GeAs: Highly Anisotropic van der Waals Thermoelectric Material

Article abstract of DOI:10.1021/acs.chemmater.6b00567

GeAs and Sn-doped GeAs were synthesized from elements. Both crystallize in a layered crystal structure in the C2/m space group (No. 12) in the GaTe structure type. The crystal structure consists of As-terminated layers separated by van der Waals gaps. ¹¹⁹Sn M?ssbauer spectroscopy reveals that in the doped compound, Sn atoms are situated in a symmetric and homogeneous environment, most probably in the form of Sn₂ dumbbells. The anisotropic crystal structure of GeAs leads to highly anisotropic transport properties. High electrical and thermal conductivities were determined along the crystallographic layers. For the perpendicular direction across the layers, a sharp drop of more than an order of magnitude was observed for the transport properties of the GeAs single crystal. As a result, an order of magnitude difference in the figure of merit, ZT, was achieved. High-temperature thermoelectric characterization of the Sn-doped compound reveals a remarkable ZT with a maximum of 0.35 at 660 K.

Full text of DOI:10.1021/acs.chemmater.6b00567

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Article
GeAs: Highly anisotropic van der Waals thermoelectric material
Kathleen Lee, Saeed Kamali, Tore Ericsson, Maverick Bellard, and Kirill Kovnir
Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b00567 • Publication Date (Web): 18 Mar 2016
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Page 1 of 19
Chemistry of Materials
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GeAs: Highly anisotropic van der Waals thermoelectric
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Kathleen Lee,§ Saeed Kamali,# Tore Ericsson,& Maverick Bellard,§ Kirill Kovnir§,*
§Department of Chemistry, University of California, Davis, One Shields Avenue, Davis, CA 95616
#Mechanical, Aerospace & Biomedical Engineering Department, University of Tennessee Space Institute,
Tullahoma, TN 37388
&Department of Chemistry, Ångström Laboratory, Uppsala University, Box 538, SE-75121 Uppsala, Sweden
Layered Arsenide, crystal structure, anisotropy, thermoelectric
ABSTRACT: GeAs and Sn-doped GeAs were synthesized from elements. Both crystallize in a layered crystal structure in
the C2/m space group (No. 12) in the GaTe structure type. The crystal structure consists of As-terminated layers separated
by van der Waals gaps. 119Sn Mössbauer spectroscopy reveals that in the doped compound, Sn atoms are situated in a
symmetric and homogeneous environment, most probably in the form of Sn2 dumbbells. The anisotropic crystal structure
of GeAs leads to highly anisotropic electronic and thermal transport properties. High electrical and thermal conductivities
were determined along the crystallographic layers. For the perpendicular direction across the layers, a sharp drop of more
than an order of magnitude was observed for the transport properties of the GeAs single crystal. As a result, an order of
magnitude difference in the figure of merit, ZT, was achieved. High-temperature thermoelectric characterization of the
Sn-doped compound reveals a remarkable ZT with a maximum of 0.35 at 660 K.
INTRODUCTION Efficient thermoelectric materials are
highly sought after for use in space applications, such as
in the Mars Rover, Curiosity. Thermoelectric materials
anharmonicity leading to low thermal conductivities and
high figures of merit.9-12 SnSe, a layered material, was
shown to have an unprecedentedly high figure of merit of
2.6 along one crystallographic direction.13 Moreover, the
compound was shown to have strongly anisotropic
transport properties along different crystallographic
directions. Anisotropic properties are not commonly
reported for layered materials since this requires growth
of relatively large single crystals. Nevertheless, the
anisotropic transport properties are important for
understanding the structure-properties correlations in
thermoelectric materials. Germanium arsenide belongs to
an underexplored family of binary van der Waals
compounds formed from tetrel (group 14) and pnicogen
(group 15) elements. Herein, we discuss the synthesis and
crystal structure of GeAs, doping with Sn, and the
anisotropic thermal and electronic transport properties
that stem from the crystal structure.
also
have
potential
domestic
applications
in
thermoelectric cooling and waste heat recovery. The
efficiency of thermoelectric materials is determined from
the dimensionless figure of merit, ZT, defined as ZT =
S2T/κρ, where
S
is the Seebeck coefficient or
thermopower, T is temperature, κ is the thermal
conductivity, and ρ is the electrical resistivity. Efficient
thermoelectric materials exhibit high thermopower, low
thermal conductivity, and high electrical conductivity. To
optimize ZT, often complex and large crystal structures
are sought after to reduce the thermal conductivity.
Another approach to reduce thermal conductivity is to
utilize the phonon glass-electron crystal (PGEC) concept1
where the compound possesses a well-defined crystal
structure to provide good electrical conductivity with
weakly bonded atoms or fragments to scatter phonons, as
in a glass. Inorganic clathrates are typical PGEC systems
since they are composed of 3D frameworks that effectively
conduct electrons with guest atoms encapsulated in large
cages that are capable of rattling to scatter phonons.2-4
Similarly, Sb- and Bi-based Zintl phases have anionic
frameworks that serve as the electron crystal with
complex structural features that scatter phonons.5-8
EXPERIMENTAL
Warning: At high temperatures the As vapor pressure
may be sufficient to damage the reaction ampoules, which
may result in an explosion releasing toxic As vapor. The
concentration of As should be kept to a minimum.
