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The effects of thermal treatment below the glass transition temperature on the refractive index of optical glass
Journal of Non-Crystalline Solids 102 (1988) 255-258 North-Holland, Amsterdam
255
THE EFFECTS OF THERMAL TREATMENT BELOW THE GLASS TRANSITION TEMPERATURE ON THE REFRACTIVE INDEX OF OPTICAL GLASS
W.W. JOCHS, H.J. H O F F M A N N and N.M. N E U R O T H Schott Glaswerke, 6500 Mainz, FRG
It is well known that the refractive index of glass depends on the annealing process starting at temperatures above the glass transition temperature Tg. However, the refractive index can also be changed by heat treatment far below Tg. These effects of heat treatment are important since they can occur during the finishing process of optical glasses, e.g., cementing, polishing and coating. We have investigated the refractive index of optical glasses before and after heat treatment at temperatures 100 K or more below Tg, followed by fast cooling to room temperature. We observed changes of the refractive index as large as 2 x 10 4 depending on the type of glass. An overview will be given on the behaviour of different glass types.
1. Introduction
The mutual distance of the ions in a glass and thus also the physical properties - depend on the annealing process, i.e., the thermal history of the glass in the temperature range around the glass transition temperature Tg. In this region the viscosity is increasing with decreasing temperature to values above 1012 Pa s and the mobility of the ions is strongly reduced. There are two principal procedures of annealing: (a) constant temperature soaking, (b) constant cooling rate. In (a) the glass is maintained at a constant temperature around Tg for a long period of time, so that the glass structure approaches a certain state. The lower the soaking temperature, the longer is the corresponding time constant for stabilisation. In (b) the glass temperature is maintained for some time at the transition temperature Tg or slightly higher. Subsequently the glass is cooled at a constant rate so that its structure is frozen in at a certain temperature, which is dependent on the cooling rate through the transition region [1-4]. 0022-3093/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Method (b) is preferred in production. The refractive index difference An of two samples cooled at different rates v 1 and v2, respectively, is An = n ( v 2 ) -- n ( v l ) = m l o g ( v 2 / v , ) .
(1)
Faster cooling causes a smaller refractive index. The value of m corresponds to the difference of refractive indices when the annealing velocity v2 is 10 times larger than vl. m is negative. Its absolute value is in the range of 3.3 x 10 -4 to 23 x 10 -4 for most of our optical oxide glasses. Relation (1) can be used when the optical glass is cooled to obtain the proper n-value. The refractive index can also be changed by thermal treatment at temperatures far below Tg. The order of magnitude of this effect can be important for applications of optical glasses. Heat Table 1 Possible temperatures during finishing processes of optical glasses Process
Part of the working piece
Temperature ( o C)
Cementing Polishing Coating
total surface total
100... 150 200 50... 350
256
W. W. Jochs et al. / Effects of thermal treatment below Tg
~4 o o
onneoIing rote
5OO
.
0,1
[K/h]
10
-'°~-~.
300
~' o
-20
200.
<=
- 30
100
1000
~.....
ho~O,o e
~
~
.
~t, 400*(
¢,
-40
IOO, -50
o-
o
lb
2'0
3b
4'0 sb time
6'0 7o
80
[mini
Fig. 1. Decrease of the furnace temperature after holding at different temperatures.
treatments occur during the finishing processes of optical glasses (table 1). In these cases the cooling is fast. Therefore we investigated the influence of heat treatment below Tg on the refractive index of several optical glasses in order to obtain an estimate of how much the refractive index can be changed by this heat treatment.
2. Experimental procedure All starting glass samples were fine annealed (typically v _< 1 K / h ) and prisms were made of a size of approximately 20 x 20 X 30 m m 3. The samples were put into a furnace and heated at a temperature of 100 K or more below Tg. The temperature was normally maintained for one hour. The electrical heating was then switched off, and the door of the furnace was opened. The temperature decreased at the beginning with velocities between 900 to 400 K / h depending on the holding temperature (fig. 1). In addition we used for fig. 2 data for slower well defined annealing rates. The refractive index was measured at 20 ° C at a wavelength of 587.6 nm by the method of minimum beam deflection. If the variation of the refractive index was smaller than 1 x 10 -5, two test samples with a size of 10 X 10 x 40 m m 3 were made. One of these was heat treated, and the change of its optical path-length was measured in a double slit interferometer [5] relative to the untreated sample.
