Synthesis, Crystal Structure, and Transport Properties of the Hexagonal Mo9 Cluster Compound Ag3RbMo9Se11

Article abstract of DOI:10.1021/acs.inorgchem.7b01200

Mo-based cluster compounds are promising candidates for thermoelectric applications at high temperatures due to their very low lattice thermal conductivity values. Here, we report on a detailed investigation of the crystal structure and transport properties measured in a wide range of temperatures (2-800 K) of polycrystalline Ag₃RbMo₉Se₁₁. Single-crystal X-ray diffraction shows that this compound crystallizes in the hexagonal space group P6₃/m. The crystal structure is formed by stacked Mo₉Se₁₁ units leaving channels that are randomly filled by Rb⁺ cations, while Ag⁺ cations are located between the Mo₉Se₁₁ units. The high disorder in the unit cell induced by these atoms and their large anisotropic thermal displacement parameters are two key characteristics that lead to very low lattice thermal conductivity as low as 0.6 W m^-1 K^-1 at 800 K. The combination of semiconducting-like electrical properties and low ability to transport heat leads to a maximum dimensionless thermoelectric figure of merit ZT of 0.4 at 800 K.

Full text of DOI:10.1021/acs.inorgchem.7b01200

Article
pubs.acs.org/IC
Synthesis, Crystal Structure, and Transport Properties of the
Hexagonal Mo Cluster Compound Ag RbMo Se
9
3
9
11
,
†
†
†
‡
‡
Patrick Gougeon,* Philippe Gall, Odile Merdrignac-Conanec, Lionel Aranda, Anne Dauscher,
Christophe Candolfi,‡ and Bertrand Lenoir
‡
†
Institut des Sciences Chimiques de Rennes, UMR 6226 CNRS−Universite
́
de Rennes 1−INSA de Rennes, 11 allee
́
de Beaulieu, CS
5
0837, 35708 Rennes Cedex, France
‡
Institut Jean Lamour, UMR 7198 CNRS−Universite
́
de Lorraine, Parc de Saurupt, CS 50840, 54011 Nancy, France
ABSTRACT: Mo-based cluster compounds are promising candidates for thermoelectric
applications at high temperatures due to their very low lattice thermal conductivity values. Here,
we report on a detailed investigation of the crystal structure and transport properties measured
in a wide range of temperatures (2−800 K) of polycrystalline Ag RbMo Se . Single-crystal X-
3
9
11
ray diffraction shows that this compound crystallizes in the hexagonal space group P6 /m. The
3
crystal structure is formed by stacked Mo Se units leaving channels that are randomly filled by
9
11
+
+
Rb cations, while Ag cations are located between the Mo Se units. The high disorder in the
9
11
unit cell induced by these atoms and their large anisotropic thermal displacement parameters
−
1
are two key characteristics that lead to very low lattice thermal conductivity as low as 0.6 W m
K
−
1
at 800 K. The combination of semiconducting-like electrical properties and low ability to
transport heat leads to a maximum dimensionless thermoelectric figure of merit ZT of 0.4 at
800 K.
m− K ). The origin of this amorphous-like heat transport is
1
−1 4,5
INTRODUCTION
■
i
a
tied to the large voids located between the Mo Se Se bi-
octahedral clusters (where i and a stand for innen and außen,
9
11
6
Thermoelectric materials possess the remarkable ability to
directly convert heat into electrical current and vice versa,
offering many prospects in waste-heat energy recovering.
Yet, a broad use of this technology has so far been prevented
due to the low conversion efficiency reached in state-of-the-art
28
+
1
−3
̈
respectively, according to Schafer’s notation ), where Ag
cations are distributed over four independent crystallographic
sites and exhibit large anisotropic thermal displacement
4
,5,17
1
−3
parameters.
This remarkable property results in a
thermoelectric compounds.
determined by the dimensionless figure of merit ZT = α T/
The thermoelectric efficiency is
2
maximum ZT of 0.65 at 800 K reached at the maximum Ag
filling level of x = 3.8.
We recently investigated the possibility to further tune the
carrier concentration of these compounds through substitutions
4
1
−3
ρ(κ + κ ).
High ZT materials should exhibit, at a given
L
e
absolute temperature T, a high thermopower α, a low electrical
resistivity ρ, and low lattice (κ ) and electronic thermal
L
18
on the Se site by either S or Te. Relative to the pristine
conductivity (κ ). Hence, the crystal structure of an ideal
e
sample, the increased metallic character of the electronic
transport did not yield enhanced ZT values. Furthermore, the
low solubility limit of both chalcogen atoms suggests that the
Mo−Se clusters are less flexible to substitutions than the Ag
sites are. Our prior studies with Tl and Cu partially replacing
Ag have shown that good thermoelectric properties could be
obtained at high temperatures with ZT values of ∼0.6 at 800 K
for the Tl and Cu compounds.
can also result in different structure types as exemplified by the
Tl-containing compound Ag Tl Mo Se crystallizing in the
thermoelectric material should show crystallographic features
scattering efficiently acoustic phonons but without being at the
expense of the mobility of the charge carriers. This unusual and
conflicting combination of transport properties makes the
design of such a material a complex challenge.
