Thermal expansion of skutterudites

Abstract

The current paper gives an overview of the newly obtained thermal expansion coefficients of skutterudites as well as those so far available in literature. Thermal expansion was determined for CoSb ₃ , Pt ₄ Sn _4.4 Sb _7.6 , for As- and Ge-based skutterudites as well as for various high-ZT skutterudites (micro- and nanostructured) with didymium (DD) and mischmetal (Mm) as filler atoms in frameworks of ( Fe _{1- x} Co _x )₄ Sb ₁₂ and ( Fe _{1- x} Ni _x )₄ Sb ₁₂ , and for double and triple-filled skutterudites such as Ca _0.07 Ba _0.23 Co _3.95 Ni _0.05 Sb ₁₂ and Sr _0.025 Ba _0.075 Yb _0.1 Co ₄ Sb ₁₂ . For low temperatures, a capacitance dilatometer was used (4–300 K), whereas for temperatures 300≪ T ≪750 K , a dynamic mechanical analyzer was employed. For a set of Ge-, P-, and Sb-based skutterudites, lattice parameters of single crystals, measured at three different temperatures, were used to derive the thermal expansion coefficient. The semiclassical model of Mukherjee [Phys. Rev. Lett. 76, 1876 (1996)] has been successfully used to quantitatively describe the thermal expansion coefficient in terms of Einstein and Debye temperatures, which compare well with the corresponding results from specific heat, electrical resistivity, or temperature depend-
ent x-ray measurements.

Full text

Page 1

Thermal expansion of skutterudites
G. Rogl,1,2,4L. Zhang,1,2,4P. Rogl,1,a?A. Grytsiv,1M. Falmbigl,1D. Rajs,2M. Kriegisch,2
H. Müller,2E. Bauer,2J. Koppensteiner,3W. Schranz,3M. Zehetbauer,4Z. Henkie,5
and M. B. Maple6
1Institute of Physical Chemistry, University of Vienna, Währingerstr. 42, A-1090 Wien, Austria
2Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, A-1040 Wien,
Austria
3Nonlinear Physics Group, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria
4Group Physics of Nanostructured Materials, University of Vienna, Boltzmanngasse 5, A-1090 Wien,
Austria
5Institute of Low Temperature and Structure Research, Polish Academy of Science, PL-50-950 Wroclaw,
Poland
6Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
?Received 24 July 2009; accepted 5 December 2009; published online 18 February 2010?
The current paper gives an overview of the newly obtained thermal expansion coefficients of
skutterudites as well as those so far available in literature. Thermal expansion was determined for
CoSb3, Pt4Sn4.4Sb7.6, forAs- and Ge-based skutterudites as well as for various high-ZT skutterudites
?micro- and nanostructured? with didymium ?DD? and mischmetal ?Mm? as filler atoms in
frameworks of ?Fe1−xCox?4Sb12and ?Fe1−xNix?4Sb12, and for double and triple-filled skutterudites
such as Ca0.07Ba0.23Co3.95Ni0.05Sb12 and Sr0.025Ba0.075Yb0.1Co4Sb12. For low temperatures, a
capacitance dilatometer was used ?4–300 K?, whereas for temperatures 300?T?750 K, a dynamic
mechanical analyzer was employed. For a set of Ge-, P-, and Sb-based skutterudites, lattice
parameters of single crystals, measured at three different temperatures, were used to derive the
thermal expansion coefficient. The semiclassical model of Mukherjee ?Phys. Rev. Lett. 76, 1876
?1996?? has been successfully used to quantitatively describe the thermal expansion coefficient in
terms of Einstein and Debye temperatures, which compare well with the corresponding results from
specific heat, electrical resistivity, or temperature dependent x-ray measurements. © 2010 American
Institute of Physics. ?doi:10.1063/1.3284088?
