Low frequency vibrational modes related to texture in silica aerogels

(1)

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Low frequency vibrational modes related to texture in

silica aerogels

J. Pelous, J.L. Sauvajol, T. Woignier, R. Vacher

To cite this version:

(2)

Low

_frequency

vibrational modes related

to

texture

in silica

aerogels

J. Pelous

_(1),

J. L.

_Sauvajol

_(2),

T.

_Woignier

₍₁₎

and R. Vacher

₍₁₎

(1)

Laboratoire de Science des Matériaux Vitreux

_(*),

F-34060

_Montpellier

Cedex

01,

France

(2)

Groupe

de

_Dynamique

des Phases Condensées

_(**),

F-34060

_Montpellier

Cedex 01, France

(Reçu

le 25

_septembre

1989,

accepté

sous

_{forme définitive}

le 15 novembre

₁₉₈₉₎

Résumé. 2014 Les modes de vibration basse

fréquence d’aérogels

de silice ont été _{étudiés par}

spectrométrie

Raman. La

_position

et la

largeur

des

_pics

observés dans l’intervalle de

_fréquence

5 à 30

_{cm-1 apparaissent}

corrélées aux conditions initiales de

_préparation

et aux traitements

thermiques

de densification. La

_fréquence

du

_pic

est

_{proportionnelle à}

_{l’inverse du rayon de}

gyration

des

_particules,

déduit des mesures de diffusion

_élastique

des neutrons aux

_{petits angles.}

Ceci _permetune détermination de la vitesse du son à l’intérieur des

_particules.

De

plus,

la

dépendance

en

_température

des spectres démontre le caractère

_harmonique

des modes

responsables

du

_pic.

Abstract. 2014 Low

_frequency

vibrational modes of silica

_aerogels

have been

_{investigated by}

Raman spectrometry. The

_position

and

lineshape

of the

_peaks

_{observed in the range from 5}to

30

cm-1

_{appear correlated}to the initial

_preparation

conditions and to the heat treatment

responsible

for the densification. The maximum

_frequency

of the

_peak

is

_proportional

to the inverse of the constitutive

_{particle gyration}

radius deduced from small

_angle

neutron

_scattering.

This

_gives

a determination of the sound

_velocity

inside these

_particles.

Moreover, the temperature

dependence

of the spectrum for one

_sample

demonstrates the harmonic character of the modes

responsible

for the

_peak.

Classification

Physics

Abstracts 63.50 - 78.30L

1. Introduction.

The vibrational

_dynamics

of

_glassy

networks is a matter of current research

_activity

_[1].

In

particular,

low-frequency

modes are

_attracting

much interest as

_they

are related to collective

motions of the disordered atoms. _{Those modes show up in}acoustic

_properties

as well as in low

frequency

Raman

_scattering

of solids.

_They

are also

_responsible

for their low

_temperature

thermal

_properties.

It is well known that all of the above

_physical

_properties

exhibit

_intriguing

anomalies in

_glasses

_and,

more

generally,

in disordered solids

[2].

Highly

anharmonic

excitations of still unknown

_microscopic

nature, in excess to « normal » acoustic

phonons,

have been

_proposed

to describe those anomalies

_[3].

At low

_temperature,

_coupling

of

phonons

with

_tunneling

_{processes of those « two-level}

systems »

(TLS)

explains

the

non-(*)

Unité associée au CNRS 1119.

(**)

Unité associée au CNRS 233.

(3)

434

Debye

behavior of

_specific

heat and thermal

_{conductivity,}

as well as sound attenuation and

dispersion [2].

At

_higher

temperatures,

the

_peaks

of acoustic and dielectric

_absorption

are

likely

to

_originate

from

_{thermally-activated}

relaxation

_[4].

More

_recently

a new kind of

anharmonic excitations has been

_proposed

as an alternative

_explanation

in disordered solids

[5].

Vitreous silica is from far the most

_extensively

studied

_material,

as it is a common

constituent of a

_large

number of

_glasses.

On a more fundamental

_viewpoint,

the

_properties

of

silica

_glass

can

_{easily by compared}

to those of its stable

_crystalline

_{counterparts.}

A

microscopic

model

_{involving coupled}

rotations of a few

_Si04

tetrahedra has been

_proposed

to

describe the

_density

of states deduced from inelastic neutron

_{scattering experiments}

_[6].

