Resistance anomaly and structural disorder in NiSi2 under high pressure

Article abstract of DOI:10.1016/j.jpcs.2006.11.025

Results of X-ray diffraction, electrical resistance, thermoelectric power measurements and electronic band structure calculations on NiSi₂ under high pressure are reported. The thermoelectric power (TEP) changes sign near 0.5 GPa (from +30 to -20 μV/K). As the pressure is increased, the value of TEP increases further in magnitude and near 7 GPa it becomes -50 μV/K. The pressure vs. resistance curve measured up to 30 GPa using diamond anvil (DAC)-based technique exhibits a broad hump near 12 GPa and exhibits hysteresis on pressure release. The ADXRD patterns up to 42 GPa show a gradual irreversible loss of long-range order in NiSi₂ with the diffraction lines progressively broadening under pressure. The FWHM of the diffraction lines show a rapid increase in the half-widths close to 0.5 GPa and also near 12 GPa. The computed band structure at a compression (without any disorder) corresponding to 12 GPa, exhibits an electronic topological transition (ETT). The rapid increase in disorder above 12 GPa implies that the ETT may be facilitating the structural disorder. It is suggested that the pressure drives the material through a region of entropic and energetic barriers and induces disorder in the material.

Full text of DOI:10.1016/j.jpcs.2006.11.025

ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 68 (2007) 367–372
www.elsevier.com/locate/jpcs
Resistance anomaly and structural disorder in NiSi2 under high pressure
Ã
Alka B. Garg, V. Vijayakumar , A.K. Verma, R.S. Rao, B.K. Godwal
High Pressure Physics Division, Purnima Laboratories, Bhabha Atomic Research Centre, Mumbai 400085, India
Received 29 June 2006; received in revised form 13 November 2006; accepted 21 November 2006
Abstract
Results of X-ray diffraction, electrical resistance, thermoelectric power measurements and electronic band structure calculations on
NiSi2 under high pressure are reported. The thermoelectric power (TEP) changes sign near 0.5 GPa (from +30 to ꢀ20 mV/K). As the
pressure is increased, the value of TEP increases further in magnitude and near 7 GPa it becomes ꢀ50 mV/K. The pressure vs. resistance
curve measured up to 30 GPa using diamond anvil (DAC)-based technique exhibits a broad hump near 12 GPa and exhibits hysteresis on
pressure release. The ADXRD patterns up to 42 GPa show a gradual irreversible loss of long-range order in NiSi2 with the diffraction
lines progressively broadening under pressure. The FWHM of the diffraction lines show a rapid increase in the half-widths close to
0.5 GPa and also near 12 GPa. The computed band structure at a compression (without any disorder) corresponding to 12 GPa, exhibits
an electronic topological transition (ETT). The rapid increase in disorder above 12 GPa implies that the ETT may be facilitating the
structural disorder. It is suggested that the pressure drives the material through a region of entropic and energetic barriers and induces
disorder in the material.
r 2006 Elsevier Ltd. All rights reserved.
Keywords: C. High pressure; C. X-ray diffraction; D. Phase transitions; D. Transport properties
1. Introduction
materials will be interesting in the context of pressure-
induced amorphization. Intermetallics with CaF2 structure
are one such class of compounds in which electronic
topological transition (ETT) is also possible.
If the energy landscape of a material has energy barriers,
then it can have metastable crystalline phases. However, to
have metastable amorphous/disordered phases, entropic
and energetic barriers are required [1]. Recent molecular
dynamics simulations on crystalline CaF2 have shown that
it is an example of a material that has regions of metastable
crystalline phases stabilized by non-energetic (entropic)
barriers alone [1]. Though there is no control on the path
taken, compressing a material will take it to a different
location of the energy landscape. Thus it may be possible to
drive CaF2 to regions with energetic barriers via a region of
entropic and energetic barriers i.e. to a region of stability of
disordered phases. Though, CaF2 does not show any
evidence of such disordered phases under compression,
several dihalogenides and dioxides with CaF2 structure do
transform to low-symmetry phases at high pressure [2].
Thus investigations under compression on related class of
Metallic phases with CaF2 structure are sparse. The
intermetallics of gold and platinum with Al, Ga, and In are
the few cases, which crystallize in the CaF2 structure [3]. All
Au compounds and PtAl2 occur in the fluorite structure
(i.e., CaF2 structure) at room temperature and it also
occurs as the high-temperature modification for PtGa2 and
PtIn2 under equilibrium conditions [4]. These phases are
entropy stabilized on compound formation due to the
volume expansion by 3–7% from the average volume of the
constituent elements. In our earlier investigations on
various intermetallics like AuGa2, AuIn2, AuAl2 and
PtAl2, structural transitions and electronic topological
transitions have been observed [5–7]. As an extension of
these studies we investigated the high-pressure behavior of
the transition metal disilicide NiSi2, which also occurs in
fluorite structure. In contrast to the intermetallics investi-
gated earlier, in NiSi2, the Ni atoms are in the interstitial
voids of the silicon lattice. In the present work, the results
Ã
Corresponding author. Tel.: +91 22 25591323.
E-mail address: vvijay0@gmail.com (V. Vijayakumar).
0022-3697/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2006.11.025

