Quaternary Pavonites A1+xSn2-xBi5+xS10 (A+ = Li+, Na+): Site Occupancy Disorder Defines Electronic Structure

Article abstract of DOI:10.1021/acs.inorgchem.7b03091

The field of mineralogy represents an area of untapped potential for the synthetic chemist, as there are numerous structure types that can be utilized to form analogues of mineral structures with useful optoelectronic properties. In this work, we describe the synthesis and characterization of two novel quaternary sulfides A_1+xSn_2-xBi_5+xS₁₀ (A = Li⁺, Na⁺). Though not natural minerals themselves, both compounds adopt the pavonite structure, which crystallizes in the C2/m space group and consists of two connected, alternating defect rock-salt slabs of varying thicknesses to create a three-dimensional lattice. Despite their commonalities in structure, their crystallography is noticeably different, as both structures have a heavy degree of site occupancy disorder that affects the actual positions of the atoms. The differences in site occupancy alter their electronic structures, with band gap values of 0.31(2) eV and 0.07(2) eV for the lithium and sodium analogues, respectively. LiSn₂Bi₅S₁₀ exhibits ultralow thermal conductivity of 0.62 W m^-1 K^-1 at 723 K, and this result is corroborated by phonon dispersion calculations. This structure type is a promising host candidate for future thermoelectric materials investigation, as these materials have narrow band gaps and intrinsically low thermal conductivities.

Full text of DOI:10.1021/acs.inorgchem.7b03091

Article
pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Quaternary Pavonites A1+xSn2−xBi5+xS10 (A+ = Li+, Na+): Site
Occupancy Disorder Defines Electronic Structure
Jason F. Khoury,† Shiqiang Hao,‡ Constantinos C. Stoumpos,† Zhenpeng Yao,‡ Christos D. Malliakas,†
Umut Aydemir,§ Tyler J. Slade,† G. Jeffrey Snyder,‡ Chris Wolverton,‡ and Mercouri G. Kanatzidis*,†
†Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
‡Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
§Department of Chemistry, Koc University, Sariyer, Istanbul 34450, Turkey
S
* Supporting Information
ABSTRACT: The field of mineralogy represents an area of
untapped potential for the synthetic chemist, as there are
numerous structure types that can be utilized to form
analogues of mineral structures with useful optoelectronic
properties. In this work, we describe the synthesis and
characterization of two novel quaternary sulfides
A
1+xSn2−xBi5+xS10 (A = Li+, Na+). Though not natural minerals
themselves, both compounds adopt the pavonite structure,
which crystallizes in the C2/m space group and consists of two
connected, alternating defect rock-salt slabs of varying
thicknesses to create a three-dimensional lattice. Despite their commonalities in structure, their crystallography is noticeably
different, as both structures have a heavy degree of site occupancy disorder that affects the actual positions of the atoms. The
differences in site occupancy alter their electronic structures, with band gap values of 0.31(2) eV and 0.07(2) eV for the lithium
and sodium analogues, respectively. LiSn2Bi5S10 exhibits ultralow thermal conductivity of 0.62 W m−1 K−1 at 723 K, and this
result is corroborated by phonon dispersion calculations. This structure type is a promising host candidate for future
thermoelectric materials investigation, as these materials have narrow band gaps and intrinsically low thermal conductivities.
occurring sulfosalts, as long as the other metal can adapt a
similar coordination environment.7,8 Incredibly, bismuth (and
other similarly sized elements, such as antimony, tin, and lead)
can also have mixed occupancy with alkali metals of
considerably smaller ionic radii so long as they can adapt the
INTRODUCTION
■
Bismuth chalcogenides have garnered widespread interest, from
semiconductors and thermoelectrics to superconductors, owing
to their incredible diversity in electronic structure.1,2 The
layered narrow gap semiconductors CsBi4Te6 and RbBi11/3Te6
are superconducting at low Tc (4.4 and 3.2 K, respectively),
which is remarkable considering that both compounds have low
carrier densities that are not typically conducive to super-
conductive behavior.2,3 Perhaps more importantly, many new
bismuth chalcogenides with relatively complex structures can be
predictably synthesized from canonical building blocks. The
diversity and complexity in structure are greatly enhanced when
group 14 elements such as Sn2+ and Pb2+ are added. These
structures form several different homologous series with
Bi2Te3-, CdI2-, and NaCl-type subunits.2,4 Further, expression
of the stereoactive lone pair from the ns2 orbital of Bi3+, Sb3+,
Pb2+, and Sn2+ allows for several unique coordination
environments, such as capped octahedra, capped trigonal
prisms, and trigonal bipyramids.3,5 These unusual perturbations
in local bonding can have broad implications on the crystal and
electronic structures of extended solids featuring Bi3+, Sb3+,
Pb2+, and Sn2+, resulting in a wide array of novel materials with
emergent properties.6
9
same coordination environment, as in the case of LiBi3S5 and
LiPbSb3S6.10 As a result of these phenomena, there have been a
considerable wealth of synthetic sulfosalts and selenosalts that
have significant site occupancy disorder, the effect of which on
their electronic properties has not been thoroughly inves-
tigated.11−13
Pavonite (AgBi3S5) is a naturally occurring sulfosalt that has
