A thermodynamic and kinetic investigation of amorphous (1−x)As2Se3 · xSb2Se3 alloys

Journal of Non-Crystalline Solids, 15 (1974) 30-44. © North-Holland Publishing Company

A THERMODYNAMIC AND KINETIC INVESTIGATION OF AMORPHOUS ( 1 - x ) A s 2 S e 3 • x S b 2 S e 3 A L L O Y S G.C. DAS, N.S. P L A T A K I S and M.B. B E V E R Department of Metallurgy and Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Received 26 June 1973 Revised manuscript received 19 November 1973

The heats of formation of amorphous (1-x)As2Se 3 • xSb2Se3 (x = 0 to 0.4) referred to crystalline As2 Se3 and Sb2 Se3 were measured by liquid metal solution calorimetry. The values of heats of formation of amorphous (l-x)As?Se 3 ' xSb2 Se3 decreased from 1.39 -+ 0.03 kcal • (g-at) -~ a t x = 0 to 1.27 -+ 0.04 kcal • (g-at)-" a t x = 0.4. The glass transition temperature and the temperatures of the maximum rates of crystallization and fusion were meaSured by differential scanning-calorimetry. The glass transition temperature increased and the temperatures of the maximum rates of crystallization and fusion decreased with increasing Sb2 Se3 content. The relaxation process in amorphous (1-x)As2Se 3 • xSb2Se3 (x = 0.3) was investigated by measuring changes in microhardness, small-angle X-ray scattering and heat capacity with time of annealing at several temperatures ranging from room temperature to 413 K. With increasing annealing time the microhardness, the height and the temperature of the glass transition peak increased whereas the intensity of small-angle X-ray scattering decreased. These changes reflect relaxation towards a more stable structure of smaller molecular mobility. The changes in the enthalpy with annealing time and the activation energy spectra for relaxation were derived from the heat capacity data. The effects of temperature and time of annealing on the various properties are explained in terms of structural changes and relaxation kinetics.

1. Introduction A m o r p h o u s chalcogenide materials have attracted m u c h a t t e n t i o n in recent years. Their established use as p h o t o c o n d u c t o r s and their potential use as the active comp o n e n t s in threshold and m e m o r y switching devices a c c o u n t for this interest. Since ifi these applications the materials are activated by light or an electrical signal, primarily their optical and electrical properties have been investigated. By contrast, little effort has been d e v o t e d to the d e t e r m i n a t i o n o f t h e r m o d y n a m i c data for these materials. The only published t h e r m o d y n a m i c i n f o r m a t i o n for the quasibinary system A s 2 S e 3 - S b 2 S e 3 appears to be the phase diagram [1 ]. The specific heats of the c o m p o u n d s As2Se 3 [2] and Sb2Se 3 [3], the heat o f f o r m a t i o n [4] and the heat o f

G.C. Das et aL, Amorphous (1 xJAs2Se3 " xSb2Se 3 alloys

31

sublimation [3] of Sb2Se 3 have also been determined. A thermodynamic investigation of the system As2Se 3-Sb2Se 3 was desirable because it would supplement data already available for this system on the devitrification kinetics [5, 6], optical and electrical properties [7-9] and threshold and memory switching characteristics [10]. In the investigation reported here the heat of formation of amorphous (1 x)As2Se 3 • xSb2Se 3 alloys was measured as a function of the composition variable x in the range x = 0 to x = 0.4. The temperatures of the maximum rates of crystallization and fusion of these alloys were also determined. Amorphous materials are unstable and relax toward the equilibrium structure. The relaxation process can be investigated by measuring the changes of various properties with time during annealing at temperatures below the glass transition temperature. Properties that have been measured are the specific volume [11], index of refraction [ 12] and viscosity [13]. Few investigations, however, have been concerned with changes in thermal properties during relaxation. In the investigation reported here the relaxation behavior of amorphous (1-x)As2Se 3 • xSb2Se 3 (x = 0.3) was investigated by hardness measurements, small-angle X-ray scattering and the determination of the heat capacity as functions of annealing time. The glass transition temperature of amorphous (1-x)As2Se 3 • xSb2Se 3 as a function o f x was also determined. The investigation continues research on amorphous selenium-tellurium alloys [14].

