J. Phys. Chem. B 2007, 111, 7003-7008
7003
Pressure-Induced Structural Transition in n-Pentane: A Raman Study
G. Kavitha and Chandrabhas Narayana*
Light Scattering Laboratory, Chemistry and Physics of Material Unit, Jawaharlal Nehru Centre for
AdVanced Scientific Research, Jakkur, Bangalore 560 064, India
ReceiVed: December 2, 2006; In Final Form: April 26, 2007
Pressure-induced Raman spectroscopy studies on n-pentane have been carried out up to 17 GPa at ambient
temperature. n-Pentane undergoes a liquid-solid transition around 3.0 GPa and a solid-solid transition
around 12.3 GPa. The intensity ratio of the Raman modes related to all-trans conformation (1130 cm-1 and
2850 cm-1) to that of gauche conformation (1090 cm-1 and 2922 cm-1) suggests an increase in the gauche
population conformers above 12.3 GPa. This is accompanied with broadening of Raman modes above
12.3 GPa. The high-pressure phase of n-pentane above 12.3 GPa is a disordered phase where the carbon
chains are kinked. The pressure-induced order-disorder phase transition is different from the behavior of
higher hydrocarbon like n-heptane.
1. Introduction
Organic molecular liquids such as short- and long-chain
alkanes have considerable importance because of their conformational stability, which is fundamental to their chemical
stability. The alkyl chain properties give insight into the
understanding of the biological phenomena in liquid phase.
Liquid n-pentane has a wide variety of applications.1 It is one
of the main components in petroleum2 and a solvent in reaction
mixtures as well as an extracting agent.3-5 It has been used as
hydrostatic pressure medium in high-pressure experiments6-8
and is relevant to biological applications. Hence, it is important
to understand its conformation, phase diagram, and molecular
arrangement under pressure. The conformation of the n-alkanes
in liquids has been actively investigated. The effect of pressure
on conformational equilibrium because of the change in volume
affects the rotational isomers leading to the change in structure.
Hydrostatic pressure changes the intra- and intermolecular forces
in the molecular systems as a result of decrease in volume. In
addition to this, n-pentane is also a model for all kinds of linear
alkanes, as it possesses the basic molecular conformational units
like all-trans (TT), single gauche (TG), and double gauche (GG)
conformers.9 Recent high-pressure Raman studies up to
4.77 GPa by Qiao and Zheng1 and infrared studies up to
2.8 GPa by Kato and Taniguchi9 showed the existence of a
liquid-solid transition around 2.5 GPa. However, there have
been no studies carried out to look at transition in the solid
n-pentane.
Recently, we have carried out high-pressure studies on
n-heptane and have shown that n-heptane transforms into an
orientationally disordered structure at a pressure of 7.5 GPa.10
The above work was motivated by a theoretical calculation by
Krishnan and Balasubramanian11 suggesting freezing of methyl
end groups at high pressures in solid n-heptane. We have carried
out high-pressure Raman spectroscopy studies on liquid npentane up to a pressure of 17 GPa to investigate the existence
of any solid-solid transition in n-pentane similar to n-heptane.
We report here the existence of a liquid-solid transition below
* To whom correspondence should be addressed. E-mail: cbhas@
jncasr.ac.in.
3.0 GPa as well as another transition around 12.3 GPa as
deduced from the Raman mode behavior of n-pentane. In this
paper, we discuss the systematics of this solid-solid transition
of n-pentane.
2. Experimental Details
To carry out the high-pressure studies, we have used
spectroscopic grade n-pentane from Sigma Aldrich without
further purification. The Raman spectra were recorded using
the standard backscattering geometry. The sample was irradiated
using a 15 mW 532 nm Nd-YAG laser (SUWTECH, China).
The Jobin-Yvon Triax 550 equipped with a liquid N2 cooled
CCD detector (Instrument SA, United States) was used to record
the Raman spectra. The details of the setup used are given
elsewhere.12 High-pressure experiments were carried out using
a Mao-Bell diamond anvil cell without any pressure-transmitting medium. We have used two, Type II, diamonds with
500 µm culet and a very low fluorescence to generate the
pressure. The pressure was estimated in situ using ruby R1 line
shift using the following equation13
P(GPa) ) 1904/B[{1 + (∆λ/694.24)}B - 1]
where ∆λ is the ruby R1 line shift in Å and B ) 7.665 for quasi
hydrostatic pressure.