More

recently,

harmonic - for

frequencies

higher

than = 0.6 THz - and anharmonic vibrational modes - at lower

_frequencies

-

were observed in excess to

_propagating

acoustic

_phonons

[7].

The same model was used to

_give

an unified

_description

of acoustic and dielectric

properties

at low

_{temperatures,}

as well as of neutron and Raman

_scattering

in the

low-frequency

domain

_[8].

This

_picture

_{is very}

attractive,

but does not account for the observation of very similar anomalies in disordered

materials,

irrespective

of their

_microscopic

structure.

Alternatively,

the

_concept

of fractons

_[9]

_provides

a

_{possible explanation}

of those

properties,

as illustrated

_by

Alexander et al. in their

_study

of the thermal

_properties

of

_quartz

amorphized by

neutron irradiation

_[10].

This was the

_{starting point}

of some

_controversy

_[11]

and stimulated a number of

_experiments

_[12].

In

_particular,

Raman

_scattering

measurements on silica

_gels

_[13],

Na-colloids

_[14],

and

_{superionic glasses}

_[15]

have

_given

evidence of a

power-law dependence

of the

_{spectral intensity,}

_{I (w ) oc co ’.}

A calculation of the

_light

scattering intensity

in fractal media was

_proposed

[13]

from which a relation between the

exponent

v, the fractal dimension

D,

the fracton dimension

d,

and the localization

exponent

dcp

[16]

was derived. The results in silica

_gels

were little sensitive to

_preparation

_conditions,

and a similar behavior was also observed M

_Vycor,

a

_weakly

_porous

_glass

obtained in a

completely

different way.

The

_study

of disordered materials

_having

a well-established fractal structure can

_help

to

clarify

the matter, inasmuch as one

_clearly

_separates

_(i)

the test of fracton

_predictions

for the

physical

properties

and

_(ii)

their

_adequation

to

_{glasses. Small-angle}

neutron

_{[17, 18]}

_(SANS)

and

_X-ray

_{[19] (SAXS)}

_{scattering experiments}

have demonstrated that silica

_aerogels

are

excellent

_examples

_{of porous solids}

_having

a fractal structure at

_length

scales L

_larger

than a

particle

size a and smaller than a correlation

_length

_e.

Below a and above

_e,

the materials is

homogeneous

[18].

of the vibrational

_dynamics

of these materials have

given

evidence of a crossover from

_{long wavelength}

acoustic

_phonons

to fractons in the Brillouin

_{scattering frequency}

_range,from = 0.5 to = 5 GHz

_[20].

_Scattering

from fractons

was observed in the very low

_frequency

Raman

_scattering

_{region, typically}

below 300 GHz

(10

cm- 1)

[21].

These studies are relevant to the

_point

_(i)

above. At

_larger

_frequencies,

which

can be

_{analyzed by}

conventional Raman

_{spectrometers,}

_scattering

of

light originates

from

surface and internal modes of the

_homogeneous

_{particles. They}

can

_give

information on the

structure of the

_{peculiar glass}

obtained

_by

the

_sol-gel

route. That

_they

are related to a

_possible

fractality

of

_glasses

-

point

(ii)

above - is still

an _open

_question.

In the

_present

_paper,we

_present

the results of a low

_frequency

Raman

_{investigation}

of silica

aerogels.

The

_frequency

_range

_explored

is

_expected

_upto the fracton

_regime

_[21].

We first compare the

spectra

obtained on two series of

_samples

_{corresponding}

to different

_preparation

conditions. The

_changes

of the low

_frequency

Raman

spectrum

during

the process of

densification to

_glass

are also

_{investigated.}

The evolution of the low

_frequency

part

of the

spectrum

is correlated with the variations of a, observed in SANS

experiments

on similar

(4)

Our results demonstrate

_that,

in the

_frequency

_{range above}

12 cm-1

_{(= 400 GHz),}

the excitations

_responsible

for Raman

_scattering

show an harmonic character.

2.

_{Sample préparation}

and

expérimental procedure.

The

_aerogels

were

_{prepared by}

_hydrolysis

and

_{polycondensation}

of

_{tetramethoxysilane}

(TMOS),

followed

_by

_{hypercritical}

_drying.

