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Structural relaxation below Tg of amorphous germanium-selenium alloys
Volume
3, number
7,8
MATERIALS
LETTERS
STRUCTURAL RELAXATION BELOW T, OF AMORPHOUS GERMANIUM-SELENIUM T. DERREY, L.E.C.A.P., Received
J.M. SAITER,
Fact&
26 February
J.P. LARMAGNAC
May 1985
ALLOYS and C. VAUTIER
des Sciences, B.P. 67, 76130 Mont-St-Aignan,
France
1985
The equilibrium relaxation time 7Cof Ge,Se, _ v bulk amorphous samples is studied for different values of y (0 Q r < 0.16). The experimental results plotted versus the average coordination number confirm the topological model given by Phillips.
1. Introduction In chalcogenide glasses, short-range interaction forces are of covalent nature and play a preponderant role in the formation of these glasses [ 11. Only the first and the second neighbours of a given atom are concerned by short-range forces which act by mechanical constraints. Phillips [2] has shown that these constraints are of two types: the first one, between two nearest neighbours is associated with bond stretching and the other one, between three atoms is associated with bond bending. The atom is in favorable coordination if the number of constraints exhausts the number of degrees of freedom. The addition of germanium (coordination 4) in an amorphous selenium matrix (coordination 2) increases the average coordination number m and consequently the average number of constraints. Structural relaxation, may be affected by these constraints. So we have studied, by DTA, the structural relaxation of bulk samples of Ge,Se, _y alloys of various compositions 0 = 0.02,0.04,0.08 and 0.16) below and at the central composition y, [2]. The samples were prepared by water quenching ( lo2 K s-1) of a mixture of Ge and Se melt in a vacuum sealed quartz tube. The value of Tg (measured 1 h after the quenching) versus the at% of Ge is in good agreement with the results of Azoulay [3] (fig. 1). In accordance with Ipser’s work [4] the samples are amorphous.
308
Tg (K)
423
I
\
_
_
Azoulay
l our results
27305 at% Fig. 1. Glass transition
Ge
temperature
versus at% of Ge.
2. Results and discussion It is known that a glass kept at a temperature TR below the glassification temperature Tg tends to a more favorable enthalpic state He [S 1. The relaxation time 7 of this isothermal and isobaric kinetics is classically given by [6,7 ] T = a exp(-&/TR)
exp [-c(H - He)] ,
where a, c, Ah are parameters which depend upon the material; H - He is the departure of the actual enthalpy from its equilibrium value. 0 167-.577x/85/$ 03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Vol~~me 3. number
MATERIALS
7.8
3.0
3.1
Fig. 2. Relaxation
3,2
time versus annealing
In this equation, the quantity a exp(-ah/Tr() = r,, is the equilibrium relaxation time. This parameter, as well as the equilibrium viscosity [8,9] is a structural characteristic of the material. Using a model described elsewhere [lo], we have determined 7, for different annealing temperatures TR and for different values ofy; plots of ln T, versus I/TR are shown in fig. 2. The curves are straight lines, the slope of which enables us to calculate the relaxation time activation
GeySe,_y m=2+2y
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May 1985
LETTERS
3,3 temperature
34 for different
3.5
values of y.
energy 4, WE = RAh). Then we have plotted this energy versus the mean coordination number m as defined by Phillips [2], i.e. m = 2 t 2~ for Geyser _Y (fig. 3). In the same figure we have also plotted the results of Nemilov [ 1 l] reported in ref. [2], about a complicated quantity S,, i.e. the entropy of activation for viscosity. It is clear that both curves have the same shape. The introduction of 2 at% of Ge, increases very slightly the number of constraints and acts only on polymeric chains of Se. For y = 0.04 and 0.08, Ge atoms are branching points for Se chains leading to a cross-linked quasi-planar structure [ 121. This structure is not favorable to the mechanism of relaxation of a-Se which takes place, following Abkowitz [ 131, by bond breaking and reformation of chains. For y = 0.16 the lack of structure relaxation leads us to suppose that the structure is blocked up in its native state. Phillips [2] has shown that for this value the number of constraints per atom is equal to the number of spatial degrees of freedom. So we notice three modes of relaxation, well corresponding to the three regions distinguished by Phillips [ 21.
