Molar volume and elastic properties of multicomponent chalcogenide glasses

294

Journal of Non-Crystalline Solids 128 (1991) 294- 309 North-Holland

Molar volume and elastic properties of multicomponent chalcogenide glasses A . N . Sreeram, A.K. V a r s h n e y a a n d D . R . S w i l e r 1 New York State College of Ceramics at Alfred University, Alfred, N Y 14802, USA

Received 10 August 1990 Revised manuscript received 7 December 1990

High purity chalcogenide glasses incorporating Ge, Sb, Se, As and Te were prepared by vacuum melting of previously distilled 5 N to 6 N pure raw materials from which the surface oxide was also removed in some cases. Molar volume and elastic properties of several isostructural chalcogenide glasses prepared by similar processing techniques were obtained from the measured values of densities and the velocities of transverse and longitudinal acoustic waves respectively. Property variations with the average coordination number, {r), were examined. Molar volume displayed a distinct minimum at (r} = 2.4, coincident with Phillips' 'percolation threshold' for each system studied. Elastic moduli, however, failed to show any dramatic changes at this threshold. Near the stoichiometric tie-line, a chemically ordered covalent network (COCN) model for the atomic arrangement in these glasses was found to be preferred over the chance coordination predicted by the random covalent network (RCN) model.

1. Introduction C h a l c o g e n i d e glasses exhibit u n i q u e I R - t r a n s mission a n d electrical p r o p e r t i e s that m a k e t h e m useful for several p o t e n t i a l a p p l i c a t i o n s such as threshold switching, m e m o r y switching, i n o r g a n i c photoresists, IR transmission and detection through lenses a n d optical waveguides, e.g., in welding a n d surgery. T h e use of chalcogenides in b u l k form is often restricted b e c a u s e of their limiting thermal a n d m e c h a n i c a l properties. The limiting mechanical p r o p e r t i e s of the chalcogenides relative to the rather strong oxide glasses clearly result from a difference in a t o m i c b o n d i n g . T h e oxide glasses have strong covalent a n d ionic b o n d s f o r m i n g a t h r e e - d i m e n s i o n a l network, whereas the chalcogenides have weak covalent b o n d s b e t w e e n 2 - c o o r d i n a t e d chalcogen a t o m s f o r m i n g a b a c k b o n e chain with cross-linking p r o v i d e d b y 3- or 4 - c o o r d i n a t e d group V a n d group IV atoms. V a n d e r W a a l s a t t r a c t i o n b e t w e e n the chains is even 1 Present address: Drakenfeld Colors, division of CIBA-Geigy, Corp., West Wylie Ave., Washington, PA, USA.

weaker. A s t u d y of m o l a r v o l u m e versus c o m p o s i tion p r o v i d e s i n f o r m a t i o n on the relative p a c k i n g of the a t o m s and, hence, gives an insight into the relative ease with which the a t o m s can be p u l l e d apart. A q u a n t i t a t i v e m e a s u r e of this force is p r o v i d e d b y the elastic properties. T h e c o n c e p t of the average c o o r d i n a t i o n n u m ber, { r ) , is useful in d e s c r i b i n g the cross-linking in a c h a l c o g e n i d e glass. M o t t [1], Phillips [2] a n d F l a n k et al. [3] have shown that the c o o r d i n a t i o n n u m b e r of c o v a l e n t l y b o n d e d a t o m s in glass is given b y the 8 - N rule, where N is the n u m b e r of the outer shell electrons. F o r a m u l t i c o m p o n e n t c h a i n - f o r m i n g c h a l c o g e n i d e glassy system, the average c o o r d i n a t i o n n u m b e r is defined s i m p l y as the a t o m - a v e r a g e d c o v a l e n t c o o r d i n a t i o n of the constituents. F i g u r e 1 shows the i s o - ( r ) lines in the three systems A ( G e - S b - S e ) , B ( G e - [ 6 6 S b 3 4 A s ] - [ 8 3 S e . 17Te]) a n d C ( G e - S b - [ 6 0 S e 40Tel). N o t e that the system A is a p u r e ternary, whereas B a n d C are p s e u d o t e r n a r y isostructural systems. T h e m o l a r v o l u m e of a given m a t e r i a l is det e r m i n e d b y d i v i d i n g the average m o l e c u l a r weight

0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

295

A.N. Sreeram et al. / Multicornponent chalcogenide glasses Y

0 ----x-- I O0

I0 ~

~

90

2o--F"

30 ---ff

M- s0

/

/

40

g"

~--

6{}

-'Z

U

Y

Y

70

(

.':

20 30 4t} 50 Fig. 1. Lines of equal average coordination number (r); X is the at.% Sb in systems A and C and at.% [66Se.34As] in systems B. Y is the at.% Se in system A, at.% [83Se.17Te] in system B and at.% [60Se-40Te] in system C. 0