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368
of electrical resistance (R), thermoelectric power (TEP),
X-ray powder diffraction measurements, and the first
principles electronic structure calculations carried out on
NiSi2 to investigate its structural evolution under pressure
are reported.
double-silicon crystal monochromator. The beam is
collimated to a circular beam of E 80 mm diameter. The
ADXRD station is based on a 345 mm image plate (IP)
area detector from Mar Research. The scanning step (pixel
size) for reading out the data is 88 mm. The X-ray
wavelength and sample to IP distance was calibrated by
collecting ADXRD data for silicon and LaB6 loaded in the
2. Experimental details
˚
DAC. The refined wavelength was 0.6965 A. Fine particles
The sample was prepared by arc melting of appropriate
amount of Ni and Si under argon atmosphere in a cooled
copper hearth. Subsequently, the sample was annealed
at 600 1C in evacuated quartz tube for 1 week. The X-ray
powder diffraction analysis showed that the compound
is in single phase (cubic CaF2 type) with a lattice con-
of the sample were loaded into a hardened stainless steel
gasket hole of 100 mm diameter along with silver as internal
pressure marker. Mthanol:ethanol was used as the
pressure-transmitting medium. The data were collected
with a typical exposure time of 15–30 min at each pressure
point depending on the beam intensity. X-ray measure-
ments under pressure were carried out up to 40 GPa. The
two-dimensional data thus obtained is converted to
standard one-dimensional pattern using FIT2D software
[11]. The individual peaks were fitted using the software
XFIT [12] to obtain d-values and half-width and full-
profile refinement using GSAS [13] was used to obtain the
lattice constant.
˚
stant of 5.4059 A in good agreement with the literature
value [8].
High-pressure TEP measurements were carried out in a
Bridgman-opposed anvil apparatus. Bridgman anvils used,
consisted of a pair of WC pistons of face diameter of
12.5 mm, with two pyrophyllite gaskets of thickness 150 mm
each. The pyrophyllite gaskets used had outer and inner
diameters of 12.2 and 3 mm, respectively, with talc filled
inside as the pressure medium. For in situ pressure
calibration, resistance transitions in Bi [I–II (2.5 GPa)
and V–VI (7.75 GPa)] that was loaded along with the
sample was used. The samples were in the form of a foil
of 0.025–0.05 mm thick, 1 mm wide and 2.5 mm long cut
from the ingot. For TEP measurements, a tempera-
ture gradient was established along the length of the
sample by a nichrome heater wire of 100 mm diameter at
one end of the sample. The portion of the heater wire,
which comes above the sample, is flattened and insu-
lated from it by a thin mica sheet. To obtain TEP, two
parallel pairs of chromel and alumel thermocouple wires
of 0.05 mm diameter were used to measure the thermo-
electric voltages developed under the temperature gradient
relative to chromel and alumel. The negligible correction
due to the variation of the thermo emf of chromel and
alumel with pressure was ignored. Full details are given
elsewhere [9].
Electrical resistance measurements were carried out up
to 30 GPa usng a clamp-type Merrill Bassett diamond anvil
cell (DAC) with a diamond culet size of 400 mm and
stainless steel gasket. Myler-embedded alumina that results
in quasi-hydrostatic conditions [10] were used as the
pressure-transmitting medium. A pair of 20 mm diameter
stainless steel wires put across the anvil culet at a
separation of ꢁ30 mm form four leads for electrical
resistance measurements. Pressure was measured by ruby
fluorescence technique. A small rectangular piece of the
sample (thickness ꢁ5 mm) was kept at the center of the
anvil face touching the leads. Full details of the techniques
are given elsewhere [10].
3. Electronic band structure computations
Total energy calculations were performed using the first
principles full-potential linear-augmented plane wave
method (FP-LAPW), as implemented in the WIEN2k
computer program [14] based on the density functional
theory. The errors in this approach are limited to the
approximation of the exchange-correlation energy func-
tional, cutoffs in the expansion of the basis functions, k-
point sampling in the integrations over the Brillouin zone,
and Born–Oppenheimer approximation. In the FP-LAPW
method there is no approximation as regards the crystal
geometry; the charge density and potential can have
arbitrary shape though the wave functions are only
variational approximations of the true wave functions in
the region of fixed energies En. Thus relatively open CaF2
structure can be tackled without losing precision. For the
exchange correlation the generalized gradient approxima-
tion (GGA) was used [15]. Muffin-tin radii (Rmt) of two
Bohr unit were used for both Ni (3p63d84s2) and Si
(2p63s23p2). The desired precision in the total energy
is achieved by using a plane wave cutoff RmtKmax ¼ 10
and a k-point sampling in the Brillouin zone (BZ) of 5000
points.
To confirm the reliability of the computations, equili-
brium volume and bulk modulus were obtained by fitting
the computed total energy at various compressions to a
fourth degree polynomial. A slightly large (2%) equili-
brium volume, than the measured one, and a bulk modulus
of 146 GPa were obtained. The estimated equilibrium
volume is within the typical accuracy obtainable with
FP-LAPW with GGA, whereas the computed bulk
modulus (B) differs from the earlier (160 GPa) estimation
[16]. However, the earlier estimate used ASA of lower
precision.
The ADXRD measurements under pressure on NiSi2
were carried out at the X-ray diffraction beam line of
Elettra synchrotron source at Trieste, Italy (proposal no.
2003599) using a DAC). X-rays are monochromatized by a