Mo-based cluster compounds provide a particularly interest-
ing area of research to find novel compounds that show
intrinsically very low lattice thermal conductivity values of ∼0.5
6
,19
Of note, such substitutions
−1
−1
4−9
W m
K
above room temperature.
In addition to being
2
2
9
11
nearly optimized with respect to the thermal transport, these
phases offer several degrees of freedom to tune their electrical
properties including the size and geometry of Mo clusters as
well as the rich variety of elements that can be inserted in the
voids left by the three-dimensional arrangement of these
̅
9
trigonal space group R3c and for which bi-octahedral Mo units
6
are connected to six neighboring cluster units. Another
example of this polymorphism is provided by the alkali element
Cs, which leads to the hexagonal compound Ag CsMo Se
11
2.6
9
20
1
0−16
(space group P6 /m). Its crystal structure also contains
clusters.
Among the phases recently studied, our initial
3
i
a
Mo Se Se bi-octahedral cluster units that form tunnels
works on the transport properties of the Ag Mo Se (3.4 ≤ x
9
11
6
x
9
11
≤
3.8) compounds revealed promising thermoelectric proper-
ties at 800 K that primarily stem from their very low lattice
thermal conductivity that nears the glassy limit at 800 K (0.5 W
Received: May 11, 2017
©
XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.7b01200
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Inorganic Chemistry
Article
running along the [001] direction, where the Cs cations reside.
+
The Ag cations occupy statistically 6h sites in the mirror
planes around the ternary axis between two adjacent Mo Se11
9
units.
Here, we report on the novel compound Ag RbMo Se that
3
9
11
crystallizes isostructurally to Ag CsMo Se . We explored its
2
.6
9
11
electrical and thermal properties in a wide temperature range
5−800 K) and show that this compound exhibits semi-
conducting-like electrical properties and very low thermal
(
conductivity values that remain well under 1 W m−1
K
−1
between 5 and 800 K, yielding a maximum ZT value of 0.4
at 800 K.
EXPERIMENTAL SECTION
■
Syntheses and Densification. All the elemental powders were
stored and manipulated in an argon-filled, dry glovebox. The synthesis
of Ag RbMo Se was realized by using powders of the precursors
3
9
11
MoSe and Rb Mo Se mixed with elemental Ag and Mo powders. Mo
2
2
6
6
powder was heated under H flowing gas at 1273 K for 10 h to
2
eliminate possible traces of oxygen. The MoSe2 precursor was
synthesized by direct reaction of Mo and Se in stoichiometric
proportions placed in an evacuated silica tube at 973 K for 48 h. The
Rb Mo Se precursor was synthesized in two steps. First, the ternary
2
6
6
compound In Mo Se was prepared by heating a mixture of InSe,
2
6
6
MoSe , and Mo powders in stoichiometric proportions at 1273 K
2
during 36 h in an evacuated silica tube. The second step consisted in
an ion-exchange reaction of In Mo Se with RbCl at 1073 K. For this
2
6
6
purpose, In Mo Se and RbCl powders were mixed in the proportion
2
6
6
of 1:2.5 and subsequently cold-pressed. The cylindrical pellet was
introduced in a long silica ampule sealed under vacuum. The end of
the ampule, where the pellet was placed, was introduced in a furnace,
heated at 1073 K during 2 d, while keeping the other end of the tube at
room temperature. All these starting compounds were single-phase
according to their laboratory powder X-ray diffraction patterns. At
Figure 1. Fourier difference maps along the c axis in Ag RbMo Se
11
2.6
9
−3
(
a) after refinement of the Mo−Se framework (step: 2 e Å ) and (b)
after the final refinement.
0.0321. The relevant parameters of the data collection and structure
refinement are listed in Table 1. The refined crystallographic
parameters and selected interatomic distances are given in Tables 2
1
473 K, single-phase powders of Ag3−xRbMo Se were observed for 0
x ≤ 0.4. Note that, here, we restricted our transport property
9 11
≤
investigation to the x = 0.0 compound.
