The effect of rare-earth filling on the lattice thermal conductivity
of skutterudites
G. S. Nolas and G. A. Slack
Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180
D. T. Morelli
Physics Department, General Motors Research and Development Center, Warren, Michigan 48090
T. M. Tritt and A. C. Ehrlich
Materials Physics Branch, Naval Research Laboratory, Washington, DC 20375
~Received 23 October 1995; accepted for publication 5 January 1996!
Polycrystalline samples of Ir4LaGe3Sb9 , Ir4NdGe3Sb9 , and Ir4SmGe3Sb9 have been made by hot
isostatic pressing of powders. The lattice thermal conductivity of these filled skutterudites is
markedly smaller than that of IrSb3 ; thus, void filling shows promise as a method for improving the
thermoelectric properties of these materials. We present the lattice thermal conductivity of these
filled skutterudites in an effort to quantify the impact of void filling in this structure. It is believed
that the atoms ‘‘rattle’’ in the voids of the structure and therefore interact with a broad spectrum of
lattice phonons, reducing their mean free paths substantially below that in the ‘‘unfilled’’
skutterudites. An additional phonon scattering mechanism is caused by phonon-stimulated
transitions between the low-lying energy levels of the 4 f electron configurations in the case of Nd31
and Sm31. Magnetic susceptibility and Hall-effect measurements are also presented. © 1996
American Institute of Physics. @S0021-8979~96!05808-X#
INTRODUCTION
Approximately 30 years ago the field of thermoelectrics
was at the height of its promise, and much study and research was undertaken. There was great promise of utilizing
thermoelectric materials to perform a variety of solid state
refrigeration needs. In the late 1950s and 1960s materials
were extensively studied and optimized for their thermoelectric application. Most of the research effort since that time
has been involved in optimizing the properties of those materials, i.e., alloys based one Bi2Te3 and Bi–Sb, in order to
improve their thermoelectric capabilities. Excellent reviews
of the thermoelectric properties of materials and thermoelectric refrigeration are given in Refs. 1–3.
The definition of a good thermoelectric material lies in
the magnitude of the material’s figure of merit2,3
Z5
a 2s
,
k
~1!
where a is the Seebeck coefficient, s the electrical conductivity, and k the total thermal conductivity ~k 5 k g 1 k e ; k g
and k e being the lattice and electronic contributions, respectively!. Since the dimensions of Z are inverse temperature, a
more convenient quantity is the dimensionless figure of merit
ZT, where T is the absolute temperature.
There has been substantial renewed interest in the field
of thermoelectrics as new materials become available and
new needs become evident. One of these groups of new materials is the promising skutterudite system. The semiconducting compound iridium triantimonide, IrSb3 , is one the
compounds with the skutterudite or CoAs3 structure.4 –9 The
basic conditions for high ZT of a large unit cell, heavy constituent atom masses, and large carrier mobility, as described
in Slack,10,11 are met in this material. Indeed, initial studies
4002
J. Appl. Phys. 79 (8), 15 April 1996
have indicated that this material shows promise as a potential
thermoelectric material.4,12 In addition to these properties,
skutterudites have large voids in the structure which can be
doped, or ‘‘filled,’’ in attempts to manipulate the thermal
conductivity. Only recently have adequate experimental studies of the properties of skutterudites been undertaken.4,13,14
In addition, Singh and Pickett15 have performed bandstructure calculations for CoSb3 , CoAs3 , and IrSb3 which
indicate that these materials are narrow-gap semiconductors.
The binary skutterudites have the cubic Im3 (T 5h ) structure and are of the form AB3 where A represents a metal
atom and B represents a pnicogen atom. There are eight formula units in the cubic unit cell. In addition there are two
large voids per unit cell in the structure. Skutterudites form
covalent structures with low coordination numbers for the
constituent atoms and so can incorporate atoms in the voids.
We have estimated the void radii of the nine binary semiconducting skutterudite4,7,16,17 compounds from x-ray crystallographic data.5–7,16,17 The radius r~B! of the B atom is taken
to be one-half of the average B–B separation. The void radius is taken as the distance d from the center of the void to
any one of the twelve surrounding B atoms minus r~B!,
r ~ void! 5d2r ~ B! .
~2!
These are listed in Table I.