SYNTHESIS The starting materials, Ge (Alfa Aesar,
99.999%), As (Alfa Aesar, 99.9999%), and Sn shot (Alfa
Aesar, 99.7) were used as received. GeAs was synthesized
by combining a stoichiometric amount of Ge with a 3-5
wt% excess of As leading to Ge:As ratios of 1:1.03-1.05. The
Anisotropy of the crystal structure adds one more level
of complexity. Anisotropic crystal structures, such as van
der Waals solids, have recently gained attention due to
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elements (total mass < 1 g) were sealed inside evacuated QUANTUM CHEMICAL CALCULATIONS Electronic
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silica ampoules. The ampoules were heated to 1373 K over
48 hours, annealed at this temperature for 4-5 days, and
then cooled inside the furnace. GeAs forms from a melt,
so the product is a single ingot. Excess As was removed
from the sample by sublimation in a sealed silica ampoule
in a temperature gradient of 300/773 K with the sample
placed in the hot temperature zone.
structure calculations and bonding analyses for GeAs
were carried out using the tight binding-linear muffin tin
orbitals-atomic sphere approximation (TB-LMTO-ASA)
program.15-19 The Barth-Hedin exchange potential was
employed for the LDA calculations.16 The radial scalar-
relativistic Dirac equation was solved to obtain the partial
waves. The basis set used contained Ge(4s,4p) and
As(4s,4p) orbitals with downfolded Ge(4d) and As(4d)
functions. The density of states and band structures were
calculated after converging the total energy on a dense k-
mesh of 24×24×26 points with 1272 irreducible k-points.
119Sn MÖSSBAUER SPECTROSCOPY 119Sn Mössbauer
spectroscopy was performed at room temperature on an
X2000 spectrometer operating in constant acceleration
mode in transmission geometry. Measurements were
performed with a Ca119SnO3 source maintained at room
temperature. Isomer chemical shifts are referenced to the
Ca119SnO3 absorber. The spectrum was least squares fitted
using the Recoil software.20 The parameters from the
fittings include the isomer shift (δ = 1.68 mm⋅s−1),
quadrupole splitting (ΔEQ = 0.44 mm⋅s−1), linewidth (Γ =
0.81 mm⋅s−1), and intensity (I = 100%). All e.s.d. are smaller
than 0.01 mm⋅s−1.
Sn-doped GeAs was synthesized using a flux method by
combining Sn:Ge:As in a 2:1:2 molar ratio inside sealed
and evacuated silica ampoules. The same heating profile
as pure GeAs was used. After annealing, the samples were
prepared for centrifugation and excess Sn and Sn4As3 were
removed by centrifuging at 873 K. The final products were
washed with a 1:1 HCl:H2O solution for several hours to
remove any remaining amounts of Sn and Sn4As3. The Sn
content was determined by energy dispersive X-ray (EDX)
spectroscopy. Compounds with smaller amounts of Sn-
doping were prepared by combining the elements in the
desired ratio, e.g., 3% Sn-doped samples were prepared by
combining the elements in a 0.03 Sn : 0.97 Ge : 1.00 As
ratio and annealed at the same conditions as above. The
products were checked for purity by powder X-ray
diffraction and no further treatment was found to be
necessary (Figure S1).
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Table 1. Data collection and structural refinement
parameters for GeAs and Sn-doped GeAs.a
DIFFERENTIAL SCANNING CALORIMETRY (DSC)
GeAs and Sn-doped GeAs were analyzed with a Netzsch
Differential Scanning Calorimeter. DSC measurements
were performed on ~30 mg of sample sealed inside
evacuated silica ampoules. The samples were heated to
1273 K and cooled to 373 K with a heating/cooling rate of
10 K/min.
Compound
Space Group
Temperature [K]
λ [Å]
GeAs
Sn0.08(2)Ge0.92As
C2/m (No. 12)
90(2)
Mo-Kα: 0.71073
X-RAY DIFFRACTION Powder X-ray diffraction (XRD)
was performed on a Rigaku 600 Miniflex employing Cu-Kα
radiation with a Ni-Kβ filter. Room temperature unit cell
parameters were calculated using NIST LaB6 SRM660c as
a standard. Single crystal XRD was performed on a Bruker
AXS SMART diffractometer employing Mo-Kα radiation
with an APEX-II CCD detector. The datasets were
collected at 90 K and recorded as ω-scans with a 0.3˚ step
width. The datasets were integrated using the Bruker
SAINT software and multiscan absorption corrections
were applied. The solutions and refinements were
performed using the SHELX suite.14 The structures of
GeAs and Sn-doped GeAs were solved in the monoclinic
space group, C2/m. A summary of pertinent information
relating to the unit cell parameters, data collection, and
refinement is provided in Table 1 and the atomic
parameters and interatomic distances are provided in
Tables S1 and S2. Details of the crystal structure
determination of the Sn-doped sample are discussed in
the Results and Discussion section.
a [Å]
15.618(3)
3.7948(7)
9.5127(17)
101.115(2)
553.20(17)
15.697(19)
3.810(5)
b [Å]
c [Å]
9.548(12)
101.122(17)
560.3(12)
β [Å]
V [Å]
Z
12
ρ [g/cm3]
μ [mm-1]
θ [degrees]
Data/param.