The resulting polycrystalline pellets of Ag RbMo Se were finely
3
9
11
Table 1. Relevant Parameters of the Single-Crystal Data
ground and densified by hot uniaxial pressing (HUP) realized under a
−2
Collection and Structure Refinement of Ag2.6RbMo Se11
9
residual argon pressure (∼1 × 10 mbar). A quantity of ∼5 g of
Ag RbMo Se was introduced into a graphite crucible (Ø = 12 mm)
3
9
11
empirical formula
molar mass (g mol−1)
temperature
symmetry
Ag2.6RbMo Se
that was before coated with boron nitride. The pressure was applied
from the beginning of the temperature increase (8 °C/min) to the end
of the high-temperature dwell of 2 h at 1473 K. The applied load was
9
11
2098.49
293(2) K
hexagonal
5
0 MPa at the beginning of the heating and was gradually augmented
up to 85 MPa when the temperature of 1473 K was obtained. The
experimental density was determined from the dimensions and weight
of the pellet and was ∼98% of its theoretical value.
space group
a (Å)
P6 /m
3
10.0384(2)
11.9930(2)
1046.62(5)
2
c (Å)
Single-Crystal and Powder X-ray Diffraction (PXRD).
Measurements were performed with a Nonius Kappa CCD
diffractometer using Mo Kα radiation (λ = 0.710 73 Å) on a small
single crystal obtained by heating a powder of Ag RbMo Se to 1573
3
V (Å )
Z
ρ (g·cm−3)
6.659
3
9
11
3
crystal size (mm )
0.08 × 0.07 × 0.06
Mo Kα (0.710 69 Å)
1.698−34.989
K, at which temperature the latter compound begins to decompose.
An absorption correction (T = 0.1121, Tmax = 0.2754) based on the
radiation
min
21
crystal shape was used. Structure solution and full matrix least-
θ range (deg)
absorption coefficient (mm−1) 28.991
squares refinements were performed using the Sir97 and SHELX
22,23
softwares, respectively.
After refinement of the Mo−Se framework,
limiting indices
−16 ≤ h ≤ 12, −10 ≤ k ≤ 16, − 19 ≤ l ≤
a subsequent difference-Fourier synthesis reveals the presence of Ag
atoms and a quasi-continuous electron density along the c axis due to
the Rb atoms (Figure 1). The latter was modeled with three partly
occupied rubidium sites using second-order tensors for the anisotropic
displacement parameters. Anharmonic treatment of the rubidium
19
reflection collected/unique
refinement method
14 329/1604
full-matrix least-squares on F2
data/parameters
1604/53
24
final R indices [I > 2σ(I)]
R indices (all data)
R1 = 0.0321, wR2 = 0.0724
R1 = 0.0399, wR2 = 0.0753
0.000 48(9)
atoms using the program JANA2000 was unsuccessful. The final
occupation factors for the Ag atoms were refined freely. Analysis of the
2
5
extinction coefficient
largest diff. peak and hole (e·
intensity data using the TwinRotMat routine of PLATON revealed
1.859 and −1.618
the studied crystal was twinned by merohedry with [100, −1−10, 00−
−3
Å
)
1
0
] as the twin matrix. The ratio of the twin components was refined to
.0175(6):0.9825(6), which lowered the R factor from 0.0425 to
2
goodness-of-fit on F
1.159
B
DOI: 10.1021/acs.inorgchem.7b01200
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
2
Table 2. Fractional Atomic Coordinates, Equivalent Isotropic Displacement Parameters (Å ), Wyckoff Positions, and Site
Occupancy Factors (s.o.f.) for Ag RbMo Se
2
.6
9
11
atom
x
y
z
Ueq (Å2)
Wyckoff
s.o.f.
Mo1
Mo2
Se1
0.176 52(4)
0.179 87(6)
0.047 81(6)
0.028 78(8)
0.3333
0.522 75(4)
0.674 82(6)
0.695 86(6)
0.377 73(8)
0.6667
0.564 10(3)
0.7500
0.010 01(9)
0.009 50(11)
0.013 04(11)
0.013 04(14)
0.014 27(16)
0.0278(2)
12i
6h
12i
6h
4f
1
1
1
1
1
0.565 33(4)
0.7500
Se2
Se3
0.106 77(7)
0.7500
Ag1
Rb1
Rb2
Rb3
−0.257 35(9)
0.0000
0.144 72(9)
0.0000
6h
4e
2a
0.869(4)
0.065(9)
0.152(13)
0.718(17)
−0.150(7)
0.2500
0.08(2)
0.0000
0.0000
0.080(8)
0.0000
0.0000
0.0000
0.280(18)
2b
and 3, respectively. More details on the crystal structure study can be
obtained from the Fachinformationszentrum Karlsruhe, 76344
Low-Temperature Transport Properties. Bar-shapes and disks
were cut from the consolidated pellet with a diamond-wire saw for
transport property measurements. Electrical resistivity, thermopower,
and thermal conductivity were measured simultaneously between 5
Table 3. Main Interatomic Distances (Å) for
3
and 300 K on bar-shaped samples (∼1.5 × 1.5 × 8 mm ) using the
Ag RbMo Se , Ag CsMo Se , and h-Mo Se
2
.6
9
11
2.6
9
11
9
11
thermal transport option (TTO) of a physical property measurement
system (PPMS, Quantum Design). Electrical and thermal contacts
were realized by gluing four copper bars with conducting silver epoxy.
