
−3
40
samples (~31.57 cm V s at n ~8.8 × 10 cm ) at room temperature.
Thermal conductivity. The temperature-dependent thermal conductivity values κtot
of K Bi Se - and K Bi Se samples are shown in Figure 7a. In general, the
2
.5 8.5
14
2.5 8.5
14-x
thermal conductivity drops with rising temperature as expected. The κ raises with
tot
increasing Se deficiencies content. For instance, the κ values significantly increase
tot
−
1
−1
−1 −1
from ~0.57 Wm K for K Bi Se - to ~0.86 Wm K for x = 0.105 sample at
2
.5 8.5
14
room temperature. Moreover, the x = 0.021 sample possesses an ultralow κ ~0.38
tot
−1 −1
Wm K at 823 K.
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The κlat was determined by subtracting κele from κ . According to the
tot
Wiedemann–Franz law, the κ can be estimated by following equation:
ele
κele = LσT
(1)
where L is the Lorenz number (See Supporting Information, with Figure S9)
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displaying the L and κ values). All K Bi Se samples exhibit remarkable low
14-x
ele
2.5 8.5
−
1
−1
κ between ~0.51−0.61 Wm K at 300 K, Figure 7b. Meanwhile, κ values for all
lat
lat
−
1
−1
samples decrease with temperature. Surprisingly, the κ of ~0.31 Wm K at ~723 K
lat
is ultralow for x = 0.021 sample. Because it is difficult to precisely estimate the
Lorenz number and heat capacity in the intrinsic excitation regime, the calculated κlat
values may be underestimated for T > 723 K. Although the κ of x = 0.021 sample is
lat
−1 −1
slightly higher than the ~0.21 Wm K at 873 K of Cl-doped K Bi Se , the value is
2
8
13
still ultralow as compared with other state-of-the-art thermoelectric materials.19, 31, 40,
4
8, 59-64
Figure 7c displays the ZT values only along the perpendicular to SPS pressing
direction. For all samples, the values increase with temperatures and the peak ZT
values are enhanced from ~0.67 for K Bi Se - to ~1.0 for the x = 0.021 sample at
2
.5 8.5
14
873 K. The simultaneous improvement of the power factor and reduction of κlat
demonstrates that the Se deficiencies doping is effective for enhancing the
thermoelectric performance of this system.
Phonon velocity. To uncover the origin of the ultralow κ , we performed phonon
lat
velocity measurements and theoretical calculations of phonon dispersions in the
lattice of K Bi Se . The phonon velocities were obtained by ultrasonic pulse echo
2
.5 8.5
14
measurements along the primary surface of the pellets (perpendicular to SPS pressure)
at room temperature. The longitudinal (v ), shear (v ) and average (v ) phonon velocity,
l
s
a
Young’s modulus (E), Poisson ratio (v ), Grüneisen parameter (γ, obtained by using
p
3
2
1 + 푣푝
the formula, γ = (
), and Debye temperature (Θ ) are shown in Table 1. A
D
2 ― 3푣푝
comparison of the room temperature elastic properties of K Bi Se with those of
2
.5 8.5
14
several other Bi-chalcogenide based thermoelectric materials with low thermal
conductivity is also shown in Table 1.
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The Young’s modulus of 35.8 GPa for K Bi Se is lower than other
2.5 8.5
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Bi-chalcogenide based thermoelectric materials (e.g. 37.1 GPa for K Bi Se1340, 76.5
2
8
GPa for BiCuSeO65 and 70.6 GPa Bi YO Cu Se ). Also, the small Young’s
66
2
4
2
2
modulus leads to a low average phonon velocity of 1610 ms−1 for K Bi Se .
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.5 8.5
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Generally, the Young’s modulus reflects the material’s stiffness and chemical bond
6
7
strength. The low Young’s modulus is attributed to weak individual atomic bonds,
which often result in low κlat.19-20
The Grüneisen parameter (γ), a measure of the lattice anharmonicity is another
means of understanding the thermal conductivity.19 The experimental Grüneisen
parameter value of ~1.96 for K Bi Se is larger than other Bi-chalcogenide based
2
.5 8.5
14
40
65
thermoelectric materials (e.g. 1.71 for K Bi Se , 1.5 for BiCuSeO and 1.71 for
2
8
13
66
Bi YO Cu Se ). The higher value suggests a larger anharmonicity in K Bi Se .
2
4
2
2
2.5 8.5
14
The substantial Grüneisen parameter likely originates from the presence of the
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8
stereochemically active ] Bi. In addition, the different coordination environments (3-
and 6-fold coordinated with Se atoms) and mixed occupancy of Bi and K atoms lead
to a more asymmetric structure, which results in stronger lattice anharmonic
vibrations.