Four moles of water _{per mole of}TMOS were

used. Two kinds of materials were

_{investigated namely neutrally}

reacted and base

catalysed

samples ;

in the latter case the water was

_brought

to a

_normality

of 0.05 of ammonia. The

samples

were oxidized at 500 °C in air

_during

15 hours. This treatment removes some residual

methyl

groups and decreases fluorescence lines which sometimes

overlap

the Raman

spectra

of the

_aerogels.

Densification was obtained

_by

heat treatment. Four

_pieces

of oxidized

_aerogel

of each series were treated at 1 050 "C for various durations. The final densities of these

_samples

are

given

as labels of the Raman

_spectra

in the

_figures.

To observe Raman

_scattering

from silica

_aerogels,

a conventional

experimental

configur-ation was used. Raman

_experiments

were

_{performed using}

a

_{« Coderg}

T800 »

_triple

monochromator

_{spectrometer.}

_Scattering

was obtained with the 5 145 nm line of an

_argon-ion

laser

_(Spectra

_Physics

_type

_2020),

with the

_output

_{power of the incident beam}

_kept

at

500 mW. The scattered

_light

was collected in

_right-angle

_{configuration}

and in VH

_{polarization.}

The instrumental linewidth was 1

cm- 1.

At room

_temperature

the low

_{frequency scattering}

was studied under vacuum to avoid

_{scattering originating}

from air in the

_sample

pores. Low

_temperature

measurements were

_performed

in a

4He

_cryostat.

As silica

_aerogels

are

very poor heat

conductors,

the

precise

determination of the

sample

temperature

becomes

more and more difficult as the

temperature

is lowered. To

_improve

heat

_exchange,

the

_sample

holder was

_directly

immersed in

_liquid

helium.

3. Results and discussion.

The Raman

_spectra

_{I ( W )}

have been

_analyzed

at room

_temperature

for the two series of

samples. Figure

1 compares the results obtained for two untreated

_samples,

one

_neutrally

reacted and the other

_prepared

under basic

_catalysis.

Here we have

_plotted

the Raman

susceptibilities, X

(co )

=

I (w )/ (n (,w ) + 1 ),

where

n (,w )

₊1 is the

appropriate

Bose Einstein

factor for Stokes

_scattering.

The

_density

p of each

sample

is indicated in the

figure.

In

agreement

with

_previous

results obtained

_by

Boukenter et al. on similar

_samples,

a broad low

frequency scattering

is observed from the instrumental limit 1, 7

cm- 1

_upto = 100

cm - 1.

The mean feature of these

_spectra

is a well-resolved

_peak.

Such

_peaks

have been

_tentatively

assigned

to _{the lowest energy torsional mode of silica}

_particles.

The mean

_particle

size

R is related to the

_peak

_frequency

_by

where _vtis the transverse sound

_velocity

inside the

_particle.

For

_neutrally

reacted

_samples,

the

_peak

is broader than for the

_{base-catalyzed}

ones. This

effect can be related either to a

_{polydispersity}

in the

_particle

size,

or to

_poorly

defined

_particle

surfaces. This agrees with SANS results in which a smooth crossover from bulk fractal to

Porod surface

_scattering

is observed in neutral

_aerogels

_[18].

(5)

436

Fig. 1.

Fig. 2.

Fig.

1. Low

_frequency

Raman

susceptibilities

X (co

= ’"

for two untreated silica

_{aerogels :}

n(c)+1

a)

neutrally

reacted

sample,

b)

base

_{catalyzed sample.}

Fig.

2. -

Evolution of the low

_frequency

Raman _spectrafor different times of heat treatment in

neutrally

reacted

_aerogels.

The labels indicate the

_{corresponding}

densities.

into the elastic line. An

_{overintensity}

is still

_present

in curve e of

_figure

_3,

_{corresponding}

to

p - 1 600

kg.m- 3 -

However the maximum is now below the

_experimental

_resolution,

and

only

allows an estimation of the

_higher

limit of the

_peak

_position.

In contrast, after the final

stage

of transformation of the

_gel

into

_glass,

the

_{low-frequency}

_intensity

_{becomes very}

_weak,

as demonstrated in curve d

_{(Fig. 2).}

The

_spectrum

of the

_{fully-densified}

_sample

is similar to

that of vitreous silica.

As illustrated

_by

the

_plot

_{of P..}vs.

