Elastic properties of fluoride glasses under pressure and temperature

Journal of Non-CrystaliineSolids 56 (1983) 105-110 North-HollandPublishingCompany

105

ELASTIC PROPERTIES OF FLUORIDE GLASSES UNDER PRESSURE AND TEMPERATURE RIKUO OTA and NAOHIRO SOGA Department of Industrial Chemistry Kyoto University Kyoto 606 JAPAN

Sound wave v e l o c i t i e s and e l a s t i c moduli were determined f o r glasses in the system ZrF4-BaF2-LaF3"NaF-AIF3. by by i n t e r ferometry and the cube resonance technique under h y d r o s t a t i c pressures up to 200MPa and temperatures ranging from 180 to 40OK. Sound v e l o c i t i e s and e l a s t i c moduli increased l i n e a r l y with pressure and decreased with temperature. The GrUneisen parameter was p o s i t i v e . The e l a s t i c n o r m a l i t y implied a c l o s e l y packed s t r u c t u r e f o r the ZrF4-based glass. INTRODUCTION Since the discovery ofZrF4-BaF2-based glass by Poulain and Lucas(1978), ZrF4-based f l u o r i d e glass has a t t r a c t e d considerable a t t e n t i o n as a p o t e n t i a l material f o r o p t i c a l f i b e r to be used in the i n f r a - r e d region. Ohsawae t ai(1981) studied the glass s t a b i l i t y and the loss charaOteristics ofsomeglass f i b e r s made of ZrF4-BaF 2LaF3-NaF-AIF 3 system. The e l a s t i c constants and t h e i r v a r i a t i o n under pressure and temperature in such glass are p a r t i c u l a r l y important since the o p t i c a l f i b e r s are supposed to be subjected to changing temperatures and pressures or stresses. Besides, there is theoretical interest in:the chemico-mechanical relationship between the glass structure and the elastic anomaly or normality inferred from the pressure and temperature dependenceof the elastic moduli for ZrF4-based fluoride glass. EXPERIMENTAL For the measurement of sound ' v e l o c i t i e s and t h e i r temperature dependence,the cube resonance method was used.: The procedure f o r t h i s method was described elsewhere by Goto and Soga(1983). A glass cube o f edge length about 5 mm was placed between two BaTi03 transducers and the resonance frequencies o f the glass were detected. By comparing the spectruni of observed resonance frequencies with that of dimensionless resonance frequencies, poisson's ratio a for the specimen was determined. The shear wave velocity vs of a cube of edge length L was calculated from the resonance frequency fn and the dimensionless resonance frequency an; vs = ~fnL/a n,

n : v i b r a t i o n mode

(I).

The l o n g i t u d i n a l wave v e l o c i t y v I was obtained from v s and a by v i : [ 2 ( I - o ) / ( I - 2 o ) ] I / 2 vs Bulk modulus Bs, Shear modulus ~ and Young's modulus Y were computed from and density p ; Bs = p(v~2 _ 4/3 Vs2)

: PVs2 Y = 2~(I + o)

(2). v I , vs (3)

(4) (5).

U l t r a s o n i c i n t e r f e r o m e t r y was used to determine the pressure dependence of the 0022-3093/83/0000-0000/$03.00 01983 North-Holland

R. Ota, N. Soga / Elastic properties of fluoride glasses

106

sound velocities and e l a s t i c moduli. The procedure was the same as reported by Ota and Kunugi(1977). A 20MHz quartz transducer was glued to a specimen of lO mm thickness, and the pulse repetition frequency f i , i = longitudinal l or shear s, was measured in the pressure range from 0 to 200 MPa at 20°C. The sound velocity v i can be calculated from f i and the thickness of specimen L by vi

= 2Lfi,

i = l or s

(6).

Pressure derivatives of sound velocities and e l a s t i c moduli were calculated from the pressure derivatives of fl and fs by eqs.(7)-(lO). d(v/vo)i/dP = -I/Bs + d ( f / f o ) i / d P ,

i = l or s

(7)

dBs/dP = 2pvl2[d(f/fo)I/dP] - (8/3)pVs2[d(f/fo)s/dP] + (l + 3~yT)/3

(8)

d~/dP = 2~[d(f/fo)s/dP ] + (~/3Bs)(l + 3~¥T)

(9)

dY/dP = [dBs/dP + 3(Bs/p)2(dp/dP)]/[(Bs/~) 2 + I / 3 ]

(lO).

