Differential scanning calorimetry study of structural relaxation of Ge-doped Se85Te15 glasses

Materials Science and Engineering, B22 (1994) 181-190

181

Differential scanning calorimetry study of structural relaxation of Ge-doped Se85Te15glasses E. Illekov~i Institute of Physics, Slovak Academy of Sciences, Ddbravsk6 cesta, 842 28 Bratislavia (Slovak Republic)

M. T. Clavaguera-Mora, M. D. Bar6 and S. Surifiach Fisica dels Materials, Departament de Fisica, Universitat Aut6noma de Barcelona, 08193 Bellaterra (Spain) (Received December 14, 1992)

Abstract Accurate measurements of the apparent specific heat below and through the glass transition in slowly cooled Gex(Se85Te15)100_x glasses (x = 0, 2 and 10) were performed using differential scanning calorimeter. The enthalpy released by the glasses when annealed near the glass transition was deduced. The kinetics of coordination short range ordering (CSRO), structural relaxation and the glass transition were studied by continual heating as well as by isothermal methods of thermal analysis. The activation energies of structural relaxation AE* were observed to be similar for all samples, as was the qualitative correlation of their absolute values which ranged from 120-143 kJ (g atom)-1 for CSRO processes at Ta = T~-60 K, to 217 kJ (g atom) -1 for glass transformation processes in glass having x = 10, as determined by various methods of kinetic analysis (Kissinger, Moynihan, activation energy spectrum and distribution of non-linear relaxation models). This may be explained by assuming first-order kinetics and a wide spectrum of relaxation times.

1. Introduction

Generally, atomic rearrangements in condensed matter (excluding the translational modes) can be divided into two types. In the first case only topological changes in the positions of the atoms--topological short range ordering (TSRO)--are considered, following the temperature-determined equill'brium interatomic distances. In the second case the coordination short range ordering processes (CRSOs) inside the structural elements--so-called "clusters'--of a liquid or a glass (e.g. the chemical ordering in metallic glasses or polymerization effects in glassy selenium or polymers) follow the temperature-dependent equilibrium of these elements. Thus TSRO describes changes which occur over relatively large atomic distances, while CSRO describes changes in the local surroundings of a given atom. When a glass-forming liquid is supercooled to the glass transition region, the relaxation times for atomic movements become comparable to the experimental time-scale. Therefore freezing of the liquid atomic motions (translational, TSRO, CSRO) occurs and the system falls out of thermal equilibrium. At temperatures sufficiently below the glass transition temperarare, atomic motions (except for vibrations) are 0921-5107/94/$7.00

completely frozen-in and one can consider the glass as being in a metastable solid state. On heating the glass, atomic movements become thermally activated depending on the activation free enthalpies for CSRO and TSRO, and activate the more and more pronounced relaxations of a non-equilibrium glassy structure towards its equilibrium counterpart. Finally, at the glass transition temperature Tg a softening of the frozen-in translational modes in a solid into a supercooled liquid state (SLS) completes the structural relaxation processes. Thermal relaxation of a glass at temperatures within its annealing range is a generally observed phenomenon. The linear heating of metallic glasses generally exhibits one pronounced exothermal effect and various annealing-induced endothermal effects (e.g. refs. 1 and 2) which characterize the rheological properties of the frozen-in structure. It was found [1, 3] that the exotherms reflect a high degree of non-equilibrium in TSRO of glassy samples which is caused by rapid quenching procedures. These exotherms are characterized by relatively long relaxation times; they decrease on heat treatment and probably reflect the minimization of excess free volume caused by changes in TSRO. The endotherms are related to some more complicated changes, probably of CSRO. These endo© 1994 - Elsevier Sequoia. All rights reserved

182

E. lllekowi et al.

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.~trucmral relaxation of Ge-doped S% Te/~ glasses

therms are characterized by shorter relaxation times; they increase on previous heat treatment of a sample to some saturated value when the equilibrium (determined by the annealing temperature T,) CSRO is reached. The saturated relaxation enthalpy AH~x~s (t~ = oo) was repeatedly found to depend on previous and actual temperatures. In chalcogenide glasses both exothermal and endothermal structural relaxation phenomena can be observed (e.g. refs. 4-8). Furthermore, these materials are especially appropriate for studying the transition of a glass to the supercooled liquid state (called softening or the glass transition) in the glass transition region in the vicinity of Tg. There are two methods of studying the kinetics of structural realxation of a glass: isothermal timedependent and non-isothermal continual heating methods of thermal analysis. In differential scanning calorimetry (DSC), the measured apparent specific heat Cp,a, as well as the calculated excess enthalpy changes AH~x~ (evolved or absorbed via the structural relaxation), characterize the thermodynamic state only and its evolution in a previously heat-treated, as well as in a non-treated, sample. In the present paper, the measurements of apparent specific heat cp,,( T ), as well as the evolution of excess enthalpy AH~...... c(&) of slowly cooled (SessTels)100_~Ge ~ glasses (where x = 0, 2 or 10)in the vicinity of Tg, are reported. Continuous heating as well as isothermal annealing methods of thermal analysis using a Perkin-Elmer DSC2 were used to study the kinetics of structural relaxation of the samples. As expected, the activation energies of structural relaxation AE* of all the samples, as well as the qualitative correlation of their absolute values, have been confirmed as similar when determined by various methods of kinetic analysis (Kissinger, Moynihan, activation energy spectrum (AES) and distribution of non-linear relaxation (DNLR) models ).