Hall effect measurements were performed at selected temperatures
between 5 and 300 K and under magnetic fields ranging between −1
and +1 T. The measurements were performed using a five-probe
method with the alternating current (AC) transport option of the
PPMS. The electrical contacts were realized by attaching copper wires
onto the samples using a small amount of silver paste. Specific heat
was measured from 300 to 2 K by a conventional relaxation method
using the PPMS. The sample of ∼15 mg was glued onto the sample
holder by a minute amount of Apiezon N grease.
distances
Ag2.6RbMo Se
Ag2.6Cs2.6Mo Se
h-Mo Se
9 11
9
11
9
11
Mo(1)−Mo(1)
Mo(1)−Mo(2)
Mo(1)−Mo(2)
Mo(2)−Mo(2)
Mo(1)−Se(3)
Mo(1)−Se(1)
Mo(1)−Se(1)
Mo(1)−Se(2)
Mo(1)−Se(1)
Mo(2)−Se(2)
Mo(2)−Se(2)
2.6216(7)
2.6928(5)
2.7376(5)
2.7419(10)
2.5475(8)
2.6034(6)
2.6334(6)
2.6703(5)
2.7120(6)
2.5829(9)
2.5853(9)
2.6433(6)
2.6463(10)
2.7760(7)
2.9261(9)
3.47(2)
2.6270(4)
2.6937(4)
2.7365(4)
2.7423(6)
2.5439(5)
2.6035(7)
2.6328(6)
2.6683(3)
2.7130(4)
2.5808(6)
2.5902(5)
2.6408(5)
2.6408(5)
2.7935(5)
2.8719(7)
2.6820(6)
2.7370(4)
2.7985(5
2.6838(9)
2.5234(7)
2.5909(6)
2.6000(6)
2.7026(5)
2.6090(6)
2.5672(8)
2.5893(8)
2.5357(5)
High-Temperature Transport Properties. A ZEM-3 apparatus
Ulvac-Riko) was used to measure simultaneously the electrical
(
resistivity and thermopower between 300 and 800 K on bar-shaped
Mo(2)−Se(1) (×2)
Ag(1)−Se(2)
3
samples (∼1.5 × 1.5 × 8 mm ). The thermal conductivity was
determined between 300 and 800 K through thermal diffusivity (a)
measurements using a laser flash instrument (LFA 467, Netzsch).
These measurements were conducted on disk-shaped samples (∼12
mm in diameter, ∼1 mm in thickness) spray-coated with graphite prior
to measurements to obtain a homogeneous signal absorption and
Ag(1)−Se(1) (×2)
Ag(1)−Se(3) (×2)
Rb(1)−Se(1) (×3)
Rb(1)−Se(2) (×3)
Rb(2)−Se(2) (×3)
Rb(2)−Se(1) (×6)
Rb(3)−Se(1) (×6)
3.85(3)
3.6560(7)
3.9902(5)
3.4104(5)
emission. Both quantities are related via the relation κ = αC d, where
P
C is the specific heat, and d is the density. C was evaluated using the
P
P
Dulong−Petit law (C = 3NR in which N is the number of atoms per
P
formula unit, and R is the gas constant) and, hence, was considered
temperature-independent in the covered temperature range. Here, we
neglected the temperature dependence of the density. Longitudinal
and transverse sound velocities were measured at 300 K on disk-
shaped sample using a pulse-echo method. We utilize honey to ensure
a good coupling between the sample and the ultrasonic transducers.
Eggenstein-Leopoldshafen, Germany, (fax: (49) 7247−808−666; e-
mail: crysdata@fiz.karlsruhe.de) on quoting the depository number
CSD-433045.
PXRD data were collected on bulk pieces ground into fine powders
and placed on a zero-background Si sample holder. The data were
collected at 300 K with a Bruker D8 Advance diffractometer with Cu
RESULTS AND DISCUSSION
■
Kα radiation (λ = 1.540 56 Å). Refinements were performed with the
1
Crystal Structure. The crystal structure was successfully
refined on a single crystal with the final composition
Ag RbMo Se in the hexagonal space group P6 /m. The
24,26
Fullprof and Jana2000 software.
Scanning Electron Microscopy (SEM). SEM experiments were
performed to unveil possible secondary phases, the concentration of
which is below the detection limit of PXRD. Images were collected on
polished surfaces of bulk pieces in the backscattering electron (BSE)
mode using a Quanta 650 FEG (FEI). Corresponding X-ray elemental
maps were taken to determine the distribution of the elements within
the sample.