The Debye temperature is related to the mean sound velocity and is typically <
6
7
3
00 K in low thermal conductivity materials. The value of ~126 K for K Bi Se
2.5 8.5 14
ℎ
3푁
1
/3
was obtained by using the formula, Θ =
[
] v , where h, k , N, V, and v are
a B a
푘B 4π푉
D
Planck’s constant, Boltzmann constant, number of atoms in a unit cell, unit-cell
volume and average phonon velocity, respectively. This result is lower than other
Bi-chalcogenide based thermoelectric materials (e.g. 154 K for K Bi Se with~30%
2
8
13
second phase K Bi Se , 243 K for BiCuSeO65 and 280 K Bi YO Cu Se ),
40
66
2
.5 8.5
14
2
4
2
2
−1
consistent with the low average phonon velocity (1610 ms ) and thermal
conductivity of K Bi Se .
2
.5 8.5
14
DFT electronic band structure and phonon dispersion calculations. Electronic
band structure calculations on K Bi Se indicate that it is an indirect band gap
2
.5 8.5
14
semiconductor with multiple conduction bands close to the Fermi level, Figure 8. The
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calculated band gap of 0.03 eV, is underestimated however relative to the
experimental value 0.55 eV, Figure 2c. Moreover, the partial electronic density of
states plots show that the conduction band bottom within 0.2 to 0 eV of the CBM is
mainly contributed by Bi 6p orbitals. The contribution of K orbital states in the
conduction band minimum and valence band maximum is negligible suggesting
0
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.5-
electron transport in this material is through Bi based 6p orbitals in the [Bi Se ]
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.5
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framework.
The phonon dispersions along the Γ-Z and Γ-Y directions are much lower in energy
than in the Γ-X direction, which is determined by the significantly shorter lattice
parameter b (4.206(1) Å) compared to a (17.534(4) Å) and c (21.387(5) Å), Figure 9a.
The lower energy vibrations along the Γ-Z and Γ-Y directions also indicates that the
Debye temperatures in the a and c directions are much smaller than in the b direction
and point to lower lattice thermal conductivity along a and c. As shown in Figure 9b,
the theoretically calculated κ of K Bi Se in the a and c directions are as low as 0.4
lat
5
17
28
−
1
−1
−1 −1
Wm K and 0.3 Wm K at 300 K, respectively. The larger Debye temperature in
the b direction, together with relatively lower calculated Grüneisen parameters, result
−
1
−1
in a higher κ of 1.3 Wm K at 300 K along the b direction, Figure 9c.
lat
To compare with the experimental results from the polycrystalline SPSed samples,
we consider the average of the calculated κlat over the three lattice directions, as
−
1
−1
shown in black squares in Figure 9b. The calculated value of 0.68 Wm K at 300 K
−
1
−1
gradually decreases to 0.3 Wm K at 900 K. The higher average values than the
experimental lattice thermal conductivity near room temperature can be attributed to
the fact that we consider an ordered crystalline structure of K Bi Se in the DFT
5
17
28
calculation without taking into account the partial occupancy of both K and Bi
species. In addition, we only include normal and Umklapp scattering processes of
acoustic phonons in a pure single crystal without including other phonon scattering
mechanisms present in real samples, such as point defects and grain boundary
contributions. Thus, the calculated thermal conductivities are ideally larger than the
experimental ones.
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The ultralow κ is consistent with the very low calculated phonon velocities as
lat
shown in the Table 2. The low velocities primarily originate from low frequency
acoustic vibrations because of the heavier Bi atoms with minimal contribution from K
atoms, Figure 9d. Indeed, more than half of the PDOS for the acoustic phonons (< 40
1
1
1
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0
-1
cm ) stems from Bi atoms. Of course, accounting for the site occupancy disorder of K
3
4
and Bi atoms within the calculations may affect these results. Lastly, the highly
anisotropic structure induces relatively large Grüneisen parameters in the Γ-Y and
Γ-Z directions, Figure 9c, hence very low κ in the a and c directions.
lat
CONCLUSIONS
The as-made undoped K Bi Se samples exhibit ultralow lattice thermal
2
.5 8.5
14
−1 −1
conductivity of 0.34 Wm K at 873 K and a peak ZT value of 0.67 at 873 K.
Introducing Se deficiencies is an efficient way to control the n-type doping behavior
of the mateirals and can be used to increase the ZT value to ~1 at 873 K. Phonon
velocity measurements and phonon dispersion calculations suggest that the physical
origins of such low thermal conductivity in K Bi Se mainly derive from the very
2
.5 8.5
14
strong anharmonicity in the structure and low phonon velocities imposed by the
complex low-symmetry, heavy atom crystal structure and large unit cell.
Conflicts of interest
The authors declare no competing financial interest.
