Photoelastic effects in some fluoride glasses based on the ZrF4BaF2 system

Journal of Non-Crystalline Solids 112 (1989) 341-346 North-Holland, Amsterdam

341

P H O T O E L A S T I C EFFECTS IN S O M E F L U O R I D E G L A S S E S B A S E D O N T H E ZrF4-BaF 2 S Y S T E M Kazumasa MATUSITA, Hiroshi KATO and Takayuki KOMATSU

Department of Chemistry, Nagaoka University of Technology, 1603-1 Kamitomiokaeho, Nagaoka, Niigata-ken 940-21, Japan M a m o r u Y O S H I M O T O a n d N a o h i r o SOGA Department of Industrial Chemistry, Faculty of Engineering, Kyoto University, Yoshidahonmachi, Sakyoku, Kyoto 606, Japan

The stress-optical coefficients and elastic moduli of some fluoride glasses based on ZrF4-BaF2 were measured, and the photoelasticity mechanisms were analyzed based on the equations expressing the relation among the photoelastic constants, the elastic moduli and the refractive index of glasses. The stress-optical coefficients and the strain-optical coefficients of fluoride glasses were found to be extraordinarily small, being almost zero. It was concluded that the small photoelasticities of fluoride glasses were due to the ionic bond in fluoride glasses.

1. Introduction

different refractive index, n a a n d n 3. T h e stresso p t i c a l coefficient, C, is d e f i n e d as

W h e n i s o t r o p i c a m o r p h o u s solids are e x p o s e d to m e c h a n i c a l stresses, they show b i r e f r i n g e n c e called photoelasticity. If a glass is subjected to a u n i a x i a l tensile stress, o, along the O x a axis a n d the light p r o p a g a t e s along the O x 2 axis as shown in fig. 1, the light separates i n t o two p o l a r i z e d c o m p o n e n t s ; one vibrates in the O x a d i r e c t i o n a n d the o t h e r in the O x 3 d i r e c t i o n a n d each has a

A n = n I -- n 3 = C o ,

(1)

In the p r e v i o u s r e p o r t s [1-3], the following e q u a t i o n was d e r i v e d expressing the relation a m o n g the stress-optical coefficient, C, shear m o d u l u s , G, a n d refractive index, n, as C = ( n 3 / 4 G )( p l z - - p a l ) = ( n Z / 2 G )( P - q ), (2)

~'

x2 ~---Z 0

i,,I- . . . . . . . t+, I

/

Fig. 1. Propagation of light in uniaxially stretched glass. 0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

where P12 a n d P l l are the P~Sckels s t r a i n - o p t i c a l coefficients a n d p a n d q are the N e u m a n n s t r a i n - o p t i c a l coefficients [4]. T h e s t r a i n - o p t i c a l p h e n o m e n o n can be d i v i d e d into two p a r t s : one is the lattice effect a n d the o t h e r is the a t o m i c effect [1-3,5]. T h e lattice effect is caused b y the c h a n g e of a t o m i c p o s i t i o n s p r o d u c e d b y the stress. This effect is a function only of the refractive i n d e x of u n d e f o r m e d glass a n d c o n t r i b u t e s to the n e g a t i v e p h o t o e l a s t i c effect. T h e a t o m i c effect is c a u s e d b y the d e f o r m a t i o n of electron c l o u d s a n d c o n t r i b u t e s to the positive p h o t o e l a s t i c effect. M o s t o x i d e glasses show positive p h o t o e l a s t i c effects [1-3,5], i n d i c a t i n g that the a t o m i c effect is m o r e significant.

K. Matusita et al. / Photoelastic effects in some fluoride glasses

342

2. Experimental procedure

In the previous reports [1-3], we analyzed the photoelastic mechanisms of borate, silicate and phosphate glasses in which the chemical compositions were changed systematically. It was found that the bridging oxygen with a highly covalent bond raises the atomic effect and the non-bridging oxygen with an ionic bond lowers the atomic effect [2,3]. Recently, much attention has been directed to the fluoride glasses as an infrared optical device [6]. Various properties, crystallization behavior and glass structure have been studied [6-11]. The photoelastic effect is also one of the important properties of optical devices, although few studies on photoelastic effects of fluoride glasses have been reported. In the present study, the stress-optical coefficients and elastic moduli of some fluoride glasses based on the ZrFn-BaF 2 system were measured and the photoelastic mechanism of fluoride glasses are analyzed and discussed by comparison with oxide glasses.

