arXiv:cond-mat/0503439v1 [cond-mat.dis-nn] 17 Mar 2005
Characterization of the glass transition in vitreous silica
by temperature scanning small-angle X-ray scattering
R. Br¨ uning1(∗), C. Levelut2, A. Faivre2, R. LeParc2, J.-P. Simon3, F. Bley3
and J.-L. Hazemann4
1Physics Department, Mount Allison University, 67 York Street, Sackville (NB), Canada
2Laboratoire des Verres, UMR 5587 CNRS-Universit´ e Montpellier II, cc 69, 34095
Montpellier Cedex, France
3LTPCM-ENSEEG-INPG, UMR-CNRS 5614, B.P. 75, 38042 St. Martin d’H` eres Cedex,
4Laboratoire de Cristallographie, UPR 5031, CNRS, B.P. 166, 38042 Grenoble, France
PACS. 64.70.Pf – Glass transition.
PACS. 42.70.Ce – Glasses, quartz.
PACS. 61.10.Eq – X-ray scattering (including small-angle scattering).
Abstract. – The temperature dependence of the x-ray scattering in the region below the
first sharp diffraction peak was measured for silica glasses with low and high OH content (GE-
124 and Corning 7980). Data were obtained upon scanning the temperature at 10, 40 and 80
K/min between 400 K and 1820 K. The measurements resolve, for the first time, the hysteresis
between heating and cooling through the glass transition for silica glass, and the data have
a better signal to noise ratio than previous light scattering and differential thermal analysis
data. For the glass with the higher hydroxyl concentration the glass transition is broader and
at a lower temperature. Fits of the data to the Adam-Gibbs-Fulcher equation provide updated
kinetic parameters for this very strong glass. The temperature derivative of the observed X-ray
scattering matches that of light scattering to within 14%.
nication, technology and science, there has been a relative paucity of data regarding its glass
transition. In overviews of the properties of glasses, pure vitreous SiO2 had to remain a
missing data point . Scanning calorimetry is perhaps the most commonly used tool to de-
termine the glass transition temperature, Tg, and the relaxation state of glasses. For vitreous
silica, due to the high Tg, this method cannot be used without some difficulty, and the first
in situ temperature scanning experiment for this material monitored the light scattering .
More recently, differential thermal analysis (DTA) measurements have determined the step in
the specific heat at the glass transition. An unusual endothermic process takes place during
annealing , which can be attributed to the diffusion of water/hydroxyl groups . The
Although vitreous silica is of great importance for fiber optics commu-
(∗) E-mail: firstname.lastname@example.org
c ? EDP Sciences
response of vitreous silica to quenching at different rates has been investigated by a molecular
dynamics simulation . High temperature small-angle X-ray scattering (SAXS) experiments
have been proven as a sensitive method to detect the glass transition, and changes of the state
of the glass [6,7]. The relation between thermal analysis methods and temperature scanning
SAXS has been established , and here we use this method to obtain reference data of high
quality for the glass transition in vitreous silica.
Experimental Method. –
set-up at the European Synchrotron Radiation Facility (ESRF) at a wavelength of λ = 0.677˚ A.
Polished plates of GE-124 (six samples) and Corning 7980 (three samples) were measured. The
hydroxyl content of the samples was determined with infrared spectroscopy. For the GE-124
samples, [OH] = (2±1) wt. ppm, did not change during the experiment. For Corning 7980, the
samples in the as-received state contained (900±6) wt. ppm, and the average [OH] decreased to
(832±6) wt. ppm in the course of the measurements. Samples, with dimensions of 1×4×12
mm3, were placed inside a molybdenum furnace equipped with Kapton windows [6, 7, 9].
During the SAXS transmission mode measurements the temperature was scanned at rates of
10, 40 and 80 K/min, while helium near atmospheric pressure flowed through the furnace. The
observed melting temperature of a gold foil upon heating at 40 K/min deviated 2 K from the
standard value. The heating and cooling curves obtained with the vitreous silica samples are
consistent, so that thermal gradients between samples and the thermocouples are negligible.
