Refractive index and density changes in a phase-separated borosilicate glass

Journal of Non-Crystalline Solids 24 (1977) 77-88 © North-HoUand Publishing Company

REFRACTIVE INDEX AND DENSITY CHANGES IN A PHASE-SEPARATED BOROSILICATE GLASS Joseph H. SIMMONS Inorganic Materials Division, National Bureau of Standards, Washington, DC 20234, USA

Received 1 September 1976 Revised manuscript received 6 January 1977

The refractive index and density of a soda-borosilicate glass are measured at successivestages of phase separation. Two effects are observed which consist of a structural rearrangement of the homogeneous glass reflecting changes in the heat-treatment temperature, followed by a volume increase as phase separation progresses. The structural rearrangement is analyzed by a volume relaxation model originated by O.S. Narayanaswamy, and the observed increase in volume resulting from the phase separation is discussed.

1. Introduction A number of technical glasses either undergo liquid-liquid phase separation in their annealing range or have compositions bordering on miscibility gaps. Some of these find extensive applications in the chemical-ware and window-glass industry, and while their usefulness for normal duty seems not to be greatly affected by the phase transitions, it is likely that special applications, such as long anneals, will dictate heat treatments with a combination of times and temperatures favorable for the development of a large internal structure. In order better to understand the processes involved and to characterize the related changes in physical and chemical properties, an investigation of the results of heat treatments which maximize the phase separation effects in these glasses was undertaken. In previous reports [ 1,2] we considered the mechanism of phase separation and its effects on viscous flow processes in two borosilicate glasses of which one is commonly used for chemical ware. The results are described and analyzed in ref. [1]. We found that extensive phase separation occurs in both glasses near the annealing region and the viscosity undergoes increases 10 000 to 100 000 fold during an isothermal heat treatment. In the analysis of these results, a theory was developed which accounts for the viscosity change in terms of microstructure development in molten glasses. The large increase in viscosity upon phase separation will affect annealing schedules by changing the rate of stress release. For example, one of the glasses 77

78

J.H. Simmons/Refractive index and density in a borosilicate glass

investigated, Type I in Ref. [1], has a complex time and temperature dependence for viscosity in the annealing range. The isothermal viscosity at 600°C is higher than at 560°C for heat-treatment times between 10 and 100 min. This unusual behavior indicates that, for durations shorter than 100 min, isothermal heat treatments at 560°C will release internal stresses at a faster rate than at the higher temperature of 600°C. This happens because the microstructure development and its accompanying viscosity increase occur more slowly at 560 than at 600°C. The lower temperature, 560°C, is therefore a preferable annealing temperature since the stress release is rapid and the microstructure growth is slow. If a long heat treatment is needed, then an increase in temperature to 600 or 620°C after 100 min is recommended. Having characterized the microstructure development and the stress relaxation mechanism, we proceeded to measure the effect of pressure on phase separation, and to measure the loss of chemical durability accompanying the two-phase formation. The potential effect of pressure or stress on the thermodynamic conditions controlling phase separation are reflected in the behavior of the density, refractive index and thermal expansion coefficient and is reported herein. The chemical durability of the glass as measured by the amount of alkali released from the glass when exposed to an aqueous environment is reported elsewhere [3]. Of the two glasses studied in the early part of this work [ 1,2] only Type II, the glass commonly used for chemical ware, is suitable for this study. Type I, the simple sodiumborosilicate glass, has a very low chemical durability following phase separation which can greatly complicate the density measurements since the density liquids are likely to alter its chemical makeup. Therefore, measurements of density, index of refraction and thermal expansion coefficient on the Type II glass only are reported below.

2. Experimental procedure 2.1. Glass samples

The glass chosen (Type II in our previous work [1 ]) is of the Pyrex type and has a composition consisting of SiO2, B203, Na20 and A1202 in the proportions: 81 : 12.6 : 3.9 : 2.4 by weight, as determined by chemical analysis. Its phase transition temperature is 649°C where its viscosity is 1011 p. It separates into a phase which is almost exclusively silica with a volume fraction of 0.55. The second phase, rich in soda and boron trioxide, occupies a volume fraction of 0.45. The samples were in the form of rectangles 0.1 X 0.6 × 1.0 cm for the density and index of refraction tests and rods 1/4 in. by 2 cm long for the thermal expansion coefficient tests.