2. Experimental details

Bulk samples were prepared by melt-quenching [6] weighed amounts of elemental Se, Te and Ge of 5 N purity. To avoid any significant uncontrolled relaxations [6], the slowly cooled samples were always prepared directly in DSC apparatus from initial melt-quenched glasses. These glasses were heated up to T~=400 K for Se85Te15 o r (SessTels)98Ge 2 and to T~= 420 K for (Se85Te15)90Ge10 , to their supercooled liquid state, and then subsequently cooled at fl-~ = - 2 0 K m i n -1to T i = 2 7 0 K . The calorimetric experiments were performed on approximately 10 mg of material under a dynamic

argon atmosphere. The apparent specific heat cp,~,(1 ) consists of the "true" specific heat of the sample Cp(1) as the main parameter as well as contributions from the excess heat capacity dHe,ce,~s/d T due to the eventual thermal effects (e.g. structural relaxation, crystallization, etc. ) occurring in the sample• The absolute values of Cp•,(T) have an error of less than 2% for the glassy form but only approx. 0.5% for the supercooled liquid state of samples at temperatures from T i to Te; these were measured and calculated using a Perkin-Elmer differential scanning calorimeter [9] at a heating rate of fl+= + 20 K min-1 and using sapphire as a standard. The changes of excess enthalpies AH ...... = J ACp.,.ii_21(T)dT 1i = j [Cp,a,(l)(T ) - Cp,a,(2)( T)] d T

were calculated by integration of the excess specific heats ACp,a,ii_2/(T ) (which were the differences between the heat-treated (annealed) c0,,,il)(T ) and untreated Cp,.,(2i(T) sample properties (Fig. 1)) from rigid glassy to equilibrium supercooled liquid temperatures. The temperature measurements were accurate to within +0.2 K• The samples were annealed in an thermostat at a temperature of T. < Tg-25 K, stabilized to within + 0.5 K.

8O

'7

"" 100 OI ,-.-1

..

6O --,

80 ,.,..) CP,a,(I)

4O

6o

A C p,o,( 1-2 )

40

CP, O,I 2} ......

20

•\

[ 320

1__ 340

I

(.

/'/

/

I

I

-J - - ~ - 380

360 T

-20 400

[K]

Fig. 1. Relation between the apparent specific heat of meltquenched sample aged at Ta=300 K for & = 4 0 0 0 h, cp.a,ll!(T), the true specific heat of the non-annealed slowly cooled sample, c p..( a 2)( T ), and the excess specific heat measured on an annealed (SessTels)90GeH) sample, Acp,.,r.,,,(T)(heating rate fl+ = 2 0 K rain- 1).

E. Illekovf et al.

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183

Structural relaxation o f Ge-doped Se85 Te ts glasses

The materials studied show considerable relaxation effects (which are called the ageing effects) even when kept at room temperature, To, as well as partial crystallization, especially after initiation by heating the samples to the supercooled liquid state. The glass transition, crystallization and melting temperature Tg, Tx and Tm are seen in Fig. 2. At room temperature the specific heats of frozen-in glassy forms, as well as of the equilibrium supercooled liquid forms, of all the investigated samples do not change significantly with the content of Ge (see Table 1). Excess contributions due to the lower equilibrium state of the water-quenched samples in relation to the slowly cooled samples

ACp,a,(as_q_g) ~ 0 was observed in metallic glasses [10], usually with a positive sign. Analysing all the possible contributions to the heat capacity of the studied sample (e.g. the harmonic vibrational heat capacity, anharmonic contributions, electronic or magnetic contributions, irradiation contributions and configurational contributions) the only interpretation of the negative sign of Acpa(as_q_g ) s e e m s to be that the measured ACp,a,(as-q/iTo) does not represent the "steady-state" specific heat of a water-quenched glass by a quantity apparently diminished by the relaxation exotherm started at much lower temperatures of T< To. The difference between the extrapolated heat capacities of the frozen-in glassy and equilibrium supercooled liquid states at Tg

ACp, a,(as_q_g)(To) = Cp,a,(as_q) (To) - Cp,a,(g)(To)

m Cp, a,(SLS_g)(Tg) = Cp, a,(SLS)(Tg)- Cp, a,(g)(Tg)

3. Results

(2)

made apparent Cp,a,(as_q)(To) of all water-quenched samples about 8% lower. The phenomenon of

r\

o

_ . . o. . . . .

j.

g

Q~Q

\

I

ii

L

I

I

[

I

I

I

I

/

/

,I

1i

I

300

/

[ k._. I

'----

I

~..

400

I

,

,

I

I

500 T [K]

Fig. 2. Experimental temperature dependences of specific heats of melt-quenched (Se85Te~5)100.~Ge~ glasses aged for about 4000 h at room temperature. (a) x=O, (b) x = 2, (c) x--- 10. The y axes are not equivalent but modified in order to show the anomalies

(fl+ = 20 K min-1).