Here, y is the thermodynamic Gr~neisen parameter given by Yth = 3~BsV/Cp

(ll)

where ~ is the linear thermal expansivity, V mean atomic volume, and Cp the specific heat at constant pressure. The glass density was measured at room temperature by the Archimede's method using kerosene as the l i q u i d medium. The thermal expansion of the glass was measured by dilatometry. The specific heat of the glass was measured at 27°C using the adiabatic calorimeter which Hirao, Soga and Kunugi (1979) described previously. RESULTS AND DISCUSSION The fluoride glasses obtained for the present study contained ZrF4, BaF2 and LaF3 as major components and NaF and AIF3 as minor additives. Table 1 summarizes the sound velocities and the e l a s t i c moduli observed for the glasses. Table I. Sound v e l o c i t i e s , elastic moduli, poisson's r a t i o and Debye temperatures of glasses in the system ZrF4-BaF2-LaF3-NaF-AIF3 measured at zero pressure at 20°C. _Debye temperature OD was computed from mean sound v e l o c i t y vm, mean atomic weight M and density by 0D = (h/k)(3pN/4~M) I/3 Vm, and vm = [3/~vi-3 + 2Vs-3]I/3. GLASS COMPOSITION SOUND VELOCITY BULK SHEARYOUNG'SPOISSON'SDEBYE GLASS MOL% LONG. SHEAR MODULUSMODULUSMODULUS RATIO TEMP. Bs ~ Y a 0D vs NO. ZrF4 BaF2 LaF3 NaF AIF3 _ Vl _ GPa GPa GPa K kms-l kms-l 51.36 22.83 59.65 0.3064 316 l 58.3 18.4 14.6 5.8 2.9 4.317 2.281 2

55.0 27.6

9.4 4.0 4.0

4.204

2.231

49.45

2 2 . 3 0 58.16

0.3040

307

3

54.9 22.5 14.7 3.9 3.9

4.168

2.211

47.57

21.44

0.3041

305

4

50.0 24.0 18.0 4.0 4.0

4.212

2.238

48.64

2 2 . 0 2 5 7 . 4 1 0.3033

309

55.92

The bulk moduli of the fluoride glasses are shown in the bulk modulus -mean atomic volume diagram (Bs - V diagram) in Fig. I. Fig. l includes a l k a l i halide and alkaline earth fluoride crystals, the moduli of which were taken from Anderson and Naf~ (1965). The fluoride glasses were found to l i e between the a l k a l i halide and the alkaline earth fluorides on the NaF-BaF2 line. For an ionic crystal with a Born power law repulsive potential, the bulk modulus should be proportional to the ionic charge product ZlZ2, and to -4/3th power of V, Bs = const x ZlZ2 • V-4/3 (12).

R. Ota, N. Soga / Elastic properties o/fluoride glasses

lO0 9O 80 70 60

L i h O. p = e s s ~ r e ~

Figure 1

I GLASS~ aF2 NaF~I

Bulk modulus Bs - mean atomic volumeVdiagram. The pressure arrow and the temperature arrow indicate, respectively, the direction of Bs change associated witha change of V by compression and thermal expansion.

