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Influence of thermal treatments on the heat capacity of zerodur from 0.4 K to 20 K
Journal of Non-Crystalline Solids 70 (1985) 291-295 North-Holland. Amsterdam
291
Letter to the Editor
INFLUENCE OF THERMAL TREATMENTS ON THE HEAT CAPACITY OF ZERODUR FROM 0.4 K TO 20 K S.J. COLLOCOTT CS1RO Division of Applied Physics, Sydney, Australia 2070 Received 26 June 1984 Revised manuscript received 2 October 1984
Recent papers [1,2] have reported on the thermophysical properties of Zerodur, a glass-ceramic manufactured by Schott, Mainz, Federal Republic of Germany. One of these papers [2] reported the heat capacity Cp of Zerodur in the range 1.8 K to 20 K and showed for 1.8 K ~< T ~< 5.5 K, that Cp(~tjg-lK 1) = 6.1T+ 0.71T 3 + 0.036T 5.
(1)
Measurements of the longitudinal and transverse sound velocities in the same specimen lead to a limiting value for the coefficient of the Debye T3-term of 0.655 ~tJ g-~ K - 4 , which is smaller than the calorimetric value of 0.71 /~J g-] K -4 above. The presence of a T-term, and a TB-term larger than that predicted by the Debye model, are well known features of glasses at low temperatures. The T-term is usually attributed to two-level tunnelling states of unknown origin (for a review see Pohl [3]). It is notable that the coefficient of the T-term for Zerodur is much larger than that for vitreous silica (1.2/~J g-1 K - 2 ) despite the fact that approximately 70% of the material is crystalline. The T-term is of similar magnitude to that found in Cer-Vit (5 /LJ g-~ K -2) by Leadbetter et al. [4]. In this work the heat capacity measurements on Zerodur have been extended down to 0.4 K. New measurements have been made between 0.4 K and 20 K on samples that have had different heat treatments which produce a systematic variation in crystal size and content. The results have been examined to see if any variation in the heat capacity can be correlated with crystal size, crystal content or density. Zerodur is a glass-ceramic made by Schott to have a near-zero expansion coefficient at room temperature. It is produced by the partial devitrification of a Li20-AlzO3-SiO 2 parent glass, giving material that is typically 30% glassy and 70% crystalline (by weight), with the crystals having a high-quartz type of structure [4]. O. Lindig of Schott kindly provided a number of samples for which the heat treatment had been varied during the ceramisation process to produce different crystal sizes and content (see table 1). Precise details of the heat treament process are not available from the maker. (For a detailed 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
292
S.J. Collocott / Influence of thermal treatments on heat capacity
discussion of glass-ceramics and the glass-ceramic process see McMillan [5].) The heat capacity of each sample (mass 20 to 65 g) was measured between 0.4 K and 20 K using an adiabatic-heat-pulse calorimeter. A complete description of the experimental apparatus and procedure has been given by Collocott [6]. Measurements on the 1965 Calorimetry Conference Copper Standard material indicate an overall inaccuracy in the heat capacity measurements of +0.5% above 2 K, rising to + 1% below 1 K. Densities were measured here by Mr J.B. Patterson of the Density Section, CSIRO Division of Applied Physics (National Measurement Laboratory). From 3 K to 20 K the heat capacity per gram is the same within experimental accuracy for all three samples. The results are presented in fig. 1 as a single curve in a plot of C p / T 3 against T. For comparison Cer-Vit [4], v-SiO 2 [7], cristobalite [8] and a-quartz [9] are also shown. All show a heat capacity in excess of that predicted by Debye theory from elastic moduli, with a peak in C p / T 3 near 12 K. The peak in C p / T 3 is a characteristic of oxide glasses, amorphous organic polymers and amorphous Se, As, Ge [10]. A maximum is also seen in C p / T 3 for crystalline solids. It is due to the effects of dispersion, is usually less pronounced, and occurs at higher temperatures than in glasses. The identical behaviour of C p / T 3 for the three Zerodur samples indicates that the contributions to the heat capacity from the glassy/crystalline phases present were unaffected by the heat treatment process. The density of the samples increases by about 1.6% as the degree of crystallinity increases, yet the heat capacity remains constant. Assuming the glassy and crystalline phase differ in density by 15 to 20%, which is the difference between vitreous silica and a-quartz, then a 1.6% density increase is consistent with the increase in crystal content. In the case of pure vitreous silica above 3 K an increase in density is accompanied by a marked decrease in Cp [11,12], due presumably to closer packing of the SiO 4 tetrahedra inhibiting the low lying transverse acoustic modes and any low frequency optic modes. Bohn [13] has examined the behaviour of Li20-A1203-SiO 2 glasses and Table 1 Details of the Zerodur samples. ZerodurN refers to Schott's normal product, whilst ZerodurA and ZerodurB receiveda non-standard heat treatment Melt number: Density (gcm- 3) Averagecrystal size (nm) Content of crystals (%) T-termcoefficient (,ttJ g-lK-2)
ZerodurN 890162 2.52
ZerodurA 890069 2.54
ZerodurB 890069 2.56
50
68
135
70
74
81
6.2
5.4
7.8
S.J. Collocott / Influence of thermal treatments on heat capacity
293
cristobalite
4
'~
I
v-Si02
3
Zerodur
.~
_
Cer-Vit
,,2
/
0
/
0
,
0
1
J
I
4
]
1
t
I
,
1
a
8
t
12
,
I
,
I
16
~
I
,
20
T (K) Fig. 1. C p / T 3 against T for some silica-based materials. Data sources are cristobalite [8], v-SiO: [7], Zerodur (this work), Cer-Vit [4] and a-quartz [9]. The arrow denotes the limiting value for the coefficient of the Debye T3-term for Zerodur.