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40
20
8
Loading
Unloading
NiSi2
7
6
5
4
3
2
1
0
-20
-40
-60
NiSi2
1
2
3
4
5
6
7
Pressure (GPa)
0
4
8
12
16
20
24
28
32
Fig. 1. Pressure variation of TEP for NiSi2 up to 10 GPa.
Pressure(GPa)
Fig. 2. Pressure variation of electrical resistance for NiSi2 up to 30 GPa.
4. Results and discussion
The TEP of NiSi2 changes its sign near 0.5 GPa (from
+30 to ꢀ20 mV/K, Fig. 1). This implies major changes in
electronic structure or energy dependence of scattering of
electrons near the Fermi level. As the pressure is increased,
the TEP increases further in magnitude and near 7 GPa it
becomes ꢀ50 mV/K. Fig. 2 shows the electrical resistance
(R) variation with pressure (P) up to 30 GPa. The
resistance is stable in the low-pressure region (i.e. up to
1 GPa), falls fast in the 1–7 GPa region. A remarkable
feature in the pressure vs. resistance curve is a broad hump
near 12 GPa. Above 20 GPa it saturates. The resistance
exhibits hysteresis on unloading. In the following
sections, by examining the crystal and electronic structure
evolution, it is concluded that the structural disordering of
NiSi2 under pressure is the origin of the interesting TEP
and resistance behavior. Thus, NiSi2 under appropriate
doping may turn out to be an excellent thermoelectric
material.
strongest lines of NiSi2 and the (1 1 1) line of Ag with
pressure. The NiSi2 lines show rapid increase in the half-
widths at very low pressure and also above 12 GPa. It is
clear from the FWHM of silver (also plotted in Fig. 4) that
the effect of freezing of the pressure medium on line width
is very small (the change in FWHM of Ag and sample are,
respectively, 20% and 380% in the full pressure range of
measurement). On pressure release, the sample lines do not
fully recover though the Ag lines do (Fig. 3b). Also, the
fact that on pressure release the sample lines remains broad
confirms that the broadening of the lines is an intrinsic
behaviour of the materials under pressure and not the
artifact of the freezing of the pressure transmitting
medium. It also indicates that the high-pressure disordered
phase is quenchable. Thus the results of X-ray diffraction
measurements indicate a quenchable structural disordering
in NiSi2 under pressure with accelerated changes occurring
near 0.5 and 12 GPa.
The evolution of X-ray diffraction pattern with pressure
is shown in Fig. 3a and b. It is clear from these figures that
the sample lines get broadened and their intensities get
reduced as the pressure is increased, whereas the pressure
calibrant (silver) lines do not broaden appreciably. The
broadening starts from very low pressure where there is no
possibility of any pressure gradient due to freezing of
pressure medium (methanol:ethanol). Also, it is the low d
lines of the powder pattern that start broadening first,
indicating the gradual loss of long-range ordering. Above
10 GPa, the peaks are substantially broad, but no new lines
appear. By 42 GPa, all sample lines except the (2 2 0) line
have merged with background, but Ag lines are clearly
seen. Fig. 4 shows the variation of FWHM of three
In spite of the different pressure media used for electrical
resistance, TEP, and X-ray diffraction (Myler-embedded
alumina, talc and ethanol–methanol, respectively), the data
corroborate one another. The change in sign of TEP near
0.5 GPa, coincides with the onset of disorder in the X-ray
pattern. The rapid increase in FWHM near 12 GPa is
reflected as a hump in the R vs. P curve. It may be noted
that unlike methanol:ethanol that freezes above 10 GPa, in
Myler-embedded alumina, there will not be any change in
pressure gradient in the region, where the hump in R is
observed. This clearly indicates that the features observed
in R, and X-ray diffraction pattern are the intrinsic
property of the material and not induced by any pressure
gradient that may be present.

