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Anomalous heat capacity of vitreous silica: Effect of interstitial 4He
Journal of Non-Crystalline Solids 41 (1980) 251-256 © North-Holland Publishing Company
ANOMALOUS HEAT CAPACITY OF VITREOUS SILICA: EFFECT OF INTERSTITIAL 4He *
R.A. FISHER Low Temperature Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94720, USA Received 4 April 1980
4He (gas or liquid) sorbs into SiO2 glass at liquid helium temperatures. The term in the heat capacity of vitreous silica which is linear in temperature is increased by the presence of interstitial 4He. (The linear term is believed to be generally characteristic of glasses.) A number of experiments on SiO2 glass are suggested using H2, 3He, and 4He as probes of mass 2, 3, and 4 to explore the mechanism which is responsible for the anomalous heat capacity.
1. Introduction In 1959 Anderson [1] found that the heat capacity of vitreous silica in the liquid helium range of temperatures was larger than that of quartz single crystal. In particular, it was larger than expected based on its elastic properties, suggesting the presence of additional low-frequency vibrations in the glassy state. Shortly thereafter, Rosenstock [2], in 1962, suggested a simple explanation for the excess heat capacity found by Anderson [1 ]. He pointed out that at low temperatures the low frequency lattice vibrations must be broken down into elastic and non-elastic modes for a disordered solid. Rosenstock postulated that vibrations" of loosely held particles in microscopic cavities in the glass were the origin of the non-elastic modes. The model was made quantitative by calculating the heat capacity for a particle-in-a-box, which Rosenstock suggested would represent an upper limit to the heat capacity due to the particle--cavity entities [3]. It should be noted that weakly bound particles are not necessarily impurities, but could be atoms or molecules of the amorphous substance. Thus, purification of the material would not necessarily eliminate the excess heat capacity of a glass. However, the presence of foreign particles in the cavities should enhance the effect, while decreasing the nufiaber of cavities (by annealing or other means) should reduce it.
* This work was supported in part by a grant from the National Science Foundation. 251
252
R.A. Fisher/Anomalous heat capacity
In 1968 we became interested in using SiO2 glass for magnetothermodynamic apparatus. Measurements of heat capacity [4] and thermal conductivity [5] were made on a sample of Amersil SiO2 glass [6] * over the temperature range 0 . 5 4.2 K. Over this temperature interval we found the heat capacity to be larger than that of single crystal quartz [7], and to have a term linear in temperature. (The thermal conductivity had a term proportional to T 1"7s.) Zeller and Pohl [8] made measurements on several other amorphous insulators and showed that these systems had also the same type of deviation from crystalline behavior as did SiO2 glass. Subsequent investigations by others on a number of glassy insulator systems have shown that these deviations ate probably universal
[9]. 2. Models Two theories have been developed to explain the difference in behavior of amorphous insulators from the crystalline state. One of these is the particle-cavity model of Rosenstock [2.3,10] and the other a tunnelling model by Anderson et al. [11], Phillips [12] and Stevens [13]. According to the tunnelling model, glassy solids have trapped particles which can quantuum mechanically move between two localized potential minima. This double-weU potential system is assumed to arise from disorder present in the network of glassy material [11,12]. A reasonable energy level distribution for these doublewell potentials leads to .a linear temperature term in the heat capacity [13]. Rosenstock's [10] particle-cavity model has an appealing simplicity. He shows that for a reasonable distribution of cavity sizes, a linear temperature dependence of heat capacity results at low temperatures. Despite its physical appeal, however, Rosenstock's model has been ignored generally, with most of the attention being given to the tunnelling model. Recent measurements [ 14,15] have shown that at sufficiently low temperatures (T < 0.5 K) there are departures from the C = T heat capacity behavior. At these very low temperatures C cc T l+n, where n has been found to vary from 0.3 to 0.5. Lasjaunias et al. [16] have modified the tunnelling model [11-13] to explain this T l+n behavior, while maintaining the linear form at higher temperatures. Rosenstock's model [10] also exhibits non-linear T behavior of heat capacity depending on the choice of cavity size distribution. It has been suggested that changing the structure of an amorphous solid by the introduction of impurities (such as OH-) in a controlled fashion might change the physical properties (e.g., heat capacity) in such a way that some conclusions on the
* Impurities were: <5 ppm Fe, < 1 0 p p m A1, < 1 0 ppm Ca, <1 ppm Mg, 5 ppm Li and 1 ppm B.