J.H. Simmons / Refractive index and density in a borosilicate glass

79

2.2. Refractive index measurements The samples were heat treated in a furnace with an inconel core. The samples were dropped into and out of the furnace, thus effecting a rapid temperature change in each case. The reproductibility of the quench was checked by heat treating several samples at the same temperature and comparing the index differences. No discrepancy was found between the readings [4]. A Grauer refractometer was used to measure the index of refraction. The data for isothermal heat treatments between 526 and 620°C are shown in fig. 1. 2.3. Density measurements The samples were heat treated in the same manner as for the index measurement. The density was measured using the sink-float technique by immersing the samples in a thermostatically controlled density liquid. The latter was a mixture of iso-propyl salicylate (38.1%) and s-tetrabromoethane (61.9%) [5]. The liquid mixture was calibrated with two density standards giving the values 2.219 82 at 27.396°C and 2.232 38 at 21.495°C. This yielded the following equation for the

1.4720

o°

o

•

o

o

I

" 526 °C

o

&

x

•

"'~'~" '~x .

o,

o

J

85°c

v 620 °C

,, V

x

565 °C

•

,x mmm °

V

x

147mi •

o

•x

V

e

x • X xOo

x~

o o

%

1.4710

x

i

I

lO

I

i

J

1,000

10.000

100.000

HEAT-TREATMENT TIME (min)

Fig. 1. Dependence of refractive index on heat-treatment time for a variety of temperatures during phase separation.

80

J.H. Simmons / Refractive index and density in a borosilicate glass

unknown density/922 normalized to 22°C. p = [ 2 . 2 3 2 3 8 - 0.002 1 2 8 ( T - 27.396°C)] [1 + 1.5 × 10-S(T - 22°C)],

(1)

where p is in g/cm 3 and T in °C. The temperature was measured with a four-lead Pt resistance thermometer calibrated at NBS with a constant current of 1.0 ma through the thermometer. The measurement was effected by slowly raising the temperature of the bath (0.0035°C/rain) and recording the temperature at which the sample changed from a floating to a sinking condition. The sample was restrained 6 cm below the surface of the density liquid in order to avoid evaporative cooling effects. The coefficient of thermal expansion of the glass was measured at 5 X I0-6/°C which added a small change in the density measurement as the temperature of the liquid was varied. While the correction was included in the calculation, owing to the small changes in liquid temperature effected during the measurements this step was not necessary for this glass, since the maximum density change due to expansion of the glass in the density liquid during the measurements was calculated to be 3 × 10 - s g/cm 3. The accuracy of the measurement depends directly upon the density standards which were certified to +0.0005 g/cm 3 by the manufacturer * but not verified by us. The precision of the measurement is approximately -+3 × 10 -6 g/cm 3 or Ap/p = -+1.5 X 10 -6, when the expansion correction is made. Samples were measured and heat treated in succession. Several samples were used for each isothermal study but none were heat-treated at more than one temperature. The resulting isothermal density data are plotted as a function of heattreatment time in figs. 2 and 3. 2. 4. Thermal expansion coefficient measurement

The coefficient of thermal expansion was measured in a modified beam-bending viscometer [6]. The cylindrical samples were placed in an inconel box within a furnace, and the expansion of the glass during heating was measured by recording the position of a long silica rod resting on top of the sample cylinder with the sensing element of a linear deflection transducer attached to the other end. A concentric silica cylinder resting on the box was used to support the outer portion of the transducer. This arrangement allowed a measurement of the difference between the expansion of the sample and an equal length of silica. The furnace was heated at 2°C/rain and the temperature was monitored with a Pt-10% P t - R h thermocouple touching the sample. Temperature gradients within the chamber were less than 5°C. The transducer output was recorded on the y-axis, and the voltage generated by the thermocouple on the x-axis, of a recorder. The glass samples were first heat treated between 565 and 620°C for various * R.P. Cargille Laboratories, Inc., Cedar Grove, NJ 07009, USA.

J.H. Simmons / Refractive index and density in a borosilicate glass

1.4720

/

o

2.22200

81

I 565 °C

2.22100

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u ~oFRACTIVE INDEX

DENSITY~ . , ,.z

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-1.4715

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2.21900

\1.4710 2.21800

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1.000 '

lOO

10.000 '

lOO,OOO

HEAT- TREATMENTTIME (min) Fig. 2. Density and index data at 565°C.

times, and then were tested for measurement of the coefficient of thermal expansion.

