Magnetotransport properties of the ternary carbide Ti
3
SiC
2
: Hall effect, magnetoresistance,
and magnetic susceptibility
P. Finkel, J. D. Hettinger, and S. E. Lofland
Department of Chemistry and Physics, Center for Materials Research and Education, Rowan University, Glassboro, New Jersey 08028
M. W. Barsoum and T. El-Raghy
Department of Materials Engineering, Drexel University, Philadelphia, Pennsylvania 19104
Received 28 June 2001; published 28 December 2001
In this study we report on the transport properties of the Ti-based ternary carbide Ti
3
SiC
2
. The Hall effect
and longitudinal magnetoresistance have been measured as a function of temperature in the 4 –300 K range and
at magnetic fields up to 5 T. The magnetoresistance is dominated by a positive quadratic field dependence at
low temperatures. The Hall voltage is a linear function of magnetic field over the range of temperatures
investigated. The effective carrier concentration and mobilities were calculated based on the sign and value of
the Hall coefficient. These results are discussed in terms of a two-band model and compared to the single-band
approximation. The magnetic susceptibility 4.1 10
-6
was found to be independent of temperature and
field. These results were used to evaluate the charge concentration in light of Pauli paramaganetism theory.
DOI: 10.1103/PhysRevB.65.035113 PACS numbers: 72.15.Eb, 72.15.Gd, 71.20.Be
I. INTRODUCTION
In recent years there has been considerable interest in the
study of a new class of ternary carbide and nitrides, which
possess an unusual and sometimes unique combination of
properties.
1–10
These so-called MAX phases have the general
formula M
n +1
AX
n
, where n =1–3, M is an early transition
metal, A is an A-group element mostly IIIA and IVA, and X
is either C and/or N. They are all hexagonal ( P 6/mmc ) with
hexagonal nets of pure A-group element layers interleaved
with Ti
n +1
X
n
layers. There are over 50 known M
2
AX or 211
phases, three 312 phases, Ti
3
SiC
2
, Ti
3
GeC
2
, and Ti
3
AlC
2
,
and one 413 phase, Ti
4
AlN
3
. What renders these solids
unique is a combination of metalliclike bonding, the activa-
tion of basal dislocations even at room temperature and the
propensity of layers to delaminate without fracture. The lat-
ter is why they are referred to as thermodynamically stable
nanolaminates.
3
To date the most studied of this group of materials is
Ti
3
SiC
2
. It is anomalously soft for a transition-metal carbide
Vickers hardness values from 2 to 4 GPa and readily ma-
chinable with a manual hacksaw or regular high-speed tool
steels with no lubrication or cooling required. Ti
3
SiC
2
is
elastically stiff Young’s modulus 300 GPa,
1,9,10
damage
and thermal-shock tolerant, and behaves quasiplastically un-
der compression.
9
In the last few years several band structure calculations of
Ti
3
SiC
2
have been performed.
11–13
Two of those papers
11,12
predict a density of states at the Fermi level N ( E
F
) of about
5 states/eV unit cell. These values are in excellent agreement
with the values calculated from low-temperature heat capac-
ity measurements.
7
The Debye temperature of Ti
3
SiC
2
is also
quite high and ranges from 715 to 780 K depending on the
method of measurement.
7,8
It is a good thermal and electrical conductor. The room-
temperature electrical conductivity is 4.510
6
( m)
-1
,
roughly twice that of pure Ti and more than 4 times that of
near-stoichiometric TiC.
1,5,6
Recently, Yoo et al. have shown
that the thermoelectric power of Ti
3
SiC
2
is negligible at least
over the 300– 850 K temperature range.
5
This fact led Bar-
soum et al. to the conclusion that Ti
3
SiC
2
is a compensated
conductor,
6
in which the concentration of electrons, n, was
equal to the concentration of holes, p. In addition, to account
for the fact that the Hall coefficient fluctuated around zero,
the mobilities of the holes and electrons were also assumed
to be equal. As this work shows, the Hall coefficient is not
zero. Part of the problem in the previous work can be traced
to the fact the latter were performed in relatively low 0.8 T
magnetic fields, causing the Hall voltage to be around the
noise level of the measurements.
In this work, we characterize the electronic transport in
Ti
3
SiC
2
by performing electrical conductivity, Hall constant,
and magnetization measurements over the 4 –300 K tempera-
ture range and magnetic fields up to 5 T. In what follows, we
discuss the electronic properties of Ti
3
SiC
2
derived from
these experimental results. Insight is obtained into the elec-
tronic conduction mechanism in Ti
3
SiC
2
in light of the two-
band model.
II. EXPERIMENTAL METHODS
Three samples two six-probe Hall bars and one parallel-
epiped shaped specimen of various thicknesses 0.2–1.3
mm were cut from a Ti
3
SiC
2
sample with extra large 1–2
mm grains fabricated using the following sequence: reac-
tive sintering, hot forging, followed by annealing at 1600 °C
for 24 h. The forging oriented the grains and the annealing
allowed them to grow to millimeter sizes. The fabrication
details and microstructure are described elsewhere.
9
Despite
the fact that the grains were quite large, the samples are to be
considered polycrystalline, albeit with few grain boundaries.
The Hall voltage and magnetoresistance MR=
( H )
- ( H =0) / ( H =0), where is the resistivity and H the
magnetic field, were measured sequentially using pairs of the
six leads in a gas flow cryostat for temperature T between 4
PHYSICAL REVIEW B, VOLUME 65, 035113
0163-1829/2001/653/0351134/$20.00 ©2001 The American Physical Society 65 035113-1