(3)

is an integral quantity and is also sensitive to the degree of crystallinity of the sample. The temperatures, Tg, are sensitive to the Ge as well as GeSe 2 content. Figure 3 shows the linear temperature dependences of frozen-in glassy and supercooled liquid states as well as the A-shaped anomalies of Cp,a(T) in the glass transition regions of the investigated samples. The annealing-induced peaks closely preceding these transformation anomalies are the result of annealing effects induced during ageing, and annealing by continual heating; their relative magnitudes reflect their relative kinetics which are inversely proportional to Tg. Therefore, the reproducible reference state of samples that have an equivalent thermal history (represented by the annealing-induced endotherm seen in Fig. 3) was defined to be the state of samples slowly cooled to T i at fl- = - 20 K rain- 1 just after their preparation, having unchanged values of ACp,a,(SLS_g) and Tg.

3.1.Dependence of Tg on heating rate fl + The heating rate dependence of Cp,a(T) curves of chalcogenide glasses is well known, e.g. ref. 6. Using DSC we have studied the variation of Tg with heating

T A B L E 1. Characteristic specific heats and activation energies of slowly cooled Gex(Se85Te~5)100_ x glasses: Cp,a.(gI (300 K) is for a glassy sample, Cp,a./ULSl(400 K) for a supercooled liquid state sample and A Cp,a.(a~_q-gI( 300 K) is the difference between the meltquenched and slowly cooled samples; AEM* is the Moynihan, AEK* the Kissinger, AEAEs* the activation energy spectrum and A E DNLR*the distribution on non-linear relaxation model activation energies

Sample

SeasTe15 (Se85Tels)98Ge2 (SessTels)90GeHj

[Jg-lat-I K-l]

[jg-lat-tK-1]

[ J g - l a t - l K -l] [kJg -1 at-X]

ACp.a,ias_q_g)

AEM* AEK*

[kJg -1 at - l ]

[kJg -~ at-l]

25.53 + 0.45 25.53 + 1.64 25.53+0.71

40.63 + 0.1 40.34 + 0.1 39.67+0.1

- 1.5 - 2.0 -2.2

259 223 217

203 169 192

116-136 120-143

Cp.a.(g)

Cp.a.(ULS

)

Note: The reference value for the absolute cp.a( T ) quantities of all samples was taken to

AEAEs*

AEDNLR* AS*

[kJg -1 at-I]

[ J g - ] a t -1 K -1 ]

184 156

239 162

be Cp,a,(g)(300K) = 25.53

J g- 1 at- 1 K - I.

K

-

1.3 0

184

E. lllekov6 et al. .

~-50 F

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.

.

.

.

.

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.

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5'tructural relaxation of Ge-doped Ses5"fe/~glasses

.

-6

[ T - - - S n -

........

-7 I\'

~ ...........

.......

w

r

-

~'~\ \"

~

,

i 30

t

-9

./

q

t 20[

, 300

350

400

-ll

T[K]

Fig. 3. Experimental temperature dependence of specific heats of slowly cooled (Se85Tels)mo_xGex glasses. (a) x= 0, (b) x = 2, (c) x = l0 (fl+ = 20 K min- 1). The error is indicated by an error bar.

I

I 0.028

0.0z7

o.o29 0.030 l/T,,

o.o31

It/K]

Fig. 5. Ln[fl+/(Tg4)2] VS. 1/Tg4 plotted in order to determine the Kissinger activation energy AEK* of structural relaxation for slowly cooled (Se85Te15)9oG%0 (0), (Se85Tels)98Ge2 (v) and Se85Tel5 (cz) glasses. For (SessTels)9oGeu~ the line leads to AEK* = 192 kJ g atom- 1.

5O 5

-12

10 20 40

~ 40 o 0

J

30

20

~5 {E

I

I

I

300

I

I

~J~

,,-4 ,'-3 I

I

I

I

I

I

I

I __

\

400

350 T [K]

Fig. 4. Heating rate influence on Cp,~(T) measured on slowly cooled (Se85Tels)9oGeu,glass (the heating rate fl+ is the variable parameter).

I

Tgl

I I

1

%3

Tg5 T

I

O.0024

rate for (SessTe15)90Ge10, (SessTe15)98Ge2 and Se85Te15 glasses. Tg always increases with increasing /3 +. For slowly cooled non-relaxed (SessTe15)9oGe m glass this dependence is shown in Fig. 4. Figures 5 and 6 show the dependence of TL(see its several definitions in Fig. 6) on /3+ in the Kissinger plots (In/3+/(Tg4 2) vs. l/Tg4) and the Moynihan plots (ln fl+ vs. 1/Tgl, 1/Tg 2, 1/Tg 3, 1/Tg4)for all samples. It can be seen that the slopes of the straight lines obtained in Kissinger coordinates and in Moynihan coordinates do not change significantly with the Ge content nor with the degree of conversion from glass to supercooled liquid state (except for the Tg~ dependence). As temperature Tg5 is the last moment of both structural relaxation and glass transition it was difficult to define because the temperature interval from Tg5 to T~ was too short for the definition of Cp,a,(SLs)(T ) to avoid initiation of crystallization of samples. By comparing the heating and cooling Cp,,(T) curves, the annealing effect inducing C S R O relaxations in the sample, even during the course of a heat measurement, was evident.