Fig. 2. Decrease of refractive index An of BK7 glass after treatment at different temperatures below the glass transition temperature Tg = 5 5 9 ° C for one hour and different cooling rates. The starting samples were cooled at 0.5 ° C / h .
Table 2 Decrease of the refractive index due to heat treatment at 100 K below the glass transition temperature Tg and fast annealing Glass type
Main components of the chemical composition a)
An (10-6)
F K 1...5 F K 51, 52 PK 2 PK 50 PSK 3 BK BaLK 3 K ZK BaK 4 SK KF BaLF 4 SSK 52 LaKN 16 LLF 1 BaF LF 2 F 2 F N 11 BaSF LaF LaSFN 9 SF SFL TiF 2 . . . N 5 TiF 6 TiSF 1 TiK 1 KzF 2 KzFS LgSK 2
Si B R F P E A1 F Si B R P A1 R Si B Ba Si B R Si R Si R Si R Zn Si Ba Zn Si B E Si Pb R Si Ba Zn Si Ba B B La Si Pb R Si Ba Si Pb R Si Pb Si Ti Si Pb E Si B La Ba Si Ba La Ti Si Pb Si Ti Ba Si Ti R(F) P Ti R Si Ti K Si B A1 R Si B Sb B Pb A1 As B AI F
51-56 16, 18 43 24 51 41-48 72 43-71 18-40 52 4-20 39-58 48 18 22 61 14-22 43 36 64 1-9 18-29 54 6-39 121-134 135-201 96 230 55 46 13-16 10
a) Only the cations of oxides are given. R means alkali ions, E means alkaline earth ions
W. W. Jochs et al. / Effects of thermal treatment below Ts
3. Results
3.1. Influence of the cooling rate and the holding temperature on the refractive index Samples of BK 7 glass which had been fine annealed (0.5 K / h ) were treated at different temperatures below Tg for one hour and then cooled at different rates. Fig. 2 shows the measured decrease An of the refractive index as a function of the cooling rate. In this case A n is proportional to the logarithm of the cooling rate. With decreasing holding temperature An becomes smaller. However, the treatment of B K 7 at as low as 2 0 0 ° C still causes a remarkable change of the refractive index. Fig. 3 shows the change of the refractive index of several glass types after treatment at different temperatures below Tg. The time of holding at each temperature is one hour. The order of
I ". -..'---....
I
~<'-% -..FKmo
\i"-.~
\
.. +Kt+,
,o + 0l 1 <
"'~-..~.
|
~
TiKlo
B~7 • ," +=4.
K7,',
/
-100 0
, 200
, 100
, 300
, 400
harding temperature
, 500
o c <
-150-
\
-200 +
b)
~ " ~ SFL56 • " t ~ SFL 6 o SFN64Zx
\ \
\ • TiF 1 •
-250
o
t6o
26o holding
300 temperature
46o
3.2. Influence of chemical composition We have listed (table 2) the change of the refractive index for a selection of different glass types which have been heat treated at a temperature 100 K below Tg for one hour. Most of the glass types have a medium effect in the range of An = 20 x 10 - 6 tO 60 x 10 -6. Rather small effects can be seen for lead-silicate, lead-barium-silicate, alkaline earth-alumo-boro-silicate, phosphate and fluoro-phosphate glasses. Alkali-silicate glasses show medium effects. In our investigation the largest effects occurred for titanium-oxide containing glasses: titanium-alkali-silicate glasses and titanium-alkali-boro-silicate glasses. In several lead containing glasses the lead was replaced by titanium. By this variation of the composition the change of the refractive index due to the heat treatment increased by more than a factor of two. Glasses with higher alkali content ( > 15%) show an effect even at low holding temperatures (100 and 200 ° C).
4. D i s c u s s i o n
~100-
\', \
magnitude of A n and its dependence on the holding temperature is sensitive to the glass composition. There are types of optical glasses for which A n is already negligible at 200 K below Tg, whereas other types show an effect even at a holding temperature 400 K below Tg.
