LIQUID-GLASS TRANSFORMATION IN SE-BASED ALLOY
E.Bormashenkoa, R.Pogreb a, S.Sutovsky a, V.Lusternik b, A.Voronelb
a
The College of Judea and Samaria, The Research Institute, 44837,
Ariel, Israel
b
Tel-Aviv University, Ramat Aviv, 66978 Tel-Aviv, Israel
Abstract
Properties of glassy selenium and selenium based chalcogenide
glasses: Se55As45, Se67.5As20Ge12.5 and Se57I20As18Te3Sb2 were first
studied using dynamical mechanical analysis (DMA). DMA method
gave the valuable information about complex Young’s modulus of the
glassy materials. In parallel with the study of mechanical properties of
pure Se and Se-based chalcogenide glasses there also has been cleared
the character of the glass transition process. The results of DMA study
were compared with data obtained by differential calorimetry. It was
established that glass transition temperature, established by calorimetric
measurements is lower than the temperature, which corresponds to the
peak of loss modulus for all kinds of materials under study.
Keywords: dynamic mechanical analysis, selenium, chalcogenide glass,
storage modulus, loss modulus, glass transition, calorimetry, infrared.
1. Introduction
The problem of glass transition in amorphous media has been the
subject of much theoretical and experimental investigation recently. In
spite of that exhausting understanding of the phenomenon was not
attained yet. Standard identification of glass transition temperature T g is
based on calorimetric experiments. At the same time analysis of
transport coefficients and scattering experiments indicate the existence
of a critical temperature Tc, located above Tg in the region of the
supercooled liquid state (1). Near this temperature the dynamic crosses
over from the behavior, which is typical for a normal liquid to that
which is characteristic for a glass.
33
Theoretical coupling mode approach, based on the theory of liquids
predicts critical temperature Tc located at 50 to 100 degrees K above the
calorimetric glass transition temperature (2). Alternatively the VogelFulcher law describes the viscous flow as a thermally activated process,
and the Vogel-Fulcher temperature is found 50 to 100 K below T g. Thus
one explanation postulates the important changes at a temperature above
Tg and the other at a temperature well below Tg. And neutron scattering
data, obtained with liquid and glassy selenium, presented by Buchenau
and Zorn (3) demonstrate that solidlike structure of the liquid, based on
single-particle approach is more relevant to experimental data.
Se is generally amenable object for glass transition process study: on
one hand kinetic and thermodynamic characteristics of selenium were
investigated thoroughly (4,5), on the other hand Se gives rise to a large
variety of Se-based chalcogenide glasses (6-7), which demonstrate
relatively low melting points, and are handy for experimental work. The
novelty of our approach to glass transition study in amorphous Se and
Se-based lies chalcogenide glasses lies in application of dynamical
mechanical analysis (DMA) for this purpose.
DMA method was developed generally for a study of mechanical
properties and glass transition transformation of polymer materials (7),
and wasn’t applied for the study of glasses previously, because of
temperature instrumental limitations: as a matter of fact glasses
demonstrate softening temperatures much more than those of polymer
materials. Low softening point of the glassy materials under
investigations allowed DMA method application.
2. Experimental
2.1. Materials and Experimental Details
Pure Se (99.99+%) in pellets (d<4 mm) was supplied by SigmaAldrich Co. Se-based chalcogenide glasses were supplied by St.
Petersburg Research Institute of Optical Materials. These glasses were
developed for IR optics applications, they are distinguished for their
exclusive transparency in wide middle and far IR-bands. Certain of
properties of Se-based chalcogenide glasses, important for IR-optics
applications were studied thoroughly (5,6) and they are summarized in
Table 1.
34
Table 1
The properties of Se-based chalcogenide glasses.
Chalcogenide
Glass
Density,
g/cm3
Se55As45
Se67.5As20Ge12.5
Se57I20As18Te3Sb2
4.74
4.48
4.40
Linear
thermal
expansion
coefficient
Α·10-7,
°C-1
0, 00220
0.00220
-
Transmission
Range,
Μm
Dispersion,
n1.8-n2.2
Refraction
index
λ = 2 μm
1.5-17
1.2-12
1.2-12
0.0138
0.0118
-
2.80
2,73
2.39
Mechanical properties of pure Selenium and Se-based
chalcogenide glasses were was studied using dynamic mechanical
analysis (DMA) method. DMA method was developed generally for a
study of mechanical properties and glass transition transformation of
polymer materials, and wasn’t applied for the study of chalcogenide
glasses previously, because of temperature instrumental limitations: as a
matter of fact glasses demonstrate softening temperatures much more
than those of polymer materials. Low softening point of the glass under
investigations allowed to apply DMA method, realized using PerkinElmer DMA 7 device
When material is studied with DMA method, it is subjected to a
forced mechanical vibration at a fixed frequency (1 Hz in our case) and
amplitude of oscillatory stress. For polymers, the most common
experiment is a temperature sweep under the fixed parameters of
vibration. We choose this well developed experimental procedure and
raised the temperature from –15 °C to 250 °C under the rate 3 °C/min.