I\',L\A

j

0.0028

0.0032 1/Tg k [ l / K ]

Fig. 6. Ln(fl + vs. 1/Tg~ plotted in order to determine the Moyniban activation energy AEM* of glass transformation, where Tgk= Tg2 for slowly cooled (Se85T%5)90Gelo(0), (Se85Tels)98G~2 V) and SessTel5 (n) glasses. For (Se85Tels)9oGelo the lines depending on the position of 7".k lead to the sequence of Agu*(Tgz)=217 kJ (g atom) -I lo), AEra*(T,3)=204 kJ (g atom)- 1 (m) and AEM*( T~4) = 199 kJ (g atom)- r( • ). Temperatures Tgl, Tg2, Tg3 Tg4 and Tg5 are defined in the inset.

That is why the Tgl(fl + ) dependence was not considered, being strongly influenced by this error. 3.2. Dependence of AHexcess on annealing temperature Ta and time ta The evolution of an annealing-induced endotherm due to a previous annealing for a constant heating rate (fl+ = 20 K min -1) was measured. Figure 7 shows the dependency of Cp,a.T.,ta(T) obtained after isothermal annealing of (SessTe15)90Ge10 at T a = 3 2 0 K. The dependence of the relaxation enthalpy AHe ...... r,(ta) of

E. Illekovd~ et al. / Structural relaxation of Ge-doped Se85Tels glasses (Se85Tels)90Gel0 glass on annealing time at several annealing temperatures is calculated from eqn (1) using these sets of thermograms, as shown in Fig. 8. On increasing the annealing time for a given annealing temperature, the annealing-induced peak shifts to higher temperatures and the area of the peak increases. All AHe~c~,,r.(t,) and Tg4,r.(ta) dependences show saturation effects with kinetics inversely proportional to AT= T g - T a. According to observations on SeTe glasses [8], the saturated relaxation enthalpies AHexc~,T.(ta= oo) seem to show some annealing temperature dependence though these are not reached in the experimental time-scale. These facts will be studied further [ 1 1].

ate study of the three relaxation phenomena defined in the Introduction. 1. The excess enthalpy Hexce~s( T, t) is spontaneously minimized by TSRO relaxations of a sample at every temperature. 2. The excess enthalpy Hexc~s~(T,t) is modified (increased or lowered) by CSRO relaxations depending on previous annealing at Ta and actual measuring temperatures T, 3. Finally, the 2-shaped Cp,a( T ) anomaly follows the phase transition from frozen-in glass to the supercooled liquid state at Tg. These phenomena contain: thermodynamic contributions which characterize the degree of non-equilibrium (which is proportional to, for example, AHexc,~,(T, t, Ta, ta)) and are related to the whole thermal history of the sample, especially the method of its preparation and all its annealings; and kinetic contributions (e.g. d(AHexcess)/dt ) which depend on fl+ employed for the measurement. In our studies, it can be assumed that sequences of measurements characterized by Figs. 7 and 8, reflecting the evolution of some endotherms induced by previous annealing, represent only ordering phenomena of the CSRO type because the second heating rate Cp,a,(2)(T), following the c h a r a c t e r i s t i c Cp,a,(1),Tda(T) runs, were always the curves seen in Fig. 3. These did not change with the number of measurements, e.g. the samples did not relax irreversibly by means of TSRO processes. The Cp,~,(2)(T) curves, representing a first approximation to the glass transition phenomenon, have always been subtracted from Cp,a,(l),Tvt,(T) curves in our AHex..... r,(ta) calculation technique (eqn. (1) and Fig. 1), and have thus also eliminated contributions from this quantity. In the case of heating rate-dependent sequences of measurements, characterized by Figs. 4 to 6, neither TSRO processes (for the same reason as before) nor

4. Interpretation

The recovery of a non-equilibrium glass to the equilibrium supercooled liquid state is a thermally activated kinetic process. The Cp,a( T ) dependence enables separ-

x ~6 o, 100

h e

2

c

~ 50 o Q

1

I

320

i

340

I

I

360

I

I

380

400

T{KI Fig. 7. Measurementof %.,(T ) on slowlycooled (SessTeas)90Ge10 glass previously annealed at Ta= 320 K (t. being the variable parameter: (a) 0, (b) 1, (c) 2, (d) 4, (e) 16, (f) 24, (g) 48, (h) 143 h). Curve (a) having ta= 0 h represents the reference non-annealed line equivalentto line (c) in Fig. 3 (fl+ = 20 K rain- 1). 3BO

~

~

,

~

,

~

,

185

~

320 280

z4o 2OO

ioo i 120 "r ,,~

8O 40 0

-2

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-1

0

1

2

3

4

5

6

7

8

L
186

E. lllekovtJ et aL

/

Structural relaxation of Ge-doped Sea.,Te l~ glasses

CSRO contributions took place, because without heat treatment the samples were always in the same thermodynamic state. It is generally known that for a description of structural relaxation in glasses it is necessary to use the concept of a spectrum of independent processes g(AEj*, T,, ta) with a spectrum of activation energies, where gj is related to processes having activation energy AE/* available to relax. Then, by using some kinetic analysis method, an effective activation energy value AE~ff* ( Ta, ta) is measured. The glass transition phenomenon, as well as the ordering phenomenon of CSRO type in a glass, are assumed to be thermally activated processes of firstorder kinetics

db(T,t,~,t~)