shown promise as a thermoelectric material due to its extremely
low thermal conductivity and good electrical properties.14
Pavonite is a three-dimensional structure with a layered rock-
salt motif containing two distinct slabs. The first, thicker PbS-
type slab consists of BiS6 octahedra oriented as diagonal chains,
and these chains are flanked by the thinner SnSe-type slabs
consisting of AgS6 octahedra surrounded by BiS5 square
pyramids.14 The structure pavonite is part of the homologous
series M′n+1Bi2Qn+5, where the M′ cations can be bismuth, alkali
metal, lead, silver, or copper, and the Q anions are sulfur,
Many of these materials are known for having considerable
Received: December 13, 2017
amounts of site occupancy disorder in several naturally
© XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.7b03091
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Inorganic Chemistry
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Table 1. Crystal Data and Structure Refinement for LiSn2Bi5S10 and NaSn2Bi5S10 at 298 K
a
b
empirical formula
formula weight
temperature
Li0.97(3)Sn2.06(2)Bi4.97(2)S10(0)
1609.90
Na1.04(2)Sn1.84(0)Bi5.11(3)S10(0)
1631.95
298 K
298 K
wavelength
0.71073 Å
0.71073 Å
crystal system
space group
monoclinic
monoclinic
C2/m
C2/m
unit cell dimensions
a = 13.148(3) Å, α = 90°
b = 4.0186(8) Å, β = 93.93(3)°
c = 16.607(3) Å, γ = 90°
875.4(3) Å3
a = 13.311(3) Å, α = 90°
b = 4.0470(8) Å, β = 93.64(3)°
c = 16.794(3) Å, γ = 90°
902.8(3) Å3
volume
Z
2
2
density (calculated)
absorption coefficient
F(000)
6.108 g/cm3
6.003 g/cm3
53.820 mm−1
53.326 mm−1
1356
1376
crystal size
0.1745 × 0.1049 × 0.0112 mm3
2.459 to 29.207°
−18 ≤ h ≤ 16, −5 ≤ k ≤ 5, −22 ≤ l ≤ 22
4242
0.0964 × 0.0531 × 0.0164 mm3
2.430 to 25.974°
−16 ≤ h ≤ 16, −4 ≤ k ≤ 4, −18 ≤ l ≤ 20
θ range for data collection
index ranges
reflections collected
independent reflections
completeness to θ = 26.000°, 25.974°
refinement method
data/restraints/parameters
goodness-of-fit
3187
1349 [Rint = 0.0434]
99.7%
full-matrix least-squares on F2
1008 [Rint = 0.0649]
99.9%
full-matrix least-squares on F2
1349/0/61
1008/0/60
1.090
1.279
final R indices [I > 2σ(I)]
R indices [all data]
extinction coefficient
largest diff peak and hole
Robs = 0.0390, wRobs = 0.0932
Rall = 0.0490, wRall = 0.0972
0.00084(11)
Robs = 0.0675, wRobs = 0.1661
Rall = 0.0814, wRall = 0.1710
N/A
1.717 and −1.585 e·Å−3
2.945 and −5.082 e·Å−3
a
2
Li0.97(3)Sn2.06(2)Bi4.97(2)S10(0): R = ∑||Fo| − |Fc||/∑|Fo|, wR = {∑[w(|Fo|2 − |Fc|2)2]/∑[w(|Fo|4)]}1/2 and w = 1/[σ2(Fo ) + (0.0557P)2 + 4.8554P]
b
where P = (Fo2 + 2Fc2)/3. Na1.04(2)Sn1.84(0)Bi5.11(3)S10(0): R = ∑||Fo| − |Fc||/∑|Fo|, wR = {∑[w(|Fo|2 − |Fc|2)2]/∑[w(|Fo|4)]}1/2 and w = 1/[σ2(Fo ) +
2
(0.0523P)2 + 238.6890P] where P = (Fo + 2Fc2)/3.
2
selenium, or tellurium.. The original pavonite mineral is the n =
5 member of this homologous series.
occupancy disorder. Phonon dispersion calculations are used to
create simulated lattice thermal conductivity of LiSn2Bi5S10,
with the simulated values being much higher than the actual
values, likely due to the significant site occupancy disorder and
minor impurity phase of the experimental compound.
For AgBi3S5, it has been proposed that its low thermal
conductivity is the result of a “double rattling” mechanism with
the phonon modes of the Ag and Bi atoms in the structure,
causing a phonon dampening effect that reduces lattice thermal
conductivity of the material.15 The double rattling mechanism
is where both Ag and Bi atoms have two peaks in the partial
density of states as a function of frequency, suggesting that both
atoms are responsible for suppressing the lattice thermal
conductivity of AgBi3S5. This mechanism is distinct from the
concerted rattling effect in CsAg5Te3, where the Ag sublattice
atoms all oscillate in the same phase and only one broad peak
in the partial density of states is observed.16 Rattling effects in
materials with complex crystal structures allow for an additional
method of scattering acoustic phonons without sacrificing
performance in their electrical properties, therefore making
them attractive candidates for thermoelectric materials.
In this work, we describe the synthesis, crystal structure, and
characterization of two novel quaternary bismuth chalcogenides
ASn2Bi5S10 (A = Li+, Na+) with the n = 5 pavonite structure.
Although both compounds have the same structure type, their
differences in site occupancy disorder cause noticeable changes
in their electronic structures and optical properties. Electrical
measurements on LiSn2Bi5S10 show that it behaves like a doped
n-type semiconductor with a conductivity of 165 S/cm and
carrier concentration of 1.21 × 1019 cm−3 at room temperature.
LiSn2Bi5S10 has ultralow thermal conductivity of 0.625 W m−1
K−1 at 723 K, which is lower than that of synthetic pavonite at
the same temperature, likely due to its considerable site
EXPERIMENTAL SECTION
■
Reagents. All chemicals in this study were used as obtained:
bismuth metal (99.9%, Strem Chemicals, Inc., Newburyport, MA),
sulfur pieces (99.998%, Sigma-Aldrich, St. Louis, MO), tin chunks
(99.999%, American Elements, Los Angeles, CA), lithium metal rods
(99.9%, 12.7 mm diameter, Sigma-Aldrich, St. Louis, MO), and
sodium metal (99.95%, Sigma-Aldrich, St. Louis, MO). Li2S and Na2S
were synthesized from stoichiometric amounts of the constituent
elements reacted in liquid ammonia, as described in the Supporting
Information.