Chalcogenide glass samples with dimensions 1.50x15.0x4.1 mm we
prepared by die-casting process.
When a material is subjected to forced mechanical vibration at a
fixed frequency a fraction of the energy is absorbed and a fraction is
returned elastically. The complex resolve of the material is resolved into
elastic or storage modulus G' and the viscous or loss modulus G''. A
complex modulus G* and loss tangent tanδ can then be constructed
G* = G' +i G''
(1a)
tanδ = G''/ G'
(1b)
35
In parallel we studied the temperature dependence of thermal
capacity using scanning differential calorimeter, under heating rates
varied from 0.6 K/min up to 3K/min.
2.2. Results and Discussion
Fig. 1-1a show the DMA and calorimetric tests result for pure
selenium. The storage modulus G' of the material is practically stable up
to 323 K and equals 2.2-2.3 GPa. It is worth to sign that the absolute
value storage modulus couldn’t be compared directly with those
obtained with tensile-testing machine, because of the difference in the
loading conditions.
3
storage modulus
loss modulus
9
Modulus x 10 Pa
2.5
2
1.5
1
0.5
0
273
283
293
303
313
323
333
343
353
T, K
Fig.1 Temperature dependencies of the storage and loss modulus of pure Se
(heating rate 3 K/min, frequency 1 Hz).
At 325 K the storage modulus G' falls abruptly. We can see that
the peak of loss modulus G'', which is conventionally identified as the
glass transition temperature takes place at temperature 334 K; tanδ
achieves maximum at 338 K. Three temperatures could be distinguished
36
by DMA testing: T0 – temperature which corresponds to the pronounced
change of the storage modulus, Tc – temperature corresponding to the
maximum loss modulus and Tδ – temperature corresponding to the tanδ
maximum value.
1
0.9
tan /t anmax, Cp/Cpmax
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
270
280
290
300
310
320
330
340
T,K
Fig. 1a Temperature dependencies of the normalized to maximal values
thermal capacity and tanδ of pure selenium (Cp(T) – studied by Stephens
(4))
○ - tanδ/ tanδmax
◊ - Cp/Cpmax
DMA data, which deal with glass transition transformation need
comparison with those obtained by independent experimental technique.
Glass transition in selenium has been studied thoroughly by Stephens (4)
using calorimetric measurements, and he obtained Tg = 314 K. It can be
seen that Tg obtained by calorimetric experiments lower than critical
temperatures obtained by DMA technique.
In order to generalize obtained results we studied various Sebased chalcogenide glasses using DMA, and in parallel we studied the
temperature dependence of thermal capacity using scanning differential
calorimeter. The results of our experiments are plotted in Fig.2-4.
37
4.5
4
storage modulus
loss modulus
Modulus Pa x 10
9
3.5
3
2.5
2
1.5
1
0.5
0
290
310
330
350
370
390
410
430
450
470
490
510
T, K
Fig.2 Temperature dependencies of the storage and loss modulus of the
Se55As45 glass (heating rate 3 K/min, frequency 1 Hz).
Cp temperature dependence was obtained when heating rate
equals to those of DMA method - 3.0 K/min. Fig 7 demonstrates that Tg ,
obtained by calorimetric technique practically doesn’t depend on the
heating rate, when varied from 0.6 K/min to 3 K/min, in both cases Tg =
313 K. We didn’t recognize the dependence of T g on heating rate for all
materials under study (such slight dependence was established in Se3As2
chalcogenide glass in (9). It have to be signed that T g in (9) was obtained
mechanically, by pressing of cylindrical indenter in the bulk of the glass,
so these results couldn’t be compared directly with our calorimetric
data). Anyway we kept the same heating rate 3.0 K/min in all our DMA
and calorimetric experiments.
The experimental results are summarized in Table 2. It can be
concluded that critical temperatures obtained for all studied glasses
obtained by DMA and calorimetric investigation don’t coincide.
38
Cp/Cpmax;tan /tan max
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
280
300
320
340
360
380
400
420
440
460
480
500
520
T,K
Fig. 2a Temperature dependence of the normalized to maximal values loss
tangent and thermal capacity of Se55As45 chalcogenide glass.
