Brillouin scattering in a glassforming BiCl3KCl mixture

Journal of Non-Crystalline Solids 56 (1983) 93-98 North-Holland Publishing Company

93

BRILLOUIN SCATTERING IN A GLASSFORMING BiCI3-KCI MIXTURE. Lena M. Torell Department of Physics, Chalmers University of Technology, S-412 96 G~teborg, Sweden.

The B r i l l o u i n scattering spectra of a glassforming BiCI 3KCl system have been obtained through the transformation temperature from l i q u i d to s o l i d - l i k e behaviour. The spectra revealed both l o n g i t u d i n a l and transverse acoustic phonons. From the observed frequency s h i f t s , the l o n g i t u dinal and the transverse v e l o c i t i e s were determined along with the e l a s t i c constants and the modulii of the glass. INTRODUCTION Recently, preparations of some unusual glasses based on d i f f e r e n t compositions of bismuth chloride and potassium c h l o r i d e have been reported (Angell and Ziegler (1981)). These glasses are transparent in the v i s i b l e and infrared range and are characterized by a high r e f r a c t i v e index, varying from 1.90 to 2.28 depending on composition, and low Abbe numbers, around 13. The glass systems have been suggested as i n t e r e s t i n g optical glasses with possible p r a c t i c a l applications as laser ion host glasses and as optical communication f i b e r s . We report here a high frequency (GHz) B r i l l o u i n scattering study of the l o n g i t u d i nal and transverse sound v e l o c i t y of a 41.25 mol % KCI and 58.75 mol % BiClR mixture through the glass t r a n s i t i o n temperature. The hypersonic v e l o c i t y dat~ have permitted the evaluation of the e l a s t i c constants and the modulii of the glass. In B r i l l o u i n s c a t t e r i n g , t h e spectrum of the l i g h t scattered through an angle 9, when a sample is i l l u m i n a t e d with monochromatic l i g h t (frequency ~o and wavelength ~o),is studied. The p r i n c i p a l components of the scattered l i g h t are the Rayleigh l l n e , R , centered at the incident frequncy ~o and a pair of dopplershifted l i n e s , the B r i l l o u i n l i n e s , L, due to l o n g i t u d i n a l phonons in the m a t e r i a l , see Fig. I . In a glass where both compressional and shear restoring forces are present,the spectrum also contains a weaker doublet, T, which arises from the presence of transverse phonons. The s h i f t s v L and v T are related to the l o n g i t u d i n a l and transverse sound v e l o c i t i e s , v L and VT, by v L = VLkl2~

(I)

v T = VTk/2~

(2)

where k is the wave vector of the phonon given by k = (4~nl~sine/2 0022-3093/83/0000-0000/$03.00© 1983 North-Holland

3)

L.M. Torell / Brillouin scattering

94

L

R

Fig. I. Brillouin scattering spectrum for a 41.25 mol % KCI and 58.75 mol % BiCl 3 system at a temperature of 45°C. The Rayleigh (R), the longitudinal (L) and the transverse (T) peaks are indicated.

I

i

15

J

I0

I

L

I

5 0 5 10 FREOUENCY GHz

I

15

where n is the refractive index of the medium. From the values of the longitudinal and transverse elastic wave velocities,the constants which characterize the glass can be calculated, i.e. the elastic constants, c11 and c44, Young's modulus Y, shear modulus p, bulk modulus B and Poissons ratio ~ by using the relations (Mason (1972)) c11 = PVL2

(4)

c44

(5)

Y: = B= =

PVT2

c44[(3c11 - 4c44)/(C11 - c44) I c44 c11 - 4/3c44 Y/2U - I

(6) (7) (8) (9)

EXPERIMENTAL

I LASER

I

L5 A1

A2 ~ .

^

1 ~

v

I L

, , ~ v ~ 2

0

I I

0 L1 TH

Fig. 2. Schematic diagram of the triple-pass Fabry-Perot spectrometer system. L: lenses, TH: thermostat with scattering c e l l , A: apertures, F.P.: Fabry-Perot interferometer, P.M.T.: cooled photomultiplier tube, STAB: Burleigh stabilization system, RAMP: rampgenerator for piezocrystals, MCA: multichannel analyzer.