R.A. Fisher /Anomalous heat capacity
253
nature of the two-level system could be drawn [17,18] During our investigation of the heat capacity of vitreous silica [4], we discovered that 4He sorbed into the glass in the liquid helium range of temperatures. (3He did not go into the glass, which we attributed to the fact that 4He has a lower zero-point energy than 3He.)
3. Interstitial 4He The adsorbed 4He increased the heat capacity of the vitreous silica; in particular, the linear term increased [4]. We showed that we were dealing with 4He in the interior of the glass, and not with a surface effect. The vitreous SiO2 calorimeter had a superficial specific surface area of 2.71 cm2/g SiO2, and the greatest amount of 4He sorbed was 2.7 × 10 -4 mol/g SiO2. This amount is about 103 times more than the amount of 4He which would normaUy be expected to adsorb on the surface. In addition, the sorbed 4He could not be removed after prolonged pumping at high vacuum (<10 -6 Torr) at 4.2 K. We suggested that the 4He atoms entered the SiO2 glass as though into a maze and became trapped.
3.0
I
I
I
SiO 2 4"
SINGLE CRYSTAL QUARTZ • SOLID CYLINDER o HOLLOW CYLINDER + HOLLOW CYLINDER AFTER GLAS! CONTACT WITH 4He (g) AT
2.5 ÷
2.C
4-
4-
i i
4,2"K AND I ATM FOR 67 HRS.
++ 4"
1.5
::L ~ " 1.0 I--
4"
(L
CT-3 =0.33 T~ + 0.271 +0.O22 T2 +
+ q
+
0.5
~
0
4"
+
4"
+
0 -
CT-3 = O. 146 0
+
t I
.
J 2
. i 3
.0165 T2 t 4
5
T, *K
Fig. 1. The heat capacity of SiO2 (single crystal and solid cylinder), and a b o U o w cylinder before and after exposure to 4He (g) at low temperatures.
R.A. Fisher / Anomalous heat capacity
254
SiO2
6
GLASS
-'~ 4
o, ~ ~ZbC
..~
-'~
• "H+ ,N toO2 GLASS
< G~ "//~e+ ~"
2-0
I
T-I=1.38 i
° AFTER4HeREMOVA-l J
2
5
i
I 4
i 5
T, *K
Fig. 2. The effect of interstitial 4He on the low temperature heat capacity of SiO2 glass. AC = (0.26 T+ 0.243 T3 + 0.016s Ts). The 4 H e sorbed by the SiO2 was 2.7 X 10.-4 mol/g
Cob s -
SiO2.
We interpreted the excess linear heat capacity as arising from loosely bound 4He atoms in cavities within the glass, which contributed to low frequency modes. Removal of the 4He at room temperature, and recooling to liquid helium temperatures, restored the heat capacity to its original value before ever having been in contact with 3He or 4He. Figure 1 shows the heat capacity of single crystal quartz [7], a solid cylinder of vitreous Si02 [4], and vitreous SiO2 tubing [4] with and without absorbed 4He. Fig. 2 shows the increase in heat capacity of the tubing due to the absorbed 4He in the interstities of the glassy SiO2. The increase in the linear heat capacity term, caused by the interstitial 4He, was some five fold. Other experiments showed that smaller amounts of absorbed 4He led to a proportionately smaller effect [4]. Interstitial 4He atoms in the cavities of SiO2 glass should be weakly bound. They are essentially particles in a box; and, as predicted by Rosenstock [2,8,10] they exhibit a linear heat capacity term. At least in the case "of the 4He-SiO2 glass system, 4He would seem to be a useful probe for the controlled study of the anomalous physical properties of vitreous silica at low temperatures. (Certain plastics have also been shown to have an excess heat capacity linear in temperature [9], and some plastics are porous to 4He near room temperature [ 19]. Such systems should also be investigated.)