3. Analysis 3.1. Pressure effect The volume change resulting from phase separation can be analyzed to yield the change in apparent phase transition temperature due to pressure or stress applied 2.22100

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~

T

•

"

T

620Oc V, E

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"=~ Ct:

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~: -14710

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1

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100

t

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10.000

HEAT-TREATMENTTIME (min) Fig. 3. Density and index data at 620°C.

100,'000

82

J.H. Simmons I Refractive index and density in a borosilicate glass

isothermally to the glass. Using the simple model of regular mixing to describe phase separation [7,8], the effect of pressure applied at constant temperature on the phase transition temperature can be found by differentiating the enthalpy of mixing with respect to pressure. The result is expressed as (aOlae)r = (AV(T)/2ROc/O)[1 - T A a ] ,

(2)

where 0 is the transition temperature, P the pressure, 0c the critical point of the system, AV - Vmix - Vunmix the change in volume per mole at the temperature T of phase separation, and Aa is likewise the change in linear coefficient of thermal expansion due to phase separation. The expansion coefficient in glasses is generally a small number, and, in all cases, TAa < < 1. Therefore, only the first term of eq. (2) needs to be considered. The equations show that if there is expansion during phase separation Vunmi x > Vmix, there will be a reduction in transition temperature resulting from the applied pressure, or positive stress. For simplicity, it will be assumed that 0 ~ 0c at atmospheric pressure. Equation (2) then simplifies to

(3)

(aOlaP)r = A V(T)I2R. 3.2. Coefficient o f thermal expansion

In analyzing the change in coefficient of thermal expansion with various heat treatments, care must be taken to consider the density of the material at the beginning of the test. The test generally begins at room temperature, and therefore the initial state of the glass is a function of the preceding cooling treatment. Since the physical property of interest is the change in volume per unit of matter rather than per unit volume, the coefficient of thermal expansion must be normalized by the density in order to compare materials with different thermal histories. In this context, therefore, we seek the change in density Ap with temperature: A V/M _ A p _ AT

AT

AL 3PLAT

(4) =

The density of each sample was measured prior to the measurement of the linear coefficient of thermal expansion a, and the change in density with temperature is plotted in fig. 4. The data demonstrate no apparent change with degree of phase separation, therefore the normalized thermal expansion coefficient is not significantly altered by phase separation. Since one of the phases is nearly pure silica [9], with an expansion coefficient near 0.5 × I0-6/°C, it is expected that the expansion coefficient of the individual phases will differ measurably. The average value of the bulk sample remained constant during phase separation, indicating that the dependence of the coefficient of thermal expansion on composition is linear along the tie line. This, however, does not imply that there will be no stress development during cooling of the two-

J.H. Simmons / Refractive index and density in a borosilicate glass

83

=..... I

o E

I

o&

~3

I

,,1585°C o o A & A

620°C J

c~ Ii i<32 10

L

L

I

100

1,000

10,000

HEAT-TREATMENTTIME (rain)

Fig. 4. Plot of normalized coefficient of thermal expansion for samples heat treated at 585 and

620°C for the times shown.

phase structure, since there are differences in the individual coefficients of expansion. In fact, stresses are expected and have been observed in phase-separated glasses [10]. The effect that these stresses can have on strength may be considerable and is presently under investigation.

4. Discussion

4.1. Refractive index change The refractive index data at 565,545 and 526°C indicate that two processes are occurring in the samples during the isothermal heat treatments. Initially, it appears that there is a volume relaxation in the still homogeneous glass in the direction of equilibrium at the heat-treatment temperature. This is demonstrated by the increases in refractive index observed for samples heat treated below 585°C. Secondly, there is a decrease in refractive index associated with the phase separation process. These effects are also visible in the isothermal density curves. The refractive index measurements showed no maxima for heat treatments at and above 585°C. This is the published [11] annealing temperature for this glass. Therefore, we assumed that the "as-received" samples had a thermal history and density characteristic of 585°C. Electron micrographs conducted on "as-received" samples showed no detectable phase separation [ 1]. In our previous work with this glass [ 1], we have seen that there is a long time lag before the effect of phase separation is detectable by either a viscosity increase or the appearance of phase separation. The length of this time lag is shown in table 1 as a function of temperature. It is interesting to note that at temperatures below 585°C, the maxima in refractive index occur near the time lag-durations before observation of phase separation. This indicates that most of the change due to volume relaxation occurs before the onset of phase separation. In order to analyze the volume relaxation process separately from the phase separation, we turned to the elegant model for structural relaxation in glasses near