~dj(T,t,T~,t,) +/3+~Odj(T,t,L, ta)

dt

/ r/(T,t, T,,ta)

j

0T

(4)

where 6j. is the quantity that is linearly proportional to the partial degree of non-equilibrium. In our case

6u( T, t, Ta, ta) - H( T, t, Ta, ta) - H¢q( T, t, Ta, ta)

4.2. "lhe Kissinger relation With assumptions, as above, but for temperatures of the maximal rate of conversion Tgma~(fl+)= Tg4(fl+ ) (e.g. temperatures at the inflexion points of glass transition curves or the maxima of the annealing-induced endotherms in the case of CSRO relaxation), the socalled Kissinger heating rate dependence [14] is valid: d[ln (/3 + / Tgmax2)]

- AL" K*

d(1/Tgm~x)

R

(9)

The Kissinger activation energies AEK* for our investigated samples are given by the slopes of the lines plotted in Fig. 5 and are summarized in Table 1.

4.3. The activation energy spectrum (AES) model In the case of isothermal annealing at T~ while neglecting the action of relaxation during continual heating (e.g. if/3 + ,> ( T, - Ti)/r then fl+ = 0 after reaching Ta) the dependence of the recovery of excess enthalpy AHexcess( Ta, ta) on the so-called A E S annealing time ta and temperature T.d will be valid [ 15]: AEAEs* / 1~, t o)

=H~xc~ss(T,t,T~,t,)

(5)

AHe ...... L(ta) = AH~...... ~o(ta=°° )

r/( T, t, Ta, t~) is the non-linear relaxation time related to AEj* ( Ta, t,) rj(T,t, Ta, t,) = r ° exp K6(T,t, Ta, ta)exp AE/(T~,t,)

RT

(6)

J 0

1-exp

- v °t~ exp

RTa--aJ[ d(Ae*) (lO)

RT

where K is some non-linearity material parameter, r ° and R are constants.

The frequency factor v ° is related to the constant r °. This relation defines a limiting activation energy

4.1. The Moynihan relation

AEAEs*( Za, ta)= R Ta In (V°ta)

In the case of continual heating experiments, if fl + - ( T g - Ti)/r and neglecting the isothermal relaxation effects, some sets of temperatures Tgk(fl +) for a given set of heating rates r + are defined as the temperatures at which an identical value for the degree of conversion (glass transition or CSRO relaxation) a is always observed. For example, the temperature Tg2 is defined as

stating that during isothermal annealing, at time t,, all processes with AE* AEAEs* have yet to contribute. From the known AHe ...... l;(ta) dependences (e.g. Fig. 8), the shape of the actual spectrum of activation energies hz,(AE*) = c(AHexcess,AE*)gra(AE*), where c(AHexcess, AE*) is a coupling function, and its Ta evolution can be deduced

Cp, a(Tg2) = Cp, a,(g)(Tg) + 1/2A Cp,a,(SLS_g)(Tg)

(7)

as a temperature at which the degree of conversion a = ½. For these temperatures, the so-called Moynihan or Larmagnac heating rate dependence [12, 13] is valid:

dln(fl+)

-AEM*

d(1/Tgk)

R

(8)

The Moynihan activation energies AEM* for our investigated samples are the slopes of lines plotted in Fig. 6 and are summarized in Table 1.

1

hr,(AEaEs*) = - RT~

. d [ A H e ...... r.(ta)]

(1 1)

(12)

d(ln ta)

The AHe ...... Ta(ta) dependences of a slowly cooled (Se85Te15)90Ge10 sample at four annealing temperatures ( Ta -- 300, 310, 320 and 330 K) are shown in Fig. 8. In order to calculate the form of hT.(AEAEs*), the frequency factor v ° = 1 x 1017 s-1, obtained for Se90Gel0 glass in ref. 5, was taken. The evolution of alternative relaxation processes characterized by their activation energies assuming an A E S model (AE* < AEAEs* ) in

E. Illekov6 et al.

Structuralrelaxation of Ge-doped SessTe~sglasses

/

the course of AH~x~,T,(t~)recovery, as well as their actual densities hT.(AEAEs*), are shown in Fig. 9. These results show a unique AHcxccss(AEAEs*) dependence as the master curve for any CSRO recovery in the sample within the investigated temperature range, and that the temperature-independent spectrum of activation energies of the acting processes has a bell-shaped distribution curve h(AEAEs* ) in the energy range 120-143 kJ (g atom)-1. To obtain the master curve AHexcess(AEAEs*) (Fig. 10) normalization of the y scales of the measured AH¢x~,~,T.(t~)dependences, with respect to the saturated AH~x¢~, r.( oO), had to be performed as well. As all the values of H~xc~, r.(o0) were neither measured nor could be extrapolated (this problem will be studied in more depth elsewhere [11]), the following procedure was used. It was assumed that the actual AEAEs* was the only state parameter of the relaxing glassy structure. Use of eqn. (11) gave points corresponding to all measured values of AH~xc~s,T.(ta) given by lnta=4 on In(ta) 400

