ELSEVIER
Journal of Non-Crystalline Solids 198-200 (1996) 556-558
Debye to non-Debye relaxation in As-Te-Se
glasses
S.S.K. Titus, H. Skauragi, K. Hayashi, A. Kondo, K. Shimakawa
Department of
Electronica,
Gfu
Uniwrsi~,
x
Gifu 501-I 1. Japm
Abstract
Time-dependent electrical resistivity measurements are carried out on As-Te-Se
glasses at different fixed pressure using
the Bridgman anvil system. At pressures, p < I8 kbar, the variation of electrical resistivity with time exhibits an exponential
behavior, and at pressures p > 18 kbar it shows a stretched exponential behavior. This behavior can be explained on the
basis of critical thresholds and fractal dimension of the network glasses.
1. Introduction
The time dependent
ties in materials
response
has been
of physical
known
proper-
for several
years
[l-3]. Non-Debye
relaxation
has been observed
in
many systems such as liquids, inorganic glasses,
ionic conductors, insulators, dielectrics, amorphous
semiconductors etc. [4]. The experimental manifestation of non-Debye relaxation is often described by a
stretched-exponential
function. In the present study,
we have observed for the first time, the variation of
resistivity with pressure in As-Te-Se
glasses exhibiting two types of relaxation behavior (exponential and stretched exponential) in two different pressure regimes.
2. Experimental
Bulk,
been
semiconducting
prepared
As,,Te,,Se,,,
by the melt quenching
glasses
have
method.
High
* Corresponding author. Tel.: + 81-58 293 2691; Fax: +81-M
230 1109; e-mail: [email protected].
pressure experiments are carried out using a Bridgman anvil system, consisting of tungsten carbide
anvils with a working face diameter of 12 mm.
Pyrophyllite
was used as the gasket material and
teflon as the pressure transmitting medium. Bismuth
was employed as the in situ pressure calibrant. The
high pressure system was properly checked in order
to eliminate the possibility of relaxation due to the
system in our time dependent study. Samples are
pressurized up to certain values and a clock was set
on immediately
to measure the variation of resistance with time.
3. Results
The electrical resistivity of virgin As,,,Te,,,Se,,,
glasses is around lo6 CI cm. Fig. 1 illustrates the
variation of resistivity with time at two different
pressures. It can be seen from Fig. 1 that, at pressure,
p = 13 kbar, the variation of log[(R - &)/CR,
R,)] as a function of time has a linear dependence
after abrupt initial decrease in the resistance. This
dependence is fitted by an exponential function, with
0022.3093/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All right< reserved.
SSDI 0022-3093(95)00762-S
S.S.K. Titus et al. / Journcd of Non-Crysralline
Solids 198-200
(19961 556-558
SSI
106-
J..
0
13 kbar
(3
-.
Ti
;:
.
0
0
Ooo
8
Cl
0
0
04.
0
4
R = ( R,, - K)exp(
time (Gaussian
-r/7>
relaxation),
+ R,,
as
(1)
where T is the relaxation time, R, and R, are the
initial and the saturated sample resistances respectively.
On the other hand, as shown in Fig. 2, at pressures, p = 19 kbar (a) and 26 kbar (b), the resistance
can be fitted to a function, stretched exponential with
time. The stretched exponential behavior is described
by the following function
R=(R,,-R,)exp[(-t/T)~]
+R,,
(2)
where (Y is called the dispersion parameter. This
equation indicates that the system goes from the
Debye type of relaxation to the non-Debye type of
relaxation under pressure. Fig. 3(a) and (b) show the
variation of r and a with pressure, respectively, for
the present material. The value of r is found to
b
i
b
11
t,me(x103s)
Fig. 2. The variation of log[(R - R,)/(
As3,,Te,,,Se20 glass at 19 kbar (a) and
represent stretched exponential function
3.5 X IO3 s at 19 kbar (a) and (Y= 0.45
kbar (b).
1
0
0
0 0
o
~ressure(kbar)
pressure(kbar)
(X103d
Fig. 1. The variation of log[(R - R,)/(R,
- R,)] with time
(7 =9.0X 10’ s) for As,,Te,,jSe,,,
glass at 13 kbar pressure.
a single relaxation
given below
0
12
8
t,me
0
o
lO2-
0
(b)
0.8.