I. INTRODUCTION
Thermoelectric generators directly convert heat flow into
electrical power. Energy conversion efficiency of thermo-
electric materials is a function of the dimensionless thermo-
electric figure of merit ZT=S2T/????, where S is the See-
beck coefficient, T is the temperature, ? is the electrical
resistivity, and ? is the thermal conductivity. With thermo-
electric energy conversion efficiencies of more than 10%
?ZT?1?, skutterudites have been considered as suitable ther-
moelectric generator materials for an application range 300–
700 K. For a flawless long-term and cyclic temperature per-
formance of thermoelectric devices, it is essential that
thermal expansion coefficients of p- and n-legs as well as of
contacting materials are chosen as similar as possible. Al-
ready in the 1990s in the Jet Propulsion Laboratory not only
transport behavior of skutterudites but also related problems
such as thermal expansion were investigated; however, at
that time thermal expansion coefficients were only reported
for CoSb3,1,2RhSb3,1and IrSb3.1,3,4From our comprehensive
literature search in two major electronic libraries, chemical
abstracts service ?CAS? and INSPEC, scanning entries up to
2009, it became obvious that only a few research groups
have dealt with thermal expansion ?see data and references in
Table II?. Besides these directly accessible data on thermal
expansion, all data in literature were collected, which al-
lowed us to extract thermal expansion coefficients. There-
fore, the aim of the present work is threefold: ?i? to supply
new data on thermal expansion from a series of high ZT p-
and n-type skutterudites, ?ii? to extract thermal expansion
from experimental data in literature, where expansion coef-
ficients have not yet been evaluated by the authors, and
?iii? a general discussion of all thermal expansion data
available covering antimony-, phosphorous- arsenic-, and
germanium-based skutterudites. It is interesting to note that
our literature search did not reveal any expansion data on
arsenide skutterudites. The experimental work presented
herein is concerned with skutterudites ?micro- and nanostruc-
tured? where didymium ?DD? ?4.76% Pr and 95.2% Nd? and
mischmetal ?Mm? ?50.8% Ce, 28.1% La, 16.1% Nd,
and5.0%Pr?
actasfiller
works of ?Fe1−xCox?4Sb12and ?Fe1−xNix?4Sb12. From these
series of samples, we selected those with a ZT?1
?DD0.68Fe3.2Ni0.8Sb12 and DD0.76Fe3.4Ni0.6Sb12?, including
nanostructured ?ball milled ?BM?? as well as micro-
structuredmaterials.These
andDD0.44Fe2.1Co1.9Sb12
Mm0.70Fe4Sb12BM, and DD and Mm-samples with the same
nominal composition ?DDFe4Sb12 BM and MmFe4Sb12
BM?.5,6We compare the thermal expansion of the above-
mentionedsamplesnotonly
atomsinthe frame-
were
BM,
DD0.44Fe2.1Co1.9Sb12
Mm0.76Fe4Sb12
and
withmultifilledn-type
a?Author to whom correspondence should be addressed. Tel.: ?43-1-4277-
52456.FAX:
?43-1-4277-95245.
peter.franz.rogl@univie.ac.at.
Electronic mail:
JOURNAL OF APPLIED PHYSICS 107, 043507 ?2010?
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107, 043507-1
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Page 2

skutterudites,
Sr0.025Ba0.075Yb0.1Co4Sb12,8
CoSb3, and Pt4Sn4.4Sb7.6but also with values reported in the
literature.9–15The semiclassical model of Mukherjee16will
be used to quantitatively evaluate the thermal expansion and
to derive Einstein and Debye temperatures for all those
samples where lattice parameters or dilatometric data are
available as a function of temperature over a larger tempera-
ture range starting from 4.2 K.
Ca0.07Ba0.23Co3.95Ni0.05Sb12
?Ref.7?
and
which both have a ZT?1,
II. EXPERIMENTAL DETAILS
All DD and Mm samples, CoSb3, Pt4Sn4.4Sb7.6as well as
Ca0.07Ba0.23Co3.95Ni0.05Sb12, and Sr0.025Ba0.075Yb0.1Co4Sb12,
were prepared via an optimized melting reaction technique.