2. Experimental

procedures

2.1. Preparation o f specimens

Amorphous As2Se 3 and crystalline Sb2Se 3 were prepared from high-purity (99.999+%) As, Sb and Se. These binary compounds were used in preparing specimens of amorphous (l-x)As2Se 3 • xSb2Se 3. In all cases a special technique [15], which insured homogeneity, was used. The constituents were weighed to + 10 -5 g and placed in a quartz ampoule, which was then evacuated to a pressure of 10 -6 mm Hg and sealed. The ampoule was attached to the horizontal shaft of a motor, introduced into a horizontal furnace and rotated at approximately 125 rpm. The temperature was raised to 1023 K and held there for 1 h. The ampoule was then withdrawn from the furnace and quenched in air while still being rotated. Most specimens of crystalline As2Se 3 needed as a reference material for solution calorimetry were prepared by the vapor transport method: amorphous As2Se 3 held in an evacuated and sealed quartz ampoule was heated in a temperature gradient. A few specimens of crystalline As2Se 3 were also prepared by annealing amorphous material at 688 K for ten days. Both methods yielded fully crystalline specimens of As2Se 3 . Crystalline specimens of (1-x)As2Se 3 - xSb2Se 3 were prepared by annealing amorphous materials.

32

G.C. Das et al., Amorphous (1-x)As2Se 3 • xSb2Se 3 alloys

2.2. Characterization o f specimens

Specimens prepared by the rapid cooling technique were amorphous at all compositions within the range o f x = 0 to 0.5, but above x = 0.5 some crystalline material was always present. In this investigation amorphous specimens containing up to 0.4 g-at fraction of Sb2Se 3 were used. The amorphous state of these specimens was confirmed by X-ray diffraction. Electron microprobe analysis, capable of revealing chemical inhomogeneities with a resolution of approximately 2/am, did not reveal phase separation. Also optical and scanning electron microscopy combined with etching experiments did not indicate any chemical or structural inhomogeneities. The scanning electron microscope was used in the X-ray mode to test for chemical homogeneity from point to point, and in the secondary electron mode to check for phases having the same chemical composition but a different structure. The assumption was made for the latter mode that chemically identical but structurally different phases would react at a different rate with the etchant; this would create a surface topography which should have been observed by scanning electron microscopy in the secondary mode. Several etchants were used. 2.3. Liquid metal solution calorimetry

The heats of formation of amorphous (1-x)As 2 Se 3 • xSb2Se 3 (x = 0, 0.1,0.2, 0.3, 0.4) referred to crystalline As2Se 3 and Sb2Se 3 were measured by liquid metal solution calorimetry with bismuth as solvent. Heats of formation of some crystalline (l-x)As2Se 3 • xSb2Se 3 specimens were also determined [16]. The calorimetric equipment and procedure have been described elsewhere [I 7]. Samples were added from 273 K to the bath at 623 K. Successive additions consisted of amorphous samples, crystalline samples and the corresponding mechanical mixtures of crystalline As2Se 3 and Sb2Se 3 . The calorimeter was calibrated with bismuth. A value of 4.96 kcal • (g-at) -1 was taken for the heat content H623K-H273K of bismuth [18]. The heat effects of the additions of the specimens were plotted against the average of the atom fractions of selenium in the bath before and after each addition. 2. 4. Annealing o f specimens

In order to investigate their relaxation behavior amorphous specimens of (1-x)As2Se 3 - xSb2Se 3 (x = 0.3) were given annealing treatments for various times at room temperature and at 323,373 and 413 K. For annealing above room temperature the specimens were placed in a continuously evacuated tube which was immersed in an oil bath controlled to -+ 0.5 K.