R.A. Fisher/Anomalous heat capacity
255
4. Suggested experiments In this section a number of experiments are suggested which could be carried out on the vitreous SiO2 system using interstitial molecules as probes. Other glassy systems might also be investigated using interstitial molecules. (1) Both 3He and 4He will penetrate vitreous SiO2 at room temperature. Hydrogen also goes into SiO2 glass at elevated temperatures. Each of these molecules could be trapped by quenching. Thus, a study of the effect of interstitial particles of atomic mass 2, 3 and 4 could be made. The amount of 4He, 3He and H2 absorbed should be quantitatively varied, and the effect on the heat capacity, thermal conductivity, and acoustic properties measured. The measurements should be extended below 0.5 K in order to observe the region where the heat capacity is a function of T l+n. (2) Quartz single crystals have a density of 2.65 g/cm 3 and fused silica has a density of 2.20 g/cm 3. Hence, SiO2 glass has 0.07 cm 3 of cavities per gram. If it is assumed that 4He in the cavities at liquid helium temperatures would have the density of 4He liquid (0.15 g/cm3), then the 2.7 × 10 -~ mol 4He/g SiO2 found in our experiment would be enough to fill the cavities to approximately 10%. We had no indication that this amount was a maximum [4]. Consequently, it would be interesting to see if a saturation situation could be approached at 4.2 K, and how this would affect the thermal and acoustic properties. (3) Figure 1 shows that two samples of fused silica (solid cylinder and tubing) have different heat capacities. This suggests that methods of preparation and heat treatment might affect the number and size of cavities present, and hence both the elastic and non-elastic lattice modes. Methods of preparation and annealing should be varied to see if some systematic difference can be found. (4) Similar studies could be carried out on other glass systems with H2, 3He, or 4He. (Due to an absence of cavities, helium probably cannot be trapped in single crystal quartz. However, if investigation shows that helium can be trapped, a study should be made to see how the thermal and acoustic properties.are altered.) Although we feel that Rosenstock's particle-cavity model [10] is conceptually better, the tunnelling model cannot be ruled out. For both cases, at present, there is no knowledge of the type of particle in the cavity or what it is that tunnels. A parameter in Rosenstock's theory is the frequency co = (k/m) 1/2, where k is the spring constant for a weakly attached particle of mass m. By utilizing H2, 3He, and 4He, m can be varied and k should be related to the heat of physical adsorption (about 1 kcal/mol). Similarly, if the tunnelling entities are known, then a test of this model should also be possible.
References [1] O.L. Anderson, J. Phys. Chem. Solids 12 (1959) 41. [2] H.R. Rosenstock, J. Phys. Chem. Solids 23 (1962) 659.
256
R.A. Fisher/Anomalous heat capacity
[3] H.R. Rosenstock, Am.J. Phys. 30 (1962) 38. [4] E.W. Homung, R A. Fisher, G.E. Brodale and W.F. Giaugue, J. Chem. Phys. 50 (1969) 4878. [5] R.A. Fisher, G.E. Brodale, E.W. Hornung and W.F. Giauque, Rev. Sci. Instr. 40 (1969) 365. [6] Amersil Division, Englehard Industries, Inc., Hillside, NJ 07205. [7] N.S. Natarajan, Ind. J. Pure Appl. Phys. 5 (1967) 372. [8] R.C. Zeller and R.O. Pohl, Phys. Rev. B4 (1971) 2029. [9] R.B. Stevens, Phys. Rev. B13 (1976) 852. [10] H.B. Rosenstock, J. Non-Crystalline Solids 7 (1972) 123. [11] P.W. Anderson, B.I. Halperin and C.M. Varma, Phil. Mag. 25 (1972) 1. [12] W.A. Phillips, J. Low Tern. Phys. 7 (1972) 351. [13] R.B. Stevens, Phys. Rev. B8 (1973) 2896. [14] J.C. Lasjaunias, D. Thoulouze and F. Pernot, Sol. St. Commun. 14 (1974) 957. [15] J.C. Lasjaunias, A. Ravex, M. Vandorpe and S. Huntlinker, Sol. St. Commun. 17 (1975) 1045. [16] J.C. Lasjaunias, R. Maynard and M. Vandorpe, J. Phys. 39 (Suppl. 8) (1978) C6-973. [17] M. v. Schickfus, C. Laermans, W. Arnold and S. Huntlinker, Proc. 4th Int. Conf. Phys. of Non-Cryst. Solids, Clausthal-Zellerfeld (1976). [18] H.Y. L6hneysen and B. Picot, J. Phys. 39 (Suppl. 8) (1978) C6-976. [19] W.F. Giauque, T.H. Geballe, D.N. Lyon and J.J. Fritz, Rev. Sci. Instr. 23 (1952) 169.
