Internal friction and relaxation mechanism of F-doped SiO2 glasses

Article abstract of DOI:10.1016/S0921-4526(98)01377-5

The internal friction and the Young's moduli of pure SiO₂, SiO₂-4 mol% F and -8 mol% F glasses were measured in the temperature range of 1.6-250 K. The temperature dependencies of the internal friction were not different except for their peak values, which showed differences of a few percent at 35 K. In contrast, the Young's moduli of F-doped SiO₂ glasses were 7.5% (-4 mol% F) and 15% (-8 mol% F) less than that of pure SiO₂ glass, respectively. Both temperature dependencies were analyzed on the basis of Debye relaxation by the distributed double-well potential model.

Full text of DOI:10.1016/S0921-4526(98)01377-5

Physica B 263—264 (1999) 346—349
Internal friction and relaxation mechanism
of F-doped SiO glasses
ꢀ
!ꢁ
"
#
H. Kobayashi *, Y. Kogure , T. Kosugi
!
National Research Laboratory of Metrology, 1-1-4 Umezono, Tsukuba, Ibaraki 305-8563, Japan
"
Teikyo University of Science & Technology, Uenohara, Yamanashi 409-0193, Japan
#
Faculty of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
Abstract
The internal friction and the Young’s moduli of pure SiO , SiO —4 mol% F and —8 mol% F glasses were measured in
ꢀ
ꢀ
the temperature range of 1.6—250 K. The temperature dependencies of the internal friction were not different except for
their peak values, which showed differences of a few percent at 35 K. In contrast, the Young’s moduli of F-doped SiO
ꢀ
glasses were 7.5% (—4 mol% F) and 15% (—8 mol% F) less than that of pure SiO glass, respectively. Both temperature
ꢀ
dependencies were analyzed on the basis of Debye relaxation by the distributed double-well potential model. ( 1999
Elsevier Science B.V. All rights reserved.
Keywords: Internal friction; Young’s modulus; SiO glass; Fluorine
ꢀ
tributed to the lateral motion of the bridging oxy-
gen atoms across the Si—O—Si bridge.
1. Introduction
It is well-known that the incorporation of fluor-
SiO glass is one of the materials for studying
complex systems in which many scientists have
recently shown a strong interest. We have been
measuring both the low-temperature dependencies
of the internal friction and the Young’s moduli
ꢀ
ine reduces the optical refractive index of SiO
ꢀ
glass. Fluorine-doped SiO glass possesses many
ꢀ
advantages as the cladding glass of an optical
waveguide, and is expected to have a transmission
higher than that made by Ge-doped glass. Fluorine
of Ge-doped, O-excessive and O-deficient SiO
glasses [1,2]. Analysis using the thermal relaxation
ꢀ
doped in the glass has the formation of an SiO F
ꢂ
tetrahedron substituted by an oxygen atom at its
model with a double-well potential has succeeded
in providing an explanation of these phenomena
[3]. With this model, the internal friction is at-
\ꢃ
corner. Dumas et al. reported that a 945 cm
Raman band corresponds to a l (Si—F) stretching
vibration of an SiO F tetrahedron, in which the
ꢂ
fluorine atom is only bonded to one Si atom [4].
In the present paper, we report the low-temper-
ature measurements of the internal friction and the
*Corresponding author. Fax: #81-298-50-1464; e-mail:
kobayasi@nrlm.go.jp.
Young’s moduli of fluorine-doped SiO glasses,
ꢀ
0921-4526/99/$ — see front matter ( 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 3 7 7 - 5