glass-ceramics between 1.5 K and 6 K. He found that as the tool.% of SiO2 is increased (Li20 and A1203 decreased) the T3-term for both the glass and glass-ceramic increases (typically from T 3 #J g-~ K -~ to 2.8T 3/~J g i K 1 for the glass-ceramics). The coefficient of the T3-term has the following features: its rate of change is much more rapid for the glass-ceramics than for the glasses, and differences in its magnitude are most pronounced in both glasses and glass-ceramics that have more than 75 mol.% SiO/. For the 15 mol.% Li20-16 tool.% A1203-66 tool% SiO2 sample (closest to the Zerodur samples) the coefficient of the T3-term is similar in magnitude in both the glass and glass-ceramic, making this term insensitive to small changes in crystallinity a n d / o r small changes in the mol.% of SiO2. The stability of the coefficient of the T3-term for the Zerodur samples is not surprising as it reflects the similar behaviour of the contributions of the glassy and crystalline phases. Above 1.8 K the data for all three samples were identical within experimental accuracy, and were found to lie on the curve given by eq. (1). Only at temperatures below 1.8 K do differences become apparent (fig. 2). The coefficient of the T-term (values given in table 1) for each sample for T < 1.8 K
294
S.J. Collocott / Influence of thermal treatments on heat capaei(v 18
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I
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I
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T2(K2) Fig. 2. C p / T against T 2 for ZerodurN ( + ), ZerodurA (O) and ZerodurB ([]) in the range 0.4 K to 3.2 K.
were deduced from the intercept of the data on the Cp/T axis in fig. 2. The magnitudes of the coefficients of the T-term are similar to those of the related glass-ceramic Cer-Vit and larger than those for vitreous silica or borosilicate glass (Corning Code 7740) (see table 2). Bohn [13] shows that the coefficient of the T-term varies fin a manner different from the coefficient of the T3-term, namely as the tool.% of SiO 2 decreases (Li20 and A1203 increased), the T-term increases from 2.3T/~J g K -1 to 11.9T/~J g-~ K -1 for the glass-ceramic. The rate of increase of the coefficient of the T-term is very rapid for glass-ceramics with a silica content less than 74 mol.%. The coefficient of the T-term is about three times larger in the glass-ceramic than in the glass for 65 mol.% SiO 2 content. It might be expected then that an increase in crystallinity would result in an increase in the coefficient of the T-term, but this is not obvious for Zerodur (table 1). The cellular model of Baltes [14] for the heat capacity of amorphous solids
S.J. Collocott / Influence of thermal treatments on heat capaci O'
295
Table 2 Values of the coefficients of the T and T3-terms for various materials. Data are from [4] for Cer-Vit. whilst the rest are from [3]
ZerodurN Cer-Vit SiO2 Corning Code 7740 Corning Code 9700
T-term coefficient (/.tJg -1K -2)
T3-term coefficient (/LJg 1K 4)
6.2 5 1.2 - 1 1.5
0.71 0.8 1.8 2.2 3.62
at low temperatures is based on a g r a n u l a r structure of the solid. He shows that the coefficient of the T-term c~ r - 2 where r is the radius of a spherical cell. The g r a n u l a r model allows an upper limit to be put on the m e a n crystal diameter for vitreous materials of - 7 nm, which is a factor of ten smaller than the crystal size in the Z e r o d u r samples. The coefficient of the T-term for the Z e r o d u r samples (table 1) does not scale inversely with the square of crystal size, as the cellular model requires. It is a p p a r e n t that the heat t r e a t m e n t process has affected the T-term below 1.8 K, b u t there is no clear p a t t e r n correlating it with crystal size, crystal c o n t e n t or density. The author thanks O, Lindig of Schott for s u p p l y i n g the samples, C. A n d r i k i d i s for p r e p a r i n g a n d m o u n t i n g the samples, a n d J.B. Patterson for d e t e r m i n i n g the density of the samples. T h a n k s are due also to Drs G.K. White a n d J.G. Collins for helpful discussions.
