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The specific heat of solid argon
dense first layer for adsorbed helium 7 is actually two quite distinct layers. Heat capacity measurements of adsorbed helium-3 and helium-4 were made with a calorimeter consisting of a sponge sintered into a sealed copper container, with a heater varnished to the outside, and a carbon resistance thermometer epoxied to the container. The empty calorimeter (i.e. without adsorbed helium) had the same heat capacity as an equivalent mass of copper metal from 0.2 to 4.0 ° K. The thermal relaxation time after the heating period at 0.2 ° K was approximately 7 s, with or without adsorbed helium. Much of this time lag may have been due to thermal resistance between the heater and the copper container. With regard to the possible use of these sponges as a medium for thermal contact to liquid helium-3 or helium-4 at low temperatures, it may be seen from Figure 2 that somewhat less than 1 per cent of the helium in the container may be expected to be in the first three layers next to the sponge surface. Also, it is possible for this application that precoating of the surface with a gas such as argon might help reduce the
thermal boundary resistance, by helping to match acoustic impedances at the surface. This work was sponsored in part by the Air Force Office of Scientific Research, Grant AFAFOSR-923-65. REFERENCES I. GOODSTEIN,D. L., McCoRMICK, W. D., and DASH, J. G. Proc. 9th int. Conf. low Temp. Physics, p. 368 (Plenum, New York, 1965) 2. GOODSTEIN,D. L., DASH, J. G., and McCORMICK, W. D. Phys. Rev. Lett. 15, 447 (1965) 3. GOODSXEIN,D. L., and McCoRMICK, W. L. Phys. Rev. Lett. 16, 8 (1966) 4. GOODSTEIN,D. L., and MCCORMICK,W. D. Bull. Am. phys. Soc. U, 125 (1966) 5. N.D.60 Druid Copper; Metals Disintegrating Division, Martin Marietta Corpn, Elizabeth B., New Jersey 6. See, for example, YOUNG, D. M., and CROWELL, A. D. Physical Adsorption of Gases, p. 148 (Butterworths, London, 1962) 7. See, for example, LONG,E., and MEYER,L. Advanc. Phys. 2, 1 (1953)
THE SPECIFIC HEAT OF SOLID ARGON H.-J. H U E B S C H E R Physikalisch-Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Germanyt Received 17 August 1965
THE specific heat of solid argon shows a remarkable rise above 60 ° K. Beaumont