Synthesis. LiSn2Bi5S10. Li2S (0.2529 g, 5.504 mmol), Sn (1.2594 g,
10.609 mmol), Bi (6.6250 g, 31.702 mmol), and S (1.8620 g, 58.079
mmol) were loaded in a 13 mm carbon coated silica tube in a dry,
nitrogen glovebox. The tube was flame-sealed under vacuum at
approximately 2 × 10−3 mbar, heated to 800 °C in 8 h, held there for 2
h, and water quenched to room temperature. This compound was then
sealed in a second 13 mm carbon coated fused silica tube, heated to
800 °C in 24 h, held there for 2 h, and cooled to room temperature in
48 h. The above 1:1:3:6 molar ratio of Li:Sn:Bi:S with this process
resulted in a bulk pure material, but the original 1:2:5:10 ratio had
minor impurities. This excess of lithium accounts for glass attack with
the tube, and the deficiency of tin is most likely the result of the bulk
material being tin deficient compared to the ideal stoichiometry. Bulk
pure LiSn2Bi5S10 was synthesized by this process, and crystals suitable
for single crystal diffraction were obtained by breaking up the ingot.
The reaction produced the product in quantitative yield and is stable
in open air at room temperature.
B
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Article
NaSn2Bi5S10. Na2S (0.2600 g, 3.331 mmol), Sn (1.4602 g, 12.301
mmol), Bi (6.4264 g, 30.751 mmol), and S (1.8735 g, 58.428 mmol)
were loaded in a 13 mm carbon coated fused silica tube in a dry,
nitrogen glovebox. Na2S had a 10% molar excess to account for glass
attack with the silica tube. The tube was flame-sealed under vacuum at
approximately 2 × 10−3 mbar, heated to 800 °C in 8 h, held there for 2
h, and water quenched to room temperature. The reaction produced
the product in quantitative yield with minor impurities present in the
powder X-ray diffraction pattern, and is stable in open air at room
temperature.
Powder X-ray Diffraction. Powder X-ray diffraction (PXRD)
patterns were taken using a Rigaku Miniflex powder X-ray
diffractometer with Ni-filtered Cu Kα radiation (λ = 1.5406 Å) with
a 30 kV voltage and 15 mA current. The diffraction pattern had a scan
width of 0.02° and a scan rate of 10°/min. Simulated PXRD patterns
were created using the software Mercury. Synchrotron X-ray
diffraction was measured on LiSn2Bi5S10 using the high-resolution
diffractometer 11BM-B at the Advanced Photon Source of Argonne
National Laboratory. The synchrotron sample was measured at 295 K
with a nominal 2θ step size of 0.001° and a scan rate of 0.1 step/s. The
wavelength of synchrotron radiation was λ = 0.412642 Å.
Single Crystal X-ray Diffraction. An IPDS 2T single crystal X-ray
diffractometer, running at 50 kV and 40 mA with Mo Kα radiation (λ
= 0.71073 Å), was used to gather data on the crystal structures of
LiSn2Bi5S10 and NaSn2Bi5S10. Single crystals of both compounds were
adhered to a glass fiber with super glue, and all data were collected at
room temperature. The data were collected, analyzed, and integrated
using the X-AREA17 software, where X-RED integrated the data and
X-SHAPE applied the numerical absorption correction based on the
crystal’s shape and composition. The data was solved with SHELXT
using Direct Methods, and refined with SHELXL using the Least
Squares method.18 The crystallographic information for both
structures can be found in Tables 1−3. Additional crystallographic
information can be found in the Supporting Information.
Scanning Electron Microscopy and Energy Dispersive
Spectroscopy (EDS). Images and quantitative analysis (apart from
lithium) were performed with a Hitachi S-3400 scanning electron
microscope that was equipped with a PGT energy-dispersive X-ray
analysis instrument. Lithium cannot be detected by EDS due to its low
electron count, so the results of LiSn2Bi5S10 do not have lithium in the
atomic percentages. To account for this, X-ray photoelectron
spectroscopy (XPS) and inductively coupled plasma optical emission
spectroscopy (ICP-OES) were used to confirm the presence of lithium
in the structure. EDS was performed at 25 kV, 70 mA probe current,
and a 60 s acquisition time. The chemical compositions of each crystal
were the result of averaged compositions from multiple single-point
data collections.
Differential Thermal Analysis (DTA). Differential thermal
analysis (DTA) was performed using a Netzsch STA 449 F3 Jupiter
simultaneous thermal analysis (STA) instrument. The samples were
ground to a fine powder, loaded into carbon-coated silica ampules
(approximately 40 mg in each ampule), and flame-sealed under
vacuum. Each sample was compared to a sealed silica ampule
containing aluminum oxide (Al2O3) of comparable mass. Each sample
was heated to 800 °C at a rate of 10 °C/min, held at 800 °C for 5 min,
and cooled back down at a rate of 10 °C/min. Each sample went
through two cycles to show that the behavior was repeatable. After
DTA was performed, a PXRD of each compound (see Supporting
Information) was taken to determine if they melted congruently.
Fourier-Transform Infrared Spectroscopy (FTIR). Fourier-
transform infrared spectroscopy (FTIR) was performed using a
Nicolet 6700 IR spectrometer under constant flow of nitrogen with a
diffuse reflectance setup (Figure 4). A metal mirror was used as a 100%
reflectance standard that all of the spectra were compared to.
Absorbance (α/S) data were calculated from the FTIR reflectance data
using the Kubelka−Munk equation (α/S = (1 − R2)/2R), where α is
the absorption coefficient, S is the scattering coefficient, and R is
reflectance.19 The band gap of the material was estimated by using a
linear fit of the absorption edge.