1342

~ 40 tempe rature •

.J

Li Cl

30 o

O~

KF

Li Br O0 p r e s s u r e NaCI ~ _ NaBr % ~ KC1

20

kiI

Nal

I ~ 0 RbCl KBr ~ " < _ CsBr t e m p e r a t u r e K I ~ RbB Cs]I

15 lO

107

3

, 4

i o , , n m 5 6 7 8 910

i

,

15

20

Rbl ex , 30 40

MEAN ATOMIC VOLUME/cm3mol-I Based on eq.(12), however, one can suspect that the observed elastic moduli of ZrF4-based glasses are smaller than expected for a large value of ZlZ2= 3.3 compared with CaF2, for example, which has ZlZ2 = 2 and about the same V as that of the fluoride glass. Table 2 compares the glass molar volume Vg with the additive molar volume Vc computed from the molar volume Vci of i-th crystalline componentby Vc = ~ x i V c i (13). where xi is the molar fraction of i - th component. Vg is very close to Vc. I t can be seen that each component (such as ZrF4, BaF2, etc.) in the glass has substantially the same packing state as for its crystalline state. Table 2. Comparison of the molar volume Vq of glass with the additive molar volume Vc calculated from the molar volume of crystalline ZrF4, BaF2, LaF3, NaF and AIF3. COMPOUND

MOL. MEANAT. NOL. MEANAT. MOL. MEANAT. DENSITY WEIGHT WEIGHT VOLUNE VOLUME VOLUME VOLUME DIFFERENCE p M ~ Vg ~q Vc Vc (Vg-Vc)/V ( gcm-3 gmol-l gmol-l cm3mol-l cm3mol-l cm3mol-l cm3mol-l %

GLASS l GLASS 2

4.387 4.481

149.68 36.45 155.51 38.06

34.12 34.70

8.308 8.494

33.65 34.51

l. 4 0.6

GLASS 3 GLASS 4

4 . 3 8 4 i48.35 36.85 4 . 3 9 8 144.45 37.04

33.84 32.84

8.406 8.422

33.35 32.66

1.5 0.6

ZrF4

4.54

1 6 7 . 2 2 33.44

36.8

7.36

BaF2 LaF3

4.828 4.49

175.36 58.45 195.92 48.98

36.32 43.6

NaF

2.79

41.99 21.00

15.1

7.53

AIF3

2.882

83.98 21.00

29.14

7.285

12.11 I0.9

R. Ota, N. Soga /Elastic properties of fluoride glasses

108

The temperature dependence of the sound v e l o c i t i e s was measured f o r Glass 1 over the range from -93 ° to 120°C. The temperature dependence of the sound v e l o c i t i e s is i l l u s t r a t e d in Fig. 2. The sound v e l o c i t i e s and the e l a s t i c moduli were found to decrease l i n e a r l y with temperature, see temperature d e r i v a t i v e s shown in Table 3 4.5

|

4.4 4.3 >

•

•

|

•

Figure 2

longitudinal

vI

4.2 shear •

00

• •

|

!

I

200

250

300

2.4~ 2.3

vs •

00

!

350

Temperature dependence of sound wave v e l o c i t i e s of Glass l measured at zero pressure.

2.2 I

400

2.1

TEMPERATURE /K

Table 3. Temperature d e r i v a t i v e s of sound wave v e l o c i t i e s , e l a s t i c moduli and thermodynamic constants ~s and Yth of Glass 1 measured at zero pressure. dvl/dTkms-IK-I

dvs/dT kms-IK-I

dBs/dT GPaK- I

d~/dT GPaK-I

dY/dT GPaK-I

6s

Yth

-7.98xi0 -4

_4.22xi0 -4

_2.00xlO -2

-9.25xi0 -3

-2.41xi0 "2

7

O~

According to Anderson (1965), the temperature change of the bulk modulus is given as functions of s p e c i f i c heat Cp and atomic volume V, (3Bs/aT)p = -y6sCp/V

(14).

Here 6s is a constant to be computed by 6s : -(3~Bs)-I(3Bs/3T)p (15). For Glass I , 6s was calculated to be 7 using the thermal expansion ~ : 1.8 x 10-5 at 20°C. A value of O.665J~gK was observed f o r the s p e c i f i c heat of Glass 1 at 27°C and tile GrUneisen constant Yth was 0.95. as has another physical meaning related to the Bs - V diagram. When volume changes with temperature, the bulk modulus changes also, the slope of which in the Bs - V diagram (alnBs/61nV) p is shown to be -a s as (~InBs/BlnV)p = (31nBs/~T)p/(31nV/3T)p = (3~Bs)-l(~Bs/~T)p

(16).