Fig. 3. Activation energy of relaxation time and entropy of activation for viscosity (after ref. [ 21) versus average coordination number.
309
Volume 3, number 7,8
MATERIALS LETTERS
References
[ll A. Winter, Verres Refractaires 36 (1982) 259. PI J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. 131 R. Azoulay, M. Thlbierge and A. Brenac, J. NonCryst. Solids 18 (1975) 33. [41 M. Ipser, M. Gambino and W. SchusIer, Monatsh. Chem. 113 (1982) 389. 151 A.J. Kovacs, J.J. Aklonis and A.R. Ramos, J. Polym. sci. 17 (1979) 1097. 161 C.T. Moynihan, A.J. Easteal, J. Wilder and J. Tucker, J. Phys. Chem. 78 (1974) 2673. [71 OS. Narayanaswaymy, J. Am. Ceram. Sot. 54 (1971) 491.
310
May 1985
[8] A. Eisenberg and A.V. Tobolsky, J. Polym. Sci. 46 (1960) 19. [ 91 A. Eisenberg and A.V. Tobolsky, J. Polym. Sci. 6 1 (1962) 483. [lo] J.P. Larmagnac, J. Grenet and P. Michon, J. Non-Cryst. Solids 45 (1981) 157. [ 111 S.U. Nemilov, Soviet J. Phys. Chem. 37 (1964) 1026. [ 121 J.D. Malaurent and J. Dixmier, J. NonCryst. Solids 35/36 (1980) 1227. [ 131 M. Abkowitz, in: The physics of selenium and teIluriurn, eds. E. Gerlach and P. Grosse (Springer, Berlin, 1979) p. 178.
3, number
7,8
MATERIALS
LETTERS
STRUCTURAL RELAXATION BELOW T, OF AMORPHOUS GERMANIUM-SELENIUM T. DERREY, L.E.C.A.P., Received
J.M. SAITER,
Fact&
26 February
J.P. LARMAGNAC
May 1985
ALLOYS and C. VAUTIER
des Sciences, B.P. 67, 76130 Mont-St-Aignan,
France
1985
The equilibrium relaxation time 7Cof Ge,Se, _ v bulk amorphous samples is studied for different values of y (0 Q r < 0.16). The experimental results plotted versus the average coordination number confirm the topological model given by Phillips.
1. Introduction In chalcogenide glasses, short-range interaction forces are of covalent nature and play a preponderant role in the formation of these glasses [ 11. Only the first and the second neighbours of a given atom are concerned by short-range forces which act by mechanical constraints. Phillips [2] has shown that these constraints are of two types: the first one, between two nearest neighbours is associated with bond stretching and the other one, between three atoms is associated with bond bending. The atom is in favorable coordination if the number of constraints exhausts the number of degrees of freedom. The addition of germanium (coordination 4) in an amorphous selenium matrix (coordination 2) increases the average coordination number m and consequently the average number of constraints. Structural relaxation, may be affected by these constraints. So we have studied, by DTA, the structural relaxation of bulk samples of Ge,Se, _y alloys of various compositions 0 = 0.02,0.04,0.08 and 0.16) below and at the central composition y, [2]. The samples were prepared by water quenching ( lo2 K s-1) of a mixture of Ge and Se melt in a vacuum sealed quartz tube. The value of Tg (measured 1 h after the quenching) versus the at% of Ge is in good agreement with the results of Azoulay [3] (fig. 1). In accordance with Ipser’s work [4] the samples are amorphous.
308
Tg (K)
423
I
\
_
_
Azoulay
l our results
27305 at% Fig. 1. Glass transition
Ge
temperature
versus at% of Ge.