The thermal history of the samples was reset by heating to the top of the temperature range,
followed by cooling and heating at the desired rate. For each sample the cool-heat cycle was
repeated, typically three times. At the sample surface a small amount of crystallization is
visible after the measurements, but no correlation between the SAXS signal and the progress
of surface crystallization was found. The SAXS was observed with a fiber optic coupled CCD
camera. The acquisition time was 20 s (10 s for 80 K/min scans). Distortions and cosmic
tracks in the CCD signal were corrected before integrating it in the azimuthal direction. The
x-ray was monitored before the furnace, m0, and after the furnace, m1, by scattering part of
the beam with a Kapton foils onto scintillation counters. Between sample changes the SAXS
signal of the empty furnace, IB(q), was measured. Here q = 4πλ−1sinθ is the scattering
vector, and θ is half of the scattering angle. This background originated mainly from the
Kapton windows and air scattering. Based on the measured signal with the sample in place,
IS+B(q), the signal originating from the sample was calculated according to
SAXS measurements were carried with the D2AM experimental
I(q) ∝ (tln1/t)−1[IS+B(q)/mS+B
where the transmission factor t = mS+B
and orientation of the sample. The scattered intensity was converted to absolute values, in
electron units per SiO2composition unit, by scaling the data to the measured signal obtained
with water. We assumed the value of 6.37 e.u. per H2O molecule, which is approximately
constant from q = 0.3 to 0.7˚ A−1. The probable error of the conversion factor is 4%.
The analysis of the data follows the procedure described in . Fig. 1 shows I(q), on a
logarithmic scale, as a function of q2. Most of the data range corresponds to the low-q tail
of the first sharp diffraction peak (FSDP) of vitreous silica . The small structure in the
spectrum around q2= 0.07˚ A−2is due to residual scattering originating from the Kapton
windows. Precision SAXS data show that the SAXS intensity in vitreous silica continues to
decrease down to q = 0.01˚ A−1[10,12], so that the rise observed here at low angles is not an
inherent property of the material. The linear regime in this plot, extending from q2≈ 0.04 to
0.4˚ A−2, is well described by I(q) = I(0)exp(bq2). For each temperature, the parameters b and
I(0) are obtained by linear regression. The data range included in the regression calculation is
1) allows for changes in the thickness
R. Br¨ uning et al.: Characterization of the glass transiton etc.
Fig. 1 – Logarithm of the scatted intensity of GE-124 plotted versus q2at two temperatures. The
solid lines are obtained by linear regression of the data between the dashed vertical lines, and I(q = 0)
is obtained as one of the regression parameters.
indicated by the broken vertical lines in fig. 1. The regression parameters depend only weakly
on the range of data.
The extrapolated intensity, I(0), rises with increasing temperature, while the slope b de-
creases (fig. 1). This temperature dependence is qualitatively similar to results obtained with
a fragile glass . For brevity we restrict the discussion to I(0), which has lower experimental
uncertainty. For GE-124, the overall change of I(0) is about 20% over the whole temperature
range of about 1400 K, fig. 2(a). In the successive temperature scans on the same sample,
I(0) changes slowly by about 2%, and, once upon a refill of the synchrotron, I(0) increased by
3%. Hence we attribute these effects to changes of the incident beam (e.g. of the energy, the
direction or position) which are not fully eliminated by normalizing the signal to the measured
X-ray flux before the sample. Linear corrections (less than 2.5%) were applied to the traces
shown in fig. 2(a) in order to align the end points of the traces obtained with a given sample .
Results and Discussion. –
the standard features of the glass transition: I(0) changes gradually with temperature in
the glass state, whereas the supercooled liquid state depends more strongly on temperature.
In addition to the change of slope, the glass transition is marked by a hysteresis between
the heating and cooling curves. The Tg of Corning 7890 vitreous silica, with a higher water
content, is (232±14) K lower than the Tgof GE-124. Outside the glass transition regime the
slopes of the curves are constant. The results of multiple measurements on a given sample, as
well as on equivalent samples, agree. A slight difference can be seen in the heating curves for
the water-rich sample, which may be caused by the partial loss of water at the sample surface.