Density Functional Theory (DFT) Calculations. The total
energies and relaxed geometries were calculated by DFT within the
generalized gradient approximation (GGA) of Perdew−Burke−
Ernzerhof, the exchange correlation functional with Projector
Augmented Wave potentials.20 We use periodic boundary conditions
and a plane wave basis set as implemented in the Vienna ab initio
simulation package.21 The total energies were numerically converged
to approximately 3 meV/cation using a basis set energy cutoff of 500
eV and dense k-meshes corresponding to 4000 k-points per reciprocal
atom in the Brillouin zone.
To do a DFT band structure calculation for a material with
experimentally determined mixed occupancy of the individual sites, we
first identified the lowest energy configuration of LiSn2Bi5S10 and
NaSn2Bi5S10 from many geometrically distinct Bi/Li(Na)/Sn
possibilities. In simpler terms, we enumerate all structural possibilities
within a 72-atom cell and rank their electrostatic energies. For the 10
structures with the lowest electrostatic energies, we perform further
DFT calculations to determine the most favorable (lowest energy)
structure. The details of searching for the most favorable structures
have been applied to other materials and are described in Supporting
Information.22 After implementing this strategy, we that found the
ground state structures of LiSn2Bi5S10 and NaSn2Bi5S10 are quite
different even though the two materials have the same composition.
Phonon Dispersion Calculations. To quantitatively explore the
origin of very low lattice thermal conductivity at the atomic level, we
employed the Debye−Callaway model to quantitatively evaluate the
lattice thermal conductivity of LiSn2Bi5S10. It is known that the
Table 2. Bond Lengths [Å] for LiSn2Bi5S10 at 293(2) K with
Estimated Standard Deviations in Parentheses
label
distances
Bi(1)−S(1)
Bi(1)−S(3)
2.582(4)
2.774(2)
2.642(4)
2.745(2)
2.878(3)
2.780(3)
2.665(3)
2.825(2)
2.825(2)
2.479(4)
Bi(2)/Li(1)−S(3)
Bi(2)/Li(1)−S(5)
Bi(3)/Sn(1)−S(2)
Bi(3)/Sn(1)−S(4)
Bi(3)/Sn(1)−S(5)
Sn(2)−S(2)
Sn(3)−S(1)
Sn(3)−S(3)
Table 3. Bond Lengths [Å] for NaSn2Bi5S10 at 293(2) K with
Estimated Standard Deviations in Parentheses
label
distances
Bi(1)/Na(1)−S(1)
Bi(1)/Na(1)−S(4)
Bi(1)/Na(1)−S(5)
Bi(2)/Na(2)−S(1)
Bi(2)/Na(2)−S(3)
Bi(2)/Na(2)−S(5)
Bi(3)/Na(3)−S(2)
Bi(3)/Na(3)−S(3)
Sn(1)/Bi(4)−S(2)
Sn(1)/Bi(4)−S(3)
Sn(2)−S(4)
2.882(7)
2.800(8)
2.678(11)
2.952(10)
2.685(10)
2.761(7)
2.644(11)
2.757(7)
2.855(7)
2.733(12)
2.914(15)
Gruneisen parameters, which characterize the relationship between
̈
phonon frequency and crystal volume change, allow us to estimate the
lattice anharmonicity and better understand the physical nature of
lattice thermal conductivity. The phonon and Gruneisen dispersions
̈
are calculated using first-principles DFT phonon calculations within
the quasi-harmonic approximation. The LiSn2Bi5S10 phonon dis-
persions are calculated on a 108 atom cell at two volumes: one is the
C
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equilibrium volume V0, and another one is the isotropically
compressed volume 0.98V0.
Electrical Conductivity and Seebeck Measurements. Elec-
trical conductivity and Seebeck coefficient measurements were
obtained using an ULVAC Riko ZEM-3 instrument under a low-
pressure helium atmosphere from room temperature to 600 °C. The
sample was cut perpendicular to SPS pressure with approximate
dimensions of 3.5 × 3.5 × 10 mm3, and were coated with a thin layer
of boron nitride on all sides except the points of electrical contact to
minimize melting during the measurement. The electrical conductivity
measurement had an uncertainty of about 10%.25
The Debye−Callaway formalism23 has been shown to produce
accurate values of lattice thermal conductivity, compared to experi-
ment, for low-conductivity thermoelectric compounds.24 The total
lattice thermal conductivity can be written as a sum over one
longitudinal κLA and two transverse κTA and κTA′ acoustic phonon
branches: κLatt = κLA + κTA + κTA′. The partial conductivities κi (i
corresponds to TA, TA′, and LA modes) are given by
Hall Effect and Carrier Concentration Measurements. Room
temperature Hall coefficient and carrier concentration of LiSn2Bi5S10
were measured on an SPS-obtained pellet (thickness <2 mm) using
the van der Pauw technique under a magnetic field of 2 T using
pressure-assisted tungsten electrodes.25 Room temperature electrical
resistivity was also measured. See Supporting Information for
additional details.