_{P in}

_figure

_4,

the

_peak

occurs at

_{higher frequencies}

in the

_spectrum

taken on the

_{sample prepared}

under neutral

conditions,

than on the

_gel

of the same

_density

obtained under basic

_catalysis.

This is in excellent

_agreement

with SANS results and confirms the known result that the addition of a basic

_catalyst

favors the formation of

larger particles

in the

_gel

_[22].

We observe here that these differences between

_catalysis

conditions remain for

_partially

densified

_{samples ;}

however _{the gap decreases}

_during

the

densification _process.

It can be also noted that a linear

_{extrapolation}

of the

v a,, (P )

curves

_intercept

the

for

₍₀₎

neutral untreated and densified

_aerogels,

₍₀₎

base

_catalyzed

untreated and densified

aerogels.

vitreous silica which is the final material obtained

_by

densification. The low

_frequency

Raman

scattering

spectrum

for the

_{fully-densified aerogel,}

shown in

_figure

_2d,

_{is very similar}to that of bulk vitreous silica.

SANS data

_{published previously}

_[23]

in the same

_samples

allow a determination of the characteristic size of the

_particles

constitutive of the silica

_gels,

which can be correlated to the

(7)

438

has been observed in

aerogels.

It

_gives

an estimation of the

_gyration

radius

_R.

of a

_particle,

as

qRg -

1 at the crossover. In

_figure

5 we have

_plotted

the maximum

_frequency

of the

_peak

observed in Raman

susceptibility

vs.

Rg

1 deduced from SANS

_experiments.

Within the

accuracy of the

experiments,

the two

quantities

appear

proportional.

Independently

of any

model,

this result

is,

to our

_knowledge,

the first direct and

_convincing

evidence for a

correlation between the low

_frequency

Raman

_spectra

and a structural information on

aerogels.

Assuming

that the relation between

_Rg

and v max is

given by equation

(1),

the measurements

of both

_Rg

_{and v max}can thus be used to obtain an estimate of the sound velocities at the

particle

scale. The

_quantity

is

_plotted

vs. R =

Rg 3 in

figure

6. The somewhat

_{large scattering}

of

_{points originates}

from uncertainties in the determination of

_Rg.

_However,

we can deduce a mean

_velocity

v - 2 150

m. s - 1.

This value is

_{significantly}

lower than the transverse

_velocity

of sound in

vitreous silica

_{(’" 3 700 m.s - 1)}

and

_implies

an excess

_{Debye density}

of states than in bulk

silica ;

as a matter of fact an excess has been

_really

observed

_by

neutron

_scattering

investigation

[24]

which can be related to this low value of the sound

_velocity.

The low value for the sound

_velocity

at the

_particle

scale can be related to an intemal structure different from that of vitreous

_silica,

_indicating

a more _openstructure or a residual

_{microporosity}

in the

aerogel particle.

The

_nearly

constant value found for the

_velocity

_{(Fig. 6)}

would

_imply

that this

_{microporosity}

is identical whatever the

_catalysis

conditions,

and remains in the first

densification

_stages.

Some indications for differences between the local structure of bulk vitreous silica and that of

_aerogels

have been observed in the

_{high-frequency}

_part

of the

Fig. 5.

Fig. 6.

Fig.

5. - Maximum

_frequency

of the

_peak

v max observed in the low

frequency

Raman spectra versus the inverse

_gyration

radius of the

_particules

constituve of the

_aerogels.

_Rg

was

deduced from the small

angle

neutrons

_scattering

results

_[23].

The results concerns neutral, base

_catalyzed

untreated and also densified

_samples.

Fig.

6. - Sound velocities _v

(8)

Raman

_spectrum

_[25].

_Moreover,

an

_analysis

in terms of

_composite

structure of the elastic moduli of silica

_gels

leads to a similar conclusion

_[26].

Another

_explanation

for this

_discrepancy

could be that the numerical factor in

_equation

₍₂₎

is

_inadequate.

This factor

_depends

on the

_shape

of the

_particle.

The value 0.8 is relevant to

spherical particles,

while for

_particles

of different

_shape

the numerical coefficient is not

known. The relation

₍₂₎

can be also erroneous if the

_particles

are

_coupled.

_However,

it is

worth

_noticing

that the data

_points

in

_figure

5 for

_neutrally

reacted and base

_catalyzed

aerogels collapse

on the same

_straight

line. As electron

_microscopy

has demonstrated _very

different

_{particle shapes}

for these two kinds of

_samples

_[27],

the above

_explanation

_appears

unlikely.