600
[°C ]
.ll
~o
257
~6o
0oo
[°C ]
Fig. 3. Decrease of the refractive index after heat treatment at different temperatures below the glass transition temperature for one hour and fast cooling.
Our investigations show that the refractive index of optical glasses can be changed by rapid annealing even at temperatures far below Tg. The size of this change depends on the m a x i m u m temperature during the cycle and on the cooling rate. This effect has not been paid much attention until now. However, small possible changes of the refractive index An due to fast thermal cycling below Tg have to be taken into account for optical components, for which the refractive index has to be maintained precisely. Thus, in order to minimize An, one has to cool the glass at about the same rate as during its l~revious annealing. This can be important for glasses with a large content of titania, which show in general a large decrease
258
W. W. Jochs et al. / Effects of thermal treatment below Tg
of the refractive index due to the heating cycles below Tg with fast cooling rates. On the other hand, there are some glasses, e.g., flint glasses with large lead content, for which the refractive index is nearly unchanged by thermal cycling sufficiently below Tg. The refractive index is known to decrease with the cooling rate if the cooling starts at temperatures above Tg. The variations of n in this case can be understood by the variations of the nearest neighbor configurations of the glass ions with the cooling rate. With decreasing temperature the glass structure has to relax into configurations with decreasing free energy. During cooling at sufficiently high temperatures T > Tg, the glass can follow a sequence of equilibrium states as long as these states are accessible during the cooling process. With decreasing temperature the corresponding relaxation times increase. Thus, during the cooling process, more and more configurations become inaccessible, since the relaxation times become too long. Bonds between neighboring ions with large binding energy are frozen-in at rather high temperatures, whereas bonds and consequently ions with lower binding energy can be still readjustable, until at lower temperatures even the latter are also frozen-in. The network forming ions are frozen in at rather high temperatures whereas the alkali ions, e.g., can readjust even at lower temperatures far below Tg. The chance for rearrangement during the cooling process depends on the cooling rate. The slower the cooling rate the closer the relaxation to a configuration with low free energy. However, the fraction of bonds which can be readjusted tends to smaller values with decreasing temperature. Besides the refractive index there are other physical quantities which depend on the short range configuration in a glass, e.g., the density. These quantities are expected to depend on the cooling rate with starting temperatures T > Tg in a similar way as An in eq. (1). The effects due to the annealing at temperatures below Tg, which have been reported in the present paper, fit into the same scheme. By heating a glass sample to a temperature T < Tg some bonds between nearest neighbors and thus some ions can rearrange. The longer the time duration
at the maximum or holding temperature T < Tg during the heating cycle, the better the chance to rearrange into a more favorable configuration with less free energy at temperature T. Except for T sufficiently close to Tg, the time interval of one hour used in the present investigation is too short to cause a large variation of the refractive index, if the samples are cooled as slowly as during the prior fine annealing process. Fast cooling from T < Tg, however, causes a significant effect. A small amount of relaxation, which can take place during fine annealing at temperatures T < Tg, is no longer possible, since the cooling rate is too fast. For lower holding temperatures the rearrangement of nearest neighbor configurations becomes less probable during holding at T < Tg, since the relaxation times become too long and an increasing fraction of bonds are frozen in, disregarding the variation caused by the cooling rate. This can clearly be seen by the decrease of An with decreasing holding temperature for a given cooling rate in fig. 2. The refractive index depends on the density of oscillators. Therefore we have also measured the variation of the mass density 0 of some samples due to the thermal cycling below Tg. We observed that the changes of the refractive index are not correlated to the changes of the mass density Ap in a simple way. Indeed one expects that the energy levels of the bonding and antibonding states in a glass are shifted because of the rearrangement of the ions. Consequently, the eigenfrequencies and the oscillator strengths of the UV resonances are modified, too. This explains the fact that changes of the mass density AO alone cannot account for the observed changes of the refractive index.
References [1] A. Winter, J. Am. Ceram. Soc. 27 (1944) 266. [2] N.M. Brandt, J. Am. Ceram. Soc. 34 (1951) 332. [3] P.B. Macedo and A. Napolitano, J. Res. NBS 71 A (1967) 231. [4] T.S. Izumitani, Optical Glass, Tokyo, Japan, Trans. by LLNL, Univ. of California (1984) p. 3-18 to 3-24. [5] F. Reitmayer and E. Schuster, Appl. Opt. 11 (1972) 1107.