Filled skutterudites of the form TM4B12 have been
prepared18 –30 where T, most often a rare-earth element, occupies the voids which are surrounded by the pnicogen atoms, B, in the unfilled structure, where M5Fe, Os, or Ru
and B5P, As, or Sb. Large x-ray thermal parameters have
been observed for the filler atoms in these structures.18,19,22,26
In the case of lanthanum, La, in LaFe4B12 ,19 the thermal
0021-8979/96/79(8)/4002/7/$10.00
© 1996 American Institute of Physics
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TABLE I. Lattice parameters a 0 and void radii r in Å of nine unfilled
semiconducting skutterudites.
CoP3
CoAs3
CoSb3
a 0 57.7073
r51.763
a 0 58.205
r51.825
a 0 59.0385
r51.892
RhP3
RhAs3
RhSb3
a 0 57.9951
r51.909
a 0 58.4507
r51.934
a 0 59.2322
r52.024
IrP3
IrAs3
IrSb3
a 0 58.0151
r51.906
a 0 58.4673
r51.931
a 0 59.2503
r52.040
parameter of the trivalent lanthanum ion, La31, was the largest in LaFe4Sb12 , smaller in LaFe4As12 , and the smallest in
LaFe4P12 . In other words, La31 seems to ‘‘rattle’’ more
readily when it is in a larger void. A similar observation was
made in alkaline earth-filled skutterudites.26 As previously
pointed out by one of the present authors,4,10 the rattling of
atoms in the voids of these structures should produce significant phonon scattering and reduce significantly the thermal
conductivity of these compounds.
In the present study we have succeeded in putting rareearth ions into the voids of IrSb3 , chosen because it has the
largest size voids ~as seen in Table I! as well as having good
thermoelectric properties, in an attempt to study their effect
on the lattice thermal conductivity k g . The reduction of k g
of a crystalline compound by introducing ‘‘guest’’ atoms, or
molecules, into ‘‘openings’’ in the crystal structure has been
studied in clathrate hydrates31 and rare-earth borides32–34
such as YB66 . One of the present authors30 has begun the
investigation of filled skutterudites by studying several lowtemperature transport and magnetic properties of CeFe4Sb12 .
In particular, the thermal conductivity in this compound was
reduced substantially with respect to unfilled skutterudites.
In the present article, a systematic study of the effects of
filling the voids of the IrSb3 system with different trivalent
rare-earth ions in order to understand and quantify their effect on the lattice thermal conductivity is presented. In addition, we present magnetic susceptibility and Hall-effect measurements. The potential of filled skutterudites for
thermoelectric applications is also discussed.
SAMPLE PREPARATION
Single-phase polycrystalline samples of Ir4LaGe3Sb9 ,
In4NdGe3Sb9 , and Ir4SmGe3Sb9 were similarly prepared as
follows. First the lanthanum ~La!, neodymium ~Nd!, or samarium ~Sm! rare earth ~R, 99.99% pure!, in lump form, was
reacted with germanium ~Ge, 99.9999% pure! powder, in the
stoichiometric ratio 1:3 at 960 °C for 4 days, in order to
obtain an intimate mixture of R with Ge ~RGe21Ge!. All R
elements and R compounds were handled in an argon atmosphere since high-purity R elements are very reactive in air.
The resulting mixture was ground to a fine powder with a
boron carbide ~B4C! mortar and pestle. It was then mixed
and reacted with the proper stoichiometric amounts of iriJ. Appl. Phys., Vol. 79, No. 8, 15 April 1996
dium ~Ir, 99.99% pure! and antimony ~Sb, 99.9999% pure!
powders at 960 °C for 2 days. In both cases the powder was
held in a chemically vapor deposited 2.67-cm-diam, 6.5-cmtall pyrolytic boron nitride ~BN! crucible which itself was
sealed inside an evacuated, fused quartz ampule. This ampule was heated in an external atmosphere of flowing argon
in order to prevent the inward diffusion of air and water
vapor during the run. The product was removed from the
ampule, ground in the B4C mortar and pestle, cold pressed
into cylindrical pellets, reloaded into a BN crucible, and rereacted for another 2 days at 960 °C as described above.
After removal, the resulting charge was ground into fine
powder using a planetary micromill ~Fritsch GmbH ‘‘pulverisette 7’’! with tungsten carbide vials and balls, passed
through a 400 mesh sieve, again cold pressed into cylindrical
pellets, and then sealed inside of an evacuated Pyrex ampule.