10

by its density. Density or molar volume measurements in chalcogenide glasses have been reported by several authors: G e - S e by Ruska and Thurn [4], Ota et al. [5], Feltz et al. [6] and Fuxi [7], A s - S e by Ota et al. [8], Feltz et al. [6], and Fuxi [7], A s - S by Tsuchihashi and K a w a m o t o [9] and Maruno and N o d a [10], G e - S by K a w a m o t o and Tsuchihashi [11] and Fuxi [7], G e - A s - S e by Tille et al. [12], G e - A s - S by Myuller et al. [13], A s S b - S e by Giridhar and Mahadevan [14], G e - S b Se by Borisova and Pazin [15], Savage et al. [16], Giridhar et al. [17], Mahadevan et al. [18] and Swiler [19] and G e - A s - S e - T e by Loehman et al. [20]. Nearly all of these data, when plotted as molar volume vs. ( r ) , display a distinct minimum in molar volume at ( r ) = 2.4. In addition, according to Mahadevan et al. [18], local maxima exist in the G e - S b - S e system at compositions that lie on the line joining Sb203-GeSe 2 stoichiometric compositions. However, based upon the data by Feltz et al. [6], on the A s - S e and Myuller et al. [13] on G e - A s - S , Tanaka [21] suggested that the molar volume maximum occurs at ( r ) = 2 . 6 7 . Since

Fuxi's data [7] on A s - S e show the maximum to be at ( r ) = 2.50, there appears some controversy regarding the location of the local maximum. Elastic properties have been measured by Ota et al. [5] for G e - S e glasses, Nichols et al. [22] for As2S 3 and As2Se 3 glasses, Thompson and Bailey [23] for G e - A s - T e , Tille et al. [12] and Halfpap and Lindsay [24] for G e - A s - S e , Mahadevan et al. [18] and Swiler [19] for G e - S b - S e , Giridhar et al. [14] for A s - S b - S e , Hayes et al. [26] for G e - S b - S , and Frischat et al. [27] for S n - A s - S e . Measurement by Mahadevan et al. [18] of the elastic constants of highly cross-linked G e - S b - S e glasses showed an increase in all the elastic constants with increased cross-linking. They attributed this behavior to a combination of the decreasing molar volume and increasing cross-linking as these units are added. The only comment regarding the Poisson's ratio was that it decreased with increasing Ge content. Similar trends were also observed by Giridhar et al. [25] for A s - S b - S e glasses. Frischat et al. [27] correlated the elastic properties to the molar volumes of glasses in the S n - A s - S e system.

296

A.N. Sreeram et al. / Multicomponent chaleogenide glasses

They believed that increasing cross-linking decreased the molar volume because atoms became more tightly bound, and as the molar Volume decreased, all the physical properties such as Tg, the elastic constants and the microhardness increased. The present paper deals with the variation of molar volume and the elastic properties as a function of coordination in various 'isostructural' G e Sb-As-Se-Te m u l t i c o m p o n e n t chalcogenide glasses belonging to the three ternary and pseudo-ternary systems described by fig. 1.

2. Experimental procedure Six-N pure Ge, Sb, As and 5-N + pure Te and 5-N pure Se were used as starting raw materials acquired from the suppliers *. Before batching, the raw materias were further purified; the glasses from the same melt were also used to measure optical properties, the results of which shall be discussed in a forthcoming publication. The method for glass preparation has been discussed by us elsewhere [28,29]. An infrared spectrophotometer was used to look for the impurities present in the glasses in order to determine their optical quality. The glass-forming regions for glasses made by our preparation technique was determined using a combination of results from X-ray diffraction pattern and viewing the samples under an IR-microscope with a detector * * sensitive to a wavelength of 2.2 ~m. IRmicroscopy revealed the absence of any bubbles larger than - 5 ~m in diameter for all of our glasses. The molar volumes of the glasses were calculated from the density as discussed above. The density, accurate to _+0.5%, was determined using the Archimedes method. Odorless kerosene was used as the immersion liquid. The kerosene was calibrated for any room temperature fluctuations. Elastic constants were determined by the pulse-echo technique. Shear and longitudinal pulses with a frequency of 10 M H z were supplied * J o h n s o n - M a t t h e y / A E S A R Group, 892 Lafayette Road, Seabrook, N H , USA. * * Electrophysics, Nutly, N J, USA.

and detected by piezoelectric transducers. The ultrasonic pulses were transmitted accross a flat, parallel sample disk, 13 m m dia. × - 5 m m thick, and reflected off the opposite surface. An Aerotech § transducer provided the compressive wave for determination of longitudinal sound velocity, and a Panametrics §§ transducer was used to determine the shear wave velocity. The signals were provided by a Metrotek + MR101 receiver mounted in a Tektronics ++ TM515 power module. The signal was analyzed using a Tektronics 2235 100 M H z oscilloscope that measured the time between the reflection peaks. In most cases, the time for multiple echos were read to improve the accuracy of the test. The Young's moduli and Poisson's ratio were calculated from the longitudinal velocity, shear velocity, density and thickness of the specimen. The following relationships were used to calculate the elastic properties of the glasses: G = V~,

(1) -

where Vt is the shear (transverse) wave velocity, V1 is the longitudinal wave velocity, 0 is the density, 1, is the Poisson's ratio and G is the shear modulus. The Young's modulus, Y, and the bulk modulus, K, of the glass were calculated from the well-known expressions, 1, = ( Y / 2 G ) - 1 and K = Y / 3 1 1 - 2p]. The Poisson's ratio, measured repeatedly for the same composition, was accurate to +2.5%. Because of the added error in the density measurement, the shear modulus measurements were accurate to +2.5%, and hence the derived moduli (Young's modudlus and bulk modulus) were accurate to + 4.5%.