255
THE EFFECTS OF THERMAL TREATMENT BELOW THE GLASS TRANSITION TEMPERATURE ON THE REFRACTIVE INDEX OF OPTICAL GLASS
W.W. JOCHS, H.J. H O F F M A N N and N.M. N E U R O T H Schott Glaswerke, 6500 Mainz, FRG
It is well known that the refractive index of glass depends on the annealing process starting at temperatures above the glass transition temperature Tg. However, the refractive index can also be changed by heat treatment far below Tg. These effects of heat treatment are important since they can occur during the finishing process of optical glasses, e.g., cementing, polishing and coating. We have investigated the refractive index of optical glasses before and after heat treatment at temperatures 100 K or more below Tg, followed by fast cooling to room temperature. We observed changes of the refractive index as large as 2 x 10 4 depending on the type of glass. An overview will be given on the behaviour of different glass types.
1. Introduction
The mutual distance of the ions in a glass and thus also the physical properties - depend on the annealing process, i.e., the thermal history of the glass in the temperature range around the glass transition temperature Tg. In this region the viscosity is increasing with decreasing temperature to values above 1012 Pa s and the mobility of the ions is strongly reduced. There are two principal procedures of annealing: (a) constant temperature soaking, (b) constant cooling rate. In (a) the glass is maintained at a constant temperature around Tg for a long period of time, so that the glass structure approaches a certain state. The lower the soaking temperature, the longer is the corresponding time constant for stabilisation. In (b) the glass temperature is maintained for some time at the transition temperature Tg or slightly higher. Subsequently the glass is cooled at a constant rate so that its structure is frozen in at a certain temperature, which is dependent on the cooling rate through the transition region [1-4]. 0022-3093/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Method (b) is preferred in production. The refractive index difference An of two samples cooled at different rates v 1 and v2, respectively, is An = n ( v 2 ) -- n ( v l ) = m l o g ( v 2 / v , ) .
(1)
Faster cooling causes a smaller refractive index. The value of m corresponds to the difference of refractive indices when the annealing velocity v2 is 10 times larger than vl. m is negative. Its absolute value is in the range of 3.3 x 10 -4 to 23 x 10 -4 for most of our optical oxide glasses. Relation (1) can be used when the optical glass is cooled to obtain the proper n-value. The refractive index can also be changed by thermal treatment at temperatures far below Tg. The order of magnitude of this effect can be important for applications of optical glasses. Heat Table 1 Possible temperatures during finishing processes of optical glasses Process
Part of the working piece
Temperature ( o C)
Cementing Polishing Coating
total surface total
100... 150 200 50... 350
256
W. W. Jochs et al. / Effects of thermal treatment below Tg
~4 o o
onneoIing rote
5OO
.
0,1
[K/h]
10
-'°~-~.
300
~' o
-20
200.
<=
- 30
100
1000
~.....
ho~O,o e
~
~
.
~t, 400*(
¢,
-40
IOO, -50
o-
o
lb
2'0
3b
4'0 sb time
6'0 7o
80
[mini
Fig. 1. Decrease of the furnace temperature after holding at different temperatures.
treatments occur during the finishing processes of optical glasses (table 1). In these cases the cooling is fast. Therefore we investigated the influence of heat treatment below Tg on the refractive index of several optical glasses in order to obtain an estimate of how much the refractive index can be changed by this heat treatment.
2. Experimental procedure All starting glass samples were fine annealed (typically v _< 1 K / h ) and prisms were made of a size of approximately 20 x 20 X 30 m m 3. The samples were put into a furnace and heated at a temperature of 100 K or more below Tg. The temperature was normally maintained for one hour. The electrical heating was then switched off, and the door of the furnace was opened. The temperature decreased at the beginning with velocities between 900 to 400 K / h depending on the holding temperature (fig. 1). In addition we used for fig. 2 data for slower well defined annealing rates. The refractive index was measured at 20 ° C at a wavelength of 587.6 nm by the method of minimum beam deflection. If the variation of the refractive index was smaller than 1 x 10 -5, two test samples with a size of 10 X 10 x 40 m m 3 were made. One of these was heat treated, and the change of its optical path-length was measured in a double slit interferometer [5] relative to the untreated sample.
