IGCAR : Annual Report - Indira Gandhi Centre for Atomic Research

IGC
Annual Report 2007
Energy (cm -1 )
2300
2200
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100
0
R
Γ
relaxed atomic configuration
and phonon frequencies at
different
pressures.
Calculations are performed on
8 8 8 k-point grid, with 350
Rydbergs energy cutoff, using a
16-node Linux cluster. Extra
care is taken to ensure that
inter-atomic forces in the
relaxed structure remain below
10 -6 eV/Å, as otherwise phonon
dispersion at ambient pressure
shows imaginary frequencies.
Thermal expansion coefficient
is calculated from Gruneisen
parameters of all modes.
Phonon eigenvectors are used
for assignment of phonon
modes. Soft phonon modes
contributing to NTE are
identified from the high
pressure experiments and
simulations. Zn(CN) 2 procured
X
M
Fig.2 Calculated phonon dispersion curve for Zn(CN) 2
at ambient pressure
Γ
from Alfa-Aesar (purity >
99.5%), is loaded into a Mao-
Bell type diamond anvil cell
with methanol-ethanol (4:1)
mixture as pressure transmitting
medium. Ruby fluorescence is
used to measure pressure.
Raman spectra are recorded at
different pressures in the
backscattering geometry using
the 488-nm line of an argon
ion laser, using a double
monochromator, and detected
with a cooled photomultiplier
tube operated in the photon
counting mode. The spectral
range covered is 10-2400 cm -1
that also includes the
C≡N stretch mode around
2220 cm -1 .
Figure1 depicts the phonon
frequency (ω) vs. pressure (P)
for the three modes observed
by Raman spectroscopy. Inset
shows the behaviour of the
calculated mode frequencies.
Fig.2 shows the phonon
dispersion obtained for
Zn(CN) 2 from simulation at
ambient pressure. Each of the
mode frequencies in Fig.1 inset
correspond to those at the Γ
point in the phonon dispersion.
It has been suggested that
ZnC 4 /N 4 rigid units are
responsible for NTE. But our
results show that only the C≡N
bond can be treated as rigid
unit and the soft
modes correspond to the
librational and translational
modes of C≡N bond,
with librational modes
contributing more to thermal
expansion. Out of the eleven
zone-centre optical modes, six
modes exhibit negative
Gruneisen parameter. The
value of thermal expansion
coefficient, , calculated from
the Gruneisen parameters is in
excellent agreement with
experimental value. A rapid
disordering of the lattice is
found above 1.6 GPa from x-
ray diffraction. The
present calculations and
measurements provide the first
insight into the relative role of
the different phonons in
causing negative thermal
expansion in Zn(CN) 2 .
154 BASIC RESEARCH