2
⎧
⎫
τci(x)x4 ex
Θ /T
⎡
⎤
i
dx
⎪
⎪
∫
⎪
⎪
τi(x)x4 ex
τNi (ex − 1)2
⎢
⎣
⎥
⎦
Θ /T
i
0
1
3
c
κi = CiT3
dx +
⎨
∫
⎬
τci(x)x4 ex
(ex − 1)2
Θ /T
i
0
⎪
⎪
⎩
⎪
⎪
⎭
dx
∫
0
τNi τUi (ex − 1)2
(1)
Thermal Conductivity Measurements. Samples for thermal
conductivity measurements were cut from the same sintered ingot
used for the electrical measurements, and measured on a Netzsch
Laser Flash Analysis (LFA) 457 setup. The samples were cut
perpendicular to SPS pressure with dimensions of 6.0 × 6.0 × 2.0
mm3, and were coated with a thin layer of graphite to prevent any light
emission from the sample during the measurement. The samples were
measured from room temperature up to 600 °C, and were under the
presence of a persistent nitrogen atmosphere. The density for each
sintered material was approximately 93% of the theoretical value, and
the heat capacity was estimated with the Dulong−Petit law, where Cp
In this expression, Θi is the longitudinal (transverse) Debye
temperature, 1/τiN is the scattering rate for normal phonon processes,
1/τiR is the sum of all resistive scattering processes, and 1/τci = 1/τiN +
4
1/τiR, x = ℏω/kBT, and Ci = kB /2π2ℏ3vi, here, ℏ is the Planck constant,
kB is the Boltzmann constant, ω is the phonon frequency, and vi is the
longitudinal or transverse acoustic phonon velocity.
The resistive scattering rate is the sum of scattering rates due to
Umklapp phonon−phonon scattering (1/τiU), mass-difference im-
purity scattering (1/τim), boundary scattering (1/τiB), and electron−
phonon scattering (1/τie−ph). In the pure single crystal compounds
considered here, we ignore the effect of impurity scattering, and we
assume that boundary and electron−phonon scattering contributions
can be ignored at temperatures above approximately 100 K. Thus, the
resistive scattering rate is mainly determined by the Umklapp
phonon−phonon processes (1/τiR ≅ 1/τUi ). The normal phonon
scattering and Umklapp can be written as
= 3R/M (R is the ideal gas constant, and M is the average molar mass
̅
̅
of each material). The total thermal conductivity was calculated to be
κtot = DCpd, where D is diffusivity, Cp is estimated heat capacity, and d
is the experimental density value. These data were analyzed by the
Cowan model as reported previously25 (with pulse correction
included), and the uncertainty is approximately 8%.
5
kB γ 2V
1
LA
=
5 x2T5
τNLA(x)
Mℏ4vLA
RESULTS AND DISCUSSION
(2)
■
Synthesis and Purification. Although we expected
LiSn2Bi5S10 to form by stoichiometric combination of the
elements, the ratio of the starting materials was 1:1:3:6 for
Li:Sn:Bi:S. This ratio implies that the melt is rich in lithium, but
tin deficient, with bismuth and sulfur being accommodated
correctly. Interestingly, the in-house obtained PXRD pattern
did not show noticeable impurities or an amorphous back-
ground. This off-stoichiometric ratio is partially attributable to
some of the lithium reacting with the fused silica tube in the
melt despite the presence of carbon coating, requiring extra
reagent to ensure a stoichiometric ratio. To investigate this
further, we carried out synchrotron powder X-ray diffraction on
LiSn2Bi5S10 to examine impurities below the threshold of the
Rigaku Miniflex (Figure 1). The results can be seen in Figure 2,
as there is a minor secondary phase that has been fitted via
LeBail refinement of the synchrotron pattern. The lattice
parameters of the secondary phase suggest that it is an n = 4
pavonite in the Li−Sn−Bi−S homologous series, as the c
parameter is smaller and the β angle is coincident with
previously reported n = 4 pavonite compounds.26 Due to the
complicated nature of these structures, precise quantitation of
the secondary phase as well as precise identification of its
stoichiometry cannot be determined.
5
kB γTA/TA′2V
1
=
5 xT5
Mℏ4vTA/TA′
τNTA/TA′(x)
(3)
(4)
2
kB γ2
1
i
i
=
x2T3 e−θ /3T
τUi (x)
Mℏv2Θ
i
i
where γ, V, and M are the Gruneisen parameter, the volume per atom,
and the average mass of an atom in the crystal, respectively. The
Gruneisen parameter can be defined as γ = −Vω∂∂ωV , characterizing the
i
̈
i
i
relationship between phonon frequency and volume change.
Inductively Coupled Plasma Optical Emission Spectroscopy
(ICP-OES). ICP-OES measurements to detect the presence of lithium
and approximate the molar ratios for LiSn2Bi5S10 were conducted
using a Thermo iCap 7600 ICP-OES instrument. LiSn2Bi5S10 (5 mg)
was dissolved in 0.6 mL of aqua regia, and then diluted to a 10 mL
sample with a 3% (by weight) HNO3 solution. All standards and blank
samples were also diluted with the same 3% HNO3 solution. Due to
the evolution of H2S gas upon dissolving the compound in aqua regia,
the amount of sulfur was not measured when performing the
experiment.
Spark Plasma Sintering (SPS). Ingots of both compounds were
ground into fine powders and sieved (53 μm) to ensure small and
homogeneous particle sizes. These powders were then loaded into
12.7 mm graphite dies, and spark plasma sintering (SPS) with an SPS-
211LX, Fuji Electronic Industrial Co. Ltd., instrument was performed
to turn them into dense ingots suitable for cutting and polishing for
thermoelectric measurements. The sample was placed under vacuum
and 40 MPa of pressure, while the heating profile was elevated to 500
°C in 5 min, held there for another 5 min, and then cooled to room
temperature with the sintering turned off. The ingots created from SPS
achieved approximately 93% of the theoretical density of each
compound.
The ICP-OES elemental analysis data (see Supporting
Information) show a larger molar amount of tin compared to
lithium (1.12:1 ratio for Sn:Li) in the product. The Bi:Sn ratio
in the product is also 2.78:1, slightly less than the experimental
molar ratio of 3:1. Energy dispersive X-ray spectroscopy (EDS)
confirmed a 2:1 ratio of S:Bi (see Supporting Information), as
ICP-OES cannot adequately detect sulfur due to dissolution as
H2S when dissolving the compound in aqua regia. These data
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suggest that there is an excess of lithium in the sample, and this
can be explained by the presence of a lithium-rich secondary
phase that can only be detected with synchrotron X-ray
diffraction.