Glass compositions used in this study are shown in table 1. The raw materials used were reagent grade anhydrous fluorides, namely ZrF 4, BaF2, G d F 3, LaF 3 and PbF 2. Batches producing 10 g or 20 g of glass on addition of about 5 g N H 4 F - H F were placed in platinum crucibles and melted in an electrical furnace at 850 ° C for 20 min under N 2 atmosphere. The melt was cast into a brass mold to be formed into rectangles (about 4 x 4 x 10 mm3), and placed in the annealing furnace. After being kept at 270 ° C for 1 h, the specimens were cooled slowly in the furnace to room temperature. The stress-optical coefficient was measured under uniaxial compressive stress, using the apparatus made of aluminum as shown in fig. 2. The rectangle specimens, about 3 x 3 x 6 mm 3, were formed precisely by cutting and polishing each plane. Especially the two opposite planes through which the light passes were polished carefully to

Table 1 Compositions and properties of glasses studied Glass

Compositions (mol%)

No.

ZrF 4

BaF2

GdF 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

65 65 62 62 59 59 65 65 62 62 59 59 65 65 65 65 70 60

32 30 35 33 38 36 28 25 31 28 34 31 27 22 17 12 27 27

3 5 3 5 3 5

n LaF3

PbF2

7 10 7 10 7 10 3 3 3 3 3 3

5 10 15 20 10

1.522 1.522 1.522 1.523 1.523 1.523 1.523 1.523 1.524 1.524 1.525 1.525 1.535 1.546 1.557 1.568 1.521 1.545

Density

E

K

G

(g/cm3)

(GPa)

(GPa)

(GPa)

4.653 4.637 4.665 4.659 4.706 4.720 4.570 4.558 4.610 4.622 5.662 4.644 4.793 4.836 4.970 5.096 4.521 4.914

60.06 62.08 59.08 60.20 56.57 58.83 60.38 62.02 58.94 61.71 57.84 61.60 58.35 61.63 62.87 61.99 63.02 56.68

47.99 46.88 47.34 47.11 48.25 50.33 48.53 46.94 46.23 47.73 46.86 46.67 47.96 51.36 53.38 55.84 47.85 45.44

23.26 24.26 22.86 23.39 21.68 22.54 23.36 24.23 22.89 24.02 22.34 24.06 22.49 23.70 24.11 23.57 24.61 21.93

n: Refractive index; E: Young's modulus; K: Bulk modulus; G: Shear modulus; p: Poisson's ratio.

0.291 0.279 0.292 0.287 0.305 0.305 0.293 0.280 0.288 0.285 0.294 0.280 0.297 0.300 0.304 0.315 0.281 0.292

K. Matusita et aL / Photoelastic effects in some fluoride glasses

343

Table 2 Photoelastic properties of glasses Glass No.

C xl012 ( P a - 1)

(P - q)

(P12 - Pn)

L

A

1

0.11

0.0022

0.0029

- 0.1292

0.1321

2

0.20

0.0042

0.0055

- 0,1292

0.1347

3

- 0.03

- 0.0006

- 0.0008

- 0.1292

0.1284

4

0.04

0.0008

0.0011

- 0,1294

0.1305

5

- 0.20

- 0.0037

- 0.0049

- 0.1294

0.1245

6

- 0.11

- 0.0021

- 0.0028

- 0,1294

0.1266

7

0.11

0.0022

0.0029

= 0.1294

0.1324

8

0.15

0.0031

0.0041

- 0.1294

0.1336 0.1315

9

0.07

0.0014

0.0018

- 0.1297

10

0.10

0.0021

0.0027

- 0.1297

0.1324

11

- 0.03

- 0.0006

- 0.0008

- 0.1300

0.1292

12

0.02

0.0004

0.0005

- 0.1300

0.1305

13

0.10

0.0019

0.0025

- 0.1325

0.1350

14

0.08

0.0016

0.0021

- 0.1353

0.1374

15

0.06

0.0012

0.0015

- 0.1381

0.1396

16

0.04

0.0008

0.0010

- 0.1408

0.1418

17

0.30

0.0064

0.0084

- 0.1289

0.1373

18

- 0.10

- 0.0018

- 0.0024

- 0.1351

0.1327

SiO 2

Present study Heymas and Allis "~ P r i m a k and Post [16] Vedam et al. [15]

3.53 3.58 3.53 3.56

C:

Stress-optical coefficient; atomic effect. Cited in ref. [15].