3. Results
Figure 1a and b shows the Raman spectra of n-pentane at
ambient and high pressures. Because of high Rayleigh background, we are unable to clearly observe any low-frequency
mode below 300 cm-1. Figures 2-5 show the Raman mode
frequencies of n-pentane as a function of pressure. The Raman
mode frequency (ω), its pressure derivative (dω/dP), and the
Raman mode assignments are listed in Table 1. The mode
assignments were based on refs 14-29. At around 3.0 GPa,
we observe appearance of new modes as well as a sharp change
in the Raman mode frequencies of n-pentane. This is the onset
of the liquid-to-solid transition. We will not discuss this
transition any further since it has been reported earlier.1,8,9 In
the solid phase, n-pentane crystallizes in an orthorhombic crystal
10.1021/jp068285a CCC: $37.00 © 2007 American Chemical Society
Published on Web 06/02/2007
7004 J. Phys. Chem. B, Vol. 111, No. 25, 2007
Kavitha and Narayana
Figure 1. Raman spectra of n-pentane recorded at ambient conditions and at high pressures. For clarity, the spectra has been divided into two
regions: (a) 300-1500 cm-1 and (b) 2700-3200 cm-1. The 1200-1400 cm-1 region is dominated by diamond first-order peak and has not been
shown.
TABLE 1: Frequency (ω) of the Raman Modes of n-Pentane and Its Pressure Derivative (dω/dP) Observed in the Various
Phasesa
phase I (1.9 GPa)
-1
ω (cm )
a
dω/dP
1092
1157
1.7
2.9
1450
2867
2897
2924
2934
2958
2993
5.1
15.4
0.1
32.2
4.3
19.6
15.4
phase II (>3.0 GPa)
-1
ω (cm )
dω/dP
444
894
1065
1093
1162
1460
1473
2890
2932
2961
2971
2996
3017
5.4
3.4
5.5
3.4
1.5
3.6
5.0
9.6
6.2
7.5
7.4
9.0
9.9
phase III (>12.3 GPa)
ω (cm-1)
1495
1526
2979
3006
3016
3045
dω/dP
0.4
1.1
3.2
6.3
3.4
1.7
mode assignment
LAM C-C-C angle bending
methyl rocking mode (GG)
all-trans skeletal C-C stretching
skeletal C-C stretching with gauche defect
all-trans skeletal C-C stretching
CH2 and CH3 bending
symmetric out-of-plane CH3 bending
symmetric (CH2)n stretching (TT)
symmetric (CH2)n stretching (TG)
symmetric (CH2)n stretching (TG)
in-plane asymmetric methyl stretching (TG)
out-of-plane asymmetric methyl stretching (TT)
asymmetric C-H methyl stretching (TT)
Their mode assignments are given on the basis of refs 14-29.
structure with four molecules in the unit cell.14 The structure
of the n-pentane is completely different from other paraffin as
the molecular long axes are not parallel to each other. We have
classified the Raman modes observed in n-pentane into (1)
longitudinal acoustic mode LAM, (2) methyl rocking mode, (3)
C-C skeletal stretching region (1050-1150 cm-1), (4) CH2
and CH3 bending (1400-1500 cm-1), and (5) (CH2)n and CH3
stretching (2800-3100 cm-1).
3.1. LAM (C-C-C Angle Bending). The LAM of n-alkanes
is rather weak in the liquid phase in both infrared and Raman
spectra.15 In n-pentane, we could not observe the LAM below
300 cm-1 in the liquid as well as solid phase because of the
presence of a large Rayleigh background. The torsional and
bending modes exist in the region of 200-600 cm-1. In the
solid phase, we observe a high-frequency LAM around
440 cm-1. These are related to the extension of the alkyl
chains.16 The LAM mode is associated with the C-C-C bond
angle expansion or contraction in phase and is also known as
the “accordion mode”.17,18 It is mainly dependent on chain length
and its frequency is inversely proportional to the length of the
ordered chain. This mode appears above the liquid-solid
transition. Pressure behavior of LAM frequency is shown in
Figure 2a. Its disappearance around 12.3 GPa could suggest a
possible solid-solid transition, which will be discussed later.