G.C. Das et al., Amorphous {1-x)As2Se 3 • xSb2Se 3 alloys

33

2.5. X-ray diffraction

For X-ray diffraction measurements freshly prepared amorphous specimens were ground in a mortar. The powder was made into a paste with a 75% solution of collodion in alcohol. The paste was spread on a microscope slide to a thickness o f 2 mm and dried. The X-ray specimens were examined in a diffractometer with CoK~ radiation at 22 kV and 20 mA at a scanning speed of 0.125 ° ' m i n - 1. In the specimen chamber an atmosphere of helium was maintained to eliminate air scattering. Measurements were carried out at large angles (2 0 = 15 to 75 °) and small angles (2 0 = 3 to 15 °) after annealing the specimens for various times at 373 and 413 K. 2.6. Microhardness measurements

Freshly prepared amorphous specimens were cut into pieces approximately 5 mm long. The ends of these pieces were ground and polished; Vickers microhardness measurements were made on the polished surfaces with a Leitz microhardness tester with loads of 50 and I00 g. The change in the microhardness with time of annealing at room temperature and 413 K was determined. 2. 7. Differential scanning calorimetry

The glass transition of the amorphous specimens of (1-x)As2Se 3 • xSb2Se 3 was investigated with a differential scanning calorimeter (Perkin-Elmer Model DSC-1 B). Because of the high vapor pressure of arsenic and selenium the specimens were sealed in aluminum specimen holders. A scanning speed of 10 K • rain -1 and a range of 8 mcal • sec -1 for a full scale pen deflection were used. The specimens were scanned from 451 to 499 K. To determine the effect o f annealing time on the glass transition behavior amorphous specimens of (1-x)As2Se 3 • xSb2Se 3 (x = 0.3) were given annealing treatments for various times at room temperature and at 3 2 3 , 3 7 3 and 413 K before differential scanning calorimetry. Specimens annealed at 413 K were scanned between 448 and 497 K. Specimens of amorphous (1-x)As2Se 3 - xSb2Se 3 were scanned through the temperature ranges of crystallization and fusion. The temperatures o f the crystallization and fusion peaks were defined as the temperatures at which the rates of crystallization and fusion had their largest values.

3. Experimental results 3.1. Heats o f formation

The heat effects of the additions to the calorimeter of crystalline and amorphous (1-x)As2Se 3 • xSb2Se 3 and the chemical mixture of the constituent binary corn-

34

G.C. Das et al., A m o r p h o u s ( 1 - x ) A s 2 S e 3 • x S b 2 S e 3 alloys

T

I

I

I

g

0

0

I

-

l'5 I

E

o 0

~ 1.2

~"s i.i 1.0 0

[

I

1

.I .2 .~ Gram- Atomic Fraction of Sb 2 Se 3 , x

I

.4

Fig. 1. Heat of formation of a m o r p h o u s ( 1 - x ) A s 2 Se3 " xSb 2 Se 3, referred to crystalline As2 Se3 and SbzSe3, as a function of x.

pounds were endothermic and changed linearly with the composition of the bath. The heat of formation of amorphous (1-x)As2Se 3 • xSb2Se 3 was the difference between the heat effects of this material and the corresponding mechanical mixture of crystalline As2Se 3 and Sb2Se 3. Fig. 1 shows the heats of formation of amorphous (1-x)As2Se 3 • xSb2Se 3 referred to crystalline As2Se 3 and Sb2Se 3 as a function of the composition variable x.

3.2. X-ray diffraction Large-angle X-ray scattering showed only broad diffuse peaks characteristic of amorphous materials. The changes in the widths of these peaks with annealing time at various annealing temperatures were very small. The intensity of small-angle X-ray scattering for a specimen annealed at 413 K is shown in fig. 2. This intensity decreased at angles 2 0 smaller than 7 ° in the first hour of annealing; thereafter no detectable change in the intensity occurred. This does not mean, however, that no further structural changes took place after this time. As pointed out for selenium-tellurium alloys [ 14] the wavelengths of the density fluctuation could have increased substantially by coalescence while their amplitudes decreased. This coalescence would place the changes in X-ray intensity at angles below those accessible in the reflection experiments conducted in this investigation. The results for specimens annealed at 373 K were similar except that the decrease of the intensity occurred at angles smaller than 9 ° . Annealing at room temperature did not cause any detectable change in the intensity of small-angle scattering.