A 2.531023-cm-thick tantalum foil surrounded the ingot to
prevent sticking. This ampule was then placed in a hot isostatic press ~International Pressure Service ‘‘EAGLE’’ HIP!
where the ingots were consolidated at 925 °C for 2 h at
29 500 lb/in.2 of argon pressure. The resulting ingot was
slowly cooled at <2 °C/min to room temperature in order to
avoid fracturing. The Ge randomly substitutes for Sb in the
structure and is used for charge compensation of the trivalent
rare-earth ions, R31. The three Ge atoms act as ‘‘acceptors’’
for the three ‘‘donated’’ electrons from each R atom. The
resulting polycrystalline La- and Sm-filled skutterudite
samples were both 82% of theoretical density and the Ndfilled skutterudite was 72% of theoretical density, assuming a
100% filling of the voids. The density measurements were
performed by weighing a precisely cut cube of each material.
The density measurements were verified using an Olympus
System Microscope model BHT, with camera, interfaced to a
Macintosh computer. Images of polished surfaces of the
samples were digitized and the porosity was calculated automatically. An 82% dense IrSb3 polycrystalline sample was
also prepared in order to experimentally compare it to the
filled skutterudite samples. This sample was not hot isostatically pressed so that it maintained its porosity. It should be
noted that a reaction time of only several hours was adequate
to react the above samples; however, the above procedure
was maintained in order to thoroughly react the powders and
to maintain similar preparatory conditions in the samples
used in this study.
Metallographic and electron-beam microprobe ~JOEL
733 superprobe! examination of the polished surface of each
sample, after HIP, verified the stoichiometry of the samples.
The annealed samples were ground and analyzed by x-ray
diffractometry using Cu K a radiation with a powdered silicon ~Standard Reference Material 640b! internal standard.
Both a graphite-monochromatized Philips model 5520 diffractometer with a scintillation detector and a Scintag XDS
2000 diffractometer which utilizes a solid-state detector were
used. The results from these measurements showed that the
samples were single phase and were 100% filled with the
rare-earth ions.
Electron backscattering images, from the microprobe,
were used to estimate the grain size of the samples. In all
samples, the average grain size was of the order of 10 mm.
Nolas et al.
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FIG. 1. X-ray-diffraction spectra of Ir4LaGe3Sb12 and IrSb3 annealed
samples. The peaks marked with an arrow correspond to those due to the
silicon standard. All other lines correspond to the skutterudite phase. The
peaks marked with an asterisk are absent in completely filled skutterudites.
Optical microscope images taken with the Olympus microscope system, of the Ir4NdGe3Sb9 sample etched with aqua
regia, were also used to measure the average grain size.35
The average grain size of this sample was measured to be 7
mm, in general agreement with the microprobe results.
It should be noted that a gadolinium-filled-skutterudite
sample was also prepared as described above. Electron-beam
microprobe and x-ray results showed mostly skutterudite
phase, however, other phases were present. These results
showed that the skutterudite phase had approximately 40%
of the voids filled with gadolinium, Gd, with an approximate
chemical composition of Ir3.6Gd0.41Ge1.53Sb10.1. This is an
indication that the size of the ions in the rare-earth series is
beginning to be a factor for Gd. It seems that the Gd31 ion is
too small to achieve 100% void filling, even though we made
the sample with a starting composition of Ir4GdGe3Sb9 . We
have also attempted to make bismuth, Bi, substitutions in the
voids, but we have not succeeded. The Bi does not react
easily with Ir, and it ends up in a separate Bi–Sb phase.
software.36 The calculated powder pattern intensities verified
that the R atoms occupy the voids in the structure at the
100% filling level, in agreement with the microprobe results,
and also in agreement with the experimentally observed
x-ray intensities.
The x-ray-diffraction spectra of the Ir4NdGe3Sb9 and
Ir4SmGe3Sb9 samples were similar in that the intensity of the
reflections due to the addition of R atoms in the voids of the
structure were similar to that of Ir4LaGe3Sb9 shown in Fig. 1.
In addition, the x-ray-diffraction spectra after the first 2 day
reaction period of the R-filled skutterudites were identical to
that obtained with the samples taken after the second 2 day
reaction period. This is a result of the fast reaction times of
these elements in forming these filled skutterudites.
We have measured the cubic x-ray lattice parameter at
room temperature of powdered Ir4LaGe3Sb9 , Ir4NdGe3Sb9 ,
and Ir4SmGe3Sb9 using the silicon internal standard. The results are 9.103660.0015, 9.112560.0024, and 9.1586
60.0008 Å, respectively. These results show that the lattice
parameters of these filled skutterudites are smaller than that
of IrSb3 , a 0 59.250360.0003 Å.4 A lattice parameter model
calculation for unfilled Ir4Ge3Sb9 predicts a 0 59.0021 Å using r~Sb!51.452 Å, r~Ir!51.161 Å, and r~Ge!51.2249 Å.