References [1] R.B. Roberts, R.J. Tainsh and G.K. White, Cryogenics 22 (1982) 566. [2] S.3. Collocott, J. Phys. C 16 (1983) L13. [3] R.O. Pohl, Topics in Current Physics. Amorphous Solids: Low Temperature Properties, ed., W.A. Phillips (Springer-Verlag,Berlin, 1981) p. 27. [4] A.J. Leadbetter, A.P. Jeapes, C.G. Waterfield and K.E. Wycherley, Chem. Phys. Lett. 52 (1977) 469. [5] P.W. McMillan, Glass-Ceramics (Academic Press, London, 1964). [6] S.J. Collocott, Aust. J. Phys. 36 (1983) 573. [7] P. Flubacher, A.J. Leadbetter, J.A. Morrison and B.P. Stoicheff, J. Phys. Chem. Sol. 12 (1959) 53. [8] N. Bilir and W.A. Phillips, Phil. M~g. 32 (1975) 113. [9] E.F. Westrum, IVe Congress Int. du Verre, Paris (1956) 396. [10] W.A. Phillips, J. Non-Crystalline Solids 31 (1978) 267. [11] G.K. White and J.A. Birch, Phys. Chem. Glasses 6 (1965) 85. [12] J.W. Gardner and A.C. Anderson, Phys. Rev. B23 (1981) 474. [13] R.G. Bohn, J. Appl. Phys. 45 (1974) 2133. [14] H.P. Baltes, Solid St. Commun. 13 (1973) 225.
291
Letter to the Editor
INFLUENCE OF THERMAL TREATMENTS ON THE HEAT CAPACITY OF ZERODUR FROM 0.4 K TO 20 K S.J. COLLOCOTT CS1RO Division of Applied Physics, Sydney, Australia 2070 Received 26 June 1984 Revised manuscript received 2 October 1984
Recent papers [1,2] have reported on the thermophysical properties of Zerodur, a glass-ceramic manufactured by Schott, Mainz, Federal Republic of Germany. One of these papers [2] reported the heat capacity Cp of Zerodur in the range 1.8 K to 20 K and showed for 1.8 K ~< T ~< 5.5 K, that Cp(~tjg-lK 1) = 6.1T+ 0.71T 3 + 0.036T 5.
(1)
Measurements of the longitudinal and transverse sound velocities in the same specimen lead to a limiting value for the coefficient of the Debye T3-term of 0.655 ~tJ g-~ K - 4 , which is smaller than the calorimetric value of 0.71 /~J g-] K -4 above. The presence of a T-term, and a TB-term larger than that predicted by the Debye model, are well known features of glasses at low temperatures. The T-term is usually attributed to two-level tunnelling states of unknown origin (for a review see Pohl [3]). It is notable that the coefficient of the T-term for Zerodur is much larger than that for vitreous silica (1.2/~J g-1 K - 2 ) despite the fact that approximately 70% of the material is crystalline. The T-term is of similar magnitude to that found in Cer-Vit (5 /LJ g-~ K -2) by Leadbetter et al. [4]. In this work the heat capacity measurements on Zerodur have been extended down to 0.4 K. New measurements have been made between 0.4 K and 20 K on samples that have had different heat treatments which produce a systematic variation in crystal size and content. The results have been examined to see if any variation in the heat capacity can be correlated with crystal size, crystal content or density. Zerodur is a glass-ceramic made by Schott to have a near-zero expansion coefficient at room temperature. It is produced by the partial devitrification of a Li20-AlzO3-SiO 2 parent glass, giving material that is typically 30% glassy and 70% crystalline (by weight), with the crystals having a high-quartz type of structure [4]. O. Lindig of Schott kindly provided a number of samples for which the heat treatment had been varied during the ceramisation process to produce different crystal sizes and content (see table 1). Precise details of the heat treament process are not available from the maker. (For a detailed 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
292
S.J. Collocott / Influence of thermal treatments on heat capacity