84

J.H. S i m m o n s / R e f r a c t i v e i n d e x and d e n s i t y in a borosilicate glass

Table l Time lag before detection of phase separation by viscosity measurements Time (min)

Temperature (°C)

21 28 36 63 100 158 185

619 600 585 565 545 526 515

the glass transition developed by O.S. Narayanaswamy [12]. In this work, the relaxation process due to a temperature jump is treated as a single non-exponential mechanism with a constant activation energy, in order to evaluate the corresponding change in the state of the glass - the refractive index in this case. The index deviation from equilibrium is expressed as n(t) - n~ N(t) - - , n(o) - n=

(5)

where n ( t ) is the measured index during the isothermal treatment, n ( o ) is measured prior to the heat treatment and n. is the equilibrium value at the temperature of the isothermal treatment. The temperature dependence of the latter was calculated using the measured coefficient of thermal expansion, the Lorentz-Lorenz relationship and the value ofn(o) for each sample which represents the index at 585°C. By proper choice of a dimensionless time parameter ~ the index curves can be superposed since they correspond to a single relaxation time. The activation energy for the relaxation process, E, can be calculated from the appropriate constants in the fit of the relation: In ~ = In t

- E/RT.

(6)

The reduced index change is then plotted as a function of the dimensionless time parameter, n(~)

-

n~

N ( ~ ) = n ( o ) - noo '

(7)

as shown in fig. 5 and should follow a common dependence on ~ independent of temperature. By extrapolating the straight-line dependence to large values of ~, the time dependence for the change in index of refraction caused by the volume relaxation process can be estimated and compensated for in the measured values to yield the index change associated solely with the phase separation. The activation energy calculated by this approach was 84 kcal/mol - precisely

J.H. Simmons / Refractive index and density in a borosilicate glass

1.0

[]

v 526 '~C [] 545 °C 565 *C

.8

.6 y,Y

85

z~

.4

Z

, ~ z ~

.2 -45

In-~ =InI-E/RT

E=84 kcal/mol

-50

Fig. 5. Plot of the normalized refractive index N(~) against the reduced time parameter ~.

the value obtained in our earlier analysis of viscosity measured by the fiber elongation method on the same glass with heat-treatment times less than the minimum phase transition times listed in table 1 (i.e. while the glass is still homogeneous prior to phase separation) [ 1]. This result represents the activation energy for structural relaxation in the homogeneous phase before phase separation is evident. The agreement is interesting since we are comparing two different experiments measuring different physical properties of the glass. The use of two drastically different models to derive these values is not as critical as it appears, since activation energies generally result from normalization of a property with respect to temperature and are somewhat independent of models. The effect of phase separation upon the refractive index of the glass may be calculated by appropriately subtracting the increase in the index due to thermal rearrangements of the homogeneous glass at temperatures below 585°C. This is accomplished by using eq. (7) to depict the index change due to the volume relaxation process resulting solely from the temperature jump, and the following: n(T, t)p.s" = n(T, t)mea s - t/(~),

(8)

where In ~ = In t - E / R T and E = 84 kcal/mol. The result is shown in fig. 6 and exhibits a large decrease in the refractive index as a function of heat-treatment time during phase separation. 4.2. Density change

Refractive index and density data for samples heat treated at 565 and 620°C may be compared using a combination of the Clausius-Mosotti equation and the Lorentz-Lorenz formula as follows [ 14]: pP = A [(n 2 - 1)/(n 2 + 2)],

(9)

J.H. Simmons /Refractive index and density in a borosilicate glass

86

14720

:1 .... -" • _

o • • ~ ×

JD..S~_:~L.~, ~ ~" ~ "~'-.+ ' ~ " ~ -,% ~

5 2 6 °C 545°C 5 6 5 °C 5 8 5 °C 620oc

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hl >

(..)