The Ir and Sb radii were calculated from the Sb—Sb and
Ir—Sb bonds in IrSb3 as described above and the Ge radius
is from the elemental Ge crystal structure.37 The reduction in
the lattice parameter of these R-filled skutterudites compared
to that of IrSb3 is therefore presumably due to the smaller Ge
atom introduced into the structure. We note that the R atoms
EXPERIMENTAL RESULTS
The x-ray-diffraction spectrum of Ir4LaGe3Sb9 after the
second 2 day reaction period is shown in Fig. 1 along with
the pattern for ‘‘unfilled’’ IrSb3 . Note that the intensity of a
few of the x-ray reflections decreased substantially while
others increased. In particular, the first and third reflections,
marked by an asterisk in the IrSb3 pattern, disappear. These
are the @110# and @211# reflections, respectively. This is a
result of putting R atoms into the voids of the structure. The
intensity of the x-ray reflections of the filled skutterudite
samples were compared with intensities calculated for different concentrations of R atoms in the voids using POWD7
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J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
FIG. 2. Lattice thermal conductivity vs temperature for the La-, Nd-, and
Sm-filled-skutterudite samples as well as the unfilled-skutterudite sample.
The calculated minimum thermal conductivity kmin for IrSb3 is also included
in the figure. In effect, the lattice thermal conductivity cannot be made
smaller than kmin .
Nolas et al.
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in the voids do produce some lattice expansion compared to
unfilled Ir4Ge3Sb9 .
Figure 2 shows k g in the temperature range from 300 to
10 K for the La-, Nd-, and Sm-filled skutterudite samples, as
well as for the unfilled IrSb3 sample. Thermal transport measurements were carried out by the two-thermocouple, steadystate heat-flow technique which has been described in detail
elsewhere.38,39 Samples were cut with a high-speed diamond
saw in the shape of parallelepipeds with the heat flow measured along the longest axis. Since the skutterudite structure
is cubic, k g is isotropic. Due to the low thermal conductivity
k of these samples, the radiation loss, measured to be 1.2
mW/cm K at room temperature, was corrected for. We estimate the absolute error below 200 K to be 5%, which arises
primarily from the error in measuring the geometric factor of
these samples. From the measured values of the electrical
resistivity, measured using the standard four-point-probetechnique and the Wiedemann–Franz law we have estimated
and subtracted the electronic contribution to k in Fig. 2. We
have assumed the Lorenz number L 0 to be L 0 52.4431028
V2/deg2, a value experimentally verified for doped Si–Ge
mixed crystals at low temperatures.40 In addition, k g was
corrected for porosity.41,42 The values presented therefore
correspond to fully dense samples. The curve for the minimum thermal conductivity kmin was calculated following the
method given previously;4 however, we have followed Cahill, Watson, and Pohl43 in taking the minimum mean free
path of the acoustic phonons as l/2 instead of l, as used
previously.4 This gives kmin (T>2U) of 3.0631023
W/cm K. Its temperature dependence has been calculated
following the method of Slack.11
Figure 3 shows k g for the Nd-filled skutterudite sample
and IrSb3 from 300 K to 50 mK. In the case of IrSb3 , data
indicated by solid circles above 300 K are from Slack and
Tsoukala,4 and below 10 K are for an IrSb3 sample which
was 98% dense. As in Fig. 2, kmin for IrSb3 is also plotted
along with the thermal conductivity of quartz glass43 ~amorphous SiO2!. Particularly at low temperatures, Ir4NdGe3Sb9
exhibits glasslike behavior. Similar properties have been observed in disordered crystals43 as well as in ordered crystals
with internal vibrational oscillations such as YB66 ,33
Tl3AsSe3 ,10 and clathrate hydrates.10,31
The inverse magnetic susceptibility versus temperature
for Ir4LaGe3Sb9 , Ir4NdGe3Sb9 , and Ir4SmGe3Sb9 is shown in
Fig. 4. The magnetic susceptibility measurements were performed using a Quantum Design magnetometer with a field
strength of 1 T. Samples were placed inside of a polyethylene
capsule which was in turn placed inside of a polyethylene
straw. The magnetization of the empty capsule and straw
were measured separately and subtracted from the total magnetization. For the Nd- and Sm-filled skutterudite samples,
this background correction was negligible, whereas for the
La-filled sample, which has a small diamagnetic susceptibility, the correction was approximately 10% of the total magnetization.