3. 3. Microhardness The microhardness of amorphous (1-x)AszSe 3 • xSbzSe 3 (x = 0.3) is shown as a function of the time of prior annealing at room temperature and at 413 K in fig. 3.

35

G.C. Das et al., A m o r p h o u s ( 1 - x ) A s 2 S e 3 ' x S b 2 S e 3 alloys

f

I

I

I

80

!

7 7- 6 0 - ~s Quenched 2

{ -~ 4 0 m

20-

0

Anneoled A ~ , ~ for I hour ";'\'

I

l

I

I

I

l

9° 20~ Fig. 2. Intensity of small-angle X-ray scattering of amorphous (1 x)As2Se 3 • xSb2Se3, (x = 0.3) before and after annealing at 413 K.

J60

6o

3o

I

I

-

413°K i

150

o

I

o

~

v

Room Temperoture ~

o {3

140 I

1301 0

I 50 Anneoling

I

I00 Time

150

(hours)

Fig. 3. Microhardness of amorphous (1-x)As2Se 3 ' xSb2Se 3 (x = 0.3) as a function of annealing time at room temperature and 413 K.

G.C. Das et al., Amorphous ( 1 - x ) A s 2 S e 3 • xSb2Se 3 alloys

36

Table 1 Temperature o f glass transition peak of a m o r p h o u s ( 1 - x ) A s 2 S e 3 ' xSb2Se3 as a function of x. x

Temperature o f glass transition peak (K)

0 0.1 0.2 0.3 0.4

471 -+ 0.5 472 +- 0.5 473 -+ 0.5 473 -+ 0.5 474.5

The hardness increased with time and approached a constant value at each temperature. However, the observed limiting value and the rate of increase early during the annealing were larger at the higher temperature. The rate of increase in the hardness decreased with annealing time.

3.4. Heat capacity The glass transition temperatures of specimens of (1-x)As2Se 3 • xSb2Se 3 as a function of composition are listed in table 1. These specimens had been held at room temperature after preparation. The glass transition temperature increased slightly with Sb2Se 3 concentration. .2

Annealing Temperature= 373"K

/ u.rnr As Quenched

~2hrs

0 'E c, Tv

Annealing Temperature = 413 °K

o° .4

840 hrs

--'~

240 hrs--~, / ",, /

o .3

96 hrs

'0

S,,, "':":,"' /

'"il

50 h r s - - ~ i i 22hrs

/ ? " ,,

\',

.2

•I

0 450

~:.,"~

~

I 460

l

~ ..... ~

\ \2hrs 0.5 hr

i I 1 470 480 490 Temperature (°K) Fig. 4. Heat capacity versus temperature in the region of the glass transition o f a m o r p h o u s ( 1 - x ) A s 2 S e a • xSb2Se3 (x = 0.3) after annealing for various times at 373 and 413 K.

G.C. Das et al., A m o r p h o u s ( l - - x j A s 2 S e 3 " x S b 2 S e 3 alloys

37

The difference, A C p , b e t w e e n the heat capacities at 486 K (above the glass transition temperature) and at 454 K (below the glass transition temperature) was determined as a function of composition. The variation of ACp with composition was nonmonotonic and the values ranged from 0.042 + 0.002 cal • K -1 • g-1 to 0.46 + 0.003 cal • K - 1 . g-1. The effects of time and temperature of annealing on the glass transition of (1-x)As2Se 3 • xSb2Se 3 (x = 0.3) are shown in fig. 4. In this figure the heat capacity is plotted as a function of temperature for different times of prior isothermal annealing at 373 and 413 K. When the specimens were annealed at room temperature or 323 K the glass transition temperature and the height of the specific heat peak at the glass transition did not change with annealing time. At higher annealing temperatures, however, as shown in fig. 4, the glass transition peak shifted to higher temperatures and the height of the peak increased with increasing prior annealing time. This effect was more pronounced during annealing at 413 than at 373 K. As all the specimens were annealed under vacuum, the increase in peak height with time could not have resulted from a reaction between the specimen and a gas.