Acknowledgements
This work was supported by the Department of Energy, Office of Science Basic
Energy Sciences under grant DE-SC0014520, DOE Office of Science (sample
preparation, synthesis, XRD, TE measurements, TEM measurements, DFT
calculations). ZZL and QY gratefully acknowledge the National Natural Science
Foundation of China (61728401). This work made use of the EPIC facility of
Northwestern University’s NUANCE Center, which has received support from the
Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF
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ECCS-1542205); the MRSEC program (NSF DMR-1720139) at the Materials
Research Center; the International Institute for Nanotechnology (IIN); the Keck
Foundation; and the State of Illinois, through the IIN. User Facilities are supported by
the Office of Science of the U.S. Department of Energy under Contract No.
DE-AC02-06CH11357 and DE-AC02-05CH11231. Access to facilities of high
performance computational resources at the Northwestern University is
acknowledged. The authors also acknowledge Singapore MOE AcRF Tier 2 under
Grant Nos. 2018-T2-1-010 and MOE2017-T2-2-069, Singapore A*STAR Pharos
Program SERC 1527200022, the support from FACTs of Nanyang Technological
University for sample analysis.
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Supporting Information
PXRD and DTA characterizations, DFT for phonon dispersion calculations, SEM
images, DTA results, PXRD before and after DTA of K Bi Se , power factor and
2
.5 8.5
14
electronic thermal conductivity of K Bi Se - and K Bi Se
samples,
14-x
2
.5 8.5
14
2.5 8.5
temperature-dependent RH for K Bi Se -, x = 0.021 and 0.07 samples,
2.5
8.5
14
temperature-dependent Lorenz numbers, thermal diffusivity, room temperature
densities of K Bi Se (x = 0, 0.007, 0.021, 0.042, 0.063, 0.07, and 0.105),
2
.5 8.5
14−x
HAADF-STEM EDS mapping of K Bi Se . The Supporting Information is
2
.5 8.5
14
available free of charge on the ACS Publications website.
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chalcogenides as thermoelectric materials: a solid state chemistry approach. Bull.
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of Bi Bilayer Leading to Ultralow Lattice Thermal Conductivity and High
Thermoelectric Performance in Weak Topological Insulator n-Type BiSe. J. Am.
Chem. Soc. 2018, 140 (17), 5866-5872.
45. Kim, J.-H.; Chung, D.-Y.; Bilc, D.; Loo, S.; Short, J.; Mahanti, S. D.; Hogan, T.;
Kanatzidis, M. G. Crystal Growth, Thermoelectric Properties, and Electronic
Structure of AgBi S and AgSb Bi S (x = 0.3). Chem. Mater. 2005, 17 (14),
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Dravid, V. P.; Kanatzidis, M. G. Ultralow thermal conductivity and high
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7. Zhao, L. D.; Lo, S. H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.;
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power factor and thermoelectric performance in hole-doped single-crystal SnSe.
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9. Hanko, J. A.; Sayettat, J.; Jobic, S.; Brec, R.; Kanatzidis, M. G. A CuP S (A =
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K, Rb), Cs Cu P S , and K CuP S : New Phases from the Dissolution of Copper in
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transports leading to high out-of-plane ZT in n-type SnSe crystals. Science 2018, 360
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Hogan, T. P.; Chung, D.-Y.; Dravid, V. P.; Kanatzidis, M. G. High Performance
Thermoelectrics from Earth-Abundant Materials: Enhanced Figure of Merit in PbS by
Second Phase Nanostructures. J. Am. Chem. Soc. 2011, 133 (50), 20476-20487.
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1. Biswas, K.; Zhao, L.-D.; Kanatzidis, M. G. Tellurium‐Free Thermoelectric: The
Anisotropic n‐Type Semiconductor Bi S . Adv. Energy Mater. 2012, 2 (6), 634-638.
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Kanatzidis, M. G., Tang, X. F. The Role of Zn in Chalcopyrite CuFeS : Enhanced
Thermoelectric Properties of Cu1–xZnxFeS2 with In Situ Nanoprecipitates. Adv.
Energy Mater. 2017, 7 (3), 1601299.
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Hippalgaonkar, K.; Xu, J.; Yan, Q.; Wolverton, C.; Kanatzidis, M. G. n-Type SnSe2
Oriented-Nanoplate-Based Pellets for High Thermoelectric Performance. Adv. Energy
Mater. 2017, 8, 1702167.
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2. Xie, H. Y., Su, X. L., Zheng, G., Zhu, T., Yin, K., Yan, Y. G., Uher, C.,
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4. Ahn, J. Y.; Hwang, J.-Y.; Ryu, B. K.; Oh, M.-W.; Lee, K. H.; Kim, S. W.
Importance of crystal chemistry with interstitial site determining thermoelectric
transport properties in pavonite homologue Cu-Bi-S compounds. CrystEngComm
2016, 18 (8), 1453-1461.