The slopes of the straight line segments of the data in fig. 2(a) are given in table I, as
well as the corresponding slopes obtained by light scattering . The slopes are normalized
to the intensity at an arbitrary temperature above Tg, where the samples are in metastable
equilibrium (1800 K). The light scattering based slopes are higher than the SAXS based results
by 11% above Tg, and 14% below Tg. Since the data are based on very different ranges of
The temperature dependence of the SAXS in fig. 2(a) shows
Fig. 2 – (a) Scattered intensity, extrapolated to q = 0, as a function of temperature. GE-124 contains
2 wt. ppm H2O, and Corning 7980 contains 900 wt. ppm H2O. (b) Temperature derivatives of I(0),
obtained for GE-124 upon scanning the temperature at different rates. Full and open symbols show
cooling and heating data, respectively. Solid lines are fits to the AGF equation. For clarity, the
40 and 10 K/min curves were shifted up by 10 and 20 × 10−3e.u./K, respectively. (c) Temperature
derivatives of I(0) data obtained at 40 K/min for GE-124 and, shifted up by 10×10−3e.u./K, Corning
7980. Top: heat flow upon heating a sample with ≈ 120wt. ppm at 40 K/min (ref. ).
R. Br¨ uning et al.: Characterization of the glass transiton etc.
Table I – Comparison of the temperature sensitivity of SAXS and light scattering (last two columns).
Normalized temperature derivatives, [I(1800K)]−1dI/dT, in units of 10−6K−1, are evaluated below
and above the glass transition regime. The samples are GE-124, Corning 7980, and, from ref. ,
type A and type G vitreous silica.
[OH] (wt. ppm)
T < Tg
T > Tg
72 ± 2
500 ± 6
85 ± 2
561 ± 4
85 ± 3
561 ± 4
74 ± 2
500 ± 6
photon momentum transfer (extrapolation to q = 0 from the range 0.2˚ A−1< q < 0.6˚ A−1
for SAXS, and q = 1.8 × 10−3˚ A−1for the light scattering experiment), the approximate
agreement of the x-ray and light scattering results is reassuring. It shows that the temperature
dependence of density fluctuations is almost wavelength–independent below as well as above
Tg. In one-component materials, the q = 0 limit is related to the compressibility . Low–q
scattering in vitreous silica originates predominantly density fluctuations, since the chemical
order of the SiO4tetrahedra is nearly perfect [2,6]. Following the analysis of the light scattering
data, the slope below Tgis proportional to the adiabatic compressibility of the glass, and the
slope above Tgis proportional to the isothermal compressibility of the liquid [2,14]. A review
of literature data for SAXS and light scattering measurements shows that the compressibilities
determined by different methods vary by up to 25% .
As a next step we consider the temperature derivative of I(0), which provides curves that
are comparable to e.g. calorimetric measurements. While linear adjustments were made for
the traces in fig. 2(a) (as mentioned above), this was not necessary for fig. 2(b) and (c), since
differentiation reduces the effect of the slow drift of I(0). High frequencies are enhanced
by numeric differentiation. These were partially suppressed by applying a Fourier filter to
the differentiated data. The results obtained for GE-124 at three different scanning rates
are presented in fig. 2(b). The differentiated curves clearly show the expected hysteresis of
the glass state between heating and cooling. The value of Tg considered here is the low
temperature limit of the fictive temperature calculated from the cooling curve of the best fit
of the data to the AGF equation (described below). This value is close to the onset of the
glass transition, but it has the advantage that it is based on the complete cooling and heating
trace. The fitted value of Tg varies by about 4 K between repeated scans for GE-124, and
by 12 K for Corning 7980. The glass transition shifts to higher temperature with increasing
scanning rate. A Kissinger plot of ln(φT−2
rate, yields an activation energy of Ea/kB= (62±10)×103K for GE-124, in agreement with
the slope of viscosity data in an Arrhenius plot, 61.9 × 103K for a vitreous silica with [OH]
< 10 wt. ppm .
Fig. 2(c) shows the differentiated data for the GE-124 and Corning 7980 glasses, as well
as previously published DTA data obtained for annealed Corning 7980 glass with a reduced
hydroxyl content . (In order to demonstrate the degree of reproducibility, the 40 K/min
data for Corning 7980 in fig. 2 (b) and (c) are examples from different scans.) A comparison
of the SAXS-based curves shows a broader transition for the glass with the higher hydroxyl
concentration. This agrees with the slope of the equilibrium viscosity in an Arrhenius plot,
which decreases by 28% as the hydroxyl content increases from 3 to 1200 wt. ppm . The
increase of the width of the glass transition regime may be caused by the joint action of two
processes: At high temperatures direct bond-breaking and relaxation of the SiO2network take
place, while below 1100 K the site-to-site diffusion of hydroxyl groups is the faster process .