3.2. Methyl Rocking Region. The mode at 895 cm-1 is
related to methyl rocking with GG rotamers,19 and its pressure
dependence is shown in Figure 2b. It is particularly sensitive
to conformational randomness and motion of the local molecular
state.20 It is significantly important in large alkanes, because it
probes the order of the alkane chain termini and is also sensitive
to chain packing. In the present case, it appears in the solid
phase of n-pentane. This is in agreement with the observation
that n-pentane crystallizes with the molecular long axis not being
parallel.14 From Figure 2b, it is seen that the mode disappears
above 12.3 GPa. A possible phase transition at 12.3 GPa
(discussed later) could be the origin for the disappearance.
3.3. Skeletal C-C Stretching Region (1050-1200 cm-1).
The region 1050-1200 cm-1 is related to the Raman modes
associated with these conformers, and Figure 3 shows their
pressure dependence. The Raman modes associated with the
all-trans conformation (see Supporting Information (SI)) are
1060 and 1130 cm-1, where 1090 cm-1 is related to globular
gauche conformation (see SI).21-23 A strong 1090 cm-1 Raman
mode in the liquid state suggests that large numbers of gauche
rotamers are present in the liquid state. The appearance of
1060 cm-1 mode and increase in intensity of the 1130 cm-1
mode suggest that n-pentane in the condensed phase prefers to
be in all-trans conformation. Figure 6a shows the intensity ratio
Structural Transition in n-Pentane
Figure 2. The Raman modes associated with (a) LAM and (b) methyl
rocking region as a function of pressure. The solid lines through the
data points are the linear fit to the data.
Figure 3. Raman modes associated with skeletal C-C stretching
modes (a) TT, (b) TG, and (c) TT conformers as a function of pressure.
The solid lines are the linear fit to the data.
of I1130/I1090, which is a representation of the population of trans
and gauche conformers.23-28 The I1130/I1090 intensity ratio
increases with increase in pressure suggesting an increase in
TT (all-trans) population. These modes cease to exist beyond
12.3 GPa because of a possible phase transition.
3.4. CH2 and CH3 Bending Region (1400-1500 cm-1). The
mode 1455 cm-1 is related to the CH2 and CH3 bending while
1460 cm-1 is related to the symmetric out-of-plane CH3 bending
mode. Figure 4 shows the Raman mode frequencies of these
modes as a function of pressure. The pressure effects on the
bending region of the spectra in the solid state are mainly due
to relative changes in the conformational isomers.10,24 These
J. Phys. Chem. B, Vol. 111, No. 25, 2007 7005
Figure 4. (a) CH2 and CH3 bending and (b) symmetric out-of-plane
CH3 bending modes as a function of pressure. The solid lines are the
linear fit to the data.
modes persist up to 16 GPa which is similar to our earlier Raman
work on n-heptane.10 There is a distinct change in the mode
frequency of these modes beyond 12.3 GPa, and they become
stiff beyond 12.3 GPa. This is an indication for a possible phase
transition at 12.3 GPa (see the dω/dP in Table 1).
3.5. (CH2)n and CH3 Stretching Region (2800-3100 cm-1).
There are a bunch of modes appearing in the region 28003100 cm-1, which are related to polymethylene stretching. These
modes have a strong dependence on chain length of the
hydrocarbon. Figure 5 shows the pressure dependence of these
modes. The symmetric methylene stretching mode (see SI)
involves three bands: (a) a narrower band at 2850 cm-1 (TT),
(b) a broad band at 2880 cm-1 (TG), and (c) a shoulder near
2922 cm-1 (TG).19,26 The mode at 2940 cm-1 (TG) is related
to in-plane asymmetric methyl stretching, the mode at
2950 cm-1(TT) is related to out-of-plane asymmetric CH3
stretching, and the mode at 2980 cm-1 (TT) is due to asymmetric
C-H stretching of CH3 (skeletal plane mode).19,28 These modes
are sensitive to alkyl chain conformation and chain packing
arrangement.30,31 The changes in the Raman spectra in this
region around 12.3 GPa suggest a possible phase transition
because of conformational changes. We have plotted the relative
intensity ratio of 2850 cm-1 and 2922 cm-1 modes (I2850/I2922)
in Figure 6b, which gives the populations of the two conformational isomers.28,32,33 There is a monotonous increase in this
ratio in the solid phase between 3.0 and 12.3 GPa suggesting
an increase in all-trans conformation population in this region.