2. Results and discussion It is known that a glass kept at a temperature TR below the glassification temperature Tg tends to a more favorable enthalpic state He [S 1. The relaxation time 7 of this isothermal and isobaric kinetics is classically given by [6,7 ] T = a exp(-&/TR)
exp [-c(H - He)] ,
where a, c, Ah are parameters which depend upon the material; H - He is the departure of the actual enthalpy from its equilibrium value. 0 167-.577x/85/$ 03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Vol~~me 3. number
MATERIALS
7.8
3.0
3.1
Fig. 2. Relaxation
3,2
time versus annealing
In this equation, the quantity a exp(-ah/Tr() = r,, is the equilibrium relaxation time. This parameter, as well as the equilibrium viscosity [8,9] is a structural characteristic of the material. Using a model described elsewhere [lo], we have determined 7, for different annealing temperatures TR and for different values ofy; plots of ln T, versus I/TR are shown in fig. 2. The curves are straight lines, the slope of which enables us to calculate the relaxation time activation
GeySe,_y m=2+2y
i 330
I -
I ! ‘I
2 5
60_
‘\
b
E 2
I t
LO_
2 J w 20_
z I>
\,
‘t---+1;
I I I I I
2!3
-2004
\
I
0
of111
-- -
I'
.our
results
II I\s‘\\ I ‘\~I ._- - -O- -P \
; ‘\ ,
--. ,._
; r
22
.
E
. ro -100;
-._-,’
I
24
m
2,6
May 1985
LETTERS
3,3 temperature
34 for different
3.5
values of y.
energy 4, WE = RAh). Then we have plotted this energy versus the mean coordination number m as defined by Phillips [2], i.e. m = 2 t 2~ for Geyser _Y (fig. 3). In the same figure we have also plotted the results of Nemilov [ 1 l] reported in ref. [2], about a complicated quantity S,, i.e. the entropy of activation for viscosity. It is clear that both curves have the same shape. The introduction of 2 at% of Ge, increases very slightly the number of constraints and acts only on polymeric chains of Se. For y = 0.04 and 0.08, Ge atoms are branching points for Se chains leading to a cross-linked quasi-planar structure [ 121. This structure is not favorable to the mechanism of relaxation of a-Se which takes place, following Abkowitz [ 131, by bond breaking and reformation of chains. For y = 0.16 the lack of structure relaxation leads us to suppose that the structure is blocked up in its native state. Phillips [2] has shown that for this value the number of constraints per atom is equal to the number of spatial degrees of freedom. So we notice three modes of relaxation, well corresponding to the three regions distinguished by Phillips [ 21.
Fig. 3. Activation energy of relaxation time and entropy of activation for viscosity (after ref. [ 21) versus average coordination number.
309
Volume 3, number 7,8
MATERIALS LETTERS
References
[ll A. Winter, Verres Refractaires 36 (1982) 259. PI J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. 131 R. Azoulay, M. Thlbierge and A. Brenac, J. NonCryst. Solids 18 (1975) 33. [41 M. Ipser, M. Gambino and W. SchusIer, Monatsh. Chem. 113 (1982) 389. 151 A.J. Kovacs, J.J. Aklonis and A.R. Ramos, J. Polym. sci. 17 (1979) 1097. 161 C.T. Moynihan, A.J. Easteal, J. Wilder and J. Tucker, J. Phys. Chem. 78 (1974) 2673. [71 OS. Narayanaswaymy, J. Am. Ceram. Sot. 54 (1971) 491.
310
May 1985
[8] A. Eisenberg and A.V. Tobolsky, J. Polym. Sci. 46 (1960) 19. [ 91 A. Eisenberg and A.V. Tobolsky, J. Polym. Sci. 6 1 (1962) 483. [lo] J.P. Larmagnac, J. Grenet and P. Michon, J. Non-Cryst. Solids 45 (1981) 157. [ 111 S.U. Nemilov, Soviet J. Phys. Chem. 37 (1964) 1026. [ 121 J.D. Malaurent and J. Dixmier, J. NonCryst. Solids 35/36 (1980) 1227. [ 131 M. Abkowitz, in: The physics of selenium and teIluriurn, eds. E. Gerlach and P. Grosse (Springer, Berlin, 1979) p. 178.