(p - q):

Neumann strain-optical coefficient;

(P12 - Pll):

P~3ckels

strain-optical coefficient; L: Lattice

effect; A: a)

Po lar ized microscope

~

mpensator

Recorder

j L o a d cett

Sample

Str tin rnel ~r

" ' - Screw

F i g . 2.

Loading a p p a r a t u s Schematic description of apparatus for measuring the stress-optical coefficient o f a small sample.

optical flatness. The loading apparatus was placed on the stage of a polarized microscope. The applied load was detected by the load cell and transformer. Monochromatic light of wavelength 589.3 nm (NaD-line) was used for the measurement. The retardation produced in the stressed specimen under various loads was measured by a Bereck compensator adapted to the polarization microscope and the stress-optical coefficient was calculated by using a least-squares method. Some of the measured values were confirmed by the Senarmon method [12,13]. The stress-optical coefficient of SiO 2 glass was also measured in order to ascertain the precision of this apparatus. The elastic moduli of the glasses were measured by a rectangular parallelepiped resonance method. The principle and procedures of the measurement were described in other reports [14]. The cubic

344

K. Matusita et al. / Photoelastic effects in some fluoride glasses

4. Discussion

4.1. Analysis of photoelastic constants

A I

£'

2

0

I

I

I

I

I

10

20

30

40

50

5tress

(Pax

60

10 -5 )

Fig. 3. The relation between birefringence, a n ( = n3 - n 1), of 65ZrF4-32BaF2•3GdF3 glass and applied stress. The accuracy of An is within _+0.01X10- 7 .

specimens, 3 × 3 x 3 m m 3, were formed precisely by polishing, and used for measurement. The error in length was within + 20/~m. The refractive index of glass was measured with an ordinary Abbe refractometer, and the density was measured by Archimedes method with kerosene as an immersing liquid.

3. Results The refractive index, n, the density, d, and the elastic moduli are shown in table 1 together with the glass compositions. It was found that the birefringence, A n ( = n 3 - n l ) , of SiO 2 glass increased linearly with applied stress, and the stress-optical coefficient was determined to be 3.53 × 10-12 Pa-1, agreeing with the reported values [15,16] as shown in table 2. Therefore, it was ascertained that the method in the present study gives the stress-optical coefficient of glass correctly. Figure 3 shows the variation of the birefringence, An, with the applied stress for 65ZrF 4 • 32BaF 2 • 3GdF 3 glass, and the stress-optical coefficient was found to be 0.11 X 10 -12 Pa -1, being much smaller than SiO 2 glass. The stress-optical coefficients of fluoride glasses measured in the present study are shown in table 2. It is seen that the stress-optical coefficients of all fluoride glasses are very small, being almost zero.

The most remarkable feature of the photoelastic behavior of the fluoride glasses is that the values of the stress-optical coefficients are extraordinarily small compared with those of oxide glasses. As is seen from eq. (2), the stress-optical coefficient is a function of elastic modulus, refractive index and the strain-optical coefficient factor, ( p - q) or ( p 12 - P ~1)- The values of ( p - q) and (Pu-Pu) calculated from eq. (2) are shown in table 2. The values of elastic moduli and refractive indices of fluoride glasses shown in table 1 are almost the same as those of oxide glasses. However, the strain-optical coefficient factors, ( p - q), are obviously very small, compared with those of oxide glasses. This means that the fluoride glasses show isotropic optical properties even when the glasses are subjected to anisotropic mechanical deformation. By comparing the values of the elastic modulus and stress-optical coefficient of fluoride glasses shown in tables 1 and 2, it is found that any proportional distinct relations expected from eq. (2) cannot be found. It is already reported [1-3] that no distinct relations were found between stress-optical coefficient and elastic modulus in oxide glasses such as borate, silicate and phosphate glasses. Therefore, the factor ( p - q) is essential in determining the photoelastic properties of glasses.