L.M. Torell / Brillouin scattering

95

Light scattering spectra were obtained at a scattering angle of 90o and recorded by the Fabry-Perot spectrometer system diagrammed in Fig. 2. The system includes a single-mode argon-ion l a s e r , a thermostat, a t r i p l e - p a s s p i e z o - e l e c t r i c a l l y scanned Fabry-Perot i n t e r f e r o m e t e r , photon-counting techniques and a m u l t i channel analyzer f o r m u l t i p l e d i g i t a l storage of the signal, see Torell (1982, 1983) f o r d e t a i l s . The BiCIR-KCI sample used in t h i s experiment was prepared elsewhere I . The sample is contaXned in a closed c y l i n d r i c a l (diameter ~25 mm) scattering cell made of pyrex and surrounded by p r o t e c t i v e gas since the glass is hygroscopic. RESULTS B r i l l o u i n spectra were obtained in a temperature range of ~50°C above room temperature. The observed range of the l o n g i t u d i n a l phonon frequency s h i f t s was 12.5-11.4 GHz. In some of the spectra,even the very weak transverse mode due to propagating shear waves could be seen, Fig. I . The measured values f o r the l o n g i t u d i n a l frequency s h i f t are p l o t t e d in Fig. 3. The transverse modes were too close to the Rayleigh l i n e to give accurate values of the s h i f t as a function of temperature. Also, the intense central l i n e may seriously a f f e c t the position of the transverse mode by a p u l l i n g e f f e c t . As can be seen from Fig. 3 the longi t u d i n a l frequency s h i f t decreases l i n e a r l y with temperature and, within the experimental accuracy, the temperature c o e f f i c i e n t is the same above and below the glass t r a n s i t i o n temperature at 45oc. This is contrary to the findings in Ca(NO3)2-KNO3, a glassforming mixture which has recently been investigated in this laboratory (Torell and Aronsson (1983)). For the l a t t e r system ,the temperature dependence abruptly changes at the t r a n s i t i o n ; the frequency s h i f t s being more temperature sensitive in the l i q u i d than in the glass. In the present case, however, the apparent absence of a change at the t r a n s i t i o n may be explained by the l i m i t e d temperature range (45-75°C) of the melt a v a i l a b l e f o r measurements. For higher temperatures, the sample c r y s t a l l i z e d and no l i g h t scattering studies were possible therefore.

N

~13 z

Fig. 3. The temperature dependence of the longitudinal frequency s h i f t in a 41.25 mol % KCI and 58.75 mol % BiCI 3 mixture,

12 IL

11

10

I 20

I ~

I t > 60 80 TEMPERATURE ('C)

L.M. Torell / Brillouin scattering

96

Table I. Results from Brillouin scattering experiments on 41.25 mol % KCI and 58.75 mol % BiCl 3 system at a temperature of 45°C. The values were derived from measured longitudinal and transverse frequency shifts.

Longitudinal shift ~L

12.06 GHz

Transverse shift ~T

7.94 GHz -I 2113 ms

Longitudinal velocity vL Transverse velocity vT

1391 ms-I

Elastic constant

c11

16.5xi09 Nm-2

. . . . Young's modulus

c44 Y

7.2xi09 Nm-2 16.0xi09 Nm-2

Bulk modulus

B

Poisson's ratio

~

7.0xlO9 NmL2 0.12

The observed longitudinal and transverse frequency shifts and the corresponding calculated velocities, elastic constants and modulii are listed in Table I for the glass transition temperature. The refractive index used in the calculation was taken from Ziegler and Angell (Ref. 2) by interpolating to the wavelength of 488.0 nm employed in the present study. The density was obtained by interpolation from values given by Addison and Halstead (1966). The estimated overall error of the longitudinal frequency s h i f t is less than ± 1%, while for the lower intensity transverse mode the s h i f t is accurate to ± 10 %. The glass transition temperature was chosen for the calculations, since for this temperature the transverse modewas distinct in the spectrum obtained and the frequency shift could be measured accurately. The corresponding room temperature values are s l i g h t l y larger, therefore, than those presented in Table I. For the temperature dependenceof the frequency s h i f t , see Fig. 3, and from e a r l i e r measured temperature dependence of the elastic constants in a similar system (Torell and Aronsson (1983)),we believe that the difference introduced for the room temperature data in the present case is less than 6 %. The ratio of the transverse to longitudinal velocity, VT/VL, for the present glass is ~O.66,which is higher than the average ratio of 0.59 ± 0.03 found in optical glasses (Heiman et al. (1979)). The result for the c44 value is ~I/4 and the c11 value is less than I/4 the corresponding values for optical glasses The BiCI3-KCI glass is characterized, thus, by small elastic constants which implies ~eak restoring forces compared to optical glasses and with a s l i g h t l y larger ratio between the shear and the compressional restoring force. ACKNOWLEDGMENT The author is indebted to C. A. Angell and D. C. Ziegler, Purdue University, Department of Chemistry, for preparing the sample of the present study. This research was supported by the Swedish Natural Science Research Council.

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REFERENCES I. 2. 3. 4. 5. 6. 7.

C. A. Angell and D. C. Ziegler, Mat. Res. Bull. 16, 279 (1981) D. C. Ziegler and C. A. Angell (manuscript, p r i v ~ e communication) W. P. Mason, in American I n s t i t u t e of Physics Handbook (McGraw-Hill, New York, 1972) Sec. 3 L. M. T o r e l l , J. Chem. Phys. 76, 3467 (1982) L. M. Torell and R. Aronsson,--J. Chem. Phys. (Feb. 1983) C. C. Addison and W. D. Halstead, J. Chem. Soc. (A), 1236 (1966) D. Heiman, D. S. Hamilton and R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979)