Lattice thermal transport in double-filled skutterudites In0.1Yb y Co4Sb12

Abstract

In order to investigate the phonon scattering mechanisms in double-filled skutterudites, the low-temperature lattice thermal conductivities of In0.1Yby
Co4Sb12 were measured and analyzed based on the Debye model. The eingenmode frequencies of In and Yb were obtained from low-temperature specific heat capacity analysis. It is found that filling these two types of guest atoms with different eingenmode frequencies into the voids in skutterudites could introduce strong point defect and resonant scattering to lattice phonons, thus lead to significant decrease in the lattice thermal conductivity.

Full text

Journal of Wuhan University of Technology-Mater. Sci. Ed. Aug.2013 677
Lattice Thermal Transport in Double-
fi lled Skutterudites In0.1YbyCo4Sb12
XU Wei1, PENG Jiangying1*, HE Jian2, ZHOU Menghan2, YANG Junyou3, FU Liangwei3
(1. School of Mechanical Science & Engineering, Huazhong University of Science & Technology, Wuhan 430074, China; 2. Department of
Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA; 3. State Key Laboratory of Material Processing and Die
& Mound Technology, Huazhong University of Science & Technology, Wuhan 430074, China)
Abstract: In order to investigate the phonon scattering mechanisms in double-fi lled skutterudites, the
low-temperature lattice thermal conductivities of In0.1YbyCo4Sb12 were measured and analyzed based on the
Debye model. The eingenmode frequencies of In and Yb were obtained from low-temperature specific heat
capacity analysis. It is found that fi lling these two types of guest atoms with different eingenmode frequencies
into the voids in skutterudites could introduce strong point defect and resonant scattering to lattice phonons, thus
lead to signifi cant decrease in the lattice thermal conductivity.
Key words: thermoelectric; thermal conductivity; phonons
©Wuhan University of Technology and SpringerVerlag Berlin Heidelberg 2013
(Received: Oct. 19, 2012; Accepted: Jan. 8, 2013)
XU Wei(徐薇): E-mail: xwfantasy1987@163.com
*Corresponding author. PENG Jiangying (彭江英): Assoc.Prof.;
Ph D; E-mail: jiangyingpeng@mail.hust.edu.cn
Funded by the National Natural Science Foundation of China
(No. 50972047, 51072062), the Scientifi c Research Foundation for the
Returned Overseas Chinese Scholars, State Education Ministry, and the
Fundamental Research Funds for the Central Universities (2011TS124,
HUST). J. He would like to acknowledge the financial support from
DOE/EPSCoR Implementation (Grant No. DE-FG02-04ER-46139) and
SC EPSCoR Offi ce/Clemson University cost sharing
DOI 10.1007/s11595-013-0751-0
1 Introduction
The CoSb3-based skutterudite materials have
drawn much attention as promising thermoelectric
materials in the past decades owing to their high
carrier mobilities, moderate Seebeck coefficients and
a complex crystal structure. This family of compounds
crystallizes in an Im 3 space group with the form MX3,
where the metal atom M can be Co, Rh, and Ir, and the
pnicogen X can be P, As, and Sb. A unit cell consists of
32 atoms (Co8Sb24), in which Co atoms form 8 subcubes
with Sb4 planar rings occupying six of them, leaving
the other two subcubes (cages) empty. Though the
intrinsic lattice thermal conductivity (κL) is somewhat
high due to the strong covalent bonding in the lattice,
the naturally formed voids (i e, the empty subcubes
or cages) can be filled with undersized guest ions,
forming fi lled skutterudites. One of the striking features
of the skutterudites is that the filled skutterudites
have been shown to have much lower lattice thermal
conductivity than their parent compounds[1-4], which is
a prerequisite for thermoelectric materials achieving a
high figure of merit. As evidenced by the abnormally
large atomic displacement parameters of the filler
atoms, experimental neutron inelastic scattering data
and specifi c heat capacity measurements, heavy atoms,
such as La, Ce, Yb, or Tl fi ll the voids and exhibit low
frequency localized atomic vibrations, called “rattlers”,
which strongly scatter heat-carrying acoustic phonons
via phonon resonant scattering and thereby decrease
the lattice thermal conductivity[4-8].
Experimentally the double-filling approach has
been proven effective in improving thermoelectric
properties. In a number of cases the double-filling
approach has decresed the κL further compared to the
single-filling[9-14]. The Debye model has been used
by Yang et al[15] and Nolas et al[16] in Yb- and La-
partially fi lled CoSb3 to identify the phonon scattering
mechanisms in these single-filled skutterudites.
Concerning the reduction of the lattice thermal
conductivity by double-fi lling, Yang et al[17] attributes
it to the dual-frequency resonant phonon scattering.
However, study on the thermal transports in the double-
filled skutterudites is less reported, while a more

