Effect of boundary scattering on the thermal conductivity of TiNiSn-based half-Heusler alloys
S. Bhattacharya,* M. J. Skove, M. Russell, and T. M. Tritt
Department of Physics, Clemson University, Clemson, South Carolina 29634, USA
Y. Xia, V. Ponnambalam, and S. J. Poon
Department of Physics, University of Virginia, Charlottesville, Virginia 22901, USA
N. Thadhani
Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
Received 22 December 2007; published 30 May 2008
TiNiSn-based half-Heusler alloys have been of significant interest for their potential as thermoelectric
materials. They exhibit promising electronic transport properties as revealed through high Seebeck coefficient
and moderate electrical resistivity values. The chief disadvantage of these materials is a comparatively high
lattice thermal conductivity. Attempts to “tune” the lattice thermal conductivity
L
in these materials have led
to the comparison and analysis of the thermal conductivity of two series of Ti- and Zr-based half-Heusler
alloys. In the first series, Ti
1-y
Zr
y
NiSn
0.95
Sb
0.05
, a significant reduction in
L
is observed, with the substitution
of large concentrations of Zr y 25% at Ti site, which is most likely due to mass fluctuation scattering. In the
second series, TiNiSn
1-x
Sb
x
, a nonsystematic increase in
L
is observed, with minute amounts of Sb doping
x 5% at the Sn site. Extensive microstructural analysis in a TiNiSn
1-x
Sb
x
series reveals a correlation
between
L
and the average grain diameter in these materials, which is in good agreement with theoretical
predictions related to phonon boundary scattering. In addition, a comparison of the calculated phonon mean
free path in each of the series of compounds shows some insight into the two different phonon scattering
mechanisms.
DOI: 10.1103/PhysRevB.77.184203 PACS numbers: 65.40.-b, 63.20.kp, 61.72.Mm
I. INTRODUCTION
The half-Heusler alloys are a group of ternary intermetal-
lic compounds with the general formula MM'X, which is
composed of transition metals M =Zr,Hf,Ti,V,Nb,Mn and
M' =Fe,Co,Ni and a nonmetal or a nonmagnetic metal X
=Sn,Sb,In,Ge,Al.
1
The half-Heusler alloys exhibit the cu-
bic MgAgAs C1
b
type of crystal structure consisting of 3
filled and 1 vacant interpenetrating fcc sublattices with 12
atoms in a unit cell. The third fcc structure is shifted by
one-fourth of the unit cell from the body diagonal of the
rocksalt structure.
2
The half-Heusler alloys are structurally
comparable to their parent compounds, the Heusler alloys
MM'
2
X, which have two sublattices occupied by M' at-
oms, and thus there is no vacant sublattice. A half-Heusler
alloy differs from the metallic Heusler alloy in being semi-
conducting or semimetallic due to the presence of a “hybrid-
ization gap” at the Fermi level.
3
The half-Heusler alloys ex-
hibit unusual electronic, optical, and magnetic transport
properties.
4–6
The MNiSn M =Ti,Zr,Hf half-Heusler alloys have been
of significant interest for their potential as thermoelectric
TE materials for several years.
7–9
The combination of high
thermopower -60 to -150 V / K and low electrical
resistivity =1 / 1–0.1 m cm in the TiNiSn-based
half-Heusler alloys has resulted in promising TE power
factor
2
T of about 0.7–1.0 W m
-1
K
-1
at 300 K. Opti-
mized doping of 5% Sb at Sn site has resulted in the largest
power factors
2
T 1.0 W m
-1
K
-1
at 300 K and
4.5 W m
-1
K
-1
at 650 K in the TiNiSn
0.95
Sb
0.05
.
10
Other
groups have also reported promising thermoelectric proper-
ties in the half-Heusler alloys. A TE figure of merit or ZT
=
2
T / 0.7 at 800 K has been reported in the
Zr
0.5
Hf
0.5
Ni
0.8
Pd
0.2
Sn
0.99
Sb
0.01
by Shen et al.
11
The highest
value of ZT=0.81 at T = 1025 K was observed by Culp et
al.
12
in the half-Heusler alloys for a composition of
Hf
0.75
Zr
0.25
NiSn
0.975
Sb
0.025
, which was found to exceed the
goal set for industrial purposes by the SiGe alloys.
The TiNiSn half-Heusler alloys exhibit a lattice parameter
of 5.94 Å.
13
The result of an “unfilled” structure in the half-
Heusler alloys due to the vacant Ni sublattice leads to inter-
esting band-structure properties. A narrow energy band gap
0.1–0.2 eVRefs. 5 and 7 at the Fermi level, possibly due
to an overlap between the d, d Ti3d
2
4s
2
, Ni3d
8
4s
2
,
and p and d Ti3d
2
4s
2
or Ni3d
8
4s
2
and Sn5s
2
5p
2
wave
functions leads to novel electronic transport properties.
2
The
position of the Fermi level with respect to the gap determines
whether these compounds are semiconducting or metallic. A
small band gap near the Fermi level not only makes the band
structure sensitive to various chemical substitutions but also
accounts for the “tunability” and variability of the electrical
resistivity 1 / 0.1–8 m cm at room temperature.
10
Although the electrical transport properties in the Ti-
based half-Heusler alloys reveal positive results, the lattice
thermal conductivity observed
L
10 W m
-1
K
-1
at
300 K is quite high and needs to be further reduced.
14
An
ideal thermoelectric material requires a high Seebeck coeffi-
cient 100–300 VK
-1
and favorable electrical con-
ductivity 10
2
–10
4
cm
-1
as exhibited by semimetals
or semiconductors with an optimal energy gap E
g
0.25 eV.
15
The Seebeck coefficient, from Mott’s equation
for metals, is given by =
2
/ 3k
2
T / edln / dE
E=E
F
,
where is the electrical conductivity and is proportional to
PHYSICAL REVIEW B 77, 184203 2008
1098-0121/2008/7718/1842038 ©2008 The American Physical Society 184203-1