R1
5.31
33.84
5.38
33.21
2.18 < θ < 30.6
977/37
0.027
2.64 < θ < 29.0
846/39
0.046
wR2
0.063
0.113
Goodness-of-fit
1.06
1.03
Diff. peak/hole
[e/Å3]
1.75/-1.23
3.82/-1.90
a
Further details pertaining to the crystal structure
determination may be obtained from the Inorganic Crystal
Structure Database (ICSD) at Fachinformationszentrum
Karlsruhe, Germany, by quoting the depository numbers
430819 (GeAs) and 430820 (Sn-doped GeAs).
SCANNING ELECTRON MICROSCOPY Elemental
analyses of selected single crystals of GeAs, Sn-doped
GeAs, and their respective sintered pellets were
performed on
a Hitachi S4100T scanning electron
microscope (SEM) with EDX (Oxford INCA Energy).
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Chemistry of Materials
SPARK PLASMA SINTERING High-density pellets were
a GeAs crystal grown from a melt.23 The reported
synthetic procedures did not yield bulk quantities of
phase pure GeAs. Our first attempt to synthesize GeAs
using a stoichiometric ratio of Ge and As resulted in the
formation of GeAs samples contaminated with unreacted
Ge and As. The addition of an extra amount (3-5 wt%) of
As ensured the complete reaction of Ge. Any remaining
unreacted As was removed from the samples by subliming
the As. The product was a single ingot composed of black
plate-like crystals. GeAs is stable against ambient
conditions and is also stable against concentrated HCl.
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pressed for GeAs (5 mm Ø) and Sn0.03Ge0.97As (12.7 mm
Ø). Samples were ground into fine powder and loaded
into graphite dies between circles of graphite foil.
Graphite plungers were used for the 12.7 mm diameter
pellet, while tungsten carbide plungers were used for the
5 mm diameter pellet to withstand high pressures. The
samples were sintered using a Dr. Sinter Lab Jr. SPS-211Lx
(Sumitomo Coal Mining Co., Ltd.) 5 mm/12.7 mm
diameter pellets were sintered by heating samples to 523
K over a period of 5 min under a uniaxial pressure of 51/8
MPa, then heated to 773 K over a period of 45 min at
which point the pressure was increased to 158/87 MPa,
and annealed at this temperature for 10 minutes.
Afterwards, the pressure was released and the sample was
allowed to cool to room temperature. Samples were
removed from the graphite dies and polished to remove
traces of the graphite foil. The relative densities of the
pellets were measured using the Archimedes method and
found to be 96% for the 5 mm GeAs pellet and 89% for
the 12.7 mm Sn0.03Ge0.97As pellet.
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The most tin-rich sample of Sn-doped GeAs was
synthesized using a Sn flux from a combination of
elements in a 2:1:2 ratio of Sn:Ge:As. The Sn-doped GeAs
sample was centrifuged at 873 K to remove excess Sn or
tin arsenides that may have formed. The samples were
additionally washed in a 1:1 HCl:H2O solution for several
hours to dissolve any remaining tin or tin arsenide
impurities. Sn-doped GeAs is not stable in concentrated
HCl, with the slow leaching of Sn from the compound
after several hours in the acid wash. The use of Sn flux
produced samples with the highest Sn content (~8%).
This is similar to the maximum substitution achieved for
Sn-doped GeP.24 Smaller doping contents can be achieved
by using the appropriate stoichiometric ratios of elements
without flux: xSn : (1-x)Ge : 1As for SnxGe1-xAs, x < 0.1.
TRANSPORT PROPERTIES Transport properties were
measured for both an oriented crystal of GeAs
(5.2x4.6x0.5 mm) and pellets of GeAs (5 mm Ø pellet) and
Sn-doped GeAs (12.7 mm Ø pellet). The crystal was
measured in the directions parallel to the layers and
perpendicular to the layers.
Differential scanning calorimetry of GeAs shows the
onset of melting at 1018(2) K and the onset of
Low temperature (< 400 K) resistivity measurements
were performed using
measurement to exclude the resistance of the leads on a
commercial multipurpose Physical Properties
a
standard 4-probe ac
crystallization at 1008(2) K (Figure S2). Sn-doped GeAs
has a lower melting point, with an onset of 1006(2) K and
a crystallization onset of 1006(2) K for the sample with a
nominal 3% Sn doping. Unlike the related GeP and Sn-
doped GeP24 where the difference in melting
temperatures were >200 K, Sn-doped GeAs and GeAs do
not have as large of a difference in melting temperature.
Previous reports state a higher equilibrium melting
temperature for GeAs (1036 K).25-27 In these works the
phase diagram was produced with measurements
conducted in an apparatus with saturated As pressure
while our experiments were conducted by placing solid
GeAs inside sealed and evacuated ampoules. The lack of
As in the gas phase below the melting point may affect
the equilibrium by decreasing the melting temperature.
Our conditions for thermal analysis are closer to the
method used by Stöhr and Klemm who reported GeAs
melting point as 1010 K which is much closer to our
reported temperature.21
Measurement System (PPMS, Quantum Design). The low
temperature thermal conductivity and Seebeck coefficient
were also measured on the PPMS using the Thermal
Transport Option. High temperature (300-700 K) thermal
diffusivity was measured on a Nietzsche LFA 457 using
Pyroceram 9606 as a reference material. The thermal
conductivity, κ, was calculated based on the thermal
diffusivity and heat capacity of the material using the
equation κ = D⋅CP⋅d, where D is the thermal diffusivity, CP
is the heat capacity, and d is the density of the pellet. The
high temperature resistivity and Seebeck coefficient were
measured on a Linseis LSR-3.