187

the T, = 300 K isotherm (these points are marked with symbols in Fig. 8). Then instead of dividing all the measured AH~xc~,r.(t~)dependences by H~c~,r.(Oo), these dependences were shifted in the directions indicated by the arrows in Fig. 8. The dependence thus obtained formed a unique master curve within the experimental errors in the whole AEAEs* range (Fig. 9). 4.4. The distribution of non-linear relaxation ( D N L R )

model[16, 17]

We assumed that the kinetic equation (4), the universal distribution function &. of non-linear relaxation times 'r

~1/2

j, eq/

(13)

i

7j],rnt,( Z~ t) = rj, eq( T ) exp "K[H~'T"(

(14)

[h]

1

2

3

4

5

6

7

B

9

10

i

i

i

i

i

i

I

~

i

i

350

0.020 0.015

300

v

0.010 ~LU

250 200

0.005 r~

15o "~

0.000 "~

100 -0.005

50 I

I

I

120000

130000

140000

0

-0.010

* [J/(g ~t)] AEAEs

Fig. 9. The data in Fig. 8 shifted in directions indicated by the arrows plotted vs. activation energy calculated from eqn. (11) at annealing temperatures 300 K (o), 310 K ( v ), 320 K (D) and 330 K ( zx ). The full line is the master curve A H e..... (AEAES*) and the dotted line is the activation energy spectrum h(AEAEs*) for the CSRO relaxation in slowly cooled (SessTe~5)90GeHj glass. The error is indicated by an error bar.

In(ta) [h] -3

-1

-2

1

0

2

3

4

5

6

7

B

400 850 300

z5o 200

I

o

150

.a.

• J"

.D.~

100 I

50 0 110000

a. ''~2 ~ I

I

lZOOOO

130000

~EA~ES[ J / ( g

140000

at)]

Fig. 10. The master curves for excess enthalpy recovery due to CSRO relaxation measured on slowly cooled (Se85Te,5)90Gelo (0), (Se85Te15)9sGe 2 ( v ) and Se85Tex5 (D) glasses. The error is indicated by an error bar.

E. lllekov6 et al. / Structurulrelaxationof Ge-dopedSe~5le F5glasses

188

1 ri ~q(T) = h-T exp [AED~LR*-Aa-~-TRT

(115)

and /~Cp.a(SLS_g)(T)= const hold in the temperature range of measurement. The enthalpy recovery 6,~.7~,,~(T) during measurement at a given heating rate /3 + is then

RL

Cp,~,-e~,,~(T ) - Cp,,,(SLSl, = ACpalSLS_g1

usually of the order of the Debye frequency (v °= 10 ~ s-~), for single atom processes, but may be rather different for processes involving cooperative motion of larger groups of atoms. Besides, a certain temperature dependence v°(T)=v'f(T) may be assumed [19] which could modify the AEAEs* definition given by eqn. ( 11 ) into AEAEs*( T~, t~)= 1 - ~

6~(T) ' "

~

g/

(16)

K[6n.r,,,.(T)] / r,.,q /3 + e x p - RT where h, k are Planck and Boltzmann constants, respectively. The best fit of all the experiments apparent specific heats Cp,a(T ) of slowly cooled (Se85Tels)90Ge10 glass, on heating at t + =2.5, 5, 10, 20 and 40 K min -~ (e.g. the curves in Fig. 4), is then obtained by taking one set of parameters [18]: AEDNLR*= 184 kJ (g atom) -1, A S * = 2 3 9 J (g atom K) -1 and K = - 1 . 3 , where AEDNLR* is the so-called DNLR activation energy (which is the general temperature coefficient for all Arrhenius-type temperature-dependent relaxation times of the active relaxation processes); AS* is the activation entropy of the slowest relaxation process; and K is the non-linearity coefficient, which modifies all relaxation times proportionally to the degree of non-equilibrium of the sample.

4. 5. General discussion In all cases mentioned above the effective activation energies AEM*, AEK*, AEAEs* and AEDNLR* for the slowly cooled (Se85Tels)90Ge10 sample have been deduced. Depending on the corresponding model used, these values represented just one of its parameters. As the assumptions of these models were consistent (in terms of linear or non-linear first-order kinetic equations having one relaxation time or an adequate spectrum of relaxation times rj(T, t, Ta, ta) and with manifold forms that can be demonstrated to be the result only of the mathematical formalism, e.g. ref. 13), these parameters are mutually related and, by knowing the other parameters of these models, they can be recalculated. Nevertheless, some comments will be given on the results obtained.

4.5.1. The activation energy spectrum model AEAEs* is a weak function of v ° (a change of two orders of magnitude in v ° changes AEAEs* by about 10%); taking a fixed value for v °, we have neglected this interdependence. The frequency factor v ° is

,

ln(v ta)

(17)

As we did not know the true material parameters y and v', we neglected this correction which might alter the calculated/~EAEs* values.