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a
b
NiSi2
NiSi2
Pressure released
9.9 GPa
8.5 GPa
6.7 GPa
42 GPa
5.6 GPa
3.8 GPa
34.0 GPa
1.3 GPa
24.1 GPa
13 GPa
0.4 GPa
Ambient pressure
10
15
20
25
30
35
40
10
15
20
25
30
35
40
Two Theta (degree)
Two Theta (degree)
Fig. 3. (a) Evolution of X-ray diffraction patterns in the low-(12 GPa) pressure region. Gradual broadening of the low d values is clear seen and (b)
evolution of X-ray diffraction patterns above 12 GPa.
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
ambient conditions crosses it near the G point at 12 GPa.
Similar to the complex band picture [18] for substitution-
ally disordered alloys, this band crossing will still be
present in the disordered phase, though smeared out. Since
the TEP measurement has been carried out using Bridgman
anvil set up where the pressure limit is 10 GPa, any change
in TEP that may occur near 12 GPa is not accessible
experimentally. However, the rapid increase in disorder
above 12 GPa (seen in X-ray data) and the band crossing
seen in the computed band structure implies that the
electronic structure change could be accelerating the
disorder. Though it is well known that ETT could be
related to phonon anomalies and structural transitions
(Lifshitz–Dagen anomalies [19]), no ETT-induced disorder
is known. No accurate simulation of disorder adaptable to
electronic structure and structural stability calculations
between crystal and disordered phases with sufficient
accuracy are available to substantiate this conjecture.
Several other mechanisms based on kinetics or structural
decomposition constraints evoked for the amorphization of
non-metallic materials [20] are not applicable to metallic
systems due to the absence of strongly bound structural
units.
(111)
NiSi2
(220)
(311)
Ag (111)
0
5
10
15
20
25
30
Pressure (GPa)
Fig. 4. Pressure variation of full-width at half-maximum (FWHM) for
three strong lines. The FWHM of (1 1 1) line of Ag that do not overlap
with gasket or sample is also plotted and shows negligible increase after
the pressure medium has frozen.
It is known that changes in Fermi surface topology can
result in anomalous variation of TEP [17]. However,
examination of band structure (Fig. 5a and b), do not show
any possibility of such an electronic transition near
0.5 GPa. Thus the anomalous behavior of TEP should
have its origin in the increased electron scattering due to
pressure-induced disorder. Such disordering of a metallic
material under pressure along with anomalous behavior of
TEP is a unique feature of NiSi2. In Fig. 5b, that shows the
band structure at a compression (without any disorder)
corresponding to 12 GPa, a band has crossed the Fermi
level. A band that is flat and below the Fermi level at
Recent results of detailed molecular dynamics simulation
of the energy landscape near CaF2 phase in CaF2 and
MgCl2 offer an interesting possibility. The fact that the
disordered phase is metastable (since the lines remain
broad on pressure release) implies that the material has
been driven to a region of entropic and energetic barriers
by pressure. Thus pressure-induced disorder that is
observed might be due to the peculiar nature of energy
surface that will stabilize an entropically and energetically
stabilized disordered phase [1]. In molecular dynamics
simulations, the entropic barriers in the energy landscape in
the absence of any energy barriers have been identified as

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Fig. 5. (a) Band structure at theoretical ambient volume and (b) band structure at compression V/V0 ¼ 0.88.
local regions of high density of states where the system can
Acknowledgments
remain for a long time. In measurements, slow kinetics is
the indication of an entropically stabilized region [1].
Amorphization/disorder under pressure in general results
from the kinetic hindrance to structural transition or
decomposition [21]. It is interesting to note that in RuO2,
the pressure-induced transition from rutile to CaF2 phase
passes through intermediates phases observed in molecular
dynamics and the entropically stabilized region exhibits
slow kinetics [22]. In CaF2, the system can get trapped in an
entropically stabilized ‘‘VIIa’’ (SG, Pmn21) configuration
region in the transition path CaF2 to CaCl2 resulting in
kinetic hindrance. Thus, if NiSi2 also is driven to an
entropically stabilized region on compression, the pressure-
induced disordering will result. In the present measure-
ments, laser heating of the sample at high pressure could
not be carried out because of its non-availability at the
beamline. EXAFS measurements on this material under
pressure can yield details of structural evolution of the
disordered phase.
ABG and VVK thankfully acknowledge the ICTP for
travel support and hospitality at Elettra. The X-ray
diffraction measurements were carried out under proposal
No. 2003599. We sincerely thank Dr. A. Lausi and Dr.
E. Bussetto for all the help during measurements at
ELETTRA.
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