The solids obtained were ground into fine powders in a WC
mortar or BM and in both cases hot pressed in an argon
atmosphere at 600 °C under a pressure of 50 MPa. For fur-
ther details, see Refs. 5–8. Pt4Sn4.4Sb7.6was prepared in the
form of cold compacted sintered pellets.
Lattice constants for polycrystalline powders were ob-
tained at room temperature from Guinier x-ray diffraction
data, applying Cu K?1 radiation and employing a least
squares evaluation with the program STRUKTUR.17Chemical
composition and microstructure were determined by electron
probe microanalysis ?EPMA?. Filling levels were obtained
from combined evaluation of EPMA and Rietveld x-ray pat-
tern refinements. Lattice parameters of skutterudite single
crystals were obtained at three different temperatures ?300,
200, and 100 K, N2cooling the crystal? from an Enraf Non-
ius Kappa charge-coupled device instrument with monochro-
matic Mo K? radiation under a flow of equilibrated nitrogen
gas from a cryostat. LaFe4As12and PrFe4As12are single
crystals, grown from elements with purities ?99.9% by us-
ing a molten metal flux method at high temperature and pres-
sure. Details on growth, structural, and physical properties
are reported elsewhere.18–20
The thermal expansion from 4.2 to 300 K was measured
in a miniature capacitance dilatometer,21using the tilted plate
principle.22,23For this measurement, the sample is placed in a
hole of the lower ringlike capacitance plate made of silver,
which is separated from the silver upper capacitor plate by
two needle bearings. All DD samples, Mm0.76Fe4Sb12,
Mm0.70Fe3CoSb12
BM,
Sr0.025Ba0.075Yb0.1Co4Sb12, and CoSb3, Pt4Sn4.4Sb7.6, and
both Ge- and As-based samples were measured with this low
temperature capacitance dilatometer. For the measurement of
the thermal expansion at a temperature range from 300 to
700 K, a dynamic mechanical analyzer DMA7 ?Perkin Elmer
Inc.? was employed. The sample is positioned in a parallel
plate mode with a quartz rod on top of the sample and data
are gained using the thermodilatometric analysis ?TDA?.
TDA is often referred to as zero force thermomechanical
analysis. With this method the change in the dimension of a
sample is measured while subjected to a temperature change
without using any force. The length of the sample is mea-
sured via the movement of the quartz rod. This movement is
detected using electromagnetic inductive coupling. The ab-
solute length l and the length change ?l are acquired with a
Ca0.07Ba0.23Co3.95Ni0.05Sb12,
resolution of 10 nm,24for further details see also Refs.
25–27. All Mm samples, except Mm0.70Fe3CoSb12 BM,
DD0.08Fe2Ni2Sb12, and Ca0.07Ba0.23Co3.95Ni0.05Sb12, were
measured with this method.24Porosity was obtained from
density measurements in distilled water, using Archimedes’
principle, and the calculation of the x-ray density dX
=?ZM?/?NV?, where M is the molar mass, Z is the number
of formula units per cell, N is Avogadro’s number, and V is
the volume of the unit cell. Resistivities of the DD alloys in
the temperature range from 4.2 to 300 K were measured
using a dc four-point technique. The resistivity curves of
DD0.68Fe4Sb12, DD0.76Fe3.4Ni0.6Sb12, DD0.44Fe2.1Co1.9Sb12,
and DD0.44Fe2.1Co1.9Sb12BM showed metallic behavior and
therefore could be fitted well with the Bloch–Grüneisen
functionyieldingalso the
details see Ref. 5. The same technique was used for
Ca0.07Ba0.23Co3.95Ni0.05Sb12.7
Time of flight of sound pulse measurements were per-
formed on cylinders with a frequency of 10 MHz using a
home made equipment27to provide the data for longitudinal
?vl? and shear ?transversal? ?vs? sound velocities.