4.5.2. The distribution of non-linear relaxation model Although the DNLR parameters (AEDN~*, AS*, K) are material parameters characterizing the complex structural relaxation of the sample independently of either the thermal history of the sample (e.g. the degree of non-equilibrium) or the actual relaxation times (which always have a unique distribution function), they are closely related to the largest equilibrium relaxation time

rmaxeq( T)= ~Texp!'AEoNLR*AS*TI/ • -Rf

(18)

If we want to relate the DNLR model parameters to those of the AES model, we have to take K ' = 0 because the AES model is a linear one. Then the DNLR fit to the experimental Cp,a(T) curves in Fig. 4 gives AEDNLR'*= 156 kJ (g atom) -1 and AS '*= 162 J (g atom K) -~ [18]. Now, the compared activation energies A E D m a ' * = I 5 6 kJ (g atom)-t and AEAES, max*= 143 kJ (g atom) -~ correlate within the range of their estimated error of + 19 kJ (g atom) -t, Alternatively, the more realistic K = - 1.3, principally shortening the actual relaxation times proportionally to the degree of non-equilibrium of the sample, prolongs them as the relaxation recovery progresses. The true value of K has to modify the master curve AHexces~(AEAEs*) too [20].

4.5.3. The Kissinger and Moynihan models Both of these models assumed knowledge of some corresponding temperatures having a defined degree of conversion. Though assuming only one type of relaxation process, the CSRO relaxations and glass transformation cannot be fully separated. That is why parameters AEK* as well as AEM* are not exact. Furthermore, the relation between AEM* and the true assumed activation energy AE* of structural relaxation is through the other parameters of this model [21].

E. lllekovti et aL / Structural relaxation of Ge-doped SessTels glasses

Coincidental with our results (Table 1), the qualitatively larger values for AEM* compared to the true AE* were observed [12]. Finally, our AEM* usually characterizes the glass transformation process as being the last relaxation process of the sample. A slight relation between AEM* and the progress of conversion a of the glass was observed (see Fig. 6). This continual decrease of AEM*(a ) was not studied deeply but it does not contradict the generally known rapid decrease of relaxation times during softening of a glass. 4.6. Structural modifications of slowly cooled Ge x (Sess Te191oo_x glasses Neither the exact atomic structure nor its relaxation changes in slowly cooled Gex(Se85Tels)100_x glasses have been studied up till now. The majority of investigations of chalcogenide glasses were focused on the structure of rapidly quenched Se glasses and evaporated amorphous films (e.g. ref. 22). Recent knowledge of the effect of composition and thermal annealing on the local short range and medium range structure of amorphous Sel00_xASx films has been obtained by direct study using electron diffraction [23]. The supposed short range structure of amorphous Sel00_xAsx in the region 8 < x< 17 is connected with the changes in size, topology and interaction of Se k polymeric chains due to linking and branching by As atoms and formation of AsSek chains closed into rings. The model also supposes the presence of an appreciable spatial structural fragment of quasimolecular (cluster) species on the base of AsSe3/2 whereas the tings and AsSek chains prevail. The availability of an approximately equal number of heterogeneous species in such an amorphous structure results in greater stability to structural changes occurring at the medium range order level during ageing and annealing. Amorphous selenium structural units were generally found to be dominant in the Se glasses with S, Te and/ or As additives. It was also noticed that the diffraction patterns of Se, and also of Sel00_xAsx filmS with low As content after annealing, are very similar to those of Se and Sex00_xASx bulk glassy samples and that these do not change substantially after structural relaxation [22, 23]. On the basis of these facts we assume that the composition-dependent structural peculiarities of SessAs15 amorphous films are also characteristic of a slowly cooled SessTe15 glass. Our observation that the activation energy AEDNLR* = 184 kJ (g atom) -1 is very close to the strength of an Se--Se bond AEs~_s~= 184.3 kJ (g atom) -~ [7] suggests that this bond breaking mostly occurs during structural relaxation and, therefore, the molecular species can interconvert. This model does not contradict the earlier proposed

189

model of an amorphous selenium-tellurium structure

[8]. On the basis of our comparative studies of the kinetics of structural relaxation of (Se85Tels)90Ge10, (Se85Tels)98Ge 2 and Se85Tels samples, the addition of low Ge content (x< 10) does not dramatically modify either their specific heat or their non-equilibrium thermodynamic properties.