Beyond 12.3 GPa, this ratio starts to decrease. This is interesting
and could mean an increase in gauche population. To the best
of our knowledge, we do not know of any other system which
shows an increase in the gauche population with an increase in
pressure. We propose a possible way this could happen in
n-pentane and the affect of this on n-pentane, and a resulting
phase transition is discussed below.
4. Discussion
In the case of molecular solid, the Raman spectrum is
sensitive to the changes in the inter- and intramolecular
7006 J. Phys. Chem. B, Vol. 111, No. 25, 2007
Figure 5. (a) (CH2)n and (b) CH3 stretching modes as a function of
pressure. The solid lines are the linear fit to the data.
Figure 6. The intensity ratios (a) I1130/I1090 and (b) I2850/I2922 of TT to
TG conformational isomer of n-pentane are plotted as a function of
pressure. The solid lines are the linear fit to the data.
vibrations because of conformations. The application of pressure
on liquid n-pentane increases the intermolecular potential
through increase in van der Waals forces and increase in
intramolecular potential because of decrease in bond distance
as a result of the decrease in volume. The 440 cm-1 (LAM
mode) appears in the solid phase of n-pentane beyond 3.0 GPa
but disappears around 12.3 GPa. There is an increase in the
TG conformers at the expense of TT conformers beyond
Kavitha and Narayana
12.3 GPa (see Figure 6b). This could mean that kinks develop
in the chain, mostly at the ends, hence making the execution of
LAM vibration difficult above 12.3 GPa leading to broadening
of this mode and its subsequent disappearance. The methyl
rocking with GG rotomers (895 cm-1) is due to end GG
conformation and appears only in the solid phase of n-pentane.
In general, higher hydrocarbons crystallize with gauche defects
as shown in the case of n-heptane,10 which slowly converts to
an all-trans conformer at higher pressures. This is true in the
case of n-pentane also, where there is end GG confirmation at
lower pressures, and with increasing pressure it tends toward
all-trans conformation up to a pressure of 12.3 GPa, as seen
from Figure 6. The presence of end GG conformation could be
the reason for n-pentane to crystallize with nonparallel molecular
long axis, unlike other longer chain paraffin. Above 12.3 GPa,
the mode associated with end GG disappears suggesting that
end GG is getting converted to either end TG or all-trans
conformers.
The increase in the intensity of C-C skeletal stretching mode
in the pressure range of 3-12.3 GPa suggests that n-pentane,
like other higher hydrocarbons, prefers to be in all-trans
conformation in the condensed phase. Interestingly, the disappearance of these modes beyond 12.3 GPa could mean that at
higher pressures because of its small chain length, n-pentane
prefers to compact itself by having end gauche defects rather
than going all trans as in the case of other n-alkanes. An initial
increase in the intensity ratio of I1130/I1090 (Figure 6a) suggests
an increase in TT conformers in the solid phase. The behavior
of these modes up to 12.3 GPa is similar to higher hydrocarbons
like n-heptane.10 There is a strong pressure dependence of the
CH3 and CH2 bending modes in the solid phase. The hardening
(increase in frequency) of these modes suggests that n-pentane
like n-heptane packs densely with pressure.10 There is a sharp
change in the mode behavior above 12.3 GPa because of the
phase transition. The persistence of these modes up to 16 GPa
suggests that n-pentane preserves its molecular structure at high
pressures similar to n-heptane.10 The methylene and methyl
stretching modes are highly sensitive to the conformation. The
intensity ratio of I2850/I2922 (see Figure 6b) is a quantitative
estimate of the all-trans and gauche conformers in n-pentane.
The decrease in intensity and the subsequent disappearance of
all-trans modes 2950 and 2980 cm-1 at 12.3 GPa suggest that
n-pentane above 12.3 GPa has end gauche conformers to
facilitate reduction in volume upon increase of pressure. Raman
is not sufficient to suggest this; other probes may be necessary
to authenticate this claim. To the best of our knowledge, this is
the first n-alkane that has gauche defects at high pressures or
higher density. The possible reason for this could be related to
the fact that n-pentane crystallizes uniquely with molecular long
axis not parallel to c-axis or to each other.14,34,35 This could
help in compacting the molecules at higher density by the
presence of end gauche (TG) conformation leading to better
packing. On the basis of the symmetry operations, one can
predict the chain packing, and it has been shown that in the
case of crossed chain alkanes like n-pentane, the density of van
der Waals contacts between the chain rows is minimal which
requires end gauche conformation in its crystal structure.36 A
similar argument could be used for n-pentane at high pressures
where the gauche conformers help in better packing in highdensity condition leading to a disordered phase above 12.3 GPa.