Debyetemperature;for
III. RESULTS AND DISCUSSION
Table I summarizes the thermoelectric properties of se-
lected DD and Mm samples,5,6Ca0.07Ba0.23Co3.95Ni0.05Sb12
?Ref. 7? and Sr0.025Ba0.075Yb0.1Co4Sb12,8published recently
and the porosity of all these alloys.
All samples are single phase except Mm0.70Fe4Sb12
?80 at. %?, which contains also FeSb2, Sb, and Mm2O3. In
all cases the Rietveld refinement showed an ordered atom
arrangement with respect to the atom site distribution among
DD/Mm, ?Fe/Co, Fe/Ni?, and Sb sublattices. DD and Mm
contents agree well with the data obtained from EPMA
which applies also for the Ba and Ca contents and Co/Ni
contribution in Ca0.07Ba0.23Co3.95Ni0.05Sb12and the Sr, Ba,
and Yb contents of Sr0.025Ba0.075Yb0.1Co4Sb12.
Figures 1 and 2 show the thermal expansion ?l/l of the
aforementioned skutterudites as a function of temperature. In
Fig. 1, the data from the low temperature measurements are
displayed, and those from the high temperature measure-
ments in Fig. 2.
From Fig. 1, it is obvious that ?l/l0of all measured
skutterudites decreases linearly in temperature from room
temperature to about 150 K, whereas for temperatures below
150 K, a nonlinear behavior is evident. The thermal expan-
sion coefficient ? follows from a temperature derivative of
the length change, i.e.,
? =???l
l0
?T?1
.
?1?
? was calculated in the temperature range from about 150 to
300 K. The thermal expansion coefficients derived in the
present article together with data available in the literature
are listed in Table II. Although the thermal expansion for all
DD samples ?9.45?10−6K−1???11.30?10−6K−1? is
slightly lower than for the Mm samples ?9.97?10−6K−1
???12.42?10−6K−1?, the difference within DD as well
as within Mm skutterudites is not high, which applies also
043507-2 Rogl et al.J. Appl. Phys. 107, 043507 ?2010?
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Page 3

for the difference between the n-type and the p-type DD
samples. As expected, the difference in ? between nanostruc-
tured ?BM? and microstructured samples and of samples with
lower or higher porosity is very small, as can be seen when
comparing the graphs of Mm0.76Fe4Sb12and Mm0.70Fe4Sb12
BM in Fig. 2 as well as DD0.44Fe2.1Co1.9Sb12
DD0.44Fe2.1Co1.9Sb12BM in Fig. 3 or the values of ? of these
samples as well as for Mm0.70Fe3CoSb12BM, measured
at low temperatures, and Mm0.70Fe3CoSb12, measured
at high temperatures ?see Table II?. However, Figs. 1 and 2
alsoshowthatbothn-type
Ca0.07Ba0.23Co3.95Ni0.05Sb12
Sr0.025Ba0.075Yb0.1Co4Sb12??=8.35?10−6K−1?, have a sig-
nificantly smaller thermal expansion. These observations
lead to the conclusion that the grain size does not influence
the thermal expansion, but filler atoms do have some influ-
ence on thermal expansion. Figure 4 shows that in DD or
Mm skutterudites, an increasing Fe-content ?and a simulta-
neously increasing filler-content? enlarges the thermal expan-
sion. This is also the case for other pairs of samples; e.g.,
La0.743Fe2.74Co1.26Sb12??=9.08?10−6K−1? ?Ref. 15? and
and
multifilled
??=9.14?10−6K−1?
skutterudites,
and
La0.9Fe4Sb12
?0.1 ??=8?10−6K−1? ?Ref. 14? and Ce0.9Fe4Sb12 ??