5. Conclusions

Experimental determination of the apparent specific heat as a function of temperature Cp,a( T ) in the vicinity of the glass transition range has been performed for Gex(SessTels)100_ x glasses with x--0, 2 and 10 using DSC. The enthalpy released by the glass when annealed near the glass transition temperature, AHexcess,was studied. The observed isothermal AHexces~.r~(ta), as well as non-isothermal Cp,a,T,,t.(T), relaxation behaviour at temperatures just below the glass transition of all the investigated glasses can be explained by assuming structural relaxation with first-order kinetic behaviour and either linear relaxation times with a wide spectrum of activation energies h(AEAEs* ) or a distribution of non-linear relaxations which assume an activation energy AEDNLR* independent of the relaxation processes and a limiting activation entropy AS* characteristic of the slowest relaxation process. Typical effective relaxation times of the order of 10 7 S were obtained in both models at room temperature. The results for the (Se85Tels)90Ge10 sample have shown a unique AHexcess(gAES* ) dependence, as the master curve for any CSRO relaxation recovery in the sample in the investigated temperature range and the Ta-independent spectrum of activation energies for the active processes having a bell-shaped distribution curve h(AEAEs* ) in the energy range 120-143 kJ (g atom)-1. The final upper limit of the spectrum of activation energies of AES qualitatively as well as quantitatively correlates with the DNLR parameter AEDNLR*, which is 156 kJ (g atom) -1 for the linear model (K= 0), but is modified to 184 kJ (g atom) -1 in the case of a nonlinear (K = - 1.3) relaxation model. Finally the relaxation processes culminate in the transformation of a glass to the supercooled liquid state having the largest activation energy proportional to AEM*, where AEM* = 217 kJ (g atom)-1. The DNLR model parameters, AEDNLR*, AS* and K, and the complex thermal history of the sample are the only factors responsible for any of the actual measured Cp,a,T.,,.(T) dependences (namely the temperatures, widths, depths and shapes of the structural relaxation exotherms and endotherms, as well as the

190

E. lllekova et al.

/

Structural relaxation of Ge-doped Se~Te l~ glasses

glass transition, the kinetics of any AHexce,~,~,(t,) curve and so on) of the glassy samples studied. The activation energy AEDNLa*= 184 kJ (g atom) -1 coincides well with the most freqeunt Se--Se binding energy of AEseSe = 184.3 kJ (g atom)-1 and therefore determines the most probable relaxation mechanism in the investigated (Se85Tels)90Ge10 sample as either distortion or breaking of the selenium--selenium bonds. The addition of Ge to Se85Te~5 glass did not influence the network or the kinetics of its structural relaxation. It crosslinks the network to the third dimension and consequently prolongs the relaxation kinetics (enlarging rj and AEAEs* as well as Tg).

Acknowledgments

This work has been supported by CICYT project No. MAT-90-0454. E.I. is grateful to UAB for financial support during the course of this work.

References 1 E. Illekov~i, Ch. Cunat, E A. Kuhnast, A. Aharoune and J. M. Fiorani, Thermochim. Acta, 203 (1992) 445. 2 M.T. Clavauera-Mora, M. D. Bar6, S. Surifiach, N. Clavaguera, J. Parellada, D. Crespo and T. Pradel, J. Phys. F, 18 (1988) 2669. 3 A. van den Beukel and S. Radelaar, Acta MetaU., 31 (1983) 419.

4 Q. Xu and K. lchikawa, J. f'hys. C, 18 (1985) 1.985:19 (1986)7145. 5 M. T. Clavaguera-Mora, M. D. Bar6, S. Surifiach and J. Saurina, J. Non-Cryst. Solids, 131 &133 ( 1991 ) 479. 6 M.T. Clavaguera-Mora, S. Surifiach and M. D. Bar6, J. NonCryst. Solids, 86 (1986) 311. 7 N. Clavaguera, M. T. Clavaguera-Mora, S. Surifiach and M. D. Bar6, J. Non-Cryst. Solids, 104 (1988) 283. 8 G. C. Das, M. B. Bever and D. R. Uhlman, J. Non-Cryst. Solids, 7(1972) 251. 9 E. Illekov~i, F. A. Kuhnast and B. Aba, Thermochim. Acta, 195 (1992) 195. 10 E. Illekov~i, F. A. Kuhnast and B. Aba, Thermochim. Acta, 19.5(1992)211. 11 E. Illekov~i, M. T. Clavaguera-Mora, M. D. Bar6 and S. Surifiach, J. Non-Cryst. Solids, in press. 12 C. T. Moynihan, A. J. Eastel and J. Wilder, J. Phys. Chem., 78(1974) 2673. 13 J. E Larmagnac, J. Grenet and E Michon, J. Non-Cryst. Solids, 45 (1981) 157. 14 H.E. Kissinger, Anal, Chem., 29 (1957) 1702. 15 M. R. J. Gibbs, J. E. Evetts and J. A. Leake, J. Mater. Sci., 18 (1983) 278; G. Hygate and M. R. J. Gibbs, J. Phys. F, 17 (1987)815. 16 Ch. Cunat, Thesis, Universit6 de Nancy, 1985. 17 Ch. Cunat, Zeit. Phys. Chem. Neue Folge, 157 (1988) 419, 425. 18 A. Aharoune, Thesis, Universit6 de Nancy, 1991. 19 A. van den Beukel and S. Radelaar, J. Non-Cryst. Solids, 83 (1986) 134. 20 Ch. Cunat, H. R. Hilzinger and G. Herzer, Mater. Sci. Eng., 97(1988) 497. 21 S.N. Cricbton and C. T. Moynihan, J. Non-Cryst. Solids, 102 (1988) 222. 22 R.B. Stephens, J. Appl. Phys., 49 (1978) 5855. 23 O. V. Luksha, V. I. Mikla, V. P. Ivanitsky, A. V. Mateleshko and D. G. Sernak, J. Non-Cryst. Solids, 144 (1992) 253.