678 Vol.28 No.4 XU Wei et al: Lattice Thermal Transport in Double-fi lled Skutterudites In...
complete understanding of the mechanisms which
underlie the thermal conductivity reduction would be
benefi cial in guiding materials research on this material
system.
We have demonstrated that the (In,Yb) double-
filling effectively reduced the lattice thermal
conductivity and enhanced the thermoelectric figure
of merit, ZT, as compared with the In or Yb single-
fi lling approach[12-14]. In this work, study on the lattice
thermal transport mechanisms in In0.1YbyCo4Sb12 (y
0.20) samples was performed and presented, with the
eingenmode frequencies of the fillers derived from
specifi c heat capacity measurements.
2 Experimental
Polycrystalline samples of In0.1YbyCo4Sb12 (y=0,
0.05, 0.1, 0.2) were prepared by melting-annealing-
hot pressing method. Details of materials synthesis,
characterization and transport property measurements
were described elsewhere[12]. XRD patterns of all the
samples showed a single-phase skutterudite structure.
All the samples had similar values of about 95% of the
theoretical density.
The samples were cut by diamond saw into
7 mm×2 mm×2 mm bars for low temperature transport
property measurements. The low temperature thermal
conductivity measurements from 25-300 K were made
on a custom designed apparatus using an advanced
research systems (ARS) closed cycle cryostat (10-300
K) with a radiation shield by the steady-state method.
The electrical resistivity measurement was measured
from 10-300 K in a custom designed apparatus using an
ARS closed cycle cryostat (6-300 K) equipped with a
radiation shield. The lattice thermal conductivity κL was
derived by subtracting the carrier thermal conductivity
κe from the total thermal conductivity κ. The κe is given
by the Weidemann-Franz relation κe = L0T/ρ, where
ρ is the electrical resistivity and the Lorentz constant
is given by L0 = 2×10-8 V2/K2, which is considered
suitable to heavily doped semiconductors[18].
3 Results and discussion
In order to discover the eingenmode frequency of
the fi ller atoms, specifi c heat capacities of two single-
filled skutterudites, In0.2Co4Sb12 and Yb0.2Co4Sb12,
were measured with respect to temperature. Details
of materials synthesis and characterization were
described elsewhere[14]. The specific heat capacity
measurements were performed on a Physical Properties
Measurement System unit by Quantum Design,
utilizing its heat capacity option from 1.8-300 K. The
focus was predominantly on the low-temperature range
of the data (T20 K), such that the experiment would
probe low-energy heat-carrying phonons without the
obscuring influences of high-energy phonons and
anharmonic effects. A number of different approaches
were employed in the analysis of heat-capacity data of
filled skutterudites, we followed the analytic approach
used by Mandrus et al[5] and fi tted the low temperature
Cp data directly with a function of the form[5]:
(1)
where, γ and β are the coeffi cients of the electronic and
lattice specific heat, respectively, β =12π4NκB/(5θD
3)
with N is the number of host atoms comprising the
skutterudite structure, θE1 and θE2 represent the Einstein
temperatures of the two guest modes necessary for the
fit with spectral weight A and B, respectively. Three
types of models, just the Debye model, the Debye
model and one Einstein mode, and the Debye model
and two Einstein modes, were tried to compare the
goodness-of-fit for all the cases. It is found that the
model with two Enistein oscillator modes included
leads to the best description of the experimental
results for both of the In0.2Co4Sb12 and Yb0.2Co4Sb12,
with results shown in Table 1. A detailed discussion
on the analysis of the specific heat Cp data can be
found elsewhere[19]. A brief outline will be given here.
The derived Debye temperature is comparable to the
reported values in the Refs.[20,21]. It is notable that the
fi rst Einstein mode temperatures (θE1,In=59 K, θE1,Yb=64
K) are close to the first Enistein mode temperature
of the La-filled skutterudite La0.9Fe3CoSb12 (θE1=70
K)[6] derived from heat capacity and inelastic neutron
scattering measurements, and especially, θE1,Yb=64 K
agrees well with the calculated value for Yb (60 K)
based on density-functional calculations[22] and the
fi rst Einstein mode (70 K) derived from heat capacity
measurements by Dimitrov IK et al[21]. The two Einstein
modes (i e, the Debye model and two Einstein modes)
have been found in a number of previous studies on