2
.6
9
11
3
substoichiometry in Ag stems from the higher temperature
1573 K) used during the crystal-growth process, which led to a
(
loss of silver as observed by the formation of silver droplets at
the top of the tube. The Mo−Se network results from
interlinked Mo Se clusters via Mo−Se bonds (Figure 2a). The
9
11
Thermogravimetry and Differential Scanning Calorimetry
TG−DSC). Bulk pieces of the dense pellets were used for TG−DSC
Mo Se unit has the point symmetry C and can be viewed as
9
11
3h
(
resulting from the uniaxial face-sharing of two Mo Se units
6
8
analysis. Data were collected using a TG−DSC 92−16.18 apparatus
Setaram). A sample of ∼48 mg was loaded into an alumina crucible.
The thermal response of the sample was monitored between 300 and
00 K under an argon flow with a constant low heating rate of 2 K
after removal of the Se atoms capping the shared faces.
(
Alternatively, the Mo Se can be viewed as the superposition
9
11
of three quasi-planar Mo Se in staggered position, instead of
8
3
3
−
1
min to obtain a good thermal coupling between the sample and the
crucible.
two in Mo Se clusters, with two additional Se atoms capping
6 8
the outer triangular faces. The Mo−Mo and Mo−Se bond
C
DOI: 10.1021/acs.inorgchem.7b01200
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Inorganic Chemistry
Article
Figure 3. Selenium environments of the Ag atoms (the thermal
ellipsoids are drawn at the 97% probability level).
Rb1 and Rb3 are each surrounded by six Se atoms forming
flattened octahedra along the ternary axis. The Rb−Se distances
spread over a wide range, 3.4104 (5)−3.9902 (5) Å. Both the
Ag and Rb sites are partially occupied, introducing strong
positional disorder in the unit cell. As in other Mo cluster
4
−12
chalcogenides,
the Ag and particularly the Rb atoms exhibit
large anisotropic thermal displacement parameters (Table 2)
that likely give rise to low-energy features in the phonon
spectrum as observed, for instance, in clathrates or tetrahe-
29−36
drites.
Phase Characterization and Thermal Stability. The
PXRD pattern of Ag RbMo Se refined in profile matching
3
9
11
method is shown in Figure 4. According to this analysis, the
Figure 2. (upper) Crystal structure of the Ag RbMo Se in
3
9
11
perspective view. (lower) Projection of the crystal structure along
the (001) plane (the thermal ellipsoids are drawn at the 50%
probability level).
lengths, shown in Table 3, are very close in the two
isomorphous compounds Ag RbMo Se and Ag CsMo Se
11
2
.6
9
11
2.6
9
but differ significantly from those determined in the empty
variant h-Mo Se . The similarity of the Mo−Mo distances
9
11
reflects faithfully the identical metallic electron count (MEC);
that is, electrons available for metal−metal bonding, equal to
3
5.6 in both compounds, while in the binary compound, the
MEC is only 32. This is also confirmed by the average distances
Mo−Mo in the Mo cluster that are 2.6922(4) and 2.6938(4)
9
Figure 4. Profile matching method refinement of the PXRD pattern
in Ag RbMo Se and Ag CsMo Se , respectively, and
2
.6
9
11
2.6
9
11
for polycrystalline Ag RbMo Se . The experimental data are shown in
3
9
11
2
.7313(7) in the binary. All these observations agree well
red, while the overlaid solid black line corresponds to the calculated
profile. The difference profile between the theoretical and
experimental patterns is shown in blue. The vertical blue ticks stand
for the Bragg reflections.
with previous studies that showed that any change in the MEC
induces variations of the Mo−Mo distances in the Mo
9
2
0,27
cluster.
The connective formula of the molybdenum−
i
i‑a
a‑i
selenium framework is [Mo Se Se
notation of Schaf
]Se
according to the
9
5
6/2
6/2
2
8
̈
er. As shown by the Figure 2b showing the
projection of the crystal structure of Ag RbMo Se onto the
polycrystalline sample was found single-phase. On the one
hand, as is often the case in chalcogenides with molybdenum
clusters exhibiting cationic disorders, the refinement in Rietveld
method has not yielded very reliable results. However, we could
deduce the composition Ag Rb Mo Se . On the other hand,
2
.6
9
11
(
a,b) plane, large hexagonal tunnels that are randomly filled by
+
+
the Rb cations run along the c-axis. The Ag cations occupy
partially positions in the mirror planes around the ternary axes
between adjacent Mo Se units located on the threefold axes.