3. Results Tables 1 - 3 show the compositions of the glasses batched. The location of the various compositions §

Aerotech/Krautkramer-Branson, Model G a m m a HP, 10 MHz, 0.25 in dia. longitudinal wave trans., Lewistown, PA, USA. Panametrics, Model V156, 5.0/0.25, 10 M H z s h e a r w a v e Trans., Waltham, MA, USA. + Metrotek Inc., Richland, WA, USA. ++ Tektronics, Beaverton, OR, USA.

A.N. Sreerarn et al. / Multicomponent chalcogenide glasses

297

the presence of crystals, and did not show a distinct Tg in a DSC run. The values of molar volumes of our glasses are also tabulated in tables 1-3. For a better understanding of the variation of molar volume as a function of composition, these values have been plotted as contour maps in figs. 3(a)-(c). Figures 4(a)-(c) represent the contour maps for the

on the ternary diagrams is shown in figs. 2(a)-(c). Also shown in these figures are the boundaries of glass formation in the three ternaries. The glasses classified as * in tables 1, 2 and 3 are those in which the presence of crystals was detected using IR-microscopy a n d / o r X-ray diffraction pattern. These compositions, however, showed a distinct Tg in a DSC run. The glasses classified as * * showed

'Fable 1 G l a s s e s p r e p a r e d a n d t h e i r p r o p e r t i e s ; c o m p o s i t i o n s are i n at.%; M r i n c m 3 / m o l ; Glass

Ge

Sb

A1

13.3

13.3

A2

18.2

18.2

A3

20.0

A4 A5 A6 A7

Se

As

Te

(r)

M~

73.4

-

63.6

-

-

2.4

-

2.55

20.0

60.0

-

-

23.3

13.3

25.0

10.0

63.7

-

65.0

-

26.7 13.3

6.7

66.7

23.3

63.4

A8

16.7

16.7

66.7

A9

20.0

10.0

70.0

A10

23.3

3.3

73.3

A11

6.7

26.7

66.6

A12

10.0

20.0

70.0

A13

16.7

6.7

A14

3.3

A15 A16 A17

Y, K , G i n G P a Y

K

G

v

17.821

18.14

13.81

7.08

0.281

17.67

20.35

15.21

7.97

0.277

2.6

17.659

21.84

14.98

8.69

0.257

-

2.6

17.936

20.24

14.73

7.96

0.271

-

2.6

18.010

18.53

13.61

7.28

0.273

-

-

2.6

18.009

18.87

13.27

7.47

0.263

-

-

2.5

17.802

21.69

15.65

8.55

0.269

-

-

2.5

17.819

20.33

14.93

7.99

0.273

-

2.5

17.836

17.81

13.25

6.98

0.276

-

-

2.5

17.820

16.94

13.44

6.57

0.290

-

-

2.4

17.621

22.34

15.98

8.82

0.267

-

-

2.4

17.699

20.61

15.91

8.02

0.284

76.7

-

-

2.4

17.867

16.61

11.93

6.55

0.268

3.3

93.4

-

-

2.1

18.288

10.90

10.21

4.12

0.322

6.7

6.7

86.6

-

-

2.2

18.281

14.69

13.02

5.60

0.312

13.3

3.3

83.5

-

2.3

17.957

14.25

11.76

5.49

0.298

10.0

10.0

80.0

-

2.3

17.939

15.17

11.87

5.89

0.287

A18

6.7

16.7

76.7

-

2.3

17.889

17.89

14.06

6.94

0.288

A19

33.3

3.3

62.3

-

2.7

**

**

**

**

**

A20

30.0

10.0

60.0

-

2.7

17.580

21.58

14.74

8.59

0.256

A21

26.6

16.7

56.6

-

2.7

*

*

*

*

*

A22

16.7

26.6

56.6

-

2.6

17.679

24.17

16.58

9.61

0.257

A23

30.0

0.0

70.0

-

2.6

17.911

16.44

12.23

6.44

0.276

A24

20.0

0.0

80.0

-

2.4

17.821

14.56

11.45

5.65

0.288

A25

10.0

0.0

90.0

-

2.2

18.234

11.16

9.39

4.29

0.302

A26

0.0

0.0

-

2.0

18.479

12.23

11.45

4.63

0.322

A27

10.0

30.0

60.0

-

2.5

**

**

**

**

**

A28

3.3

23.2

73.3

-

2.3

*

*

*

*

*

A29

3.3

13.2

83.4

-

2.2

**

**

**

**

**

A30 A31

0.0 25.0

10.0 0.0

90.0 75.0

-

-

2.1 2.5

** 18.034

** 16.99

** 12.53

** 6.67

** 0.274

A33

22.0

0.0

78.0

-

-

2.44

17.849

16.17

12.48

6.30

0.284

A34

0.0

20.0

80.0

-

-

2.2

**

**

**

**

**

A35

0.0

30.0

70.0

-

-

2.3

**

**

**

**

**

A36

0.0

40.0

60.0

-

2.4

**

**

**

**

**

-

-

100

*: G l a s s e s i n w h i c h t h e p r e s e n c e o f c r y s t a l s w a s d e t e c t e d u s i n g I R m i c r o s c o p y a n d / o r c o u l d be o b s e r v e d in a D S C run. * *: G l a s s e s s h o w e d t h e p r e s e n c e o f c r y s t a l s a n d d i d n o t s h o w a d i s t i n c t Ts i n a D S C r u n .