4.2. Contribution of lattice effect and atomic effect As is cited already, the strain-optical effect is caused by two effects: one is the lattice effect and the other is the atomic effect [1-5]. The factor (P12 - P u ) is expressed as [5] PI2 --Pu

41r(n 2 + 2)2 ~ N i ( o l ~ _ a~2) 9n4 i 2 ( n 2 - 1)2

(3)

5n 4

ti

where N~ is the concentration of t h e / - i o n and a u

K. Matusita et a L / Photoelastic effects in some fluoride glasses 0.3

Na20- SiO2 0.2

zx

a, ~ a B-__a.___.______c].~ a Na20 B203

0.1

ZrF 4. BaF2, GdF3 0.0 0.1

zx

0.2 10

I

I

I

20

30

40

Modifier Content(mol%)

Fig. 4. Comparisons of atomic effect, A, and lattice effect, L, among fluoride, silicate and borate glasses as functions of network modifier content. The accuracies of A and L are within + 0.001.

pi

and ot12 are the elements of the nonlinear polarizability. The first and second terms on the right-hand side of eq. (3) represent the atomic effect (designated as A) and the lattice effect (designated as L), respectively [1-3]. Since the lattice effect is a function of the refractive index only and the factor (P12 - P H ) was determined experimentally, the atomic effect can be obtained. The values of A and L thus obtained are shown in table 2. It was found that as the ionic character of the chemical bond increases, the atomic effect decreases, resulting in a lower photoelasticity [1-3]. The ionicity of a chemical bond can be calculated from electronegativity by the method of H a n n y and Smith [19]. The ionicities of Si-O, B - O and N a - O bonds are calculated to be 39.0, 31.6 and 61.5% respectively and those of Z r - F and B a - F are 75.1 and 84.4%. It is seen that the ionic character in fluorides is much higher than that of oxides. Figure 4 shows the comparisons of atomic effect, A, and lattice effect, L, of fluoride, silicate [2] and borate [1] glasses plotted against the content of network former. In fluoride glasses, Z r F 4 was regarded as network former [17,18]. It is clearly seen that the atomic effect of fluoride glasses is smaller than that of oxide glasses while the lattice effects of all glasses are almost the same. In highly covalent glasses such as SiO 2 glass, electrons are tightly bound to the directional covalent bonds. When stress is applied to the glass, the bond angles are forced to change and accordingly the electron clouds are distorted. The response of

345

these electrons to the alternating electrical field of light vibrating in the direction parallel to the stress would be much different from that in the direction perpendicular to the stress, giving rise to a strong atomic effect [1-3]. On the other hand, the electrons in the ionic bonds are less tightly bound to the bonds than those in covalent bonds. Therefore, the electrons in the ionic bonds could respond similarly to the electrical fields of lights vibrating in the directions parallel and perpendicular to the stress, compared with those in covalent bonds. Thus, the fluoride glasses in which the chemical bonds are highly ionic show little photoelastic behavior.

5. Summary The apparatus for measuring the stress-optical coefficients of small-size specimens were made. The stress-optical coefficients of ternary and four-component fluoride glasses based on Z r F 4BaF 2 were measured. The elastic moduli and refractive index were also measured. It was found that the stress-optical coefficients of fluoride glasses were extraordinarily small, being almost zero, compared with those of oxide glasses. The photoelastic mechanisms were analyzed by dividing into two effects: the atomic and the lattice effect. It was concluded that the highly ionic nature of chemical bonds in fluoride glasses gives rise to the very small photoelasticity. The present work was supported by the fund of Mitsubishi Cable Industries, Ltd. The authors wish to express their sincere thanks to Dr. Toshio Suzuki of the University of Tokyo for manufacturing the apparatus of stress-induced birefringence.

References

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346 [5] [6] [7] [8] [9] [10] [11] [12]

K. Matusita et al. / Photoelastic effects in some fluoride glasses

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[13] T. Kishii, in: Mechanical Properties of Ceramics (Ceram. Soc. Japan, Tokyo, 1979) p. 99. [14] T. Goto and N. Soga, Yogyo-Kyokai-Shi 91 (1983) 34. [15] K. Vedam, E.D.D. Schmidt and R. Roy, J. Am. Ceram. Soc. 49 (1966) 531. [16] W. Primak and D. Post, J. Appl. Phys. 30 (1959) 779. [17] C.M. Baldwin and J.D. Mackenzie, J. Am. Ceram. Soc. 62 (1979) 537. [18] C.M. Baldwin, R.M. Almeida and J.D. Mackenzie, J. Non-Cryst. Solids 43 (1981) 309. [19] C.F. Bell and K.A.K. Lott, Modem Approach to Inorganic Chemistry, 3rd ed. (Butterworth, London, 1972) Ch. 3.