RESULTS AND DISCUSSION
SYNTHESIS AND THERMAL STABILITY GeAs was first
reported by Stöhr and Klemm in 193921 and again by
Wadsten in 1977.22 The reported structure was assumed
based on the analogous structure of SiAs. Four years later,
Mentzen et al. reported the crystal structure of GeAs from
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Figure 1. Crystal structure of GeAs. A. Polyhedral view; B. Top view of a single layer; C. Ball and stick model; D. Fragment of GeAs
showing the shortest As-As distances and interlayer spacing. Ge: blue; As: red; Ge2@As6 polyhedra: blue and pink.
CRYSTAL STRUCTURE AND 119Sn MÖSSBAUER
SPECTROSCOPY GeAs is isostructural to other tetrel
pnictides such as GeP and SiAs, crystallizing in the GaTe
structure type28 in the space group C2/m (No. 12). Similar
to GeP, GeAs crystallizes in a layered structure. Within
each layer Ge-Ge dumbbells are surrounded by a distorted
trigonal antiprism of As atoms, as shown by the polyhedra
in Figure 1. The layer is composed of edge-sharing
polyhedra that are oriented orthogonal to each other and
either parallel to or perpendicular to the layers (Figure 1).
Two types of polyhedra rotated with respect to each other
by 90˚ are emphasized: blue Ge2@As6 where the Ge2
dumbbell is oriented perpendicular to the layers, and
pink Ge2@As6 where the Ge2 dumbbell is almost parallel
to the layers (Figures 1A and 1B). Each layer is terminated
by As atoms, with strong covalent bonding within the
layers and van der Waals interactions across the layers.
The shortest As-As distance is 3.359(1) Å and the
interlayer spacing is 1.80 Å (Figures 1C and 1D). The
structure reported by Mentzen et al.23 had smaller unit
cell parameters with a unit cell volume that is 10 Å3
smaller than the structure determined herein from the
single crystal dataset collected at 90 K. Least square
refinement of the room temperature powder diffraction
data using LaB6 as an internal standard resulted in the
Each Ge atom is coordinated by three As atoms and one
Ge atom with Ge-As distances of 2.45-2.49 Å and Ge-Ge
distances of 2.45-2.46 Å (Figure 1). While the Ge3-Ge3
distance and the range of Ge-As distances reported by
Mentzen are similar to this work, the Ge1-Ge2 distance
reported here is 0.02 Å larger than the previously reported
structure.23 The Ge-As distances are comparable to
distances found in transition metal germanium arsenides
(2.43 Å for ZnGeAs2 and 2.46 Å for CdGeAs2),29 alkaline-
earth germanium arsenides (2.42 Å for BaGe2As2,30 2.39-
2.47 Å for Ca3Ge2As4,31 2.41-2.49 Å for Sr3Ge2As4),32 and the
clathrate Ge38As8I8 (2.40 and 2.50 Å).33
Similar to Sn-doped GeP, Sn-doping into GeAs causes
significant disorder and split positions in the crystal
structure. Refinement of the simple GeAs model for the
Sn-doped compound resulted in high R-values and large
anisotropic displacement parameters for all atoms.
Moreover, all Ge positions exhibit occupancies >100%. To
achieve reasonable descriptions of the Sn/Ge positions,
they were refined in isotropic mode. A high electron
density peak was found near each Ge position and refined
as Sn with the constraints that the total occupancy was
100% for those positions and the ADPs were equivalent.
In the next cycles of refinement additional electron
density peaks were found near each As atomic position.
Those positions can be refined as either As or Ge with
identical results since Ge and As are neighbors in the
periodic system. Based on the results for the similar Sn-
doped GeP we expect a certain amount of Ge in the As
positions. For simplicity of description those positions
were finally refined in anisotropic mode as As atoms only.
unit cell a = 15.507(8) Å, b = 3.776(2) Å, c = 9.456(6) Å,
β
= 101.04(2) Å. These unit cell parameters are identical
within 2 e.s.d. to the unit cell reported by Mentzen et al,23
and smaller than the unit cell parameters determined at
90 K (Table 1). More detailed variable temperature
diffraction studies are necessary to clarify the possibility
of thermal expansion of GeAs upon cooling.
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Chemistry of Materials
Figure 2. Top: Average model of the crystal structure of Sn-
Analysis of interatomic distances indicates that the
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doped GeAs. Bottom: Enlarged local coordination of
bimetallic dumbbells showing chemically reasonable
possibilities together with interatomic distances. Sn: black,
Ge: blue, mixed Ge/Sn: grey, As: pink.
distances around the split position M1 cannot be
described simply by two separate Sn and Ge positions.
Proper distances and occupancies were achieved for the
refinement of position M1 jointly occupied with Sn and Ge
(grey atoms in Figure 2) and an additional Ge11 position in
close proximity of position M1. The bottom part of Figure
2 represents the analysis of possible interatomic distances
as well as atomic occupancies in the bimetallic dumbbells.
Ge-Ge distances of 2.32 Å, 2.46 Å, and 2.54 Å are close to
the distances in pristine GeAs, Ge-based inorganic
clathrates and binary RGe2-x phases, R = rare-earth
metal.34-37 In turn, Sn-Sn distances are significantly longer,
typically in the range of 2.75-2.9 Å.38-43
It should be kept in mind that the reported model is an
oversimplification of a complicated disordered structure.