t

I

I

I

65C

63C

'~""'~",,,~,~

o v

~61C

I'-

0 0

Cryslollizotion 0

590 -

570 O

55C

0

I

.I

I

.2

I

.3

I

.4

Grom-Atomic Froction of Sb2Se3,x Fig. 5. Temperatures corresponding to m a x i m u m rates of crystallization and fusion of amorphous ( 1 - x ) A s 2 S e 3 • xSb2Se3 as f u n c t i o n s o f composition x.

38

G.C. Das et al., Amorphous (1 x}As2Se3 • xSb2Se 3 alloys

3.5. Crystallization and fusion

When specimens of amorphous (1-x)As2Se 3 - xSb2Se 3 were scanned at a speed of 10 K - rain-1, crystallization and fusion occurred over a range of temperature; in most of the alloys these two processes overlapped. The temperatures at which the rates of crystallization and fusion attained their largest values were fairly reproducible. In fig. 5 these temperatures are plotted as functions of the composition variable x. At x = 0.3 a double peak occurred reproducibly during crystallization; the crystallization temperature was obtained from the weighted average of the two peaks.

4. Discussion 4.1. Heats or formation

Positive heats of formation of amorphous (1-x)As2Se 3 • xSb2Se 3 referred to crystalline As2Se 3 and Sb2Se 3 can be explained by the metastability of the amorphous material. Heats of formation of comparable magnitude were found for amorphous selenium-tellurium alloys [ 19]. The heat of formation of the amorphous alloys decreases with increasing Sb2Se 3 concentration from 1,39 + 0.03 kcal - (g-at) -1 for As2Se 3 to 1.27 + 0.04 kcal • (g-at) -1 for x = 0.4; the error limits represent the scatter around the mean values of the experimental data. No information on the structure of amorphous (1-x)As2Se 3 - xSb2Se 3 appears to be available to explain this slight decrease. 4.2. X-ray diffraction

The results of large-angle X-ray scattering indicate that the specimens were amorphous and remained amorphous even after annealing at temperatures as high as 413 K. The decrease in the intensity of small-angle X-ray scattering is similar to that observed in amorphous silicon [20] at high temperatures and in amorphous selenium-tellurium alloys [14] at room temperature. In contrast to these results, the intensity decrease for amorphous (1-x)As2Se 3 • xSb2Se 3 is small; also, it occurs only at very small angles (2 0 < 7 ° at 413 K) and only during the first hour of annealing. The decrease in the small-angle X-ray intensity indicates that heterogeneities in the density are reduced during annealing. The range of diffraction angle (2 0 = 3 to 7 °) at which the scattering decreases corresponds to fluctuations on a scale of approximately 10 3,. This range of diffraction angle, however, represents only the tail end of the small-angle peak which occurs near the forward scattering direction. In the reflection experiments of this investigation angles smaller than 3 ° were not accessible and the question of whether structural changes occurred on a larger scale, especially after longer annealing times, could not be answered.

G.C. Das et al., Amorphous (1 x)As2Se 3 • xSb2Se 3 alloys

39

4.3. Microhardness

The increase in microhardness with annealing time suggested that the material was relaxing towards a structure of smaller molecular mobility. In selenium tellurium alloys [14] the microhardness increased in a similar manner. At an annealing temperature close to the glass transition the hardness reached a maximum and then decreased. The specimens of (1-x)As2Se 3 • xSb2Se 3 were not annealed at high enough temperatures to explore possible analogous behavior of the hardness-time curve. The microhardness measurements indicate that the material is relaxing at room temperature, which is much lower than the glass transition temperature. The temperature and height of the heat capacity peak of the material at the glass transition do not change with time of annealing at room temperature. The type of inhomogeneities which anneal out at room temperature affect the hardness, but have no measurable effect on the glass transition and enthalpy of the specimen. 4.4. Temperatures o f glass transition, crystallization and fusion