1.4715

&

I..i n,--J 1.4710 I I0

J I00 HEAT-TREATMENT

I I000

I I0,000

I O 0 000

TIME (rnm)

Fig. 6. Refractiveindex change resulting solely from phase separation.

where p is the density, P the mean polarizability of the material and A is a numerical constant. The comparison shows that the mean polarizability is not detectably temperature or time dependent. Therefore, refractive index data were used in addition to the density data in order to calculate the volume change of the glass during phase separation. The volume change per unit mole during phase separation was obtained from the density measurements as follows: AV = P0 [(l/p0) - (1/pf)],

(10)

where Po and pf are the densities of the mixed and unmixed systems, respectively. The results are shown in fig. 7 where both density and index measurements are combined. The data show that AV is very small at the transition temperature but increases linearly with (Tc-T) as the temperature is lowered. The change in transition temperature is found by combining the results of the density measurements with eqs. (3) and (10). In this material, the change is a decrease in transition temperature, but the effect is small in magnitude: O0/OP)Tis --7 × 10 -3 K/kbar at 660Oc and - 1 9 X 10 -2 K/bar at 526°C. Measurements of the density change during phase separation in a soda-silica glass by Pye etal. [15] have shown no measurable change, indicating a linear dependence of molar volume on composition. Phase separation in this sample would therefore be unaffected by the application of pressure. It appears [16] that the density change in soda-lime-silica glasses will be large and negative, also corresponding to a decrease in phase transition temperature with applied pressure. However, it is also possible for the density to increase during

J.H. Simmons / Refractive index and density in a borosilicate glass

87

~ s e

-.0005

,

,

,

,

I

500

,

,

,

t

I

,

,

L

600

,

~

Tc

9

,

~

,

a

700

TEMPERATURE (°C)

Fig. 7. Change in molar volume during the phase separation plotted as a function of temperature. The circles represent the density measurements and the crosses the refractive index measurements.

a phase transition. This will cause an increase in transition temperature with applied pressure, leading to a number of interesting problems in glass-product manufacturing. Density data reported by Vashal et al. [17] on SiO2-A12Oa-CaO-MgO glasses doped with TiO2 indicate the possible occurrence of this effect. Calculations based on eqs. (3) and (10) show that a 5% difference in density between the mixed and unmixed states will lead to a change in transition temperature of 10°C/kbar of pressure.

5. References [1] J.H. Simmons, S.A. Mills and A. Napolitano, J. Am. Ceram. Soc. 57 (1974) 109. [2] R. Mahoney, G.R. Srinivasan, P.B. Macedo, A. Napolitano and J.H. Simmons, Phys. Chem. Glasses 15 (1974) 24. [3] B.F. Howell, J.H. Simmons and W. Hailer, Bull. Am. Ceram. Soc. 54 (1975) 707. [4] S. Spinner and A. Napolitano, J. Res. NBS 70A (1966) 147; P.B. Macedo and A. Napolitano, J. Res. NBS 71A (1967) 231. [5] Test C 729, Annual Book of ASTM Standards (ASTM, Philadelphia, 1973). [6] A. Napolitano, J.H. Simmons, D.H. Blackburn and R.E. Chidester, J. Res. NBS 78A (1974) 323. [7] J.B. Thompson, Jr., Res. Geochem. 2 (1967) 340. [8] P.B. Macedo and J.H. Simmons, J. Res. NBS 78A (1974) 53; W. Hailer, D.H. Blackburn and J.H. Simmons, J. Am. Ceram. Soc. 57 (1974) 120. [9] E.A. Porai-Koshits, V.L Averjanov, V.V. Golubkov and A.P. Titov, Mater. Res. Bull 7 (1972) 1323. [10] F. Schill, Epitoanyag 24 (1972) 453. [11] J.R. Hutchins, III and R.V. Harrington, Encycl. Chem. Technol. 10 (1966) 533. [12] O.S. Narayanaswamy, J. Am. Ceram. Soc. 54 (1971) 491. [13] J.H. Simmons, A. Napolitano and P.B. Macedo, J. Chem. Phys. 53 (1970) 1165. [14] M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959) pp. 86-87.

88

J.H. Simmons / Refractive index and density in a borosilicate glass

[15] L.D. Pye, L. Ploetz and L. Manfredo, J. Non-Crystalline Solids 14 (1974) 310. [16] I.S. Patel and S.M. Ohlberg, J. Appl. Phys. 43 (1972) 1636. [17] B.G. Varshal, N.M. Veisfeld, G.B. Knyazher and L.M. Yusim, in Phase Separation Phenomena in Glasses, ed. E.A. Porai-Koshits (Structure of Glass, Vol. 8; Consultants Bureau, New York, 1973).