=13.93?10−6K−1?,orCa0.07Ba0.23Co3.95Ni0.05Sb12
=9.14?10−6K−1? and CaFe4Sb12??=10.9?10−6K−1?.10
For CoSb3two rather different thermal expansion coeffi-
cients were found in literature: ?=13.5?10−6K−1?no de-
tails given, Ref. 1? and ?=6.36?10−6K−1?from single
crystal in a range from 300 to 930 K, Ref. 2?. Therefore,
thermal expansion was remeasured for a CoSb3sample ?BM
and hot pressed? revealing a coefficient ?=9.1?10−6K−1
?120–220 K?. This value fits well to the dependency of DD
and Mm alloys shown in Fig. 4.
The lattice parameter of a cubic material at varying tem-
peratures is in relationship to the thermal expansion coeffi-
cient gained from TDA or capacitance data via the relation
??=11.69?10−6K−1?,CexCo4Sb12,0?x
??
? =
a2− a1
a1
?T
,
?2?
where axis the lattice parameter at the temperature x. For
most of our calculations, we used the lattice parameter a2
FIG. 1. ?Color online? Temperature dependent thermal expansion ?l/l0of
various skutterudites for 4.2 K?T?300 K.
FIG. 2. ?Color online? Temperature dependent thermal expansion ?l/l0of
various skutterudites for 300 K?T?700 K.
TABLE I. Physical properties at 297 K ?ZT also at 700 K? of selected skutterudites.
SkutteruditeType
Porosity
?%?
?
??? cm?
S
??V/K?
?
?mW/cm K?
ZT ?297 K?
ZT ?700 K?
Ref.
Ca0.07Ba0.23Co3.95Ni0.05Sb12
Sr0.025Ba0.075Yb0.1Co4Sb12
DD0.08Fe2Ni2Sb12
DD0.76Fe3.4Ni0.6Sb12
DD0.68Fe3.2Ni0.8Sb12
DD0.44Fe2.1Co1.9Sb12
DD0.44Fe2.1Co1.9Sb12
DD0.86Fe4Sb12
Mm0.76Fe4Sb12
Mm0.70Fe4Sb12?not single phased?
Mm0.20Fe2.5Ni1.5Sb12
Mm0.70Fe3CoSb12
Mm0.68Fe3CoSb12
Mm0.05FeCo3Sb12
n
n
n
p
p
p
p
p
p
p
p
p
p
p
5
0.6
1.4
6.3
2.3
4.1
0.2
0.6
5.1
3.3
1.5
1.8
1.2
1.9
317
295
3730
690
552
780
900
370
449
408
¯
785
650
¯
?109
?170
?70
126
104
105
91
74
77
79
¯
113
103
¯
53
32
21
19
22
19
15
32
26
21
¯
15
17
¯
0.18
0.46
0.02
0.34
0.26
0.20
0.18
0.13
0.15
0.22
¯
0.33
0.28
¯
1.10
1.28
0.24
1.05
0.93
0.44
0.43
0.86
0.61
0.75
¯
1.16
1.09
¯
7
8
5
5
5
5
5
a
BM
BM
BM
6
6
6
6
6
6
BM
BM
BM
aThis work, prepared as described in Ref. 5.
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Page 4

TABLE II. Lattice parameters and thermal expansion coefficients of Ge-, P-, As-, and Sb-based skutterudites.
Lattice parameter a, RT ?nm?
Ref.
??10−6?K−1?
T ?K?
MethodRef.
Ge-based skutterudites
a
BaPt4Ge12
UPt4Ge12
0.86928?2?
0.85835?3?
10.2
9.15
160–245
160–245
DMb
DM
a
aa
P-based skutterudites
28
a
LaRu4P12
PrRu4P12
GdRu4P12
LaOs4P12
CeOs4P12
PrOs4P12
NdOs4P12
SmOs4P12
0.80605?2?
0.80493
0.80375
0.80932?3?