The increase in the glass transition temperature and the decrease in the temperature of the maximum rate of crystallization of amorphous (1-x)As2Se3 • xSb2Se 3 with increasing concentration x of Sb2Se 3 are similar to observations made in amorphous selenium-tellurium alloys [14]. As the Sb2Se 3 concentration increases, the tendency towards crystallization increases and it becomes more difficult to produce amorphous specimens. The limit for glass formation in (1-x)As2Se 3 • xSb2Se 3 alloys occurs at a g-at fraction of Sb2Se3, x of 0.5 [7, 21]. The temperature of the maximum rate of crystallization decreases sharply between x = 0.3 and x = 0.4. The temperature of the maximum rate of fusion also decreases with Sb2Se 3 concentration. The phase diagram of As2Se 3-Sb2Se 3 has a eutectic at a g-at fraction ofSb2Se 3 of approximately 0.14 [1]. 4.5. Heat capacity

Noticeable peaks representing the glass transition occurred in the heat capacity temperature curves when freshly prepared amorphous (1-x)As2Se 3 • xSb2Se 3 specimens were scanned in the differential scanning calorimeter. The height and the position of these peaks did not change with annealing time of specimens which had been annealed at room temperature or 323 K. On the other hand, as shown in fig. 4, the height and the temperature of the glass transition peak increased with the time of prior annealing at 373 and 413 K. At 373 K the increases were small and no further changes were observed after annealing for times in excess of 115 h. The changes were prominent and occurred over extended times of annealing at 413 K. The results of prior annealing at temperatures ranging from room temperature to 413 K indicate that measurable relaxation of the enthalpy occurs at room tern-

40

G.C. Das et al., Amorphous (1-x)As2Se 3 • XSblSe 3 alloys

perature in the very short time elapsed between the preparation of the amorphous specimen by quenching and the scanning of this specimen in the differential scanning calorimeter. Further relaxation of the enthalpy over an extended period of time, however, is possible only at higher annealing temperatures close to the glass transition. The relaxation of amorphous (1-x)As2Se 3 - xSb2Se 3 (x = 0.3) and amorphous selenium-tellurium alloys [ 14] near their respective glass transition temperatures probably involves a decrease in specific volume, fictive temperature and molecular mobility with increasing annealing time. The concept of overshooting of the equilibrium properties with increasing annealing time [14] also can be applied to amorphous (1-x)As2Se 3 - xSb2Se 3. In the discussion on the relaxation of amorphous selenium-tellurium alloys [14], attention was drawn to the large height of the glass transition peaks; the ratio of the heat capacity at the peak Cpeak to the heat capacity of the liquid C~ was as large as 5. In amorphous (1-x)As2Se 3 • xSb2Se 3 (x - 0.3) annealing at 413 K for extended periods resulted in glass transition peaks with ratios of Cpeak/C ~ = 3. As the specimens had not been annealed to equilibrium, the peak height would probably have increased further with longer annealing. The continuous increases in the peak height and peak temperature indicate continuing and extended relaxation; such increases may be characteristic of amorphous chalcogenides in general. 4. 6. E n t h a l p y and activation energy

The change in the enthalpy of amorphous (1-x)As2Se 3 • xSb2Se 3 due to relaxation during prior annealing at 413 K was determined from the scanning curves shown in fig. 4 by the method used for selenium-tellurium alloys [14]. The difference between the enthalpies at two temperatures, T 1 and 7"2, is zX/-/= H(T2) - H ( T 1 ) =

CpdT.