- tanδ/ tanδmax
- Cp/Cpmax
Table 2
Characteristic temperatures obtained with calorimetric experiments and
DMA study
Material under
Tg
Tc
Tδ
T0
study
K
K
K
K
Se
314
334
338
325
Se55As45
450
503
513
493
Se67.5As20Ge12.5
483
536
538
523
Se57I20As18Te3Sb2
313
326-329
326
320
Tg- temperature of glass transition obtained with calorimetric technique
Tc – temperature corresponding to the maximal loss modulus
T0 – temperature corresponding to the storage modulus abrupt fall
Tδ –temperature corresponding to the maximum value of tanδ
We see from the comparison of experimental results that for all
materials under investigation Tδ ≈Tc > T0 > Tg. It would appear
reasonable to identify Tc or Tδ with critical temperature predicted by
coupling mode approach (1-2). It stands to reason that maximum of
mechanical losses results from many-particle correlations.
39
We plan to study frequency dependence of critical temperatures
on the next study of our investigation.
3
2.5
Modulus Pa x 10
9
2
1.5
1
storage modulus
loss modulus
0.5
0
310
330
350
370
390
410
430
450
470
490
510
530
550
T, K
Cp/Cpm;tan  /tan max
Fig. 3 Temperature dependencies of the storage and loss modulus of the
Se67.5As20Ge12.5 glass (heating rate 3 K/min, frequency 1 Hz).
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
280
300
320
340
360
380
400
420
T,K
440
460
480
500
520
540
560
Fig. 3a Temperature dependence of the normalized to maximal values loss
tangent and thermal capacity of Se67.5As20Ge12.5 chalcogenide glass
○ - tanδ/ tanδmax
◊ - Cp/Cpmax
40
Conclusions
Selenium and Se-based chalcogenide glasses were studied in
parallel using dynamical mechanical analysis (DMA) and calorimetric
experimental techniques. DMA method supplied valuable information
about mechanical properties of explored materials. It was shown that in
selenium and Se-based chalcogenide glasses Tg obtained by calorimetric
experiments lower than critical temperatures obtained by DMA
technique. The authors suppose that critical temperatures obtained by
DMA experiments correspond to those predicted by coupling mode
approach.
5.5
5
4.5
9
Modulus (Pa x 10 )
4
3.5
3
2.5
Storage m odulus
2
Los s m odulus
1.5
1
0.5
0
-0.5
260
270
280
290
300
T, K
310
320
330
340
Fig. 4 Temperature dependencies of the storage and loss modulus of the
Se57I20As18Te3Sb2 glass (heating rate 3 K/min, frequency 1 Hz).
Acknowledgements
The authors wish to thank Israeli Ministry of Absorption and
Israeli Ministry of Science for their generous support of this work, Mr.
Avigdor Sheshnev and Mrs Yelena Bormashenko for their support in
treatment of experimental results .
41
1.1
tan/tanmax;Cp/Cpmax
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
260
270
280
290
300
310
320
330
340
350
T,K
Fig. 4a Temperature dependencies of the normalized to maximal values
tanδ and thermal capacity of the Se57I20As18Te3Sb2 glass (heating rates; 3
tanδ/tanδmaxand 0.6 K/min, frequency 1 Hz).
- tanδ/tanδmax
Cp/Cpmax - ○
heating
rate 0,6
◊ - Cp/Cpmax - heating rate 0,6 K/min
K/min
Cp/Cpmax –- Cp/C
heating
rate 3
pmax – heating rate 3 K/min
K/min
References
1. Götze W., Structural Glass Transitions, in Liquids, Freezing and
Glass Transition, edited by J.P. Hansen, D.Levesque and J.ZinnJustin (North-Holland, Amsterdam), 1991, pp. 292-503.
2. U. Bengtzelius, W.Götze and A. Sjölander, Dynamics of supercooled
liquds and the glass transition, J.Phys.C: Solid State Physics, 17,
(1984), pp. 5915-5934.
3. U. Buchenau and R. Zorn, A relation between Fast and Slow
Motions in Glassy and Liquid Selenium, Europhysics Letters, 18 (6),
(1992), pp. 523-528.
4. R.B. Stephens, The Viscosity and Structural Relaxation Rate of
Evaporated Amorphous Selenium, J. Appl. Phys. 49 (12),!978, pp.
5865-5864.
5. H. Gobrecht, Wiilers G., Wobig D., Transformations of red
amorphous and monoclinic selenium, J. Phys. Chem.Solids, Vol. 31,
1970, pp. 2145-2148.
6. S.R. Elliot, “Chalcogenide Glasses”, Chap. 7 in Materials Science
and Technology, Glasses and Amorphous Materials, Ed. J. Zarzycki,
VCH, pp.375-454, VCH, Weinheim, 1989.
7. V. Kokorina, Glasses for Infrared Optics, CRC Press, 1996.
8. K. Menard, Dynamic Mechanical Analysis, CRC Press, 1999.
9. Lubin V.M., Kolomietz B.T., Shilo V.P., About As2Se3 glass softening
point, Non-organic materials, 1971, Vol. 7 (5), pp.858-859.
42