ANOMALOUS HEAT CAPACITY OF VITREOUS SILICA: EFFECT OF INTERSTITIAL 4He *
R.A. FISHER Low Temperature Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94720, USA Received 4 April 1980
4He (gas or liquid) sorbs into SiO2 glass at liquid helium temperatures. The term in the heat capacity of vitreous silica which is linear in temperature is increased by the presence of interstitial 4He. (The linear term is believed to be generally characteristic of glasses.) A number of experiments on SiO2 glass are suggested using H2, 3He, and 4He as probes of mass 2, 3, and 4 to explore the mechanism which is responsible for the anomalous heat capacity.
1. Introduction In 1959 Anderson [1] found that the heat capacity of vitreous silica in the liquid helium range of temperatures was larger than that of quartz single crystal. In particular, it was larger than expected based on its elastic properties, suggesting the presence of additional low-frequency vibrations in the glassy state. Shortly thereafter, Rosenstock [2], in 1962, suggested a simple explanation for the excess heat capacity found by Anderson [1 ]. He pointed out that at low temperatures the low frequency lattice vibrations must be broken down into elastic and non-elastic modes for a disordered solid. Rosenstock postulated that vibrations" of loosely held particles in microscopic cavities in the glass were the origin of the non-elastic modes. The model was made quantitative by calculating the heat capacity for a particle-in-a-box, which Rosenstock suggested would represent an upper limit to the heat capacity due to the particle--cavity entities [3]. It should be noted that weakly bound particles are not necessarily impurities, but could be atoms or molecules of the amorphous substance. Thus, purification of the material would not necessarily eliminate the excess heat capacity of a glass. However, the presence of foreign particles in the cavities should enhance the effect, while decreasing the nufiaber of cavities (by annealing or other means) should reduce it.
* This work was supported in part by a grant from the National Science Foundation. 251
252
R.A. Fisher/Anomalous heat capacity
In 1968 we became interested in using SiO2 glass for magnetothermodynamic apparatus. Measurements of heat capacity [4] and thermal conductivity [5] were made on a sample of Amersil SiO2 glass [6] * over the temperature range 0 . 5 4.2 K. Over this temperature interval we found the heat capacity to be larger than that of single crystal quartz [7], and to have a term linear in temperature. (The thermal conductivity had a term proportional to T 1"7s.) Zeller and Pohl [8] made measurements on several other amorphous insulators and showed that these systems had also the same type of deviation from crystalline behavior as did SiO2 glass. Subsequent investigations by others on a number of glassy insulator systems have shown that these deviations ate probably universal
[9]. 2. Models Two theories have been developed to explain the difference in behavior of amorphous insulators from the crystalline state. One of these is the particle-cavity model of Rosenstock [2.3,10] and the other a tunnelling model by Anderson et al. [11], Phillips [12] and Stevens [13]. According to the tunnelling model, glassy solids have trapped particles which can quantuum mechanically move between two localized potential minima. This double-weU potential system is assumed to arise from disorder present in the network of glassy material [11,12]. A reasonable energy level distribution for these doublewell potentials leads to .a linear temperature term in the heat capacity [13]. Rosenstock's [10] particle-cavity model has an appealing simplicity. He shows that for a reasonable distribution of cavity sizes, a linear temperature dependence of heat capacity results at low temperatures. Despite its physical appeal, however, Rosenstock's model has been ignored generally, with most of the attention being given to the tunnelling model. Recent measurements [ 14,15] have shown that at sufficiently low temperatures (T < 0.5 K) there are departures from the C = T heat capacity behavior. At these very low temperatures C cc T l+n, where n has been found to vary from 0.3 to 0.5. Lasjaunias et al. [16] have modified the tunnelling model [11-13] to explain this T l+n behavior, while maintaining the linear form at higher temperatures. Rosenstock's model [10] also exhibits non-linear T behavior of heat capacity depending on the choice of cavity size distribution. It has been suggested that changing the structure of an amorphous solid by the introduction of impurities (such as OH-) in a controlled fashion might change the physical properties (e.g., heat capacity) in such a way that some conclusions on the
* Impurities were: <5 ppm Fe, < 1 0 p p m A1, < 1 0 ppm Ca, <1 ppm Mg, 5 ppm Li and 1 ppm B.