(1)

T1 If T 2 is taken sufficiently above the glass transition to ensure that the material is the equilibrium liquid, the change with annealing time in the enthalpy of the specimen referred to T 1 equals the change in z2Jt between T 1 and T 2. The annealing temperature was 413 K, T 1 was 452 K and T 2 was 497 K. The heat capacities at T 1 of the specimens annealed at 413 K for various times were almost the same and it may be assumed that there was no change in the enthalpy difference between 413 K (annealing temperature) and 452 K (T 1) with annealing time. The measured change in AH, therefore, represents the enthalpy change of the specimen during prior annealing at 413 K. A H h a s been found from fig. 4 by eq. (1) and is shown as a function of prior annealing time in fig. 6. AH decreases with annealing time; the inflection in the AH versus log t curve occurs at about 15 to 20 h of annealing. A distribution of the activation energies for relaxation can be derived with a first approximation analysis [22, 23]. This analysis, which is applicable to nonlinear

G.C. Das et al., Amorphous {1 -x)As2Se 3 • xSb2Se 3 alloys

- 5r . o1 [ ~

T

41

-[

-5.5

)

-6.5

0J

I

I

log t (hrs)

7'I

3I

Fig. 6. Change in enthalpy ~ / / o f amorphous (1-x)As2Se3 ' xSb2Se 3 (x = 0.3) between 452 K and 497 K as a function of time of prior annealing at 413 K. as w e l l as linear r e l a x a t i o n p r o c e s s e s , i m p l i e s t h a t p r o c e s s e s c h a r a c t e r i z e d b y a n activ a t i o n e n e r g y g m a k e a c o n t r i b u t i o n p ~ 0 ( ~ ) t o a p r o p e r t y P, w h i c h is c h a n g i n g d u e to a n n e a l i n g , at t i m e t: ,

_

1

P00(¢)-

RT

dP dlnt

(2)

I

I

I

l

I E8

_1~

T

1

I

I

I

I

I 34

3.0 o J

E t> 2.0 . oo ¢3_

o I.O

L~ 26

I I 1 50 32 (kcol g m - a t -I)

Fig. 7. Activation energy spectrum for the relaxation of amorphous (1-x)As2Se3 " xSb2Se3 (x = 0.3) at 413 K.

42

G.C. Das et aL, Amorphous {1-x)As2Se 3 • xSb2Se 3 alloys

In this relation f=RT(lnAt

+ 7),

(3)

where A is a frequency factor and 3' = 0.577. The activation energy spectrum characterizing the relaxation process of (1-x)As2Se 3 xSb2Se 3 (x = 0.3) at 413 K has been obtained by the foregoing analysis from the data for the enthalpy versus annealing time in fig. 6. A frequency factor of 1011 was assumed. As shown in fig. 7, the activation energy spectrum ranges from about 27.4 kcal • (g-at) -1 to 33.7 kcal - (g-at) -1 with a maximum at about 30.5 kcal • (g-at) -1. The distribution of activation energies is fairly symmetric. The activation energy spectrum was determined only for one annealing temperature. The enthalpy, which was the measured property, was still decreasing when the experiment was terminated. Also, the relaxation occurred at room temperature immediately after quenching; when the specimen was subsequently annealed at 413 K, the rate of decrease of the enthalpy had become quite large after about an hour of annealing. The activation energies determined do not represent the complete spectrum but rather that part which surrounds the most probable activation energy ~-for relaxation at 413 K. To obtain more complete data specimens would have to be annealed at several temperatures near the glass transition and the annealing times would have to be extended. The broad distribution of activation energies for the relaxation of (1-x)As2Se 3 • xSb2Se 3 at 413 K contrasts with the behavior of amorphous selenium-tellurium alloys [14], which shows a much narrower distribution. A distribution of activation energies may arise from a distribution of molecular processes or a nonlinear undistributed molecular process [23]. In either case the energy corresponding to the peak of the derived activation energy spectrum should be meaningful. This energy may be compared with the energies characteristic of this system. There are no reported data on the flow behavior of amorphous (1-x)As2Se 3 - xSb2Se 3 near the glass transition, but the cleavage energies E (in kcal • (g-at) -1) of relevant bonds are [24]:

