Thermal-Diffussion Induced by Temperature Gradient in the
Lithium Borate Melt
N.A. Bokov1, V.L. Stolyarova2
1
Institute of Silicate Chemistry of the Russian Academy of Sciences, SanktPetersburg, Russia
2
Sankt-Petersburg State University, Sankt-Petersburg, Russia
ABSTRACT.
The relaxation of light scattered intensity in the lithium borate melts containing
1.6 mol % Li2O induced by a temperature gradient has been investigated. It was
observed that the during relaxation process the intensity enhanced and finally
reached the steady-state value. It was found that into this stationary nonequilibrium state the scattered intensity was proportional to the square of the
temperature gradient subjected to the sample. The enhancement of scattered
intensity is connected with arising of the non-equilibrium concentration
fluctuations produced by a temperature gradient. Based on the measured the
time-dependence of a scattered intensity the diffusion coefficient D is calculated.
Introduction
Recently [1], it was found that the light scattered intensity by borate melts
subjected to a stationary temperature gradient was increased and finally reached
the steady state value. As it was suggested in [1] that the enhancement intensity
observed was connected with the growth of non-equilibrium concentration
fluctuations in binary system induced by Soret effect [2, 3]. It was shown that the
most enhancement of scattered intensity was observed in the lithium borate melts
containing 1.6 mol % Li2O [1]. Taking into account these features the borate
melt mentioned was taken out as the subject of the present study to investigate
the light scattering intensity as a function of the value of temperature gradient.
Experimental Procedure
The influence of the temperature gradient on the light scattered intensity
in borate melt was studied on a high-temperature optical diffractometer with the
use of primary radiation with the wavelength λ. = 4880 Å. The values obtained
experimentally by the light scattering method were the polarized, Vv, and
depolarized, Hv, components of the scattered intensity, where the indices denote
the polarization status of the incident beam and the capital letters stand for the
orientation of the polarizer before the detector, where “v” corresponding the
vertical orientation of the electric vector and “h” – horizontal. The scattered
radiation was recorded at the scattered angle 900.
The melt under investigation was placed in a cylindrical silica glass cell,
which was covered by mica cap and mounted on the metal table in a furnace of
the optical diffractometer.
In order to produce a temperature gradient across the sample under
investigation, the metal table was cooled by an air stream having room
temperature. The use this technique allowed us to produce the temperature
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difference ΔT approximately equal 750C between the table surface and the cell
cap. In more detail the experimental procedure was described in [1].
The sample under investigation was prepared by melting the glass pieces
placed in the silica cell directly in a furnace of the diffractometer at the
temperature range 750-8500C with the use of the glass of the corresponding
composition, which was preliminary synthesized at the temperature 12000C and
quenched on a metal plate. According to the chemical analysis data, the lithium
borate glass prepared by this way contained 1.6 mol % Li2O.
Experimental Results
As it was observed in [1] the more significant of the enhancement of light
scattered intensity was registered for lithium borate melt, contained 1.6 mol % Li2O.
It is necessary to make the following comment. It is known [4, 5] that the Li2OB2O3 system is characterized by the existence of the immiscibility region in the lowalkali concentration range. In view of the formation of the supercritical fluctuation
in this concentration range, the lithium borate melts have a more developed
fluctuation structure, which is responsible for the higher scattered intensity. Thus
the main contribution to the total scattered intensity in this subject is the intensity
induced by the concentration fluctuation.
The specificity of the lithium borate melt was discussed in [6], where it was
shown that the scattered intensity by this melt considerably exceeded the scattered
intensity by boron oxide melt in the identical temperature range. The temperature
dependencies of the polarized, Vv, component of scattered light for these subjects
were presented in Fig. 1.
140
Intensity, Vvx106сm-1
120
100
1
2
80
60
40
20
0
300
400
500
600
0
Temperature, С
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700
800
Fig. 1. Temperature dependencies of the Vv component of
scattered intensity by the lithium borate melt contained 1.6
mol % Li2O, (1) and boron oxide melt (2).
As it follows from Fig. 1 the scattered intensity by lithium borate melt
exceeded scattered intensity from boron oxide melt for the temperatures lower than
4000C at least by a factor four. Here, it should be noted that the data for lithium
borate melt presented in Fig. 1 were reversible relative to the temperature. It was
suggested that the melt in this temperature range had a single-phase state.
Since the scattered light intensity by the lithium borate melt reached the
most high values at a low temperature range we used the temperature 4070C to
study the influence of the magnitude of the temperature gradient on the scattered
light intensity.
The calculation of the temperature gradient magnitude across the sample
was the very complicated problem, which was connected with the specific character
of the experimental procedure. In order to estimate the influence of the temperature
gradient on the scattered intensity we used the value of the temperature difference
ΔT between the table surface and cell cap, which was measured by platinum
thermocouples located on the table surface and on the mica cap of the cell. We used
the following temperature differences ΔT: 5, 31, 43, 60, 71, and 780C. For the each
case the temperature corresponding the central part of the cell, where the primary
laser beam passed through the melt, was equal 4070C. For the every specified
temperature difference ΔT we measured the magnitude of the scattered intensity,
when reached a steady-state value. The experimental results obtained for the
examined temperature differences ΔT are presented in the Fig. 2.
240
220
Intensity, Vvx106сm-1
200
180
160
140
120
100
80
60
0
10
20
30
40
50
60
70
0
Temperature difference, T, С
Fig. 2. The dependence of the Vv component of scattered
intensity by the lithium borate melt contained 1.6 mol %
Li2O from the temperature difference ΔT.
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80
As follows from Fig. 2 the polarized, Vv, component of the scattered light
intensity exhibited the stationary increase with the raise of the temperature
difference magnitude ΔT. The data analysis demonstrated that this fact was
qualitatively correlated with the theoretical conclusions [2, 3].