As seen in Fig. 4, Ir4LaGe3Sb9 exhibits diamagnetic behavior, as expected, and the other two filled skutterudites are
paramagnetic. Above approximately 150 K the data for
Ir4NdGe3Sb12 obey Curie’s law, C/(T1D), with an effective
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
FIG. 3. Lattice thermal conductivity vs temperature of Ir4NdGe3Sb9 and
IrSb3 from 800 K to 100 mK. The thermal conductivity of amorphous SiO2 ,
solid line, is also included for comparison. In the case of IrSb3 , data indicated by solid circles above 300 and below 10 K are for IrSb3 samples
which were 98% of theoretical density. The dotted-dashed line is a calculation of grain-boundary scattering due to 7 mm grain size.
moment p.3.6m b ~corresponding to the moment of Nd31,44
where m b is the Bohr magneton! and U5215 K. Due to the
crystal-field splitting of the ground state, equal occupation of
the ground-state levels does not occur at lower temperatures
FIG. 4. Inverse magnetic susceptibility vs temperature of Ir4LaGe3Sb9 ,
Ir4NdGe3Sb9 , and Ir4SmGe3Sb9 . The solid line indicates x ;1/T behavior.
Nolas et al.
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TABLE II. Measured parameters: Temp5temperature ~K!; r5resistivity
~mV cm!; n5hole ~1! or electron ~2! concentration ~cm23!; m5mobility
~cm2/V s!; and a5absolute Seebeck coefficient ~mV/K!. The Hall measurements of the Nd- and Sm-filled-skutterudite samples were affected by the
magnetic effects due to those rare-earth ions.
Sample
IrSb3
Temp.
r
n
300
77
10
0.468
0.318
0.380
11.231019
11.931019
•••
18.8310
22.031023
•••
Ir4LaGe3Sb9
300
77
10
0.927
0.637
0.560
Ir4NdGe3Sb9
300
77
10
1.49
1.10
1.11
Ir4SmGe3Sb9
300
77
10
1.18
0.66
0.65
m
a
1150
724
177
135
144
•••
7.64
0.047
•••
16.4
23.5
20.1
**
**
•••
**
**
•••
10.9
28.0
22.2
**
**
•••
**
**
•••
17.2
20.2
10.3
20
and Curie’s law no longer holds. Below 50 K, x increases
continuously with decreasing temperature, characteristic of
an ion with Kramers’s degeneracy.45 For the Sm31 filledskutterudite sample, the behavior is more complex. In the
case of Sm31 ~and Eu31! compounds, in general, the energy
levels of the excited state J multiplets are not well above that
of the ground state unlike other trivalent rare-earth, R31,
ions. One must therefore take into account the occupation of
these excited state levels.45 Curie’s law must be corrected to
include these energy levels.
Room- and liquid-nitrogen-temperature electrical resistivity, carrier concentration, and mobility measurements are
summarized in Table II. These data were measured on flat,
square pieces of material using the van der Pauw technique.
Care was taken to insure that no heating of the samples occurred during the course of the measurements. In addition,
resistivity measurements at 10 K using the four-point-probe
technique and absolute Seebeck coefficient measurements
are also included in this table. Low-temperature electronic
properties of these filled skutterudites will be presented in a
subsequent publication; however, from Table II it is clear that
the thermoelectric properties of these filled skutterudites
were not optimized for thermoelectric devices. Further work
on charge compensation of the electrons donated by the R31
ions is currently underway.
DISCUSSION
The mass fluctuation scattering of phonons in the mixed
crystal Ir0.5Rh0.5Sb3 has been studied by Slack and Tsoukala4
from 720 to 300 K. At 300 K, the mixed crystal had a k g
56% of that of IrSb3 . The La-, Nd-, and Sm-filled skutterudite samples have a k g 9.4%, 6.5%, and 7.3%, respectively,
of that of IrSb3 . The Ge substitution for Sb in IrSb3 can be
estimated, and it produces a relatively small decrease in k g .
If it behaves similarly to the rhodium, Rh, substituted for Ir
where only mass fluctuation scattering is produced, we calculated k g at 300 K to be 58% of that of pure IrSb3 .46 – 48 An
additional strain field correction49 due to the difference in the
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J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
Ge and Sb radii gives an estimated further maximum reduction in k g at 300 K to 30% of that of pure IrSb3 . In the case
alloy
of
the
cold-pressed
CoSb3-based
Co0.99Ni0.01Sb2.75As0.25, a 50% reduction in k g at room temperature as compared to cold-pressed CoSb3 was reported.14
In addition, in CeFe4Sb12 , a filled skutterudite in which no
substitution on the Sb site occurs, a k g 10% of that of unfilled skutterudites was observed.30 Thus, the Ge is not the
main cause of the reduced k g in the R-filled-skutterudite
samples. In order to verify that the low k g of the Nd-filledskutterudite sample is not due to grain-boundary scattering,
we have calculated k g due to boundary scattering for a
sample with 7 mm grains, the average grain size of the Ndfilled skutterudite sample. This calculated k g is shown in Fig.