Nevertheless,

the total

_frequency

_spectrum

of the small

_{particles, including}

surface and bulk modes as calculated for instance

_by

_spectrum

on one

particular sample

with _p= 240

kg.m-3,

prepared

under basic conditions. We first

analyzed

the Stokes and the anti-Stokes

_part

of each

_spectrum,

_comparing

the ratio of intensities on

both sides at a

_given

_frequency

to the

_expected

value of

_[n(w)

+

1 ]/n(w).

We

_numerically

adjusted

the value of the

_temperature

to obtain the

_{superposition}

of the Stokes and

anti-Stokes

_part

of the

_spectrum.

The value of the

_temperature

T obtained _{in this way is}

systematically

higher

by

a few

_degrees

that

_{given by}

a thermometer fixed on the

_sample.

When the

_sample

holder is immersed into

_liquid

helium the above determination

_gives

T = 20

K,

which is the lowest

temperature

obtained in this

_experiment.

The

_comparison

of the Stokes Raman

_spectra

at 300 K and 20 K is

_given

in

_figure

_7,

where the curves have been shifted

_{arbitrarily along}

the ordinate axis. The insert in this

_figure

shows the

_{corresponding}

susceptibilities X

(w ),

in

_{log-log plot.}

The two features of each

_spectrum

are a base line with a

power-law dependence

of the

_intensity

vs.

_frequency

and a

_superimposed

well-defined

_peak.

Fig.

7. -

Comparison

of the law

_frequency

Raman spectra for a base

_{catalyzed sample}

(9)

440

The

_{background power-law dependence}

in _{this range of}

_frequency

has been attributed

previously [29]

to fractons at

_length

scales lower than the

_particle

_{size. Without any}

confirmation of a fractal

_geometry

or

_connectivity

inside the

_particle,

such an

_assignment

seems

questionable

and asks for further

investigations.

Furthermore,

the poor

signal-to-noise

ratio at low

_temperature,

a fluorescence

_background

and a residual elastic

_scattering

which

add to the Raman

_intensity

in our

_experiment

makes it difficult to conclude about the

temperature

dependence

of this

_{power-law background.}

On the other hand we note that neither the

_shape,

nor the

_{frequency position}

of the

peak

_{vary with}

_temperature.

This

similarity

demonstrates the harmonic character of the vibrational modes related to these

peaks.

The result confirms the

_previous

observation deduced from the

_temperature

dependence

of the inelastic neutron

_{scattering signal}

for lower

_{frequencies [24]}

or for the

nearly

same

_frequency

_range

[30].

References

[1]

See, e.g. Phonon

Scattering

in Condensed Matter, Eds. A. C. Anderson and J. P. Wolfe

_(Springer,

Berlin)

1986.

[2]

See, e.g.

Amorphous

Solids,

Low-Temperature

Properties,

Eds. W. A.

_{Phillips, Topics}

in Current

Physics

Vol. 24

_{(Springer, Berlin)}

1981.

[3]

ANDERSON P. W., HALPERIN B. I. and VARMA C. M., Philos.

_Mag

25

₍₁₉₇₂₎

_{1 ;} PHILLIPS W. A., J. Low

_{Temp. Phys.}

7

₍₁₉₇₂₎

351.

[4]

HUNKLINGER S. and SCHICKFUS M. V., in reference

704 ;

PAGE J. H. and MCCULLOCH R. D.,

Phys.

Rev. Lett. 57

₍₁₉₈₆₎

Phys.

Rev. Lett. 60

₍₁₉₈₈₎

2757.

(10)

[23]

VACHER R., WOIGNIER T., PHALIPPOU J., PELOUS J. and COURTENS E., Revue

4779.

[29]

ROUSSET J. L., DUVAL E., BOUKENTER A., CHAMPAGNON B., MONTEIL A., SERUGHETTI J. and DUMAS J., J.

Non-Cryst.

Solids 107

₍₁₉₈₈₎

27 ;

BOUKENTER A., CHAMPAGNON B., DUVAL _E.,ROUSSET J. L., DUMAS J. and SERUGHETTI J., J.

Phys.

C. Solid State

_Phys.

21

₍₁₉₈₈₎

L1097.