Fig. 2. Decrease of refractive index An of BK7 glass after treatment at different temperatures below the glass transition temperature Tg = 5 5 9 ° C for one hour and different cooling rates. The starting samples were cooled at 0.5 ° C / h .
Table 2 Decrease of the refractive index due to heat treatment at 100 K below the glass transition temperature Tg and fast annealing Glass type
Main components of the chemical composition a)
An (10-6)
F K 1...5 F K 51, 52 PK 2 PK 50 PSK 3 BK BaLK 3 K ZK BaK 4 SK KF BaLF 4 SSK 52 LaKN 16 LLF 1 BaF LF 2 F 2 F N 11 BaSF LaF LaSFN 9 SF SFL TiF 2 . . . N 5 TiF 6 TiSF 1 TiK 1 KzF 2 KzFS LgSK 2
Si B R F P E A1 F Si B R P A1 R Si B Ba Si B R Si R Si R Si R Zn Si Ba Zn Si B E Si Pb R Si Ba Zn Si Ba B B La Si Pb R Si Ba Si Pb R Si Pb Si Ti Si Pb E Si B La Ba Si Ba La Ti Si Pb Si Ti Ba Si Ti R(F) P Ti R Si Ti K Si B A1 R Si B Sb B Pb A1 As B AI F
51-56 16, 18 43 24 51 41-48 72 43-71 18-40 52 4-20 39-58 48 18 22 61 14-22 43 36 64 1-9 18-29 54 6-39 121-134 135-201 96 230 55 46 13-16 10
a) Only the cations of oxides are given. R means alkali ions, E means alkaline earth ions
W. W. Jochs et al. / Effects of thermal treatment below Ts
3. Results
3.1. Influence of the cooling rate and the holding temperature on the refractive index Samples of BK 7 glass which had been fine annealed (0.5 K / h ) were treated at different temperatures below Tg for one hour and then cooled at different rates. Fig. 2 shows the measured decrease An of the refractive index as a function of the cooling rate. In this case A n is proportional to the logarithm of the cooling rate. With decreasing holding temperature An becomes smaller. However, the treatment of B K 7 at as low as 2 0 0 ° C still causes a remarkable change of the refractive index. Fig. 3 shows the change of the refractive index of several glass types after treatment at different temperatures below Tg. The time of holding at each temperature is one hour. The order of
I ". -..'---....
I
~<'-% -..FKmo
\i"-.~
\
.. +Kt+,
,o + 0l 1 <
"'~-..~.
|
~
TiKlo
B~7 • ," +=4.
K7,',
/
-100 0
, 200
, 100
, 300
, 400
harding temperature
, 500
o c <
-150-
\
-200 +
b)
~ " ~ SFL56 • " t ~ SFL 6 o SFN64Zx
\ \
\ • TiF 1 •
-250
o
t6o
26o holding
300 temperature
46o
3.2. Influence of chemical composition We have listed (table 2) the change of the refractive index for a selection of different glass types which have been heat treated at a temperature 100 K below Tg for one hour. Most of the glass types have a medium effect in the range of An = 20 x 10 - 6 tO 60 x 10 -6. Rather small effects can be seen for lead-silicate, lead-barium-silicate, alkaline earth-alumo-boro-silicate, phosphate and fluoro-phosphate glasses. Alkali-silicate glasses show medium effects. In our investigation the largest effects occurred for titanium-oxide containing glasses: titanium-alkali-silicate glasses and titanium-alkali-boro-silicate glasses. In several lead containing glasses the lead was replaced by titanium. By this variation of the composition the change of the refractive index due to the heat treatment increased by more than a factor of two. Glasses with higher alkali content ( > 15%) show an effect even at low holding temperatures (100 and 200 ° C).
4. D i s c u s s i o n
~100-
\', \
magnitude of A n and its dependence on the holding temperature is sensitive to the glass composition. There are types of optical glasses for which A n is already negligible at 200 K below Tg, whereas other types show an effect even at a holding temperature 400 K below Tg.
600
[°C ]
.ll
~o
257
~6o
0oo
[°C ]
Fig. 3. Decrease of the refractive index after heat treatment at different temperatures below the glass transition temperature for one hour and fast cooling.
