Silica under hydrostatic pressure: A non continuous medium behavior
T. Deschampsa, C. Martineta, D.R. Neuvilleb, D. de Lignya, C. Coussa-Simona, B. Champagnona,*
aUniversité de Lyon, Université Lyon-1, UMR5620 CNRS, Laboratoire de Physico-Chimie des Matériaux Luminescents, Domaine scientifique de la Doua, Bât. Kastler,
10 rue Ampère, 69662 Villeurbanne, France
bPhysique des Minéraux et Magmas, CNRS-IPGP, 4 place Jussieu, 75005 Paris, France
a r t i c l ei n f o
Received 28 November 2008
Received in revised form 1 July 2009
Available online 26 September 2009
Terahertz properties and measurements
a b s t r a c t
The homogeneous/inhomogeneous structure of glasses is still a debated question. Hydrostatic high pres-
sure experiments allow us to determine if a glass behaves as an elastic continuous random network or if a
nanometer scale heterogeneity has to be taken into account. In order to get information on the homoge-
neous/inhomogeneous structure of glasses, in situ high pressure Raman experiments are performed on
silica in the elastic domain up to 4.7 GPa. A strong decrease of the Boson peak intensity is observed
between 1 bar and 3 GPa. We show that this decrease does not correspond quantitatively to the effect
of pressure on a homogeneous elastic medium. From the interpretation of the narrowing of the main
Raman band width under pressure as a narrowing of the h inter-tetrahedral Si–O–Si angle distribution
it is shown that the decrease of the Boson peak intensity is correlated to the decrease of the intrinsic inho-
mogeneity of the silica glass. These results confirm the occurrence of an intrinsic inhomogeneity at a
nanometer scale even in a single component glass like SiO2which is very important for the interpretation
of the optical or mechanical properties of the glasses.
? 2009 Elsevier B.V. All rights reserved.
The question of the homogeneity of glasses at the intermediate
scale, typically few nanometers, is still a debated question. The
maximum always observed in the low frequency inelastic scatter-
ing of light, commonly named the Boson peak, is one of the most
characteristic properties of glasses. It corresponds to an excess of
the density of states g(x) compared with the Debye theory which
established that in crystals the density of states is proportional to
the square of the frequency x2. This excess is commonly short-
handed as e-VDOS, an excess of Vibrational Density of States. This
‘‘anomaly” is observed in different experiments such as low fre-
quency Raman scattering, inelastic neutron scattering and temper-
ature dependence of the specific heat [1–4]. In order to improve
our knowledge of the micro-structural origin of Boson peak and
to discuss its dependence on the intrinsic heterogeneity of glasses,
the application of external perturbations such as hydrostatic pres-
sure is proposed.
Hydrostatic pressure experiments on silica glass lead to an elas-
tic response up to 8.6 GPa  and then to a plastic deformation
above this value. Samples recovered from pressure above the elas-
tic/plastic transition are called ‘‘densified” glasses since the final
samples are denser than the original materials. High pressure
experiments on the Boson peak of glasses were up to now mainly
performed on such permanently densified glasses, recovered from
high pressures over the elastic–inelastic limit [6–8]. In situ high
pressure Raman experiments are usually made in a Diamond Anvil
Cell and do not allow the observation of the Boson peak below
100 cm?1[5–9]. To our knowledge there are only few in situ obser-
vations [10,11] of the Boson peak under high pressure in Raman
experiments and, besides from the pioneering work of Hemley
et al.  and a 1.68 GPa measurement of Schroeder et al. ,
no experiment has been realized on silica which is however the
most extensively studied glass. Comparisons between the pressure
effects and the intensity of the Raman bands concerned very few
studies  and are limited in the cited paper to the frequency do-
main above the Boson peak.
In this work we focus on the behavior of the Boson peak of sil-
ica in the elastic domain below 5 GPa where no permanent
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* Corresponding author. Tel.: +33 4 72448334; fax: +33 472448442.
E-mail address: email@example.com (B. Champagnon).
Journal of Non-Crystalline Solids 355 (2009) 2422–2424
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densification occurs  and relate this to the evolution of the glass
inhomogeneity determined from the optical Raman active modes.
The measurements of the low frequency Raman scattering in
the region of the Boson peak in a Diamond Anvil Cell (DAC) require
special cares in the experimental set up. A special attention has to
be paid to the spectrometer’s alignments, in our case the Horiba Jo-
bin-Yvon T64000 microRaman triple spectrometer equipped with a
CCD detector of Institut de Physique du Globe Paris (confocal aper-
ture 2 lm). It has to reject the Rayleigh scattered light with a high
efficiency below 5 cm?1. The 514.5 nm line of a Coherent 70 Ar+la-
ser operating at 2.5 W was used as the exciting source with a
power of approximately 250 mW just before the DAC. Ultra-low
fluorescence diamonds are used and the transmitting medium
has also to be free of luminescence. In our experiments we used
a DAC Sidoine (Laboratoire de Physique des Milieux Condensés-
Paris) and KBr as the pressure transmitting medium. Spectra were
recorded from 10 cm?1to 660 cm?1which allows to record in the
same high pressure conditions both the Boson peak and the main
bands of silica with the excitation and the scattered beams in par-
allel polarizations using a X50 Mitutoyo microscope objective.