The temperature arrow shown in Fig. 1 shows a slope -6 s = - 7 f o r the f l u o r i d e glass. The pressure dependence of sound v e l o c i t i e s t i o n frequency f~ f o r longitudinal or shear Pressure dependence of the sound v e l o c i t i e s d e r i v a t i v e s of sound v e l o c i t i e s and e l a s t i c 4. The acoustic GrUneisen parameter Ya was

was measured on Glass I . The r e p e t i wave increased l i n e a r l y with pressure. is shown in Fig. 3. The pressure moduli were p o s i t i v e as shown in Table estimated using the r e l a t i o n s ;

YLT = [Yl(Vs/Vl) 3 + 2Ys]/[(Vs/Vl) 3 + 2]

(17).

YHT = (YI + 2¥s)/3

(18).

R. Ota, N. Soga / Elastic properties or fluoride glasses

Yi : Bs(l + 3aYthT)'l[~(f/fo)i/~P] ,

109

i : 1 or s

(19).

From the gamma modes, Y1 = 2.0 and 0.85 was found to have a positive value between YLT = 0.93 and ~HT =Y~'~ , Ya 4.35]

,

4.34

longitudinal

I

4.331

~- 4.32o~

• ••

• • • •

2.30 2.29

shear vs •O

•

Figure 3

0

• • •

4.311

~

vI

0 • 0•

0••

Q I•

••

•

••

••

•

Pressure dependence of sound wave v e l o c i t i e s of Glass 1 measured at 20°C.

O

2.28 I

I

I

50

I00

150

2.27 2OO

PRESSURE /MPa Table 4. Pressure derivatives of pulse r e p e t i t i o n frequencies, sound wave v e l o c i t i e s , e l a s t i c moduli and acoustic GrUneisen parameters of Glass 1 measured at 20°C.

dvsldP ~ - ~ ! J l d P

dYldP YLT YHT~

GPa-I

d(f/fo)s/dP GPa-I

dvl/dP kms-IGPa-I

kms'IGpall!

4.523xi0 -2

2,305xi0 -2

1.672xi0-I

3.777xl0-21 6.3 L .2 L 3.7

I

When volume changes with pressure, the bulk modulus changes also. the Bs - V diagram (81nBs/81nV)T is shown to be -(~Bs/~P)T;

I I l 0] .931L .01

The slope in

(~InBs/~lnV)T = (~InBs/~P)T/(~InV/~P)T = -(aBs/aP)T (20). The pressure arrow in Fig. 1 shows a slope -(~Bs/~P) T = -6.3 for the f l u o r i d e glass. The slope of the arrow due to compression, -6.3 as given by eq. (20), agrees f a i r l y well with the slope of the arrow due to thermal expansion, -7 as given by eq. (16). For comparison, temperature and pressure arrows are shown f o r KCl in Fig. I . The pressure arrow -(BBs/~P)T = -4.78 measured by Demarest et a l . (1977) coincides with the temperature arrow -as = -4.7 calculated from the data by Durand (1936). For tile f l u o r i d e glass and KCl c r y s t a l , a change in volume has the same e f f e c t on the bulk modulus, whether tile volume change is produced by pressure or temperature. Obviously, the volume e f f e c t on modulus ~dth pressure or temperature v a r i a t i o n d i f f e r s from that with compositional v a r i a t i o n , which is shown as a slope of -1.3 by eq, (12) or - I observed f o r a l k a l i halides and a l k a l i n e earth f l u o r i d e s in the Bs - V diagram in Fig. I. The v a r i a t i o n of e l a s t i c property of a glass under pressure and temperature can be related to the structure of the glass. Suppose the volume of a glass V is a function of the nearest bond distance r and s t r u c t u r a l f a c t o r C as given by Ota and Anderson (1977), V = ~ICr3 (21). From t h i s , bulk modulus B and i t s pressure d e r i v a t i v e ( B/ P)T can be derived as I/B : -(~InC/~P)T + I/B c

(22).