9
11
3.1
1.3
9
11
Its Se environment can be seen as a distorted square pyramid
the silver atom occupying a position 6h, the stoichiometry in
silver cannot exceed 3, and the cationic charge cannot be
with Ag−Se bond lengths ranging from 2.6463(10) to
2.9261(9) Å (Figure 3). The Rb2 cations are in distorted
greater than +4 (i.e., 36 electrons per Mo cluster), we can
9
tricapped trigonal prismatic selenium environment, while the
conclude that the stoichiometry of the synthesized powder is
D
DOI: 10.1021/acs.inorgchem.7b01200
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Inorganic Chemistry
Article
Figure 5. BSE images and corresponding elemental X-ray maps of the consolidated polycrystalline sample used for transport properties
measurements.
very close to Ag RbMo Se . This is also confirmed by the
the DSC curve up to 800 K. The small mass increase observed
in the TG curve upon heating (∼1.5% at 800 K) is likely due to
slight surface oxidation during data collection.
3
9
11
elemental mappings along with the backscattered electron
images (Figure 5), collected on a piece of the consolidated
sample, which confirm the absence of secondary phases
indicating that no thermal decomposition occurred during the
HUP process. The chemical composition, estimated by energy-
dispersive electron spectroscopy (EDXS) to be
Ag Rb Mo Se (normalized to 11 Se atoms per chemical
Electronic Transport Properties. The evolution of the
electrical properties with the chemical compositions of
compounds containing Mo cluster units can be rationalized
by the MEC. Density functional theory (DFT) calculations
have shown that the MEC is equal to 32 electrons for the
structural motif Mo Se , while a count of 36 is required to
2.9
1.1
9.2 11
formula), is close to the nominal composition. The X-ray
elemental maps indicate a homogeneous distribution of all the
elements.
9
11
37
reach a semiconducting state. These additional electrons are
provided by the elements inserted in the large channels of the
crystal structure assuming ionic interactions between these
cations and the Mo−Se clusters. For instance, in the
Ag Mo Se phase, a semiconducting state is predicted for x
According to the TG−DSC analysis shown in Figure 6,
Ag RbMo Se does not exhibit any sign of thermal
3
9
11
decomposition or phase transition in the temperature range
covered. No endothermal or exothermal event is observed in
x
9
11
= 4 supposing that the Ag atoms exhibit an oxidation state of
E
DOI: 10.1021/acs.inorgchem.7b01200
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Inorganic Chemistry
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with this prediction. ρ(T) follows an activated behavior,
indicative of a semiconducting character. As most of the Mo-
based cluster compounds studied so far, α is positive in the
investigated temperature range, suggestive of holes as the
dominant charge carriers. This behavior is consistent with a
Fermi level hosted in the top of the valence bands. As shown in
Figure 7b, α(T) increases nearly linearly to 560 K. Above this
temperature, the slope of α(T) is significantly lower, and α
reaches a maximum of ∼150 μ V/K at 800 K. This variation in
the slope of α(T) at high temperatures has also been observed
6
in the cluster compound Ag Tl Mo Se . The TG−DSC
2
2
9
11
analysis did not evidence any obvious thermal events around
5
60 K suggesting that this behavior might be purely electronic
in origin and related to modifications in the balance between
the electron and hole contributions to α.
Thermal Transport Properties. The temperature depend-
ence of the specific heat C is depicted in Figure 8a. Near 300
P
K, C approaches the Dulong−Petit value of 3NR. The C (T)
P
P
Figure 6. TG−DSC traces for polycrystalline Ag RbMo Se . The
data follow a conventional Fermi-liquid dependence C = γT +
3
9
11
P
3
solid and dashed curves correspond to DSC and TG, respectively.
βT only at very low temperatures. A fit of the C (T) data
P
following this relation confirms the semiconducting ground
state of Ag RbMo Se , synonymous with a null electronic
3
9
11
+
1. Although a semiconducting state is not reached in these
contribution γ(T) to within experimental uncertainty. The
phonon contribution characterized by the parameter β leads to
a very low Debye temperature of 130 K. This value is consistent
compounds due to the maximum Ag filling level of x = 3.8, the
overall variations of the electrical properties are in agreement
with this simple picture. Considering the similarity between
the crystal structures of Ag RbMo Se and Ag CsMo Se ,
the electronic structure of Ag RbMo Se should be very
similar to the one of the cesium analogue. Previously, density
functional calculations were performed on the model
compound Ag CsMo Se . These calculations showed that,
for an MEC of 36 electrons, the Mo−Mo bonding and
nonbonding bands are separated from the Mo−Mo antibond-
4
,5
4
−8
with those inferred in other cluster compounds.
In cagelike materials such as clathrates,
2
.6
9
11
2.6
9
11
29−33
the low-energy
2
.6
9
11
excitations associated with the encaged atoms that exhibit the
largest atomic displacement parameters (ADP) give rise to
additional contributions to the specific heat at low temper-
atures. This excess specific heat is usually evidenced as a
20
3
9
11
3
pronounced peak in the C data plotted as C /T versus T that
P
P
29−33
20
can be adequately modeled by Einstein oscillators.