Journal of Wuhan University of Technology-Mater. Sci. Ed. Aug.2013 679
specific heat Cp of the filled-skutterudites, such as
La0.9Fe3CoSb12
[6], Yb0.2Co4Sb12
[21]. The consistency of
the experimental weight of the fi rst Einstein mode with
the theoretical prediction (0.2×3R=4.99 J·mol-1·K-1) in
the In0.2Co4Sb12 and Yb0.2Co4Sb12 suggests that the fi rst
Einstein mode is predominantly fi ller atom vibrations,
and the significantly larger weight of the second
Einstein mode, in conjunction with its energy range,
implies it is predominantly low-energy Sb vibrations.
In conclusion, the specific heat Cp analysis gives out
the eingenmode frequencies of the fi llers as θE,In=59 K
and θE,Yb=64 K.
In order to investigate the phonon scattering
mechanisms in the filled skutterdites, the Debye
approximation was used with the form[23,24]:
(2)
where, the dimensionless quantity x=w/κBT, κB is
the Boltzmann constant, ω is the phonon frequency,
is the reduced Planck constant, θD is the Debye
temperature, ν is the sound velocity, and τc is the
phonon-scattering relaxation time. The overall phonon-
scattering relaxation rate is[24,25]
(3)
where, L is the grain size, ω0 is the resonance
frequency, and the coefficients A, B, and C are
the fitting parameters. The terms on the right side
of Eq. (3) represent grain boundary, point defect,
phonon-phonon umklapp, and phonon resonance
scatterings, respectively. The interaction between the
lattice phonons and the filler atoms is modeled by
an additional phonon resonance scattering term, as
employed previously by Yang et al[15] and Nolas et
al[16] in Yb- and La-partially filled skutterudites. The
phonon resonance scattering term was derived based
on a simple mechanical oscillator model. Because there
are two types of fi ller atoms with different vibrational
frequencies in the double-filled skutterudites, the
phonon-scattering relaxation rate in the double-filled
skutterudites could then be written as
(4)
where, ω01 and ω02 are the low-energy local mode
frequencies of the two distinct fillers. Eqs.(2)-(4)
were used to fit the low temperature κL in the single-
and double-filled skutterudites. The derived Debye
temperature from heat capacity of In0.2Co4Sb12, θD =298
K, is used here. ν is calculated according to Debye
theory, ν = ωD[6π2(N/V)]-1/3, where ωD is the Debye
frequency, ωD=κBθD/, N/V is the number density of
atoms, then ν=2840 m/s is obtained. The localized
mode frequencies of In and Yb derived from the
heat capacity measurements is used here (θE,In=59 K,
θE,Yb=64 K).
The results are shown as the solid line fi ts to the
measured data in Fig.1. The fi ts match the experimental
data very well over the entire temperature range. The
lattice thermal conductivity decreases with increasing
filling fraction and the change seems to be saturated
when the Yb filling fraction y is increased above 0.1.
Table 2 lists the obtained fitting parameters for each