X - r a y d i f f r a c t i o n . H o w e v e r , a d i s t i n c t Tg

A.N. Sreeram et al. / Multicomponent chalcogenide glasses

298

Young's modulus, Y. Similarly, figs. 5(a)-(c) represent contour maps for the Poisson's ratio, p. The contour maps for the bulk modulus, K, and shear modulus, G, were similar to those of Y and are included elsewhere [30].

4. Discussion Giridhar et al. [17] defined the stoichiometric tie-line for G e - S b - S e glasses as the line joining the stoichiometric crystalline compounds Sb2Se3 and GeSe 2. Any composition with Se content

Table 2 G l a s s e s p r e p a r e d a n d their properties; c o m p o s i t i o n s are in at.%; M~ in c m 3 / m o l ; Y, As

K, G in G P a

Glass

Ge

Sb

Se

Te

(r)

Ma

Y

K

G

i,

B1 B2 B3

13.3 18.2 20.0

8.9 12.1 13.3

61.1 53.0 50.0

4.4 6.1 6.7

12.3 10.6 10.0

2.4 2.55 2.6

17.809 18.044 18.126

18.36 21.95 21.84

14.04 16.19 16.47

7.16 8.61 8.54

0.282 0.274 0.279

B4 B5

23.3 25.0

8.9 6.7

53.0 54.1

4.4 3.3

10.7 10.9

2.6 2.6

18.17 **

20.65 **

15.10 **

8.12 **

0.272 **

B6

26.7

4.5

55.6

2.2

11.1

2.6

**

**

**

**

**

B7 B8 B9 B10

13.3 16.7 20.0 23.3

15.5 11.1 6.7 2.2

52.8 55.6 58.3 61.1

7.8 5.6 3.3 1.1

10.6 11.1 11.7 12.2

2.5 2.5 2.5 2.5

18.015 18.041 18.222 **

21.83 18.47 19.25 **

16.31 14.38 15.65 **

8.55 7.18 7.43 **

0.277 0.286 0.295 **

Bll

6.7

17.8

55.5

8.9

11.1

2.4

17.886

21.88

16.88

8.52

0.284

B12 B13

10.0 16.7

13.3 4.5

58.3 63.9

6.7 2.2

11.7 12.8

2.4 2.4

17.970 18.026

20.35 16.92

15.70 13.43

7.92 6.56

0.284 0.290

B14

3.3

2.2

77.8

1.1

15.6

2.1

18.723

12.73

11.72

4.83

0.319

B15

6.7

4.5

72.2

2.2

14.4

2.2

18.453

14.90

13.35

5.67

0.314

B16

13.3

2.2

69.4

1.1

13.9

2.3

18.380

14.87

13.18

5.67

0.312

B17 B18 B19

10.0 6.7 33.3

6.7 11.1 2.2

66.7 63.9 52.8

3.3 5.6 1.1

13.3 12.8 10.5

2.3 2.3 2.7

18.296 18.270 **

16.62 19.05 **

13.58 15.05 **

6.41 7.39 **

0.296 0.289 **

B20

30.0

6.7

50.0

3.3

10.0

2.7

**

**

**

**

**

B21 B22 B23

26.6 16.7 30.0

11.1 17.7 0.0

47.2 47.2 58.4

5.6 8.9 0.0

9.4 9.4 11.7

2.7 2.6 2.6

17.844 17.829 **

23.83 22.85 **

15.82 15.29 **

9.54 9.13 **

0.249 0.251 **

B24 B25 B26

20.0 10.0 0.0

0.0 0.0 0.0

66.7 75.0 83.0

0.0 0.0 0.0

13.3 15.0 17.0

2.4 2.2 2.0

17.905 18.546 18.953

16.24 14.97 12.18

13.27 12.86 11.47

6.26 5.73 4.60

0.296 0.306 0.323

B27 B28 B29 B30 B31

10.0 3.3 3.3 0.0 25.0

20.0 15.5 8.8 6.7 0.0

50.0 61.1 69.4 75.0 62.3

10.0 7.7 4.4 3.3 0.0

10.0 12.2 13.9 15.0 12.7

2.5 2.3 2.2 2.1 2.5

17.837 18.315 18.496 18.696 *

23.32 20.01 17.11 14.96 *

16.06 16.11 14.93 13.05 *

9.27 7.73 6.54 5.66 *

0.258 0.293 0.309 0.322 *

B33 B34 B35 B36 B37 B38 B39

22.0 0.0 0.0 0.0 5.0 10.0 20.0

0.0 13.3 20.0 26.7 26.7 26.7 20.0

64.7 66.7 58.3 50.0 45.8 41.7 41.7

0.0 6.7 10.0 13.3 13.3 13.3 10.0

13.3 13.3 11.7 10.0 9.2 8.3 8.3

2.44 2.2 2.3 2.4 2.5 2.6 2.5

18.031 ** ** ** ** ** **

16.21 ** ** ** ** ** **

12.93 ** ** ** ** ** **

6.28 ** ** ** ** ** **

0.291 ** ** ** ** ** **

• : Glasses in w h i c h the p r e s e n c e of crystals was d e t e c t e d using I R m i c r o s c o p y a n d / o r X - r a y diffraction. H o w e v e r , a distinct Ts could be o b s e r v e d in a D S C run. * *: G l a s s e s s h o w e d the p r e s e n c e of crystals a n d did not show a distinct Tg in a D S C run.