R,, ~ R,)] with time for
26 kbar. The solid lines
with ry = 0.36 and CY=
and 7 = 2.2X 10’ s at 26
Fig. 3. The variation of 7 (a) and LY(b) as a function of pressure
for As,,,TeioSezC, glass. The solid circles in (a) represent 7 in the
exponential function (Debye relaxation). The solid circles in (b)
represent LY= I in the exponential function.
decrease with pressure and the value of (Y increases
with pressure.
4. Discussion
A number of thresholds are observed from the
earlier studies on chalcogenide
glasses, some of
which are connected to the intrinsic network mechanical properties and some of them are associated
with phase separation [5]. Chalcogenide glasses containing large number of lower coordinate atoms such
as Te or Se are elastically soft and hence they are
prone to undergo a floppy-to-rigid transformation [6].
In the case of GeS glass [7], the first sharp diffraction peak intensity, the fractional change in linear
dimension, and the energy gap show no hysteresis
effect for pressures below 20 kbar. The change
taking place below 20 kbar is therefore elastic in
nature, whereas plastic deformation occurs above 20
kbar [7]. A change in the relaxation processes, from
Debye to non-Debye, in the present study may be
related to the floppy-to-rigid
(or elastic to plastic)
transformation described above.
Time-dependent
resistivity behavior of the present
glass can be explained by the model proposed by
Palmer et al. [S] for relaxation in strongly interacting
glassy materials on the basis of hierarchally constrained dynamics. According to this model, a statistical distribution of relaxation time, T, is assumed
across different atoms, clusters or degrees of freedom, and the additive contribution
to the relaxing
quantity, q(r), is considered as the total relaxation
time of the system. The q(r) can then be written as
q( t) =
I’w( ‘)exp(
-t/7>
d7.
558
S.S.K. Titus et al. / Journal
of Non-Cystdine Solids
where W(T) is a weight distribution function. With
the proper choice of u,(r) any q(t) can be explained
reasonably.
Chalcogenide
glasses contain compressible
volume due to the lower coordination of the chalcogen
atoms and hence would undergo a soft-to-rigid transformation under pressure. In general, such a transformation takes place in a percolation manner in these
types of network glasses which involves formation
and growth of clusters. It is believed that in As-TeSe glasses, the clusters grow in size and attain a
critical dimension around 18 kbar pressure, resulting
in a percolation transition in the material.
We speculate that as long as the cluster sizes are
small and separated (below 18 kbar), the system is
described by a single relaxation time, i.e. all the
clusters are believed to grow with a single relaxation
time. When the system is subjected to pressures
exceeding the critical pressure ( > 18 kbar), at which
the percolation transition occurs in the material, some
of these grown clusters would merge with one another. This merging is expected to bring a change in
the weight distribution function, W(T), leading to the
distribution of relaxation times. The increasing tendency of (Y in the plastic regime, at pressures greater
than 18 kbar. shows that the system goes from a
more dispersive to less dispersive relaxation with
pressure. This behavior is very much analogous to
the Monte Carlo simulations
of random .walk in
fractal dimensions,
developed for anomalous relaxation in disordered systems [9] in which the dispersion parameter,
a, increases as D/D,,
increases,
where D is the fractal dimension and D,, is the
dimension. The increase of LYin the present experiment (structural relaxation) may correspond to the
increase in the fractal dimension of the network with
pressure, although the present physical situation of
structural relaxation is different from that of diffusion (random walk) of atoms (or carriers).
198-200
(1996) 556-558
5. Conclusions
A change in the relaxation process has been observed in the time dependent resistivity studies on
As,,Te,,,Se *,, glass around 18 kbar pressures. For
pressures below 18 kbar, the samples exhibit Debye
relaxation with a single relaxation time (exponential)
and for pressures above 18 kbar the samples show
non-Debye
relaxation
(stretched
exponential).
A
floppy-to-rigid
transformation
may occur at around
18 kbar and a fractal nature, due to linkage of
clusters in a percolation manner under pressure, can
be related to dispersion parameter appeared in nonDebye type structural relaxation.
Acknowledgements
The authors wish to thank Professor Ke. Tanaka
and Dr S. Asokan for discussion. One of the authors
(S.S.K.) wishes to thank Monbusho for the financial
support given to carry out the work in Gifu University.
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