It is reliably determined that in the Ge positions there are
Ge+Sn atoms, but the distribution of Sn might be not as
simple as we refined it to be (Figure 2). In our model, long
metal-metal distances, >2.75 Å, were assigned to Sn-Sn
bonds rather than Sn-Ge or Ge-Ge bonds. To verify this
assumption 119Sn Mössbauer spectroscopy was applied,
which is sensitive to the local tin coordination to further
refine our model. Samples of Sn-doped GeAs grown from
Sn flux were used to ensure the highest concentrations of
Sn in the sample. The spectrum could be fitted with only
one doublet with an isomer shift of 1.68 mm⋅s−1 and a
small quadrupole splitting of 0.44 mm⋅s−1 (Figure 3, top).
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The resulting refined composition was Sn0.08(2)Ge0.92As.
The composition obtained by EDX spectroscopy,
Sn0.04(2)Ge1.00(2)As0.96(2), had a slight As deficiency compared
to Ge (Figure S3). In order to maintain high Ge content, it
is expected that Ge dopes slightly into the As site,
assuming the composition of [Sn0.04Ge0.96][As0.96Ge0.04].
EDX spectroscopy of the sample with the nominal
Despite
a scattered spectrum due to the low Sn
concentration and sample self-absorption, the extracted
hyperfine parameters give valuable information about the
electronic state of the Sn atoms and their environment.
The isomer shift value is characteristic for Sn that is
metallic in nature. The low value of the quadrupole
splitting indicates a relatively high symmetry around the
Sn atoms. The linewidth is relatively narrow, which is an
indication that the Sn atoms have a very homogeneous
surrounding. While the spectrum can be fitted with a
singlet, this is not probable as a singlet generally arises
from Sn atoms in a highly symmetric cubic local
symmetry.
composition Sn0.03Ge0.97As gave
[Sn0.03(1)Ge0.97][As0.98(1)Ge0.02].
a
composition of
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positions, coordination, and chemical bonding of the
dopants are scarcely studied, which hampers the
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relationships.
of
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structure-properties
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Figure 4. Band structure (top) and density of states (bottom)
for GeAs.
Figure 3. Top: 119Sn Mössbauer spectrum of Sn-doped GeAs.
Bottom: Comparison of quadrupole splittings and isomer
shifts of Sn-metal bonds in Sn-M@Pn6 and Sn-Sn@Pn6
fragments For the quaternary compounds, Mössbauer data
were taken from the listed references: Sn24P19.3(2)I8,41
Sn17Zn7P22I8,42 Sn17Sn7P22Br8,42 and Sn19.3Cu4.7As22I8.43
ELECTRONIC STRUCTURE According to the band
structure and density of states (DOS), GeAs is a narrow
bandgap semiconductor with an indirect bandgap of 0.57
eV (Figure 4). The direct transition at the M point, 0.70
eV, is similar in energy to the indirect transitions in the
vicinity of the Z point (Figure 4, top). The calculated
bandgap is in good agreement with an optical bandgap
measurement of 0.65 eV.46 Both Ge and As contribute
equally to the states in the conduction band with a
slightly higher contribution of As orbitals to the states in
the top of the valence band (Figure 4, bottom). A steep
increase of the DOS near the Fermi level is calculated
indicating the possibility for high thermopower. ELF
analysis indicates strong covalent Ge-Ge and Ge-As
bonding as well as the presence of electron lone pairs on
all terminal As atoms, similar to GeP24 (Figure S4). No
interlayer bonding was detected.
A large set of clathrate compounds where similar
fragments involving Sn atoms are present was
characterized with 119Sn Mössbauer spectroscopy.41-43 In
these clathrates, metal dumbbells, Sn-Sn or Sn-M (M =
Zn, Cu), are situated inside distorted antiprisms of
pnicogen atoms, P6 or As6 (Figure 3, bottom). Sn atoms
bonded to Zn or Cu atoms showed larger isomer shifts
and larger quadrupole splittings due to the asymmetry of
the environment and strong electronic density
redistribution. In turn, tin atoms from Sn2 dumbbells
displayed small isomer shifts and quadrupole splittings
(Figure 3, bottom). Sn-doped GeAs possessed even
smaller isomer shifts and quadrupole splittings, indicating
that the Sn atoms are located in highly symmetric
environments and present in the GeAs structure as Sn-Sn
pairs.
THERMOELECTRIC PROPERTIES The electrical
resistivity, thermal conductivity, and Seebeck coefficients
were measured for an oriented crystal and pellets at low
temperature (LT) (2-400 K). The high temperature (HT)
properties in the range of 300-723 K were measured on a
Sn-doped sample with the nominal composition
Sn0.03Ge0.97As. The Sn-doped sample had improved
This example shows the importance of the investigation
of the local structure.44,45 While doping is often used in
material science to modify materials’ properties, the exact
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||-GeAs (Figure 5, bottom right). While the GeAs pellet is
mechanical properties such that large diameter pellets
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could be pressed with lower pressures than for pure GeAs.
We were unable to press large diameter pellets of GeAs
with high enough densities for properties measurements.