A.N. Sreeram et al. /

Multicomponent chalcogenideglasses

'chalcogen-rich region' and glasses below the tielines shall be referred to as "chalcogen-deficient region'. If we compare the plots of iso-~r) (fig. 1) and iso-M,. (fig. 3) for the systems studied, it is clear that there lies a good correlation between the average coordination number, (r), and the molar volume, M,~, over the entire glass-forming chalcogen-rich region. Results of our experiments

greater than those on the tie-line was referred to as 'Se-rich region' and that with more Ge content was referred to as 'Ge-rich region'. Based on this notion, we define the stoichiometric tie-line for our systems as the lines joining '66.6' on the G e - S e / T e pseudobinary line to '40.0' on the Se/Te-Sb/As pseudobinary line in all the pseudoternary diagrams: the glasses above the tie-lines towards the S e - T e end shall be referred to as the

Table 3 Glasses prepared and their properties; compositions are in Glass

Ge

C1 C2

Sb

Se

As

Te

13.3

13.3

44.0

-

29.4

18,2

18.2

38.1

25.4

C3

20.0

20.0

36.0

24.0

C4

23.3

13.3

38.2

C5

25.0

10.0

39.0

C6

26.7

6.7

C7

13.3

23.3

C8

16.7

C9 C10

299

at.%;

M r

GPa

M~

Y

K

G

2.4

18.721

22.75

17.23

8.89

2.55

**

**

**

**

**

2.6

* *

* *

* *

* *

* *

25.5

2.6

**

**

**

**

**

26.0

2.6

* *

* *

* *

* *

* *

40.0

26.7

2.6

*

*

*

*

*

38.0

25.4

2.5

*

*

*

*

*

16.7

40.0

26.7

2.5

*

*

*

*

*

20.0

10.0

42.0

28.0

2.5

*

*

*

*

*

23.3

3.3

44.0

29.3

2.5

*

*

*

*

*

CI 1

6.7

26.7

40.0

26.7

2.4

*

*

*

*

*

C12

10.0

20.0

42.0

28.0

2.4

*

*

*

*

*

C13

16.7

6.7

46.0

30.7

2.4

18.695

21.16

15.88

8.29

0.278

C14

3.3

3.3

56.0

37.4

2.1

19.703

15.08

12.82

5,78

0.304

C15

6.7

6.7

52.0

34.6

2.2

19.285

17.13

13.66

6.63

0.291

C16

13.3

3.3

50.1

33.4

2.3

19.226

17.36

13.46

6.75

0.285

C17

10.0

10.0

48.0

32.0

2.3

19.167

18.53

15.92

7.09

0.306

C18

6.7

16.7

46.0

-

30.7

2.3

19.167

21.94

16.93

8.55

0.283

C19

33.3

3.3

37.4

-

24.9

2.7

**

**

**

**

**

C20

30.0

10.0

36.0

-

24.0

2.7

* *

* *

* *

* *

* *

C21

26.6

16.7

34.0

-

22.6

2.7

**

**

**

**

**

C22

16.7

26.6

34.0

-

22.6

2.6

* *

* *

* *

* *

* *

C23

30.0

0.0

42.0

-

28.0

2.6

* *

* *

* *

* *

* *

C24

20.0

0.0

48.0

-

32.0

2.4

18.721

17.95

13.79

6.99

0.283

C25

10.0

0.0

54.0

-

36.0

2.2

19.266

15.79

12.78

6.10

0.294

C26

0.0

0.0

60.0

-

40.0

2.0

19.953

14.15

12.74

5.38

0.315

C27

10.0

20.0

36.0

-

24.0

2.5

**

**

**

**

**

C28

3.3

23.2

44.0

-

29.3

2.3

* *

* *

* *

* *

* *

33.4

2.2

* *

* *

* *

* *

* *

36.0

2.1

* *

* *

* *

* *

* *

30.0

2.5

*

*

*

*

*

34.0

2.3

19.14

17.86

14.17

6.92

0.290

-

-

C29

3.3

13.2

50.0

C30

0.0

10.0

54.0

C31

25.0

0.0

45.0

C32

15.0

0.0

51.0

-

C33

22.0

0.0

46.8

-

C34

0.0

20.0

48.0

C35

0.0

30.0

42.0

C36

0.0

40.0

36.0

• :

* *:

-

-

{r)

in cm3/mol: Y, K, G in

0.280

31.2

2.44

*

*

*

*

*

32.0

2.2

* *

* *

* *

* *

* *

28.0

2.3

* *

* *

* *

* *

* *

24.0

2.4

* *

* *

* *

* *

* *

Glasses in which the presence of crystals was detected using IR microscopy a n d / o r X-ray diffraction. However. a distinct could be observed in a D S C run. Glasses showed the presence of crystals and did not show a distinct Tg in

a DSC

run.

lg

300

A.N. Sreeram et al. / Multicomponent chalcogenide glasses

Se A26

0 --gt--

,o

i O0

-::::::::::::::::::: ~ !..............m~%N~::::!i::i: : : ii:.:::::~;~:::i

20

": :::::

AIT/:: :

• .

,.' .: :. :.:. . .: . :. • ., : nn

: :~,~4'~[-- 80 ""':~.A3

: : ::" :::

\ • "il :i Aiii2ii: ::i

30

• :7

A:9)

;

ira:::::)::::

,~,.1:: i:::~:;i:~::i i ~.":i: ::i :: "::::::: ::~7.::: ::A2:: : •

•

~ ~

40

•

:....

.