The DTA of this compound shows a dominant melting event
at 677 °C and a shoulder melting event at approximately 690
°C, with matching crystallization events at 661 and 677 °C. The
dominant melting event and its shoulder correspond to the
primary phase LiSn2Bi5S10 and the secondary n = 4 pavonite
phase, respectively. The fact that the melting points of the two
phases are so close together further suggests that they are in the
same homology, as different n-members of homologous series
tend to have incremental changes in their physical properties.6
NaSn2Bi5S10 was synthesized at the nominal 1:2:5:10 molar
ratio of Na:Sn:Bi:S, and the PXRD showed the presence of the
intended major pavonite phase along with a minor secondary
27
phase Sn0.22Bi1.78S2.88
.
The DTA showed melting events at
673 and 625 °C for the major and minor phases, respectively,
with crystallization events at approximately the same temper-
atures for each. The compound could not be sintered into a
pellet for thermoelectric measurements, as the structure
decomposes when it is annealed. This indicates that
NaSn2Bi5S10 is a kinetic phase that is only isolable via
quenching from the melt, whereas LiSn2Bi5S10 is a more
robust, thermodynamic phase.
Structure Description. LiSn2Bi5S10 and NaSn2Bi5S10 were
determined to have the pavonite structure type, which consists
of two alternating rock-salt (either PbS- or SnSe-type) slabs
that were cut perpendicular to the [311] direction of the cubic
rock-salt lattice. (See Figure 3.) The three-dimensional
Figure 1. Powder X-ray diffraction patterns (Cu Kα radiation, λ =
1.5406 Å) and differential thermal analysis (DTA) graphs of
LiSn2Bi5S10 (A and C, respectively) and NaSn2Bi5S10 (B and D,
respectively). There is a shoulder melting event in B at 693 °C, but no
secondary phase in the PXRD pattern, suggesting the presence of a
high temperature precipitate redissovled into the matrix. The
metastable phase NaSn2Bi5S10 also has a minor secondary phase that
melts at 625 °C.
Figure 4. FTIR diffuse reflectance data for LiSn2Bi5S10 (left) and
NaSn2Bi5S10 (right), with measured band gaps of 0.31(2) and 0.07(2)
eV, respectively.
Figure 2. Synchrotron X-ray diffraction (SXRD, λ = 0.412642 Å) and
LeBail fit of LiSn2Bi5S10. The fit suggests that the lithium-rich
secondary phase is an n = 4 pavonite, as the lattice parameters of the
secondary phase are a = 13.1933(2) Å, b = 4.02963(6) Å, c =
15.0152(2) Å, β = 99.233(1)°.
structure is anisotropic and part of the homologous series
M′n+1Bi2Qn+5, where the M′ cations can be bismuth, alkali
metal, lead, silver, or copper, and the Q anions are sulfur or
Figure 3. Crystal structures of LiSn2Bi5S10 (left) and NaSn2Bi5S10 (right). Both contain the same motif of pseudolayered alternating rock-salt slabs,
but the right structure is notable in how the alkali metal is distributed across the bismuth sites.
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Figure 5. (A, B) Electronic band structures for LiSn2Bi5S10 and NaSn2Bi5S10 respectively. The Fermi level is at 0 eV in both graphs. (C, D) Partial
and full density of states for LiSn2Bi5S10 and NaSn2Bi5S10 respectively. The alkali metal is not included due to minimal contribution to either the
VBM or CBM of each structure.
selenium. The naturally occurring pavonite mineral, AgBi3S5,
along with the two compounds described in this work, are the n
= 5 member of this homologous series. In this structure type,
the thinner slab (Slab I) is invariant to changes in the n-
member and consists of [M′S6] octahedra flanked by two
[BiS5] square pyramids, forming SnSe-type layers along the
[010] direction. The thicker slab (Slab II) is a distorted PbS-
type structure fragment, incorporated in pavonite along the
[111] direction. The number of face-sharing octahedra in a
diagonal chain is equal to the number of the n-member.28
For LiSn2Bi5S10, Slab I is unique in that the M′ in the M′S6
octahedron is a site of mixed occupancy, where it is a [LiS6]
octahedron in 72% of unit cells and a [SnS6] octahedron in the
other 28%, and the surrounding coordination environments are
the same [BiS5] square pyramids that are common for this
structure. While it is remarkable that ions of such differing sizes
as Li+ and Sn2+ (0.76 and 1.18 Å, respectively) can occupy the
same site, there is precedence for this phenomenon in other
disordered pavonite structures containing lithium.9 The shorter
bond lengths are also evidence of mixed occupancy, as the
unique bonds at the mixed site (2.479(4) Å and 2.825(2) Å)
are on average shorter than that of the unmixed [SnS6] site
(2.825(2) Å and 2.888(4) Å) in the structure. The large
asymmetry of the [(Li/Sn)S6] site suggests that it is a very
axially distorted octahedron (where both axial bonds are
2.479(4) Å) that has four weaker equatorial bonds of 2.825(2)
Å in length. [(Li/Sn)S6] is similar to the AgS6 octahedron in
synthetic pavonite, where they are both axially distorted. The
axial and equatorial bonds for the AgS6 octahedron are
2.741(6) Å and 2.917(2) Å, respectively.7 Slab II is slightly
more complicated in terms of mixed occupancy, as the five
octahedra along the one-dimensional chain are either [SnS6],
[(Bi/Li)S6], or [(Bi/Sn)S6]. The Bi/Li site is split 87% to 13%
in terms of occupancy, and the Bi/Sn site is split 61% to 39%.