Pressures were determined from the shift of the2E ?4A2lumines-
cence of ruby ships. Silica samples are T3500 Saint-Gobain
Reduced Raman spectra at seven different pressures between
0.8 GPa and 4.7 GPa were recorded and plotted on Fig. 1.They show
the main band at 440 cm?1, the D1(490 cm?1) and D2(607 cm?1)
lines  and the Boson peak with a maximum below 100 cm?1. The
reduced Raman intensity corresponds to IR¼ I=½xðnðxÞ þ 1Þ?,
where nðxÞ ¼ ½expðhx=2pkTÞ ? 1??1is the Bose population’s factor
and I the Raman intensity.
Spectra recorded at the same pressure are identical during com-
pression or decompression of the sample as already observed as far
as the maximum pressure is kept below 8.6 GPa .
In this paper we focus on the intensity of the Boson peak and
onto the width of the main band of the Raman spectra at
440 cm?1in order to correlate these two evolutions. On the
Fig. 2(a) is plotted the variation of the Raman reduced intensity
of the Boson peak integrated between 25 cm?1and 160 cm?1and
normalized on the whole spectrum between 25 cm?1
660 cm?1as function of pressure. On the Fig. 2(b) the full width
at the half maximum of the main Raman band is plotted as func-
tion of pressure. Fig. 1 shows that the Boson peak intensity de-
simultaneously the main band narrows and shifts from 440 cm?1
to 500 cm?1.
The decrease of the e-VDOS corresponding to the Boson peak
with pressure was discussed by Yannopoulos et al. . They have
shown that the true e-VDOS requires the comparison of the ob-
served g(x) with gCMT(x) corresponding to the Continuous Med-
nal and transverse sound velocities, and d the density. This model
takes into account the fact that for a continuous medium the in-
crease of pressure induces an increase of sound velocities and den-
sity which correspond to a decrease of the VDOS. For silica
gCMT(x)/x2can be calculated as function of pressure up to 5 GPa
using the published data [16–18]. gCMT(x)/x2first increases as
function of pressure and then decreases with a maximum at
and4.7 GPa and that
model.Inthe CMT model
, mland mtbeing respectively longitudi-
Fig. 1. High pressure reduced Raman intensity of silica between 0.8 GPa and
Fig. 2a. Normalized Boson peak intensity IR¼ IðxÞ=½nðxÞ þ 1? x of silica integrated
between 25 cm?1and 160 cm?1as function of pressure.
Fig. 2b. Variation of the full width at the half maximum of the main band of silica
(at 440–500 cm?1) as function of pressure.
T. Deschamps et al./Journal of Non-Crystalline Solids 355 (2009) 2422–2424
2.4 GPa (Fig. 3). This demonstrates that for silica the decrease of Download full-text
the intensity of the Boson peak cannot be explained by the CMT
model. The origin of this decrease has then to be researched in a
change of the structure of silica under pressure.
As already mentioned, it can be observed that both the intensity
of the Boson peak and the narrowing of the main band (Fig. 2(a)
and (b)) evolve similarly with pressure: very fast between 0 GPa
and 3 GPa and then much slower between 3 GPa and 4.7 GPa. Dif-
ferent models or experiments [14–20] assign the maximum and
the width of the main band observed on Fig. 1 to the inter-tetrahe-
dral Si–O–Si angle h. In a first approximation we used the Lehmann
model  with the elastic coefficient of uncompressed silica.
From the position of the maximum we calculated that h decreases
of 5? between 0 GPa and 4.7 GPa with a maximum rate dh/
dP = ?1.25?/GPa at 2.6 GPa. In this same interval of pressure the
Dh distribution width narrows: at the half maximum it decreases
from 16? to 8?. The evolution of the main band can be viewed as
changes of the structure of silica towards a denser state since the
inter-tetrahedral angle maximum diminishes and towards a more
homogeneous structure since the inter-tetrahedral angles distribu-
tion decreases. These changes are not linear between 0 GPa and
4.7 GPa but occur with a similar higher rate at 2.6 GPa.
This parallel behavior of the Boson peak intensity with the main
band width has to be underlined. It demonstrates that amorphous
silica is not homogeneous at the nanometric scale. Several papers
[21–25] relate the Boson peak to the intrinsic inhomogeneity of
the glasses. In these models the intensity of the Boson peak is con-
nected with the contrast between the local elastic constants of the
nanometric domains. An external hydrostatic pressure is expected
to decrease this contrast and therefore to decrease the intensity of
the Boson peak. These evidences of the inhomogeneity of silica
have also to be related with the density fluctuations frozen near
the glass transition temperature Tg. They are responsible of
the Rayleigh scattering and are extensively studied in the case of
telecommunications fibers .