:•

~:::\ "AI9

.

:

I0

7O

:::: •

:

.~

:.T•:~::::

~::~.:~: A~: ~ i :: : : ~

. ~ 2 ! ii:i:7:.:` ;, . . . . •~ : :. •

I

Sb o

\A23 :

2(I

.....

(

(

3(I

4(1

~-

60

,o 50

Ge

835e. 1 7 T e B26

0 -----it-- 100

/\

i i Bt~ :

\

- 8O I

~: ::ti ii~: :

%::;.

/1~,8

:: I~13.: :: :

:

•

:.:: •:

;:: :::::I:I~L:

:

. B33

: .

: ~ .....

B31

30

70 • ::i: :i:i:i:i i

4 0 ---W--/

50 / 66Sb.34As 0

b

.;

l

m

: : :: 7 : . . $ , , * . v : • .: • :: : " ~.-.:: :::::

~ • :

BI9

60 t,2" "

B37

f,38 xo

T/,3,, 2o

~ 3o

( 4o

~ so 50 Ge

Fig. 2. (a) Glasses prepared and glass-forming region for system A (Ge-Sb-Se). (b) Glasses prepared and glass-forming region for system B (Gb-66Sb-34As-83Se-17Te). (c) Glasses prepared and glass-forming region for system C (Ge-Sb-60Se.40Te). The glass-forming region is shown shaded in each case.

A.N. Sreeram et al. / Multicomponent chalcogenide glasses

301

60Se.40Te ('26 0 ~

/\

I00

• (~s I ....

\

"'9 ' 20

____~ C34

" : i C17 ":: :: II. :

•

. .Clg 1'28 •

•

C I1

•

Sb

•

( I0

('22 •

(

v C24~--(!t3

C1 •

•

•

::

('lO .

•

•

70 ( '6

?3

( 2IF

•

80

" ('9

('21

(

20 30 Fig. 2 (continued).

show that the molar volume decreases with increasing ( r ) up to ( r ) - 2.4; an increase in ( r ) is indicative of an increase in cross-linking. This general trend can be explained by the fact that the cross-linking units pull the sub-structures in the glasses into proximity closer than if only van der Waals forces were present between the chains. In the chalcogen-rich region, we observe a minimum in the values of molar volume at ( r ) - 2.4 which is discussed below. However, there do appear other effects that modify the molar volume, especially along the stoichiometric tie-line. Between ( r ) - 2.4 and the stoichiometric tie-line, the molar volume increases with increasing cross-linking, and has a maximum in systems A and B at the stoichiometric tie-line rather than at a constant ( r ) = 2.67, as argued by Tanaka [21]. Such a behavior could not be observed for system C because the glass-forming region for system C does not extend beyond the stoichiometric tie-line. An increase in molar volume before the tie-line and a local maximum at the tie-line were also observed by Giridhar et al.

,~33

"

( 'g

(

40 - - ~

5O

:

:

•

~

:i

.

('12 "

30

i

60

•

( 411

50

Ge 50

[17] for the G e - S b - S e system. They interpreted the observed m a x i m u m in molar volume for stoichiometric compositions as apparently due to the larger volume requirement for attaining a completely cross-linked three-dimensional network of GeSe 2 and Sb2Se 3 structural units present in these compositions compared with the Ge-rich or Se-rich glasses of the corresponding family. A constant value of molar volume along a limited portion of the tie-line for the G e - S b - S e system, as observed by Giridhar et al. [17], is not observed throughout the entire tie-line for our systems. Another interesting observation is that the molar volume values decrease more with Ge content than with Sb a n d / o r As content. Intuitively, this makes sense as Ge gives more cross-linking to the structure than does Sb or As. It had been suggested by Phillips [2], D~Shler et al. [33] and Phillips and Thorpe [34] on the basis of topological arguments that covalent bonding in such glasses may be optimized at ( r ) = 2.4, where the number of constraints in a glass equals the number of

302

.4.N. Sreeram et aL / Multicomponent chalcogenide glasses

Se 0 ---'x-" 100

'

20

'"

~//~--

18.0

80

17.8 j

30 ~

/

/

~

7o

18.0 40 ~

..----~ ~ "r-17.6

/

so (~

.

.

x

~

60

_

/

Sb 0

10

20

30

40

50 Ge

(83Se.17Te) 0 - - A - - 100

10 --'-7(

! 8.7

~--

/

20 "-7( Y""

90

~--

80

18.3'

18.0

30

70

18.2

40 "

so

l (66Sb.34As) 0

b

. .17:8 . . . .

i/

i/

(

(

10

20

30

40

\

so 50 Ge

Fig. 3. (a) Iso-Mv curves in glass-forming region of system A. Values are in cm3/mol. (b) Iso-M~ curves in glass-forming region of system B. Values are in cm3/mol. (c) Iso-M~ curves in glass-forming region of system C. Values are in cm3/mol.