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5. Zhao, L.-D.; He, J.; Berardan, D.; Lin, Y.; Li, J.-F.; Nan, C.-W.; Dragoe, N.
BiCuSeO oxyselenides: new promising thermoelectric materials. Energy Environ. Sci.
2014, 7 (9), 2900-2924.
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6. Xiao, Y.; Pei, Y.; Chang, C.; Zhang, X.; Tan, X.; Ye, X.; Gong, S.; Lin, Y.; He,
J.; Zhao, L.-D. Electrical and thermal transport properties of layered Bi YO Cu Se .
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J. Solid State Chem. 2016, 239, 178-183.
7. Kurosaki, K.; Kosuga, A.; Muta, H.; Uno, M.; Yamanaka, S. Ag TlTe : A
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high-performance thermoelectric bulk material with extremely low thermal
conductivity. Appl. Phys. Lett. 2005, 87 (6), 061919.
68. Dutta, M.; Pal, K.; Waghmare, U. V.; Biswas, K. Bonding heterogeneity and lone
pair induced anharmonicity resulted in ultralow thermal conductivity and promising
thermoelectric properties in n-type AgPbBiSe . Chem. Sci. 2019, 10, 4905.
69. Tan, G.; Hao, S.; Zhao, J.; Wolverton, C.; Kanatzidis, M. G. High Thermoelectric
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Performance in Electron-Doped AgBi S with Ultralow Thermal Conductivity. J. Am.
Chem. Soc. 2017, 139 (18), 6467-6473.
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Figure 1. Crystal structure of K Bi Se from the approximate perspective of the b
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axis. Black, blue, red, and green spheres: Bi, K/Bi, Se, and K. K Bi Se has a
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complex 3D anionic framework that includes two different types of Bi/Se polyhedral
building blocks, NaCl- and Bi Te -type fragments, which are highlighted by the blue
2
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squares. The Bi Te -type rods are arranged one by one to form layers parallel to the
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a-axis. The NaCl-type rod fragments connect the layers to build a 3D framework with
K in the channel. The unit cell is demarcated by a solid black line.34
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Figure 2. (a) PXRD patterns of the intrinsic K Bi Se along two directions: (1) the
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scattering vector of the X-ray is perpendicular to the primary surface of the pellets
(
K Bi Se - blue pattern), (2) the scattering vector of the X-ray is parallel to the
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primary surface of the pellets (K Bi Se -, black pattern). The red curve is the
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simulated pattern of K Bi Se (ICSD 84269). The PXRD patterns indicate the
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anisotropic feature of K Bi Se ; (b) PXRD patterns of K Bi Se and
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K Bi Se
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samples; and (c) Electronic absorption spectra obtained from diffuse
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reflectance infrared spectroscopy measurement on K Bi Se at room temperature.
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Figure 3. (a) Typical HAADF-STEM image of K Bi Se specimen viewed down
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the monoclinic b-axis [010] of the unit cell, showing mainly z-contrast. Inset is the
electron diffraction pattern along [010] direction. (b) Zoom-in image with crystal
direction and atom labeled.
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Figure 4. Thermoelectric properties as a function of temperature for K Bi Se -
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and K Bi Se -: (a) Electrical conductivity, σ; (b) Seebeck coefficient, S; (c)
2.5 8.5
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Power factor, PF; (d) Total thermal conductivity, κ ; (e) Lattice thermal
tot
conductivity, κ ; and (f) Figure of merit, ZT.
lat
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Figure 5. Thermoelectric transport properties as a function of temperature for
K Bi Se - and K Bi Se
samples: (a) electrical conductivity, σ; (b) Seebeck
14-x
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Figure 6. (a) Hall coefficient, R and n at 300 K for K Bi Se - and K Bi Se
H
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2.5 8.5
14-x
samples; (b) Seebeck coefficient as a function of Hall carrier concentration with an
effective mass of 1.2 m . The short dot curves are the theoretical Pisarenko plots at
e
300 K (black), 573 K (red) and 773 K (blue). The solid black square, red circle, blue
up-triangle, dark cyan down-triangle, dark yellow right-triangle, and navy diamond
are K Bi Se -, x = 0.007, x = 0.021, x = 0.042, x = 0.07 and x = 0.105 samples at
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300 K. The half-right black square, blue up-triangle, and dark yellow right-triangle
are K Bi Se -, x = 0.021 and 0.7 samples at 573 K. The half-left black square,
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blue up-triangle, and dark yellow right-triangle are K Bi Se -, x = 0.021 and 0.7
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samples at 773 K; (c) Temperature-dependent carrier concentration, n for
K Bi Se -, x = 0.021 and 0.7 samples; and (d) Temperature-dependent µ for
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H
K Bi Se -, x = 0.021 and 0.7 samples.
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