discussion of glass-ceramics and the glass-ceramic process see McMillan [5].) The heat capacity of each sample (mass 20 to 65 g) was measured between 0.4 K and 20 K using an adiabatic-heat-pulse calorimeter. A complete description of the experimental apparatus and procedure has been given by Collocott [6]. Measurements on the 1965 Calorimetry Conference Copper Standard material indicate an overall inaccuracy in the heat capacity measurements of +0.5% above 2 K, rising to + 1% below 1 K. Densities were measured here by Mr J.B. Patterson of the Density Section, CSIRO Division of Applied Physics (National Measurement Laboratory). From 3 K to 20 K the heat capacity per gram is the same within experimental accuracy for all three samples. The results are presented in fig. 1 as a single curve in a plot of C p / T 3 against T. For comparison Cer-Vit [4], v-SiO 2 [7], cristobalite [8] and a-quartz [9] are also shown. All show a heat capacity in excess of that predicted by Debye theory from elastic moduli, with a peak in C p / T 3 near 12 K. The peak in C p / T 3 is a characteristic of oxide glasses, amorphous organic polymers and amorphous Se, As, Ge [10]. A maximum is also seen in C p / T 3 for crystalline solids. It is due to the effects of dispersion, is usually less pronounced, and occurs at higher temperatures than in glasses. The identical behaviour of C p / T 3 for the three Zerodur samples indicates that the contributions to the heat capacity from the glassy/crystalline phases present were unaffected by the heat treatment process. The density of the samples increases by about 1.6% as the degree of crystallinity increases, yet the heat capacity remains constant. Assuming the glassy and crystalline phase differ in density by 15 to 20%, which is the difference between vitreous silica and a-quartz, then a 1.6% density increase is consistent with the increase in crystal content. In the case of pure vitreous silica above 3 K an increase in density is accompanied by a marked decrease in Cp [11,12], due presumably to closer packing of the SiO 4 tetrahedra inhibiting the low lying transverse acoustic modes and any low frequency optic modes. Bohn [13] has examined the behaviour of Li20-A1203-SiO 2 glasses and Table 1 Details of the Zerodur samples. ZerodurN refers to Schott's normal product, whilst ZerodurA and ZerodurB receiveda non-standard heat treatment Melt number: Density (gcm- 3) Averagecrystal size (nm) Content of crystals (%) T-termcoefficient (,ttJ g-lK-2)
ZerodurN 890162 2.52
ZerodurA 890069 2.54
ZerodurB 890069 2.56
50
68
135
70
74
81
6.2
5.4
7.8
S.J. Collocott / Influence of thermal treatments on heat capacity
293
cristobalite
4
'~
I
v-Si02
3
Zerodur
.~
_
Cer-Vit
,,2
/
0
/
0
,
0
1
J
I
4
]
1
t
I
,
1
a
8
t
12
,
I
,
I
16
~
I
,
20
T (K) Fig. 1. C p / T 3 against T for some silica-based materials. Data sources are cristobalite [8], v-SiO: [7], Zerodur (this work), Cer-Vit [4] and a-quartz [9]. The arrow denotes the limiting value for the coefficient of the Debye T3-term for Zerodur.
glass-ceramics between 1.5 K and 6 K. He found that as the tool.% of SiO2 is increased (Li20 and A1203 decreased) the T3-term for both the glass and glass-ceramic increases (typically from T 3 #J g-~ K -~ to 2.8T 3/~J g i K 1 for the glass-ceramics). The coefficient of the T3-term has the following features: its rate of change is much more rapid for the glass-ceramics than for the glasses, and differences in its magnitude are most pronounced in both glasses and glass-ceramics that have more than 75 mol.% SiO/. For the 15 mol.% Li20-16 tool.% A1203-66 tool% SiO2 sample (closest to the Zerodur samples) the coefficient of the T3-term is similar in magnitude in both the glass and glass-ceramic, making this term insensitive to small changes in crystallinity a n d / o r small changes in the mol.% of SiO2. The stability of the coefficient of the T3-term for the Zerodur samples is not surprising as it reflects the similar behaviour of the contributions of the glassy and crystalline phases. Above 1.8 K the data for all three samples were identical within experimental accuracy, and were found to lie on the curve given by eq. (1). Only at temperatures below 1.8 K do differences become apparent (fig. 2). The coefficient of the T-term (values given in table 1) for each sample for T < 1.8 K
294
S.J. Collocott / Influence of thermal treatments on heat capaei(v 18
!