High-pressure Brillouin studies on 1:1 pentane/isopentane up
to 12 GPa, which is used as a hydrostatic medium in high-
Structural Transition in n-Pentane
J. Phys. Chem. B, Vol. 111, No. 25, 2007 7007
and has found six bands associated with the molecule in GG
state.19 This again suggests that n-pentane unlike other n-alkanes
tends to have end gauche configuration for effective packing.
In summary, high-pressure Raman spectroscopic studies on
n-pentane carried out up to 17 GPa shows two transitions: (a)
liquid-solid transition below 3.0 GPa and (b) solid-solid
transition above 12.3 GPa. This solid-solid transition above
12.3 GPa is due to reorientation of the methyl group at the end
of the molecules leading to an increase in TG conformation in
the disordered phase. We observe all the Raman modes expected
in n-pentane and have followed their pressure dependence up
to 17 GPa. There is a broadening of all the modes around
12.3 GPa, making it difficult to observe them above 12.3 GPa.
The result of the disordered phase is indicated by the disappearance of many of the n-pentane Raman modes above 12.3
GPa. The disordered phase observed in n-pentane is very
different from n-heptane and could be related to the difference
in their crystal structure in the solid phase as well as the chain
length. The X-ray diffraction, which is a prominent tool for
probing crystal structure, can give further information about this
transition.
Acknowledgment. C.N. thanks Prof. C.N.R. Rao and
Jawaharlal Nehru Centre for Advanced Scientific Research and
Department of Science and Technology for the financial support.
Supporting Information Available: The figures depicting
the all-trans conformers, end gauche conformers, and methylene
stretching modes are provided for clarity. This material is
available free of charge via the Internet at http://pubs.acs.org.
References and Notes
Figure 7. The schematic representation of possible n-pentane molecular
arrangement at pressures (a) below and (b) above the transition pressure
of 12.3 GPa.
pressure experiments, shows a glass transition around 7 GPa.37
This suggests that n-pentane could develop disorder at higher
pressure.
Figure 7 shows the schematic representation of the n-pentane
at pressures (a) below and b) above the transition temperature
of 12.3 GPa. In this schematic, we suggest that the gauche
defects are mostly end gauche and are associated with those
molecules which are not aligned parallel to the long axis in the
low-pressure phase. This could lead to a very small reduction
in volume. It has been seen from our experiments that the sample
does not show any large change in volume across this transition,
since we do not observe any microcracks in the sample. It has
been seen in the NMR studies on n-pentane that in the
temperature region 70-143.4 K the second moments of the
absorption lines were found to be smaller than the computed
rigid lattice values throughout the temperature range. It has been
suggested that the lower value is achieved by the reorientation
of the methyl group at the end of each molecule about the
adjacent C-C bond.38 This could mean that molecular rearrangements at the end of the molecule are possible in n-pentane
in the solid form. Thus, we suggest that in n-pentane we expect
a fraction of the TG conformation in the all-trans conformation
by molecular rearrangement above 12.3 GPa.38 Additionally,
using valence force field calculations, Snyder has calculated
the vibrational frequencies of n-pentane at 143 K temperature
(1) Qiao, E.; Zheng, H. Appl. Spectrosc. 2005, 59, 650.
(2) Hunt, J. M. Petrol. Geochem. Geol. 1979, 31-35.
(3) White, C. M.; Jensen, K. L.; Rohar, P. C.; Tamilia, J. P.; Shaw, L.
J.; Hickey, R. F. Energy Fuels 1996, 10, 1067.
(4) Rhlid, R. B.; Matthey, D. W.; Blank, I.; Fay, L. B.; Juillerat, M.
A. J. Agric. Food Chem. 2002, 50, 4087.
(5) Ganiev, I. M.; Timerghazin, Q. K.; Khalizov, A. F.; Andriyashina,
N. M.; Shereshovets, V. V.; Volodarsky, L. B.; Tolstikov, G. A. Tetrahedron
Lett. 1999, 40, 4737.
(6) Tkachev, S. N.; Bass, J. D. J. Chem. Phys. 1996, 104, 10059.