Mo-
ing bands by a band gap of ∼1 eV. Because of the ionic
interaction between the alkaline and the Mo−Se clusters, the
nature of the alkaline metal and its position in the channel
hardly perturb the electronic structure of Ag MMo Se (M =
based cluster compounds feature similar contributions
associated with the thermal vibrations of the cations located
in the intercluster voids. Ag
RbMo Se11 provides another
3
9
11
3
9
Rb, Cs). Therefore, we can anticipate that Ag RbMo Se
example of a system with low-energy excitations as reflected by
3
9
11
3
should be close to a semiconducting state as well, assuming
that Ag and Rb are both in a +1 state. The variations in the
electrical resistivity and thermopower as a function of
temperature, shown in Figure 7a,b, respectively, are consistent
the peak visible in the C /T (T) data (Figure 8b) at ∼3 K. Yet,
P
a detailed analysis based on Einstein oscillators in these
compounds is less straightforward due to a more complex low-
energy phonon spectrum than in clathrates.
Figure 7. Temperature dependence of the electrical resistivity ρ (a) and thermopower α (b) for Ag RbMo Se .
3
9
11
F
DOI: 10.1021/acs.inorgchem.7b01200
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
Figure 8. (a) Specific heat C as a function of temperature. The horizontal black solid line corresponds to the Dulong−Petit value. (b) Specific heat
P
3
data plotted as C /T vs T to visualize the low-temperature peak associated with the presence of low-energy excitations.
P
These characteristics are likely important ingredients that are
experimental transverse and longitudinal sound velocities,
38
at the origin of the very low thermal conductivity κ values
respectively. With ν = 1347 m/s and ν = 3287 m/s, this
T L
1
−1
−1
−1
(
Figure 9) that remain well below 1 W m−
K
between 5 and
formula yields κmin ≈ 0.43 W m K . This compound thus
makes no exception to the general fact that Mo-based cluster
compounds feature very low lattice thermal conductivity, a
property that tends to be practically independent of the size
and geometry of the clusters and of their spatial distribution
within the unit cell.
Dimensionless Thermoelectric Figure of Merit. The
temperature dependence of the ZT values is shown in Figure
1
0. Despite the low thermal conductivity values, the rather large
Figure 9. Total (red ●), electronic (green ▲), and lattice (blue ■)
thermal conductivity as a function of temperature for Ag RbMo Se .
3
9
11
The lack of data between 250 and 300 K and the slight upturn
observed above 200 K are due to thermal radiations that accompany
the low-temperature measurements. The solid black line represents the
theoretical minimum of the lattice thermal conductivity κmin
.
8
00 K. The electronic thermal conductivity κ was estimated
e
using the Wiedemann−Franz law κ = LT/ρ, where L is the
Figure 10. Temperature dependence of the dimensionless figure of
merit ZT for Ag RbMo Se .
e
Lorenz number. The variations in temperature of L were
3
9
11
approximated by a single-parabolic-band model. While below
3
00 K κ ≈ κ due to the high ρ values, κ reaches ∼30% of the
L
e
total thermal conductivity at 800 K. κ slightly diminishes when
L
−1
−1
the temperature increases to reach ∼0.6 W m
At high temperatures, these values are close to the minimum
lattice thermal conductivity which can be calculated above the
K
at 800 K.
electrical resistivity values lead to a moderate ZT of 0.4 at 800
K. Investigations of S and Te substitutions for Se in the sister
compound Ag Mo Se have shown that both elements
3.8
9
11
18
D e b y e
t e m p e r a t u r e
f r o m
reinforce the metallic character of the electronic conduction.
Hence, further optimization of the power factor of
Ag RbMo Se11 through these isovalent substitutions on the
Se sites might help to tune the electrical resistivity.
1
/3
1
π
6
−2/3
κmin
=
k V
B
(2v + v )where V is the average
( )
T
L
2
3
9
volume per atom in the unit cell, and ν and ν are the
T
L
G
DOI: 10.1021/acs.inorgchem.7b01200
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
Thermoelectric Properties of the Novel Cluster Compound
CONCLUSION
We reported on the successful synthesis of the Ag RbMo Se
■
Ag In Mo Se . Chem. Mater. 2012, 24, 2899−2908.
3
2
15 19
3
9
11
(8) Al Rahal Al Orabi, R.; Fontaine, B.; Gautier, R.; Gougeon, P.;
cluster compound. Single-crystal X-ray diffraction measure-
ments performed at 300 K evidenced the high disorder induced
by the Ag and Rb ions, both of them showing large ADP values.
Within the temperature range of 300−800 K, the title
compound is stable with no signs of phase transitions or
mass loss. Ag RbMo Se shows very low thermal conductivity
Gall, P.; Bouyrie, Y.; Dauscher, A.; Candolfi, C.; Lenoir, B. Cu
Insertion Into the Mo12 Cluster Compound Cs Mo Se : Synthesis,
2
12 14
Crystal and Electronic Structures, and Physical Properties. Inorg. Chem.