3. It is evident that the cause for the low k g is the R31 ions,
it is not grain-boundary scattering.
As seen in Fig. 2, there is more than an order-ofmagnitude decrease in k g over most of the temperature range
between 300 and 10 K for the R-filled skutterudite samples
as compared to that for IrSb3 . From the left- to right-hand
sides of the lanthanide series in the periodic table, the trivalent rare-earth ions increase in mass and decrease in radius.
This decrease is known as the lanthanide contraction.
If we assume that r~Sb!51.452 Å, and that the radii of
La31, Nd31, and Sm31 can be obtained from the rocksaltstructure compounds37 LaSb, NdSb, and SmSb, we find their
radii to be 1.79, 1.70, and 1.69 Å, respectively. These radii
are considerably smaller than the void radius of 2.040 Å for
IrSb3 given in Table I. In a hard-sphere model these ions will
move off center and at absolute zero will be contacting only
three out of the 12 surrounding Sb ions. In this condition,
their centers will be 0.32, 0.43, and 0.46 Å, respectively,
away from the center of the void. As the temperature increases they will move about inside the voids, or rattle. At
absolute zero there are 12 different, equivalent resting positions within the void, all off center. These off-center distances have been calculated assuming that the host crystal is
IrSb3 , and have not been corrected for the slightly smaller a 0
of the actual crystals produced by the Ge contraction.
The Nd31 and Sm31 ions are therefore more free to rattle
inside the voids of the skutterudite structure as compared to
La31, and are thereby able to interact with lower-frequency
phonons than in the case of the La31 ions. The result is a
larger decrease in k g . This ~guest atom!–~phonon! coupling
is an effective phonon scattering mechanism, and one that
shows promise for improving the properties of thermoelectric materials based on the skutterudite structure. In addition,
the low-lying 4 f electronic energy levels in the case of Nd31
and Sm31 also produce additional phonon scattering, reducing k g even further. The influence of paramagnetic rare-earth
ions on the thermal conductivity of rare-earth compounds is
given in a review by Smirnov and Oskotski.50
From Hund’s rule,44 the ground-state energy level of
31
Nd is tenfold degenerate, 4 I 9/2 , and that of Sm31 is sixfold
degenerate, 6 H 5/2 . Each of these degenerate energy levels is
also a doubly degenerate Kramers’s ion level. When these
ions experience an octahedral crystal field, in the case of
rare-earth antimonides, for example, the crystal field further
splits these levels into two fourfold and one twofold degenNolas et al.
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erate levels in the case of Nd31, and one fourfold and one
twofold degenerate level for Sm31. In the case of NdSb and
SmSb, the energy levels of the 4 f ground-state configuration
of Nd31 and Sm31 are within 103 K ~71.6 cm21! of the
ground state.51–54 The site symmetry of R31 in the voids of
the skutterudite structure is most likely of lower symmetry
than octahedral symmetry, since the R31 ions are presumably
not held at the center of the voids as indicated by their large
x-ray thermal parameters.18,19,22 This would lead to further
splitting of the energy levels of the R31 4 f ground state.
Since the ground state of Nd31 splits into more levels of
smaller energy separation than that of Sm31, the Nd31 ion in
Ir4NdGe3Sb9 will therefore scatter a larger spectrum of
phonons than Sm31 in Ir4SmGe3Sb9 . These would be longwavelength phonons, therefore, the result on k g would be
magnified at lower temperatures.55 As seen in Fig. 2, this is
indeed the case. Near room temperature, the Nd- and Smfilled-skutterudite samples have approximately the same k g
values; however, at lower temperatures, k g of the Nd-filledskutterudite sample is lower than that of the Sm-filledskutterudite sample by a factor of 2.