0.80751?3?
0.80813?2?
0.80790?2?
0.80731?2?
4.7
5.64
5.4
5.1
5.08
4.77
5.8
5.39
10–300
10–300
150–300
100–300
100–300
100–300
100–300
100–300
SCLPc
SCLP
LPd
LP
SCLP
SCLP
SCLP
SCLP
a
a
29
a
a
a
aa
aa
aa
aa
As-based skutterudites
18
20
Sb-based skutterudites
a
PrFe4As12
LaFe4As12
0.8310?2?
0.83273?2?
10.3
9.25
160–250
160–250
DM
DM
a
a
CoSb3
0.903484?2?
0.90345?3?
9.1
13.5
6.36
12.7
6.89
6.69
7.96
8
11
10.9
9
9.09
7.4
9.5
9.5
11.69
12.7
8
11.21
12.50
10.59
12
8.17
11.26
12.09
11.29
9.81
9.82
9.51
9.45
13.43
11.94
12.42
10.78
11.33
11.43
9.97
9.19
10.16
8.85
9
8.9
6.94
120–220
¯
300–930
¯
RT
300–673
¯
¯
100–300
150–300
100–300
¯
180–300
180–300
180–300
100–300
100–300
300
125–300
100–300
100–296
110–295
100–300
160–245
160–245
160–245
160–245
300–600
160–245
160–245
160–250
300–500
300–500
300–500
160–245
300–500
300–500
160–280
300–650
160–245
DM
¯
¯
¯
LP
LP
¯
¯
LP
LP
LP
¯
NDe
ND
ND
SCLP
LP
¯
LP
SCLP
SCLP
LP
LP
DM
DM
DM
DM
a
21
2
1
a
RhSb3
IrSb3
0.92503?3?
0.92503?3?
0.92533
9
3
1
3
1
4
10
a
NaFe4Sb12
CaFe4Sb12
CaxCo4Sb12
Ru0.5Pd0.5Sb3
Tl0.22Co4Sb12
TlCo3FeSb12
Tl0.5Co4Sb11.5Sn0.5
La0.9Fe4Sb12
Ce0.9Fe4Sb12
CexCo4Sb12?0?x?0.1?
PrFe4Sb12
Nd0.85Fe4Sb12
Eu0.93Fe4Sb12
Yb0.95Fe4Sb12
YbxCo4Sb12
DD0.86Fe4Sb12BM
DD0.68Fe3NiSb12
DD0.76Fe3.4Ni0.6Sb12
DD0.08Fe2Ni2Sb12
0.91759?3?
0.9171?4?
0.9052
0.9298
0.9056
0.9112
0.9082
0.91503
0.91406?3?
¯
0.91290
0.91412?2?
0.91725?2?
0.91586?8?
0.9048
0.91357?2?
0.91208?4?
0.91219?3?
0.90927?3?
10
33
11
12
13
13
13
a
11
12
13
13
13
a
aa
¯
a
14
a
aa
aa
34
11
a
a
11
a
aa
aa
aa
DD0.44Fe2.1Co1.9Sb12
DD0.44Fe2.1Co1.9Sb12BM
Mm0.76Fe4Sb12
0.90920?4?
0.90878?3?
0.91370?5?
a
DM
DM
DM
a
aa
aa
Mm0.70Fe4Sb12BM
Mm0.20Fe2.5Ni1.5Sb12
Mm0.70Fe3CoSb12BM
Mm0.68Fe3CoSb12
Mm0.05FeCo3Sb12
Ca0.07Ba0.23Co0.95Ni0.5Sb12
0.91384?3?
0.91009?1?
0.91165?3?
0.91167?3?
0.90624?3?
0.90665?3?
a
DM
DM
DM
DM
DM
DM
a
aa
aa
aa
aa
aa
Sr0.025Ba0.075Yb0.1Co4Sb12
La0.743Fe2.74Co1.26Sb12
0.90617?4?