2
016, 55, 6616−6624.
(9) Daigre, G.; Gougeon, P.; Gall, P.; Gautier, R.; Guillou, O.; Vaney,
J.-B.; Candolfi, C.; Dauscher, A.; Lenoir, B. Synthesis, Crystal Structure
and High-Temperature Transport Properties of the New Cluster
3
9
11
−1
−1
values (0.7 W m
K
at 800 K) due to the combination of a
complex unit cell and large ADPs of the Ag and Rb ions. The
high electrical resistivity and thermopower values are consistent
with the valence electron count predicting than Ag RbMo Se
11
should be close to a semiconducting state. A maximum ZT
value of 0.4 is reached at 800 K, indicating that substitutions on
the Ag sites might provide a route to achieving good
thermoelectric properties. Further investigations with other
substituting elements on the Ag site would be of interest and
may lead to enhanced thermoelectric performances and/or to
Compound Rb
2
Mo15Se19. J. Solid State Chem. 2016, 237, 1−6.
(10) Picard, S.; Gougeon, P.; Potel, M. Rb Mo S : A Novel
10
36 38
Reduced Molybdenum Sulfide Containing the Highest Nuclearity
Transition Metal Cluster in a Solid-State Compound. Angew. Chem.,
Int. Ed. 1999, 38, 2034−2036.
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(
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11) Picard, S.; Saillard, J.-Y.; Gougeon; Noel, H. P.; Potel, M.
Rb (Mo S )(Mo S ) (n = 1 to 4): A Novel Family of
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n
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6n 6n+2
Superconducting Molybdenum Cluster Compounds. J. Solid State
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(12) (a) Gougeon, P.; Potel, M.; Padiou, J.; Sergent, M. Synthesis,
novel crystal structures with different Mo Se cluster arrange-
ment.
9
11
Crystal Structure and Electrical Properties of the First Compound
Containing Uniquely Mo Se Cluster Units. Mater. Res. Bull. 1987,
12
14
2
2, 1087−1092. (b) Gautier, R.; Picard, S.; Gougeon, P.; Potel, M.
Synthesis, Crystal and Electronic Structures, and Electrical Properties
of Rb Mo Se Containing Trioctahedral Mo12 Clusters. Mater. Res.
ASSOCIATED CONTENT
Accession Codes
CCDC 1550722 contains the supplementary crystallographic
data for this paper. These data can be obtained free of charge
via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_
request@ccdc.cam.ac.uk, or by contacting The Cambridge
Crystallographic Data Centre, 12 Union Road, Cambridge CB2
■
2
12 14
Bull. 1999, 34, 93−101.
13) (a) Gougeon, P.; Potel, M.; Sergent, M. Structure of
Rb Mo Se Containing the New Mo15 Clusters. Acta Crystallogr.
(
3
15 17
1
989, C45, 182−185. (b) Gougeon, P.; Potel, M.; Sergent, M.
Structure of Cs Mo Se . Acta Crystallogr. 1989, C45, 1413−1415.
(
First Structural Type Containing the New Mo Se Cluster Unit.
3
15 17
14) Gougeon, P.; Potel, M.; Padiou, J.; Sergent, M. Rb Mo Se
4 18 20
1
EZ, UK; fax: +44 1223 336033.
18
20
Mater. Res. Bull. 1988, 23, 453−460.
AUTHOR INFORMATION
Corresponding Author
E-mail: patrick.gougeon@univ-rennes1.fr.
■
(15) Picard, S.; Gougeon, P.; Potel, M. Single-Crystal Structure of
Cs Mo S . Acta Crystallogr. 1997, C53, 1519−1521.
5
21 23
*
(16) Gougeon, P. Nouveaux Chalcogen
́
ures Ternaires de Molybden
̀
e
a
̀
Clusters Condenses
Thesis, University of Rennes: France, 1984.
17) Gougeon, P.; Padiou, J.; Le Marouille, J.-Y.; Potel, M.; Sergent,
M. Ag Mo Se Premier Compose Clusters Mo dans des Motifs
́
Syntheses, Structures et Proprietes Physiques.
̀
́
́
ORCID
Patrick Gougeon: 0000-0003-4778-5581
Christophe Candolfi: 0000-0002-1248-5354
Notes
(
́ ̀
a
3.6
9
11
9
Mo
18) Masschelein, P.; Candolfi, C.; Dauscher, A.; Al Rahal Al Orabi,
R.; Gougeon, P.; Potel, M.; Gautier, R.; Lenoir, B. to be published.
19) Colin, M.; Zhou, T.; Lenoir, B.; Dauscher, A.; Al Rahal Al Orabi,
Se11. J. Solid State Chem. 1984, 51, 218−226.
9
(
The authors declare no competing financial interest.
(
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