H. Kobayashi et al. / Physica B 263—264 (1999) 346—349
347
and try to explain both phenomena by the double-
well potential model which has succeeded in the
The change of the Young’s modulus, dE, due to
the relaxation is expressed as
analysis of Ge-doped SiO glasses [3].
ꢀ
ꢀ
D
G
A 1
1
D
!AdE
E
B"+ ¹DG ꢀ 1#(uq)
A
2k ¹
B
G
ꢀ
sech
dD.
ꢀ
ꢀ
ꢅ
ꢅ
G
2. Experiment and specimens
(2)
The experimental method applied to the meas-
urements of the internal friction and the Young’s
modulus is a composite oscillator type with
Eqs. (1) and (2) are fitted to the internal friction
and the Young’s modulus data by the Monte Carlo
ꢀ
method, and 50 sets of parameters (º , A , D ) are
G
G
G
ꢂ
a quartz of 50;3.5;3.5mm , which produces lon-
determined. A series of º values are chosen for the
G
gitudinal waves [5]. This method has only one
oscillational frequency of 51 kHz but the capability
of high resolution suitable for measurements of
small changes of internal friction. Glass specimens
fitted curves to be smooth.
To determine the potential distribution uniquely,
any functional form for the distribution was not
assumed. Firstly the fitting of internal friction was
made under the condition of a symmetric potential
were obtained as follows. SiO soot rods were ob-
ꢀ
tained from SiCl by the vapor-phase axial depos-
ꢄ
ꢀ
(D "0 for all i’s), and the modulus change is
G
ition (VAD) method, and then the rods were heat
calculated by using the determined A values. Sec-
G
treated at a high temperature in an atmosphere of
ꢀ
ondly, both the asymmetry parameter D ’s and the
G
relaxation strength A ’s are used as the fitting para-
G
SF and He gases. These rods were sintered at
ꢄ
a temperature of 1500°C, and SiO —4 mol% F and
meters, and the internal friction and the elastic
ꢀ
—8 mol% F glasses were obtained. Pure SiO glass
ꢀ
modulus change are fitted simultaneously. When
which was obtained by the direct method was pre-
the parameters A ’s are determined, the density
G
pared and used as the standard of SiO glasses.
of relaxation strength, P(º )"(A #A )/
ꢀ
G
G>ꢃ
G
2(º !º ), is calculated.
G>ꢃ
G
3. Analysis
4. Discussion
The observed relaxation peak around 35 K is con-
sidered to be a superposition of widely distributed
Debye-type mechanical relaxation peaks. For the
analyses the internal friction is expressed as [3,6]
The internal frictions of three types of SiO glass-
es were measured in the temperature range of
ꢀ
1.6—250 K. The results are shown in Fig. 1, in which
the symbols O, # and X show those of pure
SiO , SiO —4 mol% F and —8 mol% F glasses. At
ꢀ
D
G
A 1
uq
D
G
\ꢃ
pQ "+
ꢀ
sech
dD.
B
ꢀ
ꢀ
ꢀ
ꢀ
¹ DG ꢀ 1#(uq)
A
2k ¹
ꢅ
G
low temperatures below 5 K, the internal friction is
almost independent of temperature, which is
thought to be due to the TLS relaxation [7]. In
order to compare the values of the internal friction
of the glasses, they are normalized in Fig. 1 by those
\ꢂ
(1)
where Q is the quality factor, A is the magnitude of
G
contribution from ith Debye relaxation, ¹ is the
temperature, u is the angular frequency of sound,
D is the asymmetric energy of the double-well po-
at 2 K, which are 1.49;10
(pure SiO ),
ꢀ
\ꢂ
1.41;10
\ꢂ
(—4 mol% F), and 1.63;10
(—8
ꢀ
tential, and D is the maximum value of the distri-
mol% F). These values of three glasses are not very
different except for their peaks, which show a few
% point differences at 35 K. In Fig. 2, the Young’s
moduli of the three kinds of glasses are shown, in
which the symbols O, # and X show the values of
pure SiO , SiO —4 mol% F and —8 mol% F glasses
G
bution of the asymmetry energy for the i’s potential.
q is the relaxation time in the asymmetric potential
and given by, q"q exp(º /k ¹)sech(D/k ¹),
ꢅ
G
where º is the barrier height of the ith potential
G
and q is a constant.
ꢅ
ꢀ
ꢀ

348
H. Kobayashi et al. / Physica B 263—264 (1999) 346—349
Fig. 1. Internal friction normalized at 2 K of pure SiO , SiO —4
ꢀ
ꢀ
mol% F and —8 mol% F glasses.
Fig. 3. Determined relaxation strength density P (a), and asym-
metry parameter Dꢀ (b).
[6]. With the increment of the fluorine content, the
values of n and E decrease in the same manner,
\ꢃ
which, it is thought, cancels the change of pQ
.
When an oxygen atom moves by the applied force
over the potential height from one site to the equiv-
alent site, it is difficult to jump directly across the
Si—Si bond line in a plane. It is supposed that an
oxygen atom can move around the Si—Si line
smoothly. Kaneta suggested that an oxygen impu-
rity atom in an Si crystal exists at a bridging oxygen
site and turns round the Si—Si axis [8].
\ꢃ
The experimental data of pQ
and Young’s
modulus have satisfactorily been fitted to Eqs. (1)
and (2), respectively, and the relaxation strength
ꢀ
A and the asymmetry parameter D were deter-
Fig. 2. Young’s moduli of pure SiO , SiO —4 mol% F and —8
mol% F glasses.
G
ꢀ
ꢀ
mined, and the relaxation density P was calculated.
The results are shown in Fig. 3. It can be seen that
the oxygen atoms with the activation energy of
about 60 meV are largely contributed to the relax-
ation phenomena. The effect of the fluorine atoms
on the density P is not clearly seen in the present
analysis. It is noted that the present model can
in the temperature range of 1.6—250 K. In contrast
to the internal friction, the Young’s moduli of fluor-
ine-doped SiO glasses are 7.5% (—4 mol% F) and
ꢀ
15% (—8 mol% F) less than that of pure SiO glass,
ꢀ
\ꢃ
respectively. The thermal relaxation theory shows
reproduce the pQ and the Young’s modulus si-
\ꢃ
internal friction pQ Jn/E, where n is the number
multaneously, then this relaxation model can ex-
of particles (bridging oxygen atoms) moving in
a double-well potential and E is Young’s modulus
plain the mechanical dynamics of SiO glasses very
ꢀ
well.

H. Kobayashi et al. / Physica B 263—264 (1999) 346—349
349
References
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[7] J. Jackle, L. Piche, W. Arnold, S. Hunklinger, J. Non-
Crystal Solids 20 (1976) 365.
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