R. Ota, N. Soga / Elastic properties of fluoride glasses

110

(~B/BP) T B-2 : (321nC/Bp2)T + (BBc/~P)T Bc-2 (23). Here, Bc is the bulk modulus obtained fora constant C. (@Bc/3P)T is always positive as can be derived from eq.(12). The variation of C under pressure w i l l be affected by bond angle s h i f t or twisting of polyhedra and is restricted by the free space available for the polyhedra. Therefore, any glass that has a closely packed structure should have small (321nC/@p2)T,hence positive (3B/3P)T value according to eq. (23). While open structure can be'implied from the elastic anomaly for some fourfold coordinated glasses (Krause and Kurkjian 1968) and B203-Na20 glasses (Ota et ai..1978), a closely packed structure can be implied from the elastic normality for Se and As2Se3 glasses (Soga et a1.1973), As-Se glasses (Ota et ai.1973), Ge - Se glasses (Ota et ai.1978) and GeS2 glass (Ota and Kunugi, 1977). The normal e l a s t i c i t y inferred from positive dBs/dP and negative dBs/dT observed in Glass l implies a closely packed structure for ZrF4- based glass, which is possibly associated with the high coordination number of the fluoride cations in the glass and is supported by the volumetric consideration given above. REFERENCES [I] [2] [3]

[4] [5] [6] [7] [8] [9] [lO] [Ill [12]

[13] [14] [15]

Anderson, O.L. and Naf~, J.E., The bulk modulus-volume relationship for oxide compounds and related geophysical problems, J.Geophys.Res.,79(1965) 3951-3963. Anderson,O.L.,A derivation of Wachtman's equation for the temperature dependence of elastic moduli of oxide compounds, Phys.Rev., 144(1966) 553-557. Demarest, Jr, H.H., Ota, R. and Anderson, O.L. , Prediction of high pressure phase transition by elastic constant data, in : High- Pressure Research , Application in Geophysics, 281-301, Manghnani, M.H. and Akimoto, S.,(eds.) , (Academic Press, New York, 1977). Durand, M.A., The temperature variation of the elastic moduli of NaCl, KCI and MgO. Phys.Review, 50(1936) 449-55. Goto, T. and Soga, N., Measurement of elastic moduli of small specimen by means of rectangular parallelepiped resonance method, Yogyo-Kyokai-Shi, 91 (1983) 25-31. Hirao, K., Soga, N. and Kunugi, M., Low-temperature heat capacity and structure of alkali s i l i c a t e glasses. J.Am.Ceram.Soc., 62(1979) 570-573. Krause, J.T. and Kurkjian, C.R., Vibrational anomalies in inorganic glass formers, J.Am.Ceram.Soc., 51(1968) 226-227. Ohsawa, K., Shibata, T., Nakamura, K. and Yoshida, S.,Fluorozirconate glasses for infrared transmitting optical fibers. 7th European Conference on Optical Communication, Denmark, l . l - l ~ 4 , (1981). Ota, R. and Anderson, O.L., Variation in the mechanical properties of glass induced by high-pressure change, J.Non-Cryst.Solids, 24(1977) 235-252. Ota, R. and Kunugi, M., Temperature and pressure dependence of the elastic property of GeS2 glass. J.Phys.Chem.Solids, 38(1977) 9-13. Ota, R., Soga, N. and Kunugi, M., Elastic properties of As-Se glasses, YogyoKyokai-Shi, 81(1973) 156-161. Ota, R., Yamanaka, H. and Kunugi, M., Pressure dependence of elastic properties for B203-Na20 glasses and equations of state for glass, in:High-Pressure Science and Technology, 6th AIRAPT Conference vol. 2 , 209-215 Timmerhaus, K.D. and Barger, M.S. (eds.), (Plenum Press, New York, 1978). Ota, R., Yamate, T., Soga, N. and Kunugi, M., Elastic properties of Ge-Se glass under pressure J.Non-Cryst.Solids, 29(1978} 67-76. Poulain,M. et Lucas,J.,Une nouvelle classe de mat~riaux : Les verres fluor~s au tetrafluorure de zirconium, Verres et Refract. 32(1978) 505-513. Soga, N., Kunugi, M. and Ota, R., Elastic properties of.Se and As2Se3 glasses under pressure and temperature, J.Phys. Chem.Solids, 34(1973) 2143-2148.