CONCLUSION
We have prepared samples with the skutterudite structure
with La31, Nd31, and Sm31 ions in the voids in order to
study their effect on k g . The rattling motion of the R atoms
has a substantial influence on the phonon propagation in this
structure as seen in Figs. 2 and 3. In addition, phonon scattering due to the low-lying energy levels of the R31 4 f
ground state further reduces k g in this system. Over an orderof-magnitude reduction in k g is observed in these samples as
compared to that of the unfilled-skutterudite sample. We believe this rattling method of reducing k g is most promising
for improving the thermoelectric figure of merit of skutterudite compounds. Unfortunately, the electronic properties are
adversely effected in relation to good thermoelectric materials in the filled-skutterudite samples investigated in this
study. Other techniques for charge compensation are currently being investigated. A more promising approach would
be to fill the voids with a neutral atom or molecule. This
would scatter the phonons while minimizing the scattering
effect on the electrons.
ACKNOWLEDGMENTS
The authors wish to thank P. Vu at the Laboratory of
Atomic and Solid State Physics at Cornell University for
thermal conductivity data below 10 K, and Dr. M. Garbauskas of the General Electric Research and Development Center for x-ray powder pattern simulations. This work was supported, in part, by the U. S. Office of Naval Research, Grant
No. N00014-94-1-0341.
H. J. Goldsmid, Electronic Refrigeration ~Pion Limited, London, 1986!.
D. M. Rowe and C. M. Bhandari, Modern Thermoelectrics ~Reston Publishing, Prentice–Hall, Reston, VA, 1983!.
3
C. Wood, Rep. Prog. Phys. 51, 459 ~1988!.
4
G. A. Slack and V. G. Tsoukala, J. Appl. Phys. 76, 1665 ~1994!.
5
A. Kjekshus and G. Pederson, Acta. Crystallogr. 14, 1065 ~1961!.
6
N. N. Zhuravlev and G. S. Zhdanov, Kristallogr. 1, 509 ~1956! @Sov. Phys.
Cryst. 1, 404 ~1956!#.
1
2
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
A. Kjekshus and T. Rakke, Acta Chem. Scand. A 28, 99 ~1974!.
A. Kjekshus, Acta Chem. Scand. 15, 678 ~1961!.
9
F. Hulliger, Helv. Phys. Acta 34, 782 ~1961!.
10
G. A. Slack, in Thermoelectric Handbook, edited by D. M. Rowe ~CRC,
Boca Raton, FL, 1995!, p. 407.
11
G. A. Slack, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, and
D. Turnbull ~Academic, New York, 1979!, Vol. 34, p. 1.
12
J.-P. Fleurial, T. Caillat, and A. Borshchevsky, in Proceedings of the Thirteenth International Conference on Thermoelectrics, edited by B.
Mathiprakasam and P. Heenan, American Institute of Physics Conf. Proc.
No. 316 ~AIP, New York, 1995!, p. 40.
13
D. T. Morelli, T. Caillat, J.-P. Fleurial, J. W. Vandersande, B. Chen, and C.
Uher, Phys. Rev. B 51, 9620 ~1995!.
14
J. W. Sharp, E. C. Jones, R. K. Williams, P. M. Martin, and B. C. Sales, J.
Appl. Phys. 78, 1013 ~1995!.
15
D. J. Singh and W. E. Pickett, Phys. Rev. B 50, 11 235 ~1994!.
16
S. Rundquist and N. O. Ersson, Arkiv Kemi ~Stockholm! 30, 103 ~1968!.
17
T. Schmidt, G. Kliche, and H. D. Lutz, Acta Crystallogr. C 43, 1678
~1987!.
18
L. E. Delong and G. P. Meisner, Solid State Commun. 53, 119 ~1985!.
19
D. J. Braun and W. Jeitschko, J. Less-Common Met. 72, 147 ~1980!.
20
D. T. Braun and W. Jeitschko, J. Solid State Chem. 32, 357 ~1980!.
21
W. Jeitschko and D. Braun, Acta Crystallogr. B 33, 3401 ~1977!.
22
L. Boonk, W. Jeitschko, U. D. Scholz, and D. J. Braun, Z. Kristallogr. 178,
30 ~1987!.
23
S. Zemni, D. Tranqui, P. Chaudouet, R. Madar, and J. P. Senateur, J. Solid
State Chem. 65, 1 ~1986!.
24
D. J. Braun and W. Jeitschko, J. Less-Common Met. 76, 33 ~1980!.
25
N. T. Stetson, S. M. Kauzlarich, and H. Hope, J. Solid State Chem. 91,
140 ~1991!.
26
C. B. H. Evers, L. Boonk, and W. Jeitschko, Z. Anorg. Allg. Chem. 620,
1028 ~1994!.
27
G. P. Meisner, M. S. Torikachvili, K. N. Yang, M. B. Maple, and R. P.
Guertin, J. Appl. Phys. 57, 3073 ~1985!.