(7) Zeto, R. J.; Vanfleet, H. B. J. Appl. Phys. 1969, 40, 2227.
(8) Gelles, S. H. J. Chem. Phys. 1968, 48, 526.
(9) Kato, M.; Taniguchi, Y. J. Chem. Phys. 1991, 94, 4440.
(10) Kavitha, G.; Narayana, C. J. Phys. Chem. B 2006, 110, 8781.
(11) Krishnan, M.; Balasubramanian, S. J. Phys. Chem. B 2005, 109,
1936.
(12) Kavitha, G.; Vivek, S. R. C.; Govindaraj, A.; Narayana, C. Proc.
Indian Acad. Sci. (Chem. Sci.) 2003, 115, 689.
(13) Yousuf, Md. Semiconductors and Semimetals; Willardson, R. K.,
Suski, T., Paul, W., Eds.; Academic Press: New York, 1998; Chapter 7.
(14) Heinz, G.; Fanconi, B. J. Chem. Phys. 1973, 59, 534.
(15) Painter, P. C.; Coleman, M. M.; Koenig, J. L. The Theory of
Vibrational Spectroscopy and its Application to Polymeric Materials; John
Wiley: New York, 1982.
(16) Braden, D. A.; Parker, B. S.; Hudson, B. S. J. Chem. Phys. 1999,
111, 429.
(17) Logan, K. W.; Danner, H. R.; Gault, J. D.; Kim, H. J. Chem. Phys.
1973, 59, 2305.
(18) Snyder, R. G.; Strauss, H. L.; Alamo, R.; Mandelkern, L. J. Chem.
Phys. 1994, 100, 5422.
(19) Snyder, R. G. J. Chem. Phys. 1967, 47, 1316.
(20) Brown, K. G.; Bicknell-Brown, E.; Ladjadj, M. J. Phys. Chem.
1987, 91, 3436.
(21) Kint, S.; Scherer, J. R.; Snyder, R. G. J. Chem. Phys. 1980, 73,
2599.
(22) MacPhail, R. A.; Strauss, H. L.; Snyder, R. G.; Elliger, C. A. J.
Phys. Chem. 1984, 88, 334.
(23) Schoen, P. E.; Priest, R. G.; Sheridan, J. P.; Schnur, J. M. J. Chem.
Phys. 1979, 71, 317.
(24) Yamaguchi, M.; Serafin, S. V.; Morton, T. H.; Chronister, E. L. J.
Phys. Chem. B 2003, 107, 2815.
7008 J. Phys. Chem. B, Vol. 111, No. 25, 2007
(25) Snyder, R. G.; Cameron, D. G.; Casal, H. L.; Compton, D. A. C.;
Mantsch, H. H. Biochim. Biophys. Acta 1982, 684, 111.
(26) Snyder, R. G.; Scherer, J. R. J. Chem. Phys. 1979, 71, 3221.
(27) Pink, D. A.; Green, T. J.; Chapman, D. Biochemistry 1980, 19, 349.
(28) Wallach, D. F. H.; Verma, S. P.; Fookson, J. Biochim. Biophys.
Acta 1979, 559, 153.
(29) Kato, M.; Taniguchi, Y. J. Chem. Phys. 1990, 93, 4345.
(30) Pratt, L. R.; Hsu, C. S.; Chandler, D. J. Chem. Phys. 1978, 68,
4202.
(31) Huai, W.; Haifei, Z.; Qiang, S. Appl. Spectrosc. 2005, 59, 1498.
Kavitha and Narayana
(32) Snyder, R. G. J. Chem. Phys. 1982, 76, 3342.
(33) Snyder, R. G.; Scherer, J. R.; Gaber, B. P. Biochim. Biophys. Acta
1980, 601, 47.
(34) Norman, N.; Mathisen, H. Acta Crystallogr. 1960, 13, 1043.
(35) Mathisen, H.; Norman, N.; Pederson, B. F. Acta Chem. Scand. 1967,
21, 127.
(36) Segerman, E. Acta Crystallogr. 1965, 19, 789.
(37) Oliver, W. F.; Herbst, C. A.; Lindsay, S. M.; Wolf, G. H. Phys.
ReV. Lett. 1991, 67, 2795.
(38) Rushworth, F. A. Proc. R. Soc. London, Ser. A 1954, 222, 526.