Our investigations show that the refractive index of optical glasses can be changed by rapid annealing even at temperatures far below Tg. The size of this change depends on the m a x i m u m temperature during the cycle and on the cooling rate. This effect has not been paid much attention until now. However, small possible changes of the refractive index An due to fast thermal cycling below Tg have to be taken into account for optical components, for which the refractive index has to be maintained precisely. Thus, in order to minimize An, one has to cool the glass at about the same rate as during its l~revious annealing. This can be important for glasses with a large content of titania, which show in general a large decrease
258
W. W. Jochs et al. / Effects of thermal treatment below Tg
of the refractive index due to the heating cycles below Tg with fast cooling rates. On the other hand, there are some glasses, e.g., flint glasses with large lead content, for which the refractive index is nearly unchanged by thermal cycling sufficiently below Tg. The refractive index is known to decrease with the cooling rate if the cooling starts at temperatures above Tg. The variations of n in this case can be understood by the variations of the nearest neighbor configurations of the glass ions with the cooling rate. With decreasing temperature the glass structure has to relax into configurations with decreasing free energy. During cooling at sufficiently high temperatures T > Tg, the glass can follow a sequence of equilibrium states as long as these states are accessible during the cooling process. With decreasing temperature the corresponding relaxation times increase. Thus, during the cooling process, more and more configurations become inaccessible, since the relaxation times become too long. Bonds between neighboring ions with large binding energy are frozen-in at rather high temperatures, whereas bonds and consequently ions with lower binding energy can be still readjustable, until at lower temperatures even the latter are also frozen-in. The network forming ions are frozen in at rather high temperatures whereas the alkali ions, e.g., can readjust even at lower temperatures far below Tg. The chance for rearrangement during the cooling process depends on the cooling rate. The slower the cooling rate the closer the relaxation to a configuration with low free energy. However, the fraction of bonds which can be readjusted tends to smaller values with decreasing temperature. Besides the refractive index there are other physical quantities which depend on the short range configuration in a glass, e.g., the density. These quantities are expected to depend on the cooling rate with starting temperatures T > Tg in a similar way as An in eq. (1). The effects due to the annealing at temperatures below Tg, which have been reported in the present paper, fit into the same scheme. By heating a glass sample to a temperature T < Tg some bonds between nearest neighbors and thus some ions can rearrange. The longer the time duration
at the maximum or holding temperature T < Tg during the heating cycle, the better the chance to rearrange into a more favorable configuration with less free energy at temperature T. Except for T sufficiently close to Tg, the time interval of one hour used in the present investigation is too short to cause a large variation of the refractive index, if the samples are cooled as slowly as during the prior fine annealing process. Fast cooling from T < Tg, however, causes a significant effect. A small amount of relaxation, which can take place during fine annealing at temperatures T < Tg, is no longer possible, since the cooling rate is too fast. For lower holding temperatures the rearrangement of nearest neighbor configurations becomes less probable during holding at T < Tg, since the relaxation times become too long and an increasing fraction of bonds are frozen in, disregarding the variation caused by the cooling rate. This can clearly be seen by the decrease of An with decreasing holding temperature for a given cooling rate in fig. 2. The refractive index depends on the density of oscillators. Therefore we have also measured the variation of the mass density 0 of some samples due to the thermal cycling below Tg. We observed that the changes of the refractive index are not correlated to the changes of the mass density Ap in a simple way. Indeed one expects that the energy levels of the bonding and antibonding states in a glass are shifted because of the rearrangement of the ions. Consequently, the eigenfrequencies and the oscillator strengths of the UV resonances are modified, too. This explains the fact that changes of the mass density AO alone cannot account for the observed changes of the refractive index.
References [1] A. Winter, J. Am. Ceram. Soc. 27 (1944) 266. [2] N.M. Brandt, J. Am. Ceram. Soc. 34 (1951) 332. [3] P.B. Macedo and A. Napolitano, J. Res. NBS 71 A (1967) 231. [4] T.S. Izumitani, Optical Glass, Tokyo, Japan, Trans. by LLNL, Univ. of California (1984) p. 3-18 to 3-24. [5] F. Reitmayer and E. Schuster, Appl. Opt. 11 (1972) 1107.