680 Vol.28 No.4 XU Wei et al: Lattice Thermal Transport in Double-fi lled Skutterudites In...
composition. The typical grain size is in the range of
0.5-10 μm, as estimated from the fractured surface
SEM observation[12], and the grain size determined from
the fi ts to the data is slightly less than the experimental
value. The parameters A and C increase significantly
as the filling fraction y increases. This is reasonable
taking account of the investigated temperature range
since grain boundary scattering takes effect mainly
at very low temperatures with point defect and
resonance scatterings being dominant at intermediate
temperatures, and phonon-phonon umklapp scattering
predominantly affects the high temperature region[26].
Yang J [15] and Nolas G et al[16] have proposed that the
point defect scattering in fi lled skutterudite RyCo4Sb12
is basically due to the mass fluctuation on the 2α
crystallographic sites between mR at a concentration y
and mvoid (=0) at a concentration of (1-y). Fig.2 shows
the fitted parameter A versus ytotal(1-ytotal) (ytotal is the
sum of the filling fraction of In with that of Yb), the
solid line is a linear fit to the double-filled data. The
linear variation of the parameter A with ytotal(1-ytotal)
in the double-filled samples substantiates the above
argument, furthermore, the parameter A of the single-
fi lled In0.1Co4Sb12 falls below the solid line, consistent
with the expectation that two type of fi llers in double-
filled skutterudites would generate stronger mass
fl uctuation on the 2α sites.
Fig.3 presents the phonon resonance scattering
parameter (C1+C2) as a function of the total filling
fraction ytotal. The solid line is a linear fi t to the double-
filled data. Similarly, a linear increase in (C1+C2) is
observed as the total filling fraction increases in the
double-filled samples. This is in agreement with the
observation by Yang et al on Yb-filled CoSb3
[15]. The
partial relaxation rate for phonon resonance scattering
in Eq.(3) was derived based on a simple mechanical
oscillator model, therefore C should be proportional
to the concentration of the oscillators. Figs.1 and 3
indicate that the additional phonon scattering due to
double-fi lling can be well described by the two phonon
resonance scattering terms in Eq.(4). In double-filled
skutterudites, two types of filler atoms with different
resonant frequencies could scatter broader range of
lattice phonons compared to the single-filled ones,
thus the phonon resonant scattering in the double-fi lled
materials will be larger. This is consistent with the
observation that the data of In0.1Co4Sb12 falls below the
solid line in Fig.3.
4 Conclusions
In summary, specifi c heat capacity measurements
were performed on two single-filled skutterudtes,
In0.2Co4Sb12 and Yb0.2Co4Sb12, to probe the characteristic
low-frequency localized modes of In and Yb, with
θE,In=59 K and θE,Yb=64 K yielded. The low temperature
κL of In0.1YbyCo4Sb12 was analyzed based on the Debye
approximation, with two phonon resonance scattering
terms included to account for the additional phonon
scattering due to double-fi lling. The theoretical analysis
indicates that both phonon point defect scattering and

Journal of Wuhan University of Technology-Mater. Sci. Ed. Aug.2013 681
phonon resonance scattering increase significantly
with the increasing filling fraction. The phonon point
defect scattering is mainly due to mass fl uctuation on
the 2α crystallographic sites, and double-fi lling leads to
stronger mass fl uctuation. Furthermore, the additional
phonon scattering due to double-filling can be well
described by the two phonon resonance scattering
terms, and the phonon resonance scattering increases
with the increasing fi lling fraction.
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