303

A.N. Sreeram et aL / Multicomponent chalcogenide glasses

(60Se.40Te)

5O

Sb

0

i/

10

(

(

20 30 Fig. 3 (continued).

degrees of freedom. The experimentally observed minimum in the molar volume values (in the chalcogen-rich region) corresponds to a value of < r ) - 2.4. Thus, the minimum in molar volume occurs when the structure of the glassy system reaches Phillips' 'rigidity percolation threshold'. At cross-linking levels below this rigidity percolation threshold, the structure is 'underconstrained' and becomes 'overconstrained' at 2.4. In the 'overconstrained' region there are so many bonds that must form at specific angles that the structure no longer contracts with an increase in cross-linking but begins to expand. This is, perhaps, a manifestation of 'stearic hindrance'. The molar volume decreases along the stoichiometric tie-line in going from Ge-rich end to the Sb a n d / o r As-rich end because the Sb a n d / o r As-rich compositions are closer to an ideally constrained glass, i.e. closer to
(

40

5O 50

Ge

Compare, for instance, the molar volume values of glasses A26, B26 and C26 which show an increase in molar volume with increasing Te content. This can be attributed to the larger atomic and covalent radii of Te compared with Se and the fact that Te can go into chain structure with Se, but does not form a chain all by itself. This can lead to an increase in the bond free solid angle (BFSA), as defined by Kastner [35] which, in turn, can lead to an increase in the observed molar volume upon Te substitution. The contour maps for v follow e q u a l - ( r ) lines closely in the chalcogen-rich region (fig. 5). A plot of v vs. ( r ) for all the three systems A, B and C (in their respective chalcogen-rich regions) is shown in fig. 6. The data in the chalcogen-rich regions for the three systems fit to straight lines given by v~ = (0.512 + 0.026) - (0.095 + O.Oll), (3) v b = (0.546 _+ 0.028) - (0.108 _+ 0.012)
(4)

vc = (0.469 -4-_0.042) - (0.079 _ 0.018)(r>.

(5)

With the premise that the Poisson's ratio measure-

304

A.N. Sreeram et aL / Multicomponent chalcogenide glasses

Se 0 - - w - - 100

0/L4 __~ .."~16~ 30

_" ~ " " " ~

40 ~

'. i,~ , _

0

10

1~~....._

2

20

7(I

2

~

'

30

x

~

--- 60

40

50

(83Se.17Te) 0 - - ' x - - 100

10 --7(

X--- 90

20

80

30

70

40

so / b ( 66S b.34 As ) ~

\

"21

60

.~.~. - ~ . . . ~ . . . .

/

f l0

/ 20

( 3o

( 40

~ 50 ~,e

so

Fig. 4. (a) Iso-Y curves in glass-forming region of system A. Values are in GPa. (b) Iso-Ycurves in glass-forming region of system B Values are in GPa. (c) Iso-Y curves in glass-forming region of system C. Values are in GPa.

305

A.N. Sreeram et aL / Multicomponent chalcogenide glasses

(60Se.40Te) O -----x-- 100

lO --N

~-- 9o

'.'7--22 70

30

60

40

so Sb 0

I 10

]Ge 20

30

40

50

Fig. 4 (continued).

ments were accurate to +_2.5%, the 'goodness-offit' parameter [31], X~ (reduced chi-square), for system A, for example, was found to be 1.41. Since this corresponds to a probability level of - 12% at 18 degrees of freedom, we conclude that eq. (3) may represent the observed data, although barely. The not-so-good a fit is no surprise, because the Poisson's ratio contours begin to curve away as { r ) approaches the stoichiometric tie-line. It may be shown that the slope of the straight line given by eq. (3) is negative at a confidence level exceeding 99.9%. Support is thus provided for the observation of Mahadevan et al. [18] that Poisson's ratio decreased with increasing Ge content, except that {r) rather than Ge is the determining parameter. The contour maps for Y (and G and K which show similar trends [30]) do not follow the iso-{r) lines: a straight line similar to eq. (3) cannot represent the dependence of Y upon {r). In fact, the reduced chi-square for system A (again in the chalcogen-rich region) from a least-squares straight line is 9.08, far exceeding 2.35 which is the tabu-

lated value [31] for 0.1% probability. There is, however, a general increase in Y, G and K with ~r); clearly more with Sb than with Ge despite the fact that Ge provides more cross-linking than does Sb. In a study of elastic constants in Ge-Se, Ge-As-Se, Ge-Sb-Se, As-Sb-Se, Ge-As-S, PSe-Te and P-Se-T1, Mahadevan and Giridhar [32] noted that, when the sizes of the atoms did not differ very much, the elastic constants over 2.0 < { r ) < 2.40 also remained relatively unchanged. However, significant changes in the elastic constants were observed when the constituent atoms had widely differing sizes. On the other hand. our data (figs. 4(b) and (c)) show that Sb increases the elastic moduli more than does Te (and the case is similar for G and K [30]) despite the fact that Sb and Te are roughly of the same size. Thus, it may be concluded that the dependence of the elastic moduli on ~r) in the range 2.0-2.40 is not fully explained by the relative sizes of the constituents alone as postulated by Mahadevan and Giridhar [32]. If we consider equations (3)-(5) together, we

306

A.N. Sreeram et al. / Multicomponent chalcogenide glasses

Se 0 --A-- lO0

~0% ~ 0 ..~

0.29

/

\

30

70 0.27

40

".

,oSb (' 0

0

.

2

6

~

'

60

\ l Ge,o

(

(

¢

(

10

20

30

4(I

50

(83Se. 17Te) 0 "-"'x-- 100

10 ~

20

.....

k---- 90

80

~jO,30

~'28//

30

70

0.27 40

so [ (66Sb.34As) 0

I 10

20

30

40

Ge 50

Fig. 5. (a) Iso-v curves in glass-forming region of system A. (b) Iso-u curves in glass-forming region of system B. (c) Iso-v curves in glass-forming region of system C.