The unique bonds at the Bi/Li site (2.745(3) Å and 2.642(4)
Å) are slightly shorter than the Bi/Sn site (2.780(3) Å and
2.665(3) Å), which is unsurprising considering that the former
contains the significantly smaller lithium cation and the latter is
mixed with two atoms of almost identical ionic radii. These
bond lengths are comparable to established literature bond
lengths for bismuth sulfide and tin sulfide, with the former
ranging from 2.697(14) Å to 2.961(11) Å and the latter ranging
from 2.622(3) Å to 2.6618(19) Å.
NaSn2Bi5S10 is also an n = 5 pavonite, but there are several
notable differences in the occupancies of the metal sites in both
Slab I and Slab II of the structure. The [M′S6] octahedron in
Slab I is actually a Sn/Bi site (84% and 16% respectively) and
does not contain any monovalent alkali metals. [(Sn/Bi)S6] is
also a distorted octahedron, but not to the same extent as the
lithium analogue, as the axial bonds are 2.734(12) Å and the
weaker equatorial bonds are 2.856(7) Å. The [(Sn/Bi)S6]
octahedron is surrounded by two [(Bi/Na)S5] square pyramids,
where the occupancies are 79% and 21% respectively. In Slab II,
the different octahedra along the diagonal chains are either
[SnS6] or two unique [(Na/Bi)S6] octahedra. The Sn−S bond
lengths are comparable to similar bonds in the lithium pavonite
structure with values of 2.866(7) Å and 2.917(15) Å, and the
values of the Na/Bi bonds across all three sites range from
2.644(10) Å to 2.950(10) Å in length. In both structures, the
bismuth- and tin-containing octahedra are distorted due to their
stereoactive lone pairs (6s2 for and 5s2 for bismuth and tin,
respectively), which persists despite the presence of mixed
occupancy with alkali metals at the sites.29
Optical Measurements and Electronic Structure
Calculations. Both LiSn2Bi5S10 and NaSn2Bi5S10 are direct
band gap semiconductors with values of 0.31(2) eV and
0.07(2) eV respectively. The fact that the band gap of the
sodium analogue is significantly smaller occurs due to
differences in mixed occupancy of the individual sites. Instead
of sodium being primarily localized to the pseudo-octahedral
geometry of Slab I in the structure, it is spread out relatively
evenly across the bismuth sites in Slab II, significantly altering
the band structure of the material relative to its analogue. The
differences in site occupancy disorder for the two structures are
corroborated by the band structures of both compounds, as
DFT predicts a wider band gap for the lithium pavonite
structure compared to its sodium counterpart (Figure 5).
The band structures for LiSn2Bi5S10 and NaSn2Bi5S10 are
significantly different, as seen in Figure 5. The predicted band
gap for LiSn2Bi5S10 (0.25 eV) is in good agreement with the
true band gap of 0.31(2) eV, but the predicted gap of the
sodium analogue (0.15 eV) is actually higher than the true gap
that is measured experimentally (0.07(2) eV), an anomalous
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result given the tendency of DFT to underestimate band gaps.
The densities of states (DOS) for each structure were similar in
that the valence band maximum (VBM) of both compounds is
composed of Sn 5s and S 3p character, and the conduction
band minimum (CBM) is almost entirely Bi 6p character with
minimal contribution from Sn 5s orbitals. The alkali metal in
both cases has a negligible effect on the density of states, as
their highest occupied orbitals are not close enough in energy
to contribute to the band edges. However, even though the
alkali metals do not directly contribute to the density of states,
their presence in each structure is important due to the
differences in site occupancy disorder. Their differing ionic radii
dictate which atoms they share occupancy with, and this in turn
alters the individual DOS peaks for each atom listed, resulting
in the vastly different band structures presented in Figure 5.
The valence bands differ in that LiSn2Bi5S10 has much broader
bands, but NaSn2Bi5S10 has much more dispersive bands. The
opposite is true in the conduction bands of the two structures,
as the conduction band is much more dispersive in LiSn2Bi5S10
and broader in the sodium analogue.
example of a material that can be utilized near room
temperature for practical applications.38
LiSn2Bi5S10 behaves as a doped n-type semiconductor with a
conductivity of around 165 S/cm at room temperature. It
decreases with metal-like behavior until around 700 K, where
the conductivity stops falling and then slightly increases due to
bipolar diffusion. Hall effect measurements show a carrier
concentration of approximately 1.2 × 1019 cm−3, while the
Seebeck coefficient starts at −55 μV/K, increases in magnitude
to −160 μV/K, and undergoes a similar turnover at 700 K to
the electrical conductivity, consistent with an increase in carrier
concentration as a result of bipolar diffusion.