28
A. Gerard, F. Grandjean, J. A. Hodges, D. J. Braun, and W. Jeitschko, J.
Phys. C 16, 2797 ~1983!.
29
F. Grandjean, A. Gerard, D. J. Braun, and W. Jeitschko, J. Phys. Chem.
Solids 45, 877 ~1984!.
30
D. T. Morelli and G. P. Meisner, J. Appl. Phys. 77, 3777 ~1995!.
31
R. G. Ross, Phys. Chem. Liq. 23, 189 ~1991!, and references therein.
32
G. A. Slack, D. W. Oliver, and F. H. Horn, Phys. Rev. B 4, 1714 ~1971!.
33
D. G. Cahill, H. E. Fischer, S. K. Watson, R. O. Pohl, and G. A. Slack,
Phys. Rev. B 40, 3254 ~1989!.
34
P. A. Medwick, R. O. Pohl, and T. Tanaka, in Proceedings of the Eleventh
International Symposium on Boron, Borides and Related Compounds: J.
Appl. Phys., Series 10, Tsukuba, Japan, edited by Ryosei Uno and Iwami
Higashi, 1994, p. 106.
35
Metals Handbook, 9th ed. ~American Society of Metals, Metals Park, OH,
1985!, Vol. 9, pp. 122–134, and references therein.
36
Reports of the University of California, Lawrence Radiation Laboratory
~Smith ~1963! UCRL-7176 and ~1976! UCRL-50264!; Clark, Smith, and
Johnson, Bulletins of the College of Earth and Mineral Sciences, The
Pennsylvania State University, 1973.
37
R. W. G. Wyckoff, Crystal Structures, 2nd ed. ~Wiley–Interscience, New
York, 1963!.
38
D. T. Morelli and C. Uher, Phys. Rev. B 28, 4242 ~1983!.
39
D. T. Morelli, Phys. Rev. B 44, 5453 ~1991!.
40
G. S. Kumar, J. W. Vandersande, T. Klistner, R. O. Pohl, and G. A. Slack,
Phys. Rev. B 31, 2157 ~1985!.
41
S. L. Loeb, J. Am. Ceram. Soc. 37, 96 ~1954!.
42
J. Francl and W. D. Kingery, J. Am. Ceram. Soc. 37, 99 ~1954!.
43
D. G. Cahill, S. K. Watson, and R. O. Pohl, Phys. Rev. B 46, 6131 ~1992!.
44
See, for example, N. W. Ashcroft and N. D. Mermin, Solid State Physics
~Holt, Rinehart, and Winston, New York, 1976!, p. 657, and references
therein.
45
H. M. Rosenberg, Low Temperature Solid State Physics, Some Selected
Topics ~Oxford University Press, London, 1963!, pp. 291–304.
46
G. A. Slack, Phys. Rev. 105, 829 ~1957!.
47
G. A. Slack, Phys. Rev. 122, 1451 ~1961!.
48
M. G. Holland, Phys. Rev. 134, A471 ~1964!.
49
B. Abeles, Phys. Rev. 131, 1906 ~1963!.
7
8
Nolas et al.
4007
Downloaded¬30¬Jan¬2001¬¬to¬130.127.12.50.¬¬Redistribution¬subject¬to¬AIP¬copyright,¬see¬http://ojps.aip.org/japo/japcpyrts.html.
50
I. A. Smirnov and V. S. Oskotski, Handbook on the Physics and Chemistry
of Rare Earths, edited by K. A. Gschneidner, Jr. and L. Eyring ~Elsevier,
Amsterdam, 1993!, Vol. 16, pp. 152–178.
51
E. D. Jones, Phys. Rev. 180, 455 ~1969!.
52
M. E. Mullen, B. Luthi, P. S. Wang, E. Bucher, L. D. Longinotti, J. P.
4008
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
Maita, and H. R. Ott, Phys. Rev. B 19, 186 ~1974!.
A. Furrer, J. Kjems, and O. Vogt, J. Phys. C 5, 2246 ~1972!.
54
A. Furrer, W. J. L. Buyers, R. M. Nicklow, and O. Vogt, Phys. Rev. B 14,
179 ~1976!.
55
G. A. Slack and D. W. Oliver, Phys. Rev. B 4, 592 ~1971!.
53
Nolas et al.
Downloaded¬30¬Jan¬2001¬¬to¬130.127.12.50.¬¬Redistribution¬subject¬to¬AIP¬copyright,¬see¬http://ojps.aip.org/japo/japcpyrts.html.