307

A.N. Sreeram et al. / Multicomponent chalcogenide glasses

(60Se.40Te) 0 --x-- 100

10 --7(

/

'v--- 90

80

..I/0.27"" •

,

70

40_//

60

50 /

t/

(

(

Sb o

10

20

30

-I.0

51)

Fig. 5 (continued).

may recognize that the Poisson's ratio does not change significantly by iso-structural substitution. As an example, the average of the differences of the Poisson's ratio at each {r) between systems C and A is + 0.0045 which yields a 'student-t' value of 1.34. Since this is less than 2.1 (=/0.975,18), w e accept the hypothesis that average of the paired differences is simply zero. However, the same could O. 4 0

=

t

0.36

o.aa ~

I

- -

0

System

C

A

System

B

0

System

A

~ o

0.24

0.20

i 2.0

I

I

I

2.2

2.4

2.6



2.8

Fig. 6. ~ vs. ( r ) for systems A, B and C in their respective chalcogen-rich regions.

not be said for the elastic moduli Y, G and K. In each case, the average of the difference of paired data (system B-system A and system C-system B) at each ( r ) is statistically greater than zero. One may conclude that the moduli of elasticity (Y, G and K ) generally increase upon isostructural substitution in going from system A to B to C. Thorpe [36] and He and Thorpe [37] suggested that, for the mean field case, there should be a sudden increase in the bulk modulus as the system moves through the rigidity percolation threshold at ( r ) = 2.40. In systems where weak bonding may be present, Yun et al. [38] modified He and Thorpe's calculations to suggest that the increase in elastic moduli beyond ( r ) - 2.4 would not be as steep as originally predicted. They showed some increase in the slope of the elastic modulus for transverse waves, and reported almost no change for the longitudinal wave elastic modulus. Cai and Thorpe [39] on the other hand failed to observe any anomalous behavior in the elastic moduli at ( r ) - 2.4. The same authors, however, pointed out that measurements of phonon density of states

A.N. Sreeram et al. / Multicomponent chalcogenide glasses

308 ,

,

t800

r

24

t5.75

~.3,50 >-

/ 12

~

/

/

1t

- - Y - - - 5 2.0

.25

V/S K v/s

I

I

I

2.2

2.4

2.6

9.00 2.8



Fig. 7. Y vs. ~r) and K vs. ( r ) for system A along a pseudobinary path at Sb = 8 at.%.

(which are a measure of 'dynamic' elastic moduli) in the G e - A s - S e system using neutron scattering and MSssbauer techniques do show a gentle change in the slope at { r ) - 2.4. Our results for the bulk moduli and also for the Young's and shear moduli in all the three systems do not show any dramatic behavior at least in the 'static' region of measurements (ultrasonic frequencies and below). Plots of Y and K with respect to ~r) along a pseudo-binary path (at constant 8 at.% Sb) in the G e - S b - S e system are shown in fig. 7. There is perhaps some increase in the slope of the moduli, particularly in K, at { r ) - 2.4, above and beyond the errors of measurement. It is worth mentioning here that, because of the limited range of glass formation, such changes could not be observed by us for the systems B and C. Tatsumisago et al. [40] have suggested that the ambient temperature elastic properties of covalently bonded solids with van der Waals interactions may not be a sensitive test for rigidity percolation concepts, and that a more sensitive test could be to examine properties in the liquid state of such systems. Like the molar volume, our data for Y, G and K show small local maxima near the stoichiometric tie-line. Such a local maximum in K was also observed by Giridhar et al. [25]. This behavior presumably results from the preference of the systems towards a completely cross-linked chemically ordered covalent network (COCN) rather

than to a chance coordination predicted by the random covalent network (RCN) model. The fact that chemical ordering appears to influence the elastic properties of chalcogenide glasses has also been suggested by Tanaka [41]. Finally, we wish to draw attention to the variation of the elastic moduli in relation to that of the molar volume. The contour maps of the Poisson's ratio follow the molar volume quite closely, except in the vicinity of the stoichiometric tie-line where the molar volume has a local maximum; Poisson's ratio, on the other hand, has a minimum. The Y, G and K do show local maxima at the tie-line; however, elsewhere the contour maps are oriented differently than those of the molar volume. The similarities and the dissimilarities of their relationship to molar volume are not fully understood as yet.

5. Conclusions

The elastic properties of G e - S b - S e - A s - T e glasses do not show a sudden rise in their values at ( r ) - 2.4. A slight increase in the slope for K at ( r ) - 2.4 is observed in at least one of the three systems studied. The molar volume does show a local minima in the chalcogen-rich region at ( r ) - 2.4. For each system, the elastic moduli (Y, K and G) generally increase with {r). However, the increase in magnitudes is more with Sb than with Ge. Local maxima in the molar volumes and all the elastic moduli at the stoichiometric tie-line suggest the preference of the systems for a chemically ordered covalent network (COCN) over the chance coordination predicted by the random covalent network model (RCN). 'Iso-structural' compositions exhibit significant changes in the values of molar volumes, Y, K and G, but relatively no change in the values of Poisson's ratio.

The authors gratefully acknowledge Center for Advanced Ceramic Technology, NY, and Galileo Electro-Optics corp., Sturbridge, MA, for providing financial support towards this study.

A.N. Sreeram et al. / Multicomponent chak'ogenide glasses

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