We measured the time-dependence of scattered intensity for the largest
magnitude of the temperature difference ΔT = 780C. The obtained results are
presented in the Fig. 3. As Fig. 3 shows the experimental obtained time-dependence
of the polarized, Vv, component of the scattered light intensity monotonically
enhances and finally approaches to the stationary value.
240
220
Intensity, V V x106сm -1
200
180
160
140
120
100
80
60
0
20
40
60
80
100
120
140
160
Tim e, m in
Fig. 3. The time-dependence of the Vv component of the
scattered intensity by the lithium borate melt contained 1.6
mol % Li2O for the temperature difference ΔT = 780C.
Discussion
According to the theoretical conclusions [2, 3] the total intensity of scattered
light in the liquid solutions subjected to the stationary temperature gradient T was
enhanced proportional to magnitude of (T)2. As it mentioned above for the exact
calculation the temperature gradient value T was not possible because of the
specificity of the experimental procedure. Therefore we used the value of the
temperature difference ΔT between the table surface and the cell cap.
The Fig. 4 demonstrates the dependence of the polarized, Vv, component of
scattered intensity as a function of the square of the temperature difference ΔT. As
follows from Fig. 4 this dependence is the linear function of the values (ΔT)2. The
dashed line was drawn by the least-squares method. Hence, it appeared that the
experimental result were in agreement with the theoretical prediction [2, 3], where
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the enhancement of the scattered light intensity was connected with the nonequilibrium concentration fluctuations produced by the temperature gradient.
The analysis of the data presented in Fig. 3 are showed that the experimental
data are satisfactorily described by the equation
Vv(t) = ΔVv [1 – exp(-t/)] + Vv
(1),
where ΔVv = Vv(0) – Vv(),Vv(0) is the scattered intensity at the initial moment of
the time, when the temperature gradient is included, Vv() is the stationary value of
the intensity reached after the relaxation process, t is the time, and  is the relaxation
time. As can be seen from Fig. 3, experimental data are satisfactorily described by
Eqn. (1) (the dotted line in Fig. 3). It was obtained for our case that the value of the
relaxation time  was about 3000 sec.
240
220
Intensity, Vvx106сm-1
200
180
160
140
120
100
80
60
0
10
20
30
40
2
50
60
70
0
Т) /100, С
Fig. 4. The dependence of the Vv component of the
scattered intensity by the lithium borate melt contained 1.6
mol % Li2O from the square of the temperature difference
(ΔT)2/100.
It is well known [7] that the intensity of the scattered light by the
concentration fluctuations is described by the equation
I(q, t) = I(q, 0) exp[D(q) q2 t]
(2),
where q is the scattering vector, which value is given by (4π sinφ/2)/λ, φ is the
scattered angle, λ is the scattered radiation wavelength, D(q) is the diffusion
coefficient. Based on this consideration we found the magnitude of the diffusion
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coefficient D(q) for the lithium borate melt contained 1.6 mol % Li2O, which was
equal approximately 1.2 10-14 cm2 s-1. It should be noted that the value of a shear
viscosity for this melt at the temperature 4070C was about 107 Poises. This value is
in agreement in the frame of the order magnitude with the data obtained for the
potassium silicate glass [8]. It should be mentioned that the magnitude of the
diffusion coefficient D obtained for the polymer solution (polystyrene-toluene) in
[3] was approximately for seven orders higher.
Conclusion
The obtained results illustrated that the scattered intensity by the glass
forming melt subjected by the stationary temperature gradient increases. Its value
approached to a limit magnitude. The features of the effect observed allowed to
connect this phenomenon with the arising of the non-equilibrium concentration
fluctuations induced by the temperature gradient. The diffusion coefficient was
determined from the time-dependence of light scattered intensity for the lithium
borate melt at 4070C that suggested the new opportunities for the study of the
diffusion processes in the glass forming melts at the low temperatures.
Acknowledgement
This study was carried out based on the financial support by the Russian
Foundation for Basic Research according to the project N 10-03-00759.
References
1.
2.
3.
4.
5.
6.
7.
8.
Bokov N.A. “Experimental investigation of the influence of a temperature
gradient on the intensity of light scattering in borate melts” Glass Phys Chem
2010 36 (2) 158-165
Sengers J.V., de Zarate J.M.O. “Nonequilibrium concentration fluctuations in
binary liquid systems induced by the Soret effect” Ed W. Kohler and S.
Wiegand 2002 LNP 584 121-145
Sengers J. V., Gammon R. W., Ortiz de Zárate J. M. “Thermal-diffusion driven
concentration fluctuations in a polymer solution” Comp Stud Nanotech
Solution Therm Polym Syst Ed Dadmun et al. Kluw Acad/Plenum Pub N-Y
2000 37-44
Golubkov V.V., Titov A.P., Vasilevskaya T.N., Porai-Koshits E.A. “On the
phase separation in alkali borate glasses” Fiz Khim Stekla 1977 3 (4) 306–
311.
Bokov N.A. “Position of the spinodal in lithium borate system from the data
on light scattering in the visible region” Fiz Khim Stekla 1988 14 (1) 135–
137.
Bokov N.A., Andreev N.S., Shakhmatkin B.A. “Investigation of the
fluctuations in melts of alkali borate glasses by the light scattering technique”
Fiz Khim Stekla 1989 15 (6) 832–837.
Fabelinskii I.L. “Molecular scattering of light” Plenum N-Y 1968
Andreev N.S., Bokov N.A., Boiko G.G. “The concentration fluctuations in
potassium silicate glasses” Doc Ac Sci 1971 (6) 1375-1377.
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