In situ Raman scattering experiments on pure silica in the elas-
tic pressure range show a fast decrease of the intensity of the Bo-
son peak correlated with a fast narrowing of the main Raman
band at 440 cm?1. These observations are in agreement with a de-
crease of the inhomogeneity of the glass at the beginning of the
compression process. The quantitative analysis of these changes
shows that silica glass does not behave under hydrostatic pressure
as a homogeneous continuous random network but as a medium
with nanometric heterogeneities. These results demonstrate that
even in a single component glass like silica an intrinsic inhomoge-
neity at a nanometer scale exists which can be related to the den-
sity fluctuations frozen at Tg. This nanostructure is important both
from a basic point of view and to improve applications of glasses in
optics  and mechanics [28,29].
The authors would like to thank E. Duval (LPCML) for illuminat-
ing discussions. This work was supported by the ANR project ‘‘Plas-
tiglass” and the ‘‘Région Rhône-Alpes” program MACODEV and
extensively used the ‘‘CECOMO” facility of the ‘‘Institut de Chimie
 E. Duval, A. Mermet, L. Saviot, Phys. Rev. B 75 (2007) 0242001.
 B. Schmid, W. Schirmacher, Phys. Rev. Lett. 100 (2008) 137402.
 M.I. Klinger, J. Non-Cryst. Solids 353 (2007) 1824.
 G. Simon, B. Hehlen, R. Vacher, E. Courtens, J. Phys.: Condens. Matter 20 (2008)
 B. Champagnon, C. Martinet, M. Boudeulle, D. Vouagner, C. Coussa, T.
Deschamps, L. Grosvalet, J. Non-Cryst. Solids 354 (2008) 569.
 S. Sugai, A. Onodera, Phys. Rev. Lett. 77 (1996) 4210.
 Y. Inamura, M. Arai, M. Nakamura, T. Otomo, N. Kitamura, S.M. Bennington,
A.C. Hannon, U. Buchenau, J. Non-Cryst. Solids 293–295 (2001) 389.
 A. Monaco, A.I. Chumakov, G. Monaco, W.A. Crichton, A. Meyer, L. Comez, D.
Fioretto, J. Korecki, R. Rüffer, Phys. Rev. Lett. 97 (2006) 135501.
 R.J. Hemley, H.K. Mao, P.M. Bell, B.O. Mysen, Phys. Rev. Lett. 57 (1986) 747.
 K.S. Andrikopoulos, D. Christofilos, G.A. Kourouklis, S.N. Yannopoulos, J. Non-
Cryst. Solids 352 (2006) 4594.
 M. Yamaguchi, T. Nakayama, T. Yagi, Physica B 263&264 (1999) 258.
 R.J. Hemley, C. Meade, H. Mao, Phys. Rev. Lett. 79 (1997) 1420.
 J. Schroeder, W. Wu, J.L. Apkarian, M. Lee, L.-G. Hwa, C.T. Moynihan, J. Non-
Cryst. Solids 349 (2004) 88.
 C.H. Polsky, K.H. Smith, G.H. Wolf, J. Non-Cryst. Solids 248 (1999) 159.
 S.N. Yannopoulos, K.S. Andrikopoulos, G. Ruocco, J. Non-Cryst. Solids 352
 C. Meade, R. Jeanloz, Phys. Rev. B 35 (1987) 236.
 M. Grimsditch, Phys. Rev. Lett. 52 (1984) 2379.
 A. Polian, M. Grimsditch, Phys. Rev. B 47 (1993) 13979.
 A. Lehmann, L. Shumann, K.M. Hübner, Phys. Status Solidi B 117 (1983) 689.
 J. Neuefeind, K.D. Liss, Berichte Der Bunsen-Gesellschaft-Phys. Chem. Chem.
Phys. 100 (1996) 1341.
 E. Duval, S. Etienne, G. Simeoni, A. Mermet, J. Non-Cryst. Solids 352 (2006)
 E. Duval, L. Saviot, L. David, S. Etienne, J.-F. Jal, Europhys. Lett. 63 (2003) 778.
 E. Duval, A. Boukenter, T. Achibat, J. Phys. Condens. Matter 2 (1990) 10227.
 A. Mermet, V.N. Surovtsev, E. Duval, J.F. Jal, J. Dupuy-Philon, A.J. Dianoux,
Europhys. Lett. 36 (1996) 277.
 F. Leonforte, A. Tanguy, J.P. Wittmer, J.L. Barrat, Phys. Rev. Lett. 97 (2006)
 B. Champagnon, L. Wondraczek, T. Deschamps, J. Non-Cryst. Solids 355 (2009)
 R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I.
Flammer, J.-L. Hazemann, J.-P. Simon, J. Appl. Phys. 103 (2008) 094917.
 T. Deschamps, C. Martinet, D. de Ligny, B. Champagnon, J. Non-Cryst. Solids
355 (2009) 1095.
 D. Vadembroucq, T. Deschamps, C. Coussa, A. Perriot, E. Barthel, B.
Champagnon, C. Martinet, J. Phys. Condens. Matter 20 (2008) 485221.
Fig. 3. Variation ofgCMTðxÞ
as function of pressure for silica.
T. Deschamps et al./Journal of Non-Crystalline Solids 355 (2009) 2422–2424