Growth of large single crystals and investigation of
alternative pressing methods to produce large crystals
and pellets suitable for HT measurements are currently
underway.
more resistive than the GeAs crystal oriented in the
parallel direction and has a similar Seebeck coefficient as
the crystal oriented in either direction, the main gain to
the figure of merit stems from the low thermal
conductivity. The thermal conductivity of the pellet,
while greater than the thermal conductivity of ⊥-GeAs, is
over an order of magnitude smaller than the GeAs crystal
oriented in the parallel direction, giving an overall figure
of merit of 0.01 at 300K. This is a two orders of magnitude
increase from the figure of merit of the GeAs crystal
oriented in the perpendicular direction. The GeAs
example illustrates the necessity of characterization of the
anisotropic properties of layered thermoelectric materials
to achieve a complete understanding of thermoelectric
properties.
As expected from the crystal structure, GeAs exhibits
anisotropic properties when measured along the layers
and across the layers. The covalent bonding network
within each of the layers is an effective conductor of
charge carriers and heat-carrying phonons, while van der
Waals gaps between the layers serve as effective scatterers
of both carriers. The resistivity of GeAs along the layers
(||-GeAs) is over two orders of magnitude lower than the
resistivity perpendicular to the layers (⊥-GeAs), 44.3
mΩ⋅cm and 1520 mΩ⋅cm, respectively at 300 K (Figure 5,
top). The resistivity of GeAs measured along the
crystallographic layers is within the previously reported
range of 20-200 mΩ⋅cm at 300 K.46 The resistivity of the
GeAs pellet substantially deviates from the statistical
average of 2/3ρ|| + 1/3 ρ⊥, thus indicating the presence of
texturing in the pellet. Because GeAs grows as plate-like
crystals, the spark plasma sintering process does not
ensure a completely random orientation of particles, and
instead the plate-like crystallites may stack in a manner
that is similar to the layered crystal structure.
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The thermoelectric properties of compounds with
anisotropic crystal structures have been previously
reported. Theory suggests extreme anisotropy for single
layer materials such as graphene, phosphorene, and
arsenene.12 Bulk thermoelectric materials, Sb2Te3,50
PbSb2Te4,51 PbBi4Te7,51 and SnSe,13 all show anisotropic
properties in the thermopower, resistivity, and thermal
conductivity. Table
2 summarizes the thermal and
electronic transport properties of these compounds in
comparison with GeAs. Like GeAs, Sb2Te3 has similar
values for the Seebeck coefficient in both crystallographic
directions and anisotropic resistivity and thermal
conductivity values. PbSb2Te4, PbBi4Te7, and SnSe exhibit
higher anisotropy than Sb2Te3 in the electrical resistivity
and thermal conductivity, with an order of magnitude
difference in the figure of merit at room temperature.
GeAs has the largest anisotropy in the thermal
conductivity compared to the listed materials, with the
exception of graphite. Like graphite, which shows 2-3
orders of magnitude difference in electrical conductivity
along the layers versus perpendicular to the layers, GeAs
also shows high anisotropy in conductivity. The high
electrical conductivity coupled with high thermal
conductivity for ||-GeAs resulted in a figure of merit
similar to ⊥-GeAs with the low electrical conductivity and
low thermal conductivity.
The anisotropy in transport properties is also exhibited
in the thermal conductivity. The thermal conductivity of
GeAs in the parallel orientation is over an order of
magnitude larger than the thermal conductivity of GeAs
in the perpendicular orientation at room temperature,
12.6 and 0.4 W⋅m-1⋅K-1, respectively (Figure 5, bottom left).
Using the Wiedemann-Franz law, the total thermal
conductivity can be separated into electronic and lattice
contributions. The lattice contribution to the total
thermal conductivity dominates with minor contribution
from the charge carriers (Figure S5). The thermal
conductivity of ⊥-GeAs at 300 K is comparable to the
thermal conductivities of state-of-the-art thermoelectric
materials and materials with ultralow thermal
conductivities, such as Yb14MnSb11 (0.7 W⋅m-1⋅K-1),47
Bi0.5Sb1.5Te3 (0.7 W⋅m-1⋅K-1),48 Ba8Au16P30 (0.6 W⋅m-1⋅K-1),49
and SnSe (0.46 W⋅m-1⋅K-1 for the [100] direction).13
Sn doping improves the overall figure of merit for GeAs.
The resistivity of Sn-doped GeAs pellet was slightly lower
than the pure GeAs pellet resistivity reaching a value of 67
mΩ⋅cm at 300 K (Figure 6, top left). The thermal
conductivity of the SnxGe1-xAs pellet was slightly higher
than thermal conductivity of pure GeAs (Figure 6, bottom
left). At 300 K, the Seebeck coefficient for the SnxGe1-xAs
pellet is similar to the thermopower of pure GeAs. The
overall figure of merit for the SnxGe1-xAs pellet at 300 K is
0.02, a factor of two increase compared to the pure GeAs
pellet.
Unlike the thermal conductivity and electrical
resistivity, the Seebeck coefficients were more isotropic in
both directions, 194 μV⋅K-1 and 150 μV⋅K-1 at 300 K for ||-
GeAs and ⊥-GeAs, respectively (Figure 5, top right). The
pellet exhibited slightly higher thermopower than either
direction, 231 μV⋅K-1 at 300 K. The positive values of the
thermopower indicate that holes are the main charge
carriers. The overall figure of merit increases by over an
order of magnitude at room temperature from ⊥-GeAs to
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Figure 5. Top left: resistivity; top right: Seebeck coefficient; bottom left: thermal conductivity; and bottom right: figure of merit
plots for the GeAs pellet and the GeAs crystal measured parallel and perpendicular to the GeAs layers.
Table 2. Anisotropic thermoelectric properties at 300 K for selected layered compounds.