E

As-Se

Sb-Se

As-Sb

As-As

Sb-Sb

Se-Se

52

51

44

46

42

49

Typical van der Waals bonds have energies in the range 3 - 1 0 kcal • (g-at) -1 [25]. Activation energies of relaxation based on the change of the enthalpy with time are smaller than the bond energies between various constituent atoms, but much larger than the energies of van der Waals bonds. The relaxation of amorphous (1-x)As2Se 3 - xSb2Se3, therefore, is due neither to a breaking of bonds nor to sliding of atomic layers. It may appear that the three types of measurements reported here relate to three separate relaxation phenomena each with its own kinetics. The results, however, can be interpreted in terms of a single continuous process. The saturation of small-angle X-ray scattering in one hour can be attributed to a decrease of the smallest inhomo-

G.C. Das et al., Amorphous ( 1 - x ) A s 2 S e 3 • xSb2Se 3 alloys

43.

geneities. The larger-scale inhomogeneities may be decreasing over a longer time, but this could not be determined with the experimental method used. Hardness measurements involve complex flow mechanisms; the observed increase in hardness indicates structural changes leading to smaller molecular mobility. This decrease may be caused by the annealing out of inhomogeneities but their effect on the hardness is not known. The decrease in enthalpy results from the relaxation of the structure towards that of the supercooled liquid at the annealing temperature. In conclusion, the relaxation of amorphous (1 -x)As2Se 3 . xSb2Se 3 can be viewed as a continuous process reflecting changes in the overall structure of the material. The rates of change of various properties depend on the rates of structural changes during annealing and their effects on the properties measured.

5. Summary and conclusions (1) The heats of formation of amorphous (1-x)As2Se 3 • xSb2Se 3 referred to crystalline As2Se 3 and Sb2Sb 3 are positive. They decrease slowly from approximately 1.39 kcal -(g-at) -1 at x = 0 to 1.36 kcal • (g-at) -1 at x = 0.3 and then decrease more rapidly to 1.27 kcal. (g-at) -1 at x = 0.4. (2) The glass transition temperature of amorphous (1-x)As2Se 3 • xSb2Se 3 increases slightly with increasing Sb2Se 3 concentration. (3) The decrease in the temperature of the maximum rate of crystallization of amorphous (1-x)As2Se 3 • xSb2Se 3 with Sb2Se 3 content is consistent with the increased difficulty in preparing amorphous specimens with increasing Sb2Se 3 concentration. (4) The decrease in small-angle X-ray scattering with annealing time occurs at very small angles (2 0 = 3 to 7 °) and only during the first hour of annealing. This corresponds to the disappearance of inhomegeneities on a small scale; changes on a larger scale could not be determined by the technique used. (5) The microhardness increased with annealing time at room temperature and at 413 K; the rate of increase and the final value were larger after annealing at 413 K (6) The height and temperature of the glass transition peak in the scanning (Cp versus T) curves increased with the time of prior annealing at 373 K and 413 K. The large glass transition peaks after annealing at the higher temperature reflect continuous relaxation of the material to structures of increased stability and decreased molecular mobility. The results indicate that relaxation may be taking place in two stages. (7) The change in enthalpy occurs over an extended period whereas changes in microhardness and small-angle X-ray scattering occur early during annealing. (8) The relaxation process of amorphous (1-x)As2Se 3 • xSb2Se 3 cannot be characterized by a single relaxation time but requires a spectrum of relaxation times or activation energies for its description. (9) The relaxation phenomena in amorphous (1-x)As2Se 3 • xSb2Se 3 have many similarities with those previously reported for amorphous selenium-tellurium alloys.

44

G.C. Das et al., A m o r p h o u s ( 1 - x J A s 2 S e 3 • x S b 2 S e 3 alloys

Acknowledgments The authors are grateful to Professors D.R. U h l m a n n and H.C. Gatos for use of l a b o r a t o r y facilities. T h e y thank Professor U h l m a n n and Professor S.C. Moss for helpful discussions and Dr. A.L. Renninger for valuable assistance with the X-ray diffraction measurements.

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