LiSn2Bi5S10 has very low thermal conductivity (i.e., below 1
W m−1 K−1) of 0.80 W m−1 K−1 at room temperature. The
thermal conductivity decreases to a minimum of 0.625 W m−1
K−1 at 723 K, highlighting the intrinsically low thermal
conductivity of this structure. The pavonite structure has
been previously reported to have ultralow thermal conductivity
for several different compounds due to its lower symmetry,
complex crystal structure, and the presence of heavy elements
such as bismuth.14,26 However, the thermal conductivity of the
LiSn2Bi5S10 is comparable to that of synthetic pavonite
(AgBi3S5) at room temperature (0.75 W m−1 K−1) and lower
at high temperatures, which is most likely attributable to the
considerable site occupancy disorder and more complex
composition of its structure compared to the original mineral.14
The theoretically simulated lattice thermal conductivity,
using an ordered supercell of LiSn2Bi5S10, is significantly higher
than the actual experimental result. The higher lattice thermal
conductivity is attributable to the quantitative limitations of
DFT to accurately depict the amount of phonon scattering in a
structure with as much disorder as LiSn2Bi5S10. The higher
value is also attributable to the fact that the experimental
sample has a minor secondary phase of n = 4 pavonite, possibly
helping to scatter phonons and lowering the experimental
thermal conductivity. However, the qualitative trends are in
good agreement, as the lattice thermal conductivities both
decrease monotonically as a function of temperature in both
the experimental and simulated cases. The lattice thermal
conductivity in bismuth sulfide at room temperature is
approximately 1.3 W m−1 K−1, which is almost double that of
LiSn2Bi5S10 at the same temperature (0.743 W m−1 K−1),
supporting the claim that the lower symmetry and site
occupancy disorder of the pavonite structure play a role in its
ultralow thermal conductivity.39 In addition, the distortive
environment of the Sn and Bi atoms from the stereoactive lone-
pair s2 electrons and their pronounced repulsive interactions
may also play a role in lowering the thermal conductivity of
LiSn2Bi5S10.40
Electrical and Thermal Measurements. Thermoelectric
measurements were performed on LiSn2Bi5S10 to determine its
potential for this application (see Figure 6). Thermoelectric
Figure 6. Thermoelectric property measurements for LiSn2Bi5S10.
Electrical conductivity (A), Seebeck coefficient (B), total thermal
conductivity (C), and experimental and simulated lattice thermal
conductivity (D).
materials and their efficiency are governed by the equation
2
ZT = σS T , where ZT is the dimensionless figure of merit, σ is
The calculated phonon dispersion of LiSn2Bi5S10 shows that
the transverse acoustic phonon modes have slower velocities
(and thus lower thermal conductivity along that path) than the
longitudinal mode along all three axes (Figure 7). In the
Brillouin zone, Γ to Z corresponds to the a direction, Γ to X
corresponds to the b direction, and Γ to Y corresponds to the c
direction. The transverse modes are similar in the c direction
(through the layers), different in the a direction (between the
layers), and comparably spaced in the b direction (stacking
both slabs), with the red transverse mode being consistently
lower in every direction. The Brillouin zone highlights the
anisotropy of the pavonite structure type, as phonon transport
is significantly different depending on the crystal direction. The
phonon density of states shows that acoustic phonon transport
κ
the electrical conductivity, S is the Seebeck coefficient, T is
absolute temperature, and κ is the total thermal conductivity
(which has both lattice and electronic components). Most
attempts to improve ZT values in thermoelectric materials have
come from optimization of known, high symmetry materials
through various methods such as doping,30,31 nanostructur-
ing,32,33 and band convergence.34,35 One other paradigm for
pursuing high ZT thermoelectrics is the investigation of
materials with complex crystal and electronic structures as
well as large unit cells, such as ternary and quaternary
chalcogenides with ultralow thermal conductivity.36,37 Bismuth
chalcogenides comprise a significant portion of all thermo-
electric research, as Bi2−xSbxTe3 remains the prototypical
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AUTHOR INFORMATION
Corresponding Author
*E-mail: m-kanatzidis@northwestern.edu.
■
ORCID
Jason F. Khoury: 0000-0003-4769-6730
Constantinos C. Stoumpos: 0000-0001-8396-9578
Chris Wolverton: 0000-0003-2248-474X
Mercouri G. Kanatzidis: 0000-0003-2037-4168
Figure 7. Phonon dispersion (left) and phonon density of states
(right) of LiSn2Bi5S10. The red and purple lines in the phonon
dispersion graph correspond to the transverse acoustic phonon modes,
and the blue lines correspond to the longitudinal acoustic phonon
modes. The black lines are optical modes.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was supported by the National Science Foundation
Grant DMR-1708254, as well as the NASA Science Mission
Directorate’s Radioisotope Power Systems Thermoelectric
Technology Development. S.H. and C.W. (DFT calculations)
were supported by the Department of Energy, Office of Science
Basic Energy Sciences Grant DE-SC0014520. C.D.M. was
supported by IMSERC at Northwestern University, which has
received support from the Soft and Hybrid Nanotechnology
Experimental (SHyNE) Resource (NSF NNCI-1542205); the
State of Illinois; and International Institute for Nanotechnology
(IIN). We acknowledge the use of QUEST, the supercomputer
resource facility at Northwestern University. We thank Michael
L. Aubrey for helpful discussions, and Daniel G. Chica for
assisting in ammonia synthesis of Na2S and Li2S.
in this material is primarily based on the motions of the heavier
bismuth atoms with minimal contribution from tin. The
phonon dispersion calculations are consistent with the
intrinsically low thermal conductivity of the structure as well
as its anisotropic nature.
CONCLUSIONS
■
The crystal structures of LiSn2Bi5S10 and NaSn2Bi5S10 display
considerable site occupancy disorder of the alkali metal on both
Bi and Sn sites, and their differences in site occupancy disorder
significantly alter their band structures and their optical
properties. The thermal conductivity of LiSn2Bi5S10 is ultralow
due to the intrinsic attributes of the pavonite structure as well
as its complex composition and site occupancy disorder.
Phonon dispersion calculations highlight the anisotropic nature
of the structure, as the transverse acoustic phonon modes do
not facilitate phonon transport as easily as the longitudinal
acoustic phonon mode. The lattice contribution to thermal
conductivity should increase as the n-member in the
homologous series increases, as the structure would become
more and more isotropic and the symmetry of the structure
would trend toward a defect rock-salt such as Bi2S3. The
pavonite structure is a promising host candidate for thermo-
electric investigation, as these materials inherently have low
thermal conductivity and narrow band gaps. There is also a
considerable phase space to explore, as the respective
homologous series could lead to high performing thermo-
electric materials as well as materials with tunable electronic
properties.
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