The hydroxyl diffusion process, emergant at low temperatures, can therefore broaden the glass
transition curve. The DTA and SAXS based data in fig. 2(c) basically agree, which confirms
g ) vs. T−1
g , where φ is the temperature scanning
the results of the prior series of calorimetric measurements . However, the SAXS data are
clearly superior both in terms of the stability and linearity of the background as well as in
providing data upon heating as well as cooling. One would expect the glass transition for the
120 wt. ppm sample at a temperature 50 K higher than that of the 900 wt. ppm sample .
Next the Adam-Gibbs-Fulcher (AGF) equation is used to extract standard kinetic param-
eters from the SAXS data. Details beyond the present summary of this approach can be found
in [3,18]. The state of the glass can be approximated by a fictive temperature, Tf. Above the
glass transition, Tf is equal to the temperature, while upon cooling sufficiently far below the
glass transition Tfbecomes frozen with Tf= Tg. The AGF approximates the relaxation time
of the glass and supercooled liquid states as
τ(T,Tf) = AexpQ/[T (1 − T0/Tf)], (2)
where the temperatures Q and T0are parameters, and A is the high temperature limit of the
relaxation time. This equation extends the Vogel–Fulcher–Tammann equation, to which it
reduces in the supercooled liquid regime where Tf= T . In this case the relaxation time
diverges when T reaches T0. The relaxation time is used with the Narayanaswamy-Moynihan
equation, which desribes how Tf evolves as
Tf(T) = T∗+
1 − exp
This integral involves a Kohlrausch exponent, β, as a further parameter. Finally, the SAXS
data are fitted by treating the temperature derivative of I(0) far below and far above Tg as
further adjustable parameters. Then we obtain
The solid lines fig. 2(b),(c) are least-squares fits of the data to the AGF equation. The kinetic
parameters of the fits are given in table II.
Table II – Parameters of least squares fits to the AGF equation of the SAXS data obtained at 40
K/min for GE-124 and Corning 7980. Experimental errors are estimated from the fit parameter
variations for multiple scans obtained with the same sample.
[OH] (wt. ppm)
39 ± 9
11 ± 1
0.05 ± 0.11
0.76 ± 0.05
49 ± 5
15 ± 1
0.30 ± 0.16
0.87 ± 0.06
For GE-124 ([OH] = 2 wt. ppm), the AGF fit parameters clearly indicate the properties
of a very strong glass: T0is only 20% of Tg, β is close to one as expected , and the time
prefactor, A ∼ 10−15s, is comparable to the inverse of the Debye frequency. As a comparison,
fits to viscosity data give Q = 33.53 × 103K and T0= 0.54 × 103K . The fit parameters
are sensitive to the width and the details of the shape of the glass transition curves. The
broader SAXS curve for the high [OH] sample is reflected in the lower Q and a longer time
A. The change of Q matches the above-mentioned 28% decrease of the activation energy
for the equilibrium viscosities upon increasing [OH] . The new SAXS data provide tighter
constraints on the fit as well as a superior signal to noise ratio compared to the DTA data in fig.
2 (c), so that the present fit parameters are more reliable than the values given previously .
R. Br¨ uning et al.: Characterization of the glass transiton etc. Download full-text
glass transition in vitreous silica, including the hysteresis between cooling and heating. The
signal to noise ratio is improved over previous point-by-point SAXS, temperature scanning
light scattering and DTA measurements. Scanning the temperature at a rate of 40 K/min,
has provided the best data.The shift of Tg with heating rate matches the temperature
dependence of the viscosity. Increasing the hydroxyl concentration from 2 to 900wt. ppm
lowers Tg by (232 ± 14) K. The glass with the higher hydroxyl concentration has a broader
glass transition, in agreement with the results of non-equilibrium viscosity measurements. The
SAXS of vitreous silica is slightly less temperature dependent than the light scattering (11%
above and 14% below the glass transition). Based on the present results, the AGF parameters
for vitreous silica have been updated.
The present SAXS data provide, for the first time, a clear picture of the
∗ ∗ ∗
We wish to thank O. Geyamond, S. Arnaud, and B. Caillot for technical assistance, as
well as J.-F. B´ erar for assistance in using beamline BM02. ESRF provided the synchrotron
radiation facilities, and the Natural Science and Engineering Research Council of Canada has
supported this work through a Discovery Grant.
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