R.A. Fisher /Anomalous heat capacity
253
nature of the two-level system could be drawn [17,18] During our investigation of the heat capacity of vitreous silica [4], we discovered that 4He sorbed into the glass in the liquid helium range of temperatures. (3He did not go into the glass, which we attributed to the fact that 4He has a lower zero-point energy than 3He.)
3. Interstitial 4He The adsorbed 4He increased the heat capacity of the vitreous silica; in particular, the linear term increased [4]. We showed that we were dealing with 4He in the interior of the glass, and not with a surface effect. The vitreous SiO2 calorimeter had a superficial specific surface area of 2.71 cm2/g SiO2, and the greatest amount of 4He sorbed was 2.7 × 10 -4 mol/g SiO2. This amount is about 103 times more than the amount of 4He which would normaUy be expected to adsorb on the surface. In addition, the sorbed 4He could not be removed after prolonged pumping at high vacuum (<10 -6 Torr) at 4.2 K. We suggested that the 4He atoms entered the SiO2 glass as though into a maze and became trapped.
3.0
I
I
I
SiO 2 4"
SINGLE CRYSTAL QUARTZ • SOLID CYLINDER o HOLLOW CYLINDER + HOLLOW CYLINDER AFTER GLAS! CONTACT WITH 4He (g) AT
2.5 ÷
2.C
4-
4-
i i
4,2"K AND I ATM FOR 67 HRS.
++ 4"
1.5
::L ~ " 1.0 I--
4"
(L
CT-3 =0.33 T~ + 0.271 +0.O22 T2 +
+ q
+
0.5
~
0
4"
+
4"
+
0 -
CT-3 = O. 146 0
+
t I
.
J 2
. i 3
.0165 T2 t 4
5
T, *K
Fig. 1. The heat capacity of SiO2 (single crystal and solid cylinder), and a b o U o w cylinder before and after exposure to 4He (g) at low temperatures.
R.A. Fisher / Anomalous heat capacity
254
SiO2
6
GLASS
-'~ 4
o, ~ ~ZbC
..~
-'~
• "H+ ,N toO2 GLASS
< G~ "//~e+ ~"
2-0
I
T-I=1.38 i
° AFTER4HeREMOVA-l J
2
5
i
I 4
i 5
T, *K
Fig. 2. The effect of interstitial 4He on the low temperature heat capacity of SiO2 glass. AC = (0.26 T+ 0.243 T3 + 0.016s Ts). The 4 H e sorbed by the SiO2 was 2.7 X 10.-4 mol/g
Cob s -
SiO2.
We interpreted the excess linear heat capacity as arising from loosely bound 4He atoms in cavities within the glass, which contributed to low frequency modes. Removal of the 4He at room temperature, and recooling to liquid helium temperatures, restored the heat capacity to its original value before ever having been in contact with 3He or 4He. Figure 1 shows the heat capacity of single crystal quartz [7], a solid cylinder of vitreous Si02 [4], and vitreous SiO2 tubing [4] with and without absorbed 4He. Fig. 2 shows the increase in heat capacity of the tubing due to the absorbed 4He in the interstities of the glassy SiO2. The increase in the linear heat capacity term, caused by the interstitial 4He, was some five fold. Other experiments showed that smaller amounts of absorbed 4He led to a proportionately smaller effect [4]. Interstitial 4He atoms in the cavities of SiO2 glass should be weakly bound. They are essentially particles in a box; and, as predicted by Rosenstock [2,8,10] they exhibit a linear heat capacity term. At least in the case "of the 4He-SiO2 glass system, 4He would seem to be a useful probe for the controlled study of the anomalous physical properties of vitreous silica at low temperatures. (Certain plastics have also been shown to have an excess heat capacity linear in temperature [9], and some plastics are porous to 4He near room temperature [ 19]. Such systems should also be investigated.)