S (μV⋅K-1)
σ (S⋅cm-1)
4150
κ (W⋅m-1⋅K-1)
4600
Compound, direction
50Sb2Te3, parallel
50Sb2Te3, perpendicular
51PbSb2Te4 (SbI3 doped), parallel
σ||/σ⊥
κ||/κ⊥
ZT
73
90
26
1.4x10-4
2.2x10-4
1.6x10-5
1.8
1.8
2340
2620
2354
2910
51PbSb2Te4 (SbI3 doped),
perpendicular
10.1
4.5
107
232
650
1.2x10-4
51PbBi4Te7, parallel
51PbBi4Te7, perpendicular
13SnSe, parallel
13SnSe, perpendicular
52,53Graphite, parallel
52,53Graphite, perpendicular
a GeAs, parallel
-18
-40
510
540
3358
784
4150
1090
0.7
7.9x10-6
3.5x10-5
0.2
4.3
5
3.8
1.5
10
2
0.46
140-500
3-10
0.03
2000-4000
3.3
--
606-1212
342.3
47-50
33.2
--
194
159
22.6
12.6
0.002
0.001
a GeAs, perpendicular
0.066
0.38
a This work.
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plots for GeAs and SnxGe1-xAs pellets. LT data are shown as circles and triangles and high temperature data are shown as blue
stars.
μV⋅K-1 at 605 K, indicating a bipolar state with two
At high temperatures the thermal conductivity of the
SnxGe1-xAs pellet continues to decrease reaching a value of
0.92 W⋅m-1⋅K-1 at 777 K (Figure 6, bottom left). The small
discrepancies of the resistivity and thermal conductivity
values may be due to the fact that the LT and HT
measurements were performed on different instruments.
Moreover, each measurement was performed on the
pellet that was oriented in different directions, which may
result in alteration of properties assuming preferred
orientation of the SnxGe1-xAs crystallites within the pellet
(insets in Figure 6). The HT and LT thermal conductivity
measurements were performed perpendicular to the
pellet (parallel to the pressing direction), while the HT
and LT resistivity measurements were performed across
the pellet (perpendicular to the pressing direction). The
Seebeck coefficients were similar at low temperatures and
were measured perpendicular to the pellet for both GeAs
and SnxGe1-xAs pellets. However, the HT measurements
were performed across the pellet, which may explain the
discrepancy in Seebeck coefficient values. The Seebeck
coefficient for SnxGe1-xAs reaches a maximum value of 390
different types of charge carriers (Figure 6, top right). A
Goldsmid-Sharp bandgap estimation54 as Eg = 2e|Smax|Tmax
= 0.47 eV is slightly smaller than the values for undoped
GeAs predicted by quantum chemical calculations, 0.57
eV, and the measured optical bandgap of 0.65 eV.46
Due to the high Seebeck thermopower and low thermal
conductivity, the SnxGe1-xAs pellet exhibits a peak ZT
value of 0.35 at 660 K. This shows the general promise of
layered van der Waals compounds, which are small
bandgap semiconductors, for high temperature
thermoelectric applications.
CONCLUSION GeAs and Sn-doped GeAs were
synthesized and the crystal structures, electronic
structure, as well as the transport properties were
investigated. The anisotropy in the crystal structure is
reflected in the transport properties with orders of
magnitude difference in the resistivity of GeAs along the
layers as opposed to perpendicular to the layers. The
anisotropy is also reflected in the thermal conductivity as
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Electron-Crystal Thermoelectric Properties Nature Mater. 2004,
3, 458-463.
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the van der Waals gaps effectively inhibit phonon
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propagation. For the single crystal, the improved charge
carrier transport causes the ZT along the layers to be an
order of magnitude larger than the ZT across the layers.
Investigation of the compacted polycrystalline pellets
indicates that below room temperature, Sn-doped GeAs
exhibits similar transport properties as the pristine GeAs.
At high temperatures Sn-doped GeAs reaches a peak ZT
of 0.35 at 660 K. Studies of other tetrel-pnictides as well
as growth of large single crystals to characterize
anisotropic transport properties are currently underway.
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Zhang, C.; Peng, Z.; Li, Z.; Yu, L.; Khor, K. A.; Xiong, Q.
Controlled Growth of Bismuth Antimony Telluride BixSb2−xTe3
Nanoplatelets and Their Bulk Thermoelectric Nanocomposites
Nano Energy 2015, 15, 688-696.
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Kazem, N.; Zaikina, J. V.; Ohno, S.; Snyder, G. J.;
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Kauzlarich, S. M. Coinage-Metal-Stuffed Eu9Cd4Sb9: Metallic
Compounds with Anomalous Low Thermal Conductivities
Chem. Mater. 2015, 27, 7508-7519.
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Skoug, E. J.; Morelli, D. T. Role of Lone-Pair Electrons
ASSOCIATED CONTENT
Supporting Information
in Producing Minimum Thermal Conductivity in Nitrogen-
Group Chalcogenide Compounds Phys. Rev. Lett. 2011, 107,
235901.
Supporting Information includes tables containing selected
bond distances and atomic coordinates, powder XRD
patterns, DSC pots, EDX spectra, ELF isosurface and slice,
lattice and electronic contributions to the thermal
conductivity.
(10)
Wang, S.; Yang, J.; Wu, L.; Wei, P.; Yang, J.; Zhang, W.;
Grin, Y. Anisotropic Multicenter Bonding and High
Thermoelectric Performance in Electron-Poor CdSb Chem.