I
!
I
IG
rl
d~
+
o 14
~e
12
v~ "-a v
10 Q.
o
o
oo
o
8
°
-tt-" ~ 0 0 G
o~ 0
4 0
I
2
,
I
,
4
l
(5
J
I
B
,
10
T2(K2) Fig. 2. C p / T against T 2 for ZerodurN ( + ), ZerodurA (O) and ZerodurB ([]) in the range 0.4 K to 3.2 K.
were deduced from the intercept of the data on the Cp/T axis in fig. 2. The magnitudes of the coefficients of the T-term are similar to those of the related glass-ceramic Cer-Vit and larger than those for vitreous silica or borosilicate glass (Corning Code 7740) (see table 2). Bohn [13] shows that the coefficient of the T-term varies fin a manner different from the coefficient of the T3-term, namely as the tool.% of SiO 2 decreases (Li20 and A1203 increased), the T-term increases from 2.3T/~J g K -1 to 11.9T/~J g-~ K -1 for the glass-ceramic. The rate of increase of the coefficient of the T-term is very rapid for glass-ceramics with a silica content less than 74 mol.%. The coefficient of the T-term is about three times larger in the glass-ceramic than in the glass for 65 mol.% SiO 2 content. It might be expected then that an increase in crystallinity would result in an increase in the coefficient of the T-term, but this is not obvious for Zerodur (table 1). The cellular model of Baltes [14] for the heat capacity of amorphous solids
S.J. Collocott / Influence of thermal treatments on heat capaci O'
295
Table 2 Values of the coefficients of the T and T3-terms for various materials. Data are from [4] for Cer-Vit. whilst the rest are from [3]
ZerodurN Cer-Vit SiO2 Corning Code 7740 Corning Code 9700
T-term coefficient (/.tJg -1K -2)
T3-term coefficient (/LJg 1K 4)
6.2 5 1.2 - 1 1.5
0.71 0.8 1.8 2.2 3.62
at low temperatures is based on a g r a n u l a r structure of the solid. He shows that the coefficient of the T-term c~ r - 2 where r is the radius of a spherical cell. The g r a n u l a r model allows an upper limit to be put on the m e a n crystal diameter for vitreous materials of - 7 nm, which is a factor of ten smaller than the crystal size in the Z e r o d u r samples. The coefficient of the T-term for the Z e r o d u r samples (table 1) does not scale inversely with the square of crystal size, as the cellular model requires. It is a p p a r e n t that the heat t r e a t m e n t process has affected the T-term below 1.8 K, b u t there is no clear p a t t e r n correlating it with crystal size, crystal c o n t e n t or density. The author thanks O, Lindig of Schott for s u p p l y i n g the samples, C. A n d r i k i d i s for p r e p a r i n g a n d m o u n t i n g the samples, a n d J.B. Patterson for d e t e r m i n i n g the density of the samples. T h a n k s are due also to Drs G.K. White a n d J.G. Collins for helpful discussions.
References [1] R.B. Roberts, R.J. Tainsh and G.K. White, Cryogenics 22 (1982) 566. [2] S.3. Collocott, J. Phys. C 16 (1983) L13. [3] R.O. Pohl, Topics in Current Physics. Amorphous Solids: Low Temperature Properties, ed., W.A. Phillips (Springer-Verlag,Berlin, 1981) p. 27. [4] A.J. Leadbetter, A.P. Jeapes, C.G. Waterfield and K.E. Wycherley, Chem. Phys. Lett. 52 (1977) 469. [5] P.W. McMillan, Glass-Ceramics (Academic Press, London, 1964). [6] S.J. Collocott, Aust. J. Phys. 36 (1983) 573. [7] P. Flubacher, A.J. Leadbetter, J.A. Morrison and B.P. Stoicheff, J. Phys. Chem. Sol. 12 (1959) 53. [8] N. Bilir and W.A. Phillips, Phil. M~g. 32 (1975) 113. [9] E.F. Westrum, IVe Congress Int. du Verre, Paris (1956) 396. [10] W.A. Phillips, J. Non-Crystalline Solids 31 (1978) 267. [11] G.K. White and J.A. Birch, Phys. Chem. Glasses 6 (1965) 85. [12] J.W. Gardner and A.C. Anderson, Phys. Rev. B23 (1981) 474. [13] R.G. Bohn, J. Appl. Phys. 45 (1974) 2133. [14] H.P. Baltes, Solid St. Commun. 13 (1973) 225.