0.90971?3?
a
DM
ND
LP
DM
a
15 15
a
100–300
130–230Pt4Sn4.4Sb7.6
0.93304?2?
aa
aThis work.
bDM dilatometer measurements.
cSCLP calculated from single crystal lattice parameter.
dLP calculated from lattice parameter.
eND data from neutron diffraction.
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Page 5

gained from precise x-ray diffraction data on polycrystalline
or single crystal specimens.
Figure 5 gives an overview of the temperature dependent
lattice parameters of all measured DD and Mm samples and
shows that the slopes do not differ very much. Figures 5 and
6 demonstrate that for DD0.08Fe2Ni2Sb12, Mm0.70Fe4Sb12,
and Ca0.07Ba0.23Co3.95Ni0.05Sb12, the measurements at low
and high temperatures, with different equipment used, fit
well together. Also the values calculated for two different
measurement ranges fit within the measurable accuracy.
While in the case of DD0.08Fe2Ni2Sb12, the values for the
thermal expansion ??160–240?=9.81?10−6K−1for low and
??300–600?=9.82?10−6K−1for high temperatures are equal,
for MmFe4Sb12and Ca0.07Ba0.23Co3.95Ni0.05Sb12?see Figs. 5
and 6?, the difference in these temperature ranges is smaller
than 1?10−6K−1.
Figures 7 show temperature dependent lattice parameters
for various Ge-, P-, As- and Sb-based skutterudites. For the
calculation of the thermal expansion coefficient ?, either our
data or literature data of lattice parameters were used ?see
also Table II?. Slack3derived the thermal expansion coeffi-
cient ?=6.69?10−6K−1for IrSb3from x-ray data in the
temperature range from 300 to 673 K in good agreement
with our calculation, ?=6.89?10−6K−1, using the lattice
parameters of Kjekshus9?see Fig. 7?a??. Both values are
lower than the thermal expansion ?=8?10−6K−1found by
Kjekshus earlier.4In Fig. 7?a?, the data for the DD and Mm
skutterudites based on Sb are compared with the correspond-
ing La, Ce, Pr, Nd, Eu, and Yb skutterudites. The almost
identical slopes, i.e., the expansion coefficients ?, again
show that ? is almost insensitive to the filler elements as
already concluded above. All thermal expansion coefficients
of the P-based skutterudites were calculated from lattice pa-
rameters obtained from single crystal measurements. It is
remarkable that all thermal expansion coefficients of P-based
skutterudites MOs4P12?M=La, Ce, Pr, Nd, Sm?, in a range
?4.8–5.8??10−6K−1, are only half as large as those of Sb-
based skutterudites where ? ranges from 7.5?10−6to 14
?10−6K−1. Similarly, data of LaRu4P12?Ref. 28? with ?
=4.7?10−6K−1, PrRu4P12with ?=5.64?10−6K−1, and
GdRu4P12?Ref. 29? with ?=5.4?10−6K−1are also in this
range of relatively low thermal expansion, indicating stron-
FIG. 3. ?Color online? Temperature dependent thermal expansion ?left axis?
and calculated lattice parameter ?right axis? versus temperature for nano-
structured ?BM? and microstructured DD0.44Fe2.1Co1.9Sb12.
FIG. 4. ?Color online? Thermal expansion coefficient ? vs DD and Mm
contents ?a? and versus Fe content ?b?. The solid line is a guide to the eyes.
FIG. 5. ?Color online? Temperature dependent lattice parameters a of DD
and Mm compounds.
FIG. 6. ?Color online? Thermal expansion ?left axis? and lattice parameter
?right axis? as function of temperature for Ca0.07Ba0.23Co3.95Ni0.05Sb12with
Debye temperature ?Dand Einstein temperature ?Egained from the fit.
043507-5Rogl et al.J. Appl. Phys. 107, 043507 ?2010?
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