Mater. 2015, 27, 1071-1081.
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Nielsen, M. D.; Ozolins, V.; Heremans, J. P. Lone Pair
Electrons Minimize Lattice Thermal Conductivity Energy
Environ. Sci. 2013, 6, 570-578.
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Transport in Phosphorene: Effects of Crystal Orientation
Nanoscale 2015, 7, 10648-10654.
The Supporting Information is available free of charge on the
ACS Publications website.
Liu, T.-H.; Chang, C.-C. Anisotropic Thermal
AUTHOR INFORMATION
Corresponding Author
(13)
Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.;
Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow
Thermal Conductivity and High Thermoelectric Figure of Merit
in SnSe Crystals Nature 2014, 508, 373-377.
*Kirill Kovnir. Tel.: +1 530 752 5563; fax: +1 530 752 8995;
Email address: kkovnir@ucdavis.edu
(14)
Sheldrick, G. A Short History of SHELX Acta Cryst. A.
Notes
2008, 64, 112-122.
(15)
Program TB-LMTO-ASA 1999, Version 4.7; Max-Plank-Institut
für Festkörperforschung: Stuttgart, Germany.
The authors declare no competing financial interest.
Jepsen, O.; Burkhardt, A.; Andersen, O. K. The
ACKNOWLEDGMENT
(16)
Barth, U. v.; Hedin, L. A local exchange-correlation
We thank Prof. S. M. Kauzlarich for access to the DSC,
Linseis, LFA, and SPS. We thank Katherine Woo for
assistance with X-ray powder diffraction measurements,
Yufei Hu for assistance with high temperature TE
measurements, and Joya Cooley for helpful discussions
regarding the SPS. KL acknowledges the GAANN and ARCS
fellowships. This research is supported by the U.S.
Department of Energy, Office of Basic Energy Sciences,
Division of Materials Sciences and Engineering under Award
DE-SC0008931.
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Zhang, H.; Borrmann, H.; Oeschler, N.; Candolfi, C.;
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Ivanova, L. D., Granatkina, Yu.V., and Sidorov, Yu.A.
Schnelle, W.; Schmidt, M.; Burkhardt, U.; Baitinger, M.; Zhao, J.-
T.; Grin, Y. Atomic Interactions in the p-Type Clathrate I
Ba8Au5.3Ge40.7 Inorg. Chem. 2011, 50, 1250-1257.
Electrical Properties of Antimony Telluride Crystals Doped with
Selenium and Bismuth Neorg. Mater. 1999, 35, 44-52.
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Shelimova, L. E.; Svechnikova, T. E.; Konstantinov, P.
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Zhang, J.; Tobash, P. H.; Pryz, W. D.; Buttey, D. J.; Hur,
P.; Karpinskii, O. G.; Avilov, E. S.; Kretova, M. A.; Zemskov, V. S.
Anisotropic Thermoelectric Properties of the Layered
Compounds PbSb2Te4 and PbBi4Te7 Inorg. Mater. 2007, 43, 125-
131.
N.; Thompson, J. D.; Sarrao, J. L.; Bobev, S. Synthesis, Structural
Characterization, and Physical Properties of the Early Rare-Earth
Metal Digermanides REGe2–x (x ≈ 1/4) [RE = La–Nd, Sm]. A Case
Study of Commensurately and Incommensurately Modulated
Structures Inorg. Chem. 2013, 52, 953-964.
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Diamond, and Fullerenes: Properties, Processing, and Applications
Noyes Publications: Park Ridge, NJ, 1993, pp 61.
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Schlüter, M.; Häussermann, U.; Heying, B.; Pöttgen, R.
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Zaikina, J. V.; Kovnir, K. A.; Sobolev, A. V.; Presniakov,
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Figure 1. Crystal structure of GeAs. A. Polyhedral view; B. top view of a single layer; C. ball-and stick
model; (D) fragment of GeAs showing shortest As-As distances and interlayer spacing. Ge: blue; As: red;
Ge2@As6 polyhedra: green and pink.
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Figure 2. Top: Average model of the crystal structure of Sn-doped GeAs. Bottom: Enlarged local
coordination of bimetallic dumbbells showing chemically reasonable possibilities together with interatomic
distances. Sn: black, Ge: blue, mixed Ge/Sn: grey, As: pink.
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Figure 3. Top: 119Sn Mössbauer spectrum of Sn-doped GeAs. Bottom: Comparison of quadrupole splittings
and isomer shifts of Sn-metal bonds in Sn-M@Pn6 and Sn-Sn@Pn6 fragments. For the quaternary
compounds, Mössbauer data were taken from the listed references: Sn24P19.3(2)I8 [29], Sn17Zn7P22I8
[30], Sn17Sn7P22Br8 [30], Sn19.3Cu4.7As22I8 [31].
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Figure 4. Band structure (top) and density of states (bottom) for GeAs.
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Figure 5. Top left: resistivity; Top right: Seebeck coefficient; Bottom left: thermal conductivity; and
Bottom right: figure-of-merit plots for the GeAs pellet and the GeAs crystal measured parallel and
perpendicular to the GeAs layers.
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Figure 6. Resistivity, Seebeck coefficient, thermal conductivity, and figure-of-merit plots for GeAs and
SnxGe1-xAs pellets. LT data are shown as circles and triangles and high temperature data are shown as blue
stars.
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