R.A. Fisher/Anomalous heat capacity
255
4. Suggested experiments In this section a number of experiments are suggested which could be carried out on the vitreous SiO2 system using interstitial molecules as probes. Other glassy systems might also be investigated using interstitial molecules. (1) Both 3He and 4He will penetrate vitreous SiO2 at room temperature. Hydrogen also goes into SiO2 glass at elevated temperatures. Each of these molecules could be trapped by quenching. Thus, a study of the effect of interstitial particles of atomic mass 2, 3 and 4 could be made. The amount of 4He, 3He and H2 absorbed should be quantitatively varied, and the effect on the heat capacity, thermal conductivity, and acoustic properties measured. The measurements should be extended below 0.5 K in order to observe the region where the heat capacity is a function of T l+n. (2) Quartz single crystals have a density of 2.65 g/cm 3 and fused silica has a density of 2.20 g/cm 3. Hence, SiO2 glass has 0.07 cm 3 of cavities per gram. If it is assumed that 4He in the cavities at liquid helium temperatures would have the density of 4He liquid (0.15 g/cm3), then the 2.7 × 10 -~ mol 4He/g SiO2 found in our experiment would be enough to fill the cavities to approximately 10%. We had no indication that this amount was a maximum [4]. Consequently, it would be interesting to see if a saturation situation could be approached at 4.2 K, and how this would affect the thermal and acoustic properties. (3) Figure 1 shows that two samples of fused silica (solid cylinder and tubing) have different heat capacities. This suggests that methods of preparation and heat treatment might affect the number and size of cavities present, and hence both the elastic and non-elastic lattice modes. Methods of preparation and annealing should be varied to see if some systematic difference can be found. (4) Similar studies could be carried out on other glass systems with H2, 3He, or 4He. (Due to an absence of cavities, helium probably cannot be trapped in single crystal quartz. However, if investigation shows that helium can be trapped, a study should be made to see how the thermal and acoustic properties.are altered.) Although we feel that Rosenstock's particle-cavity model [10] is conceptually better, the tunnelling model cannot be ruled out. For both cases, at present, there is no knowledge of the type of particle in the cavity or what it is that tunnels. A parameter in Rosenstock's theory is the frequency co = (k/m) 1/2, where k is the spring constant for a weakly attached particle of mass m. By utilizing H2, 3He, and 4He, m can be varied and k should be related to the heat of physical adsorption (about 1 kcal/mol). Similarly, if the tunnelling entities are known, then a test of this model should also be possible.
References [1] O.L. Anderson, J. Phys. Chem. Solids 12 (1959) 41. [2] H.R. Rosenstock, J. Phys. Chem. Solids 23 (1962) 659.
256
R.A. Fisher/Anomalous heat capacity
[3] H.R. Rosenstock, Am.J. Phys. 30 (1962) 38. [4] E.W. Homung, R A. Fisher, G.E. Brodale and W.F. Giaugue, J. Chem. Phys. 50 (1969) 4878. [5] R.A. Fisher, G.E. Brodale, E.W. Hornung and W.F. Giauque, Rev. Sci. Instr. 40 (1969) 365. [6] Amersil Division, Englehard Industries, Inc., Hillside, NJ 07205. [7] N.S. Natarajan, Ind. J. Pure Appl. Phys. 5 (1967) 372. [8] R.C. Zeller and R.O. Pohl, Phys. Rev. B4 (1971) 2029. [9] R.B. Stevens, Phys. Rev. B13 (1976) 852. [10] H.B. Rosenstock, J. Non-Crystalline Solids 7 (1972) 123. [11] P.W. Anderson, B.I. Halperin and C.M. Varma, Phil. Mag. 25 (1972) 1. [12] W.A. Phillips, J. Low Tern. Phys. 7 (1972) 351. [13] R.B. Stevens, Phys. Rev. B8 (1973) 2896. [14] J.C. Lasjaunias, D. Thoulouze and F. Pernot, Sol. St. Commun. 14 (1974) 957. [15] J.C. Lasjaunias, A. Ravex, M. Vandorpe and S. Huntlinker, Sol. St. Commun. 17 (1975) 1045. [16] J.C. Lasjaunias, R. Maynard and M. Vandorpe, J. Phys. 39 (Suppl. 8) (1978) C6-973. [17] M. v. Schickfus, C. Laermans, W. Arnold and S. Huntlinker, Proc. 4th Int. Conf. Phys. of Non-Cryst. Solids, Clausthal-Zellerfeld (1976). [18] H.Y. L6hneysen and B. Picot, J. Phys. 39 (Suppl. 8) (1978) C6-976. [19] W.F. Giauque, T.H. Geballe, D.N. Lyon and J.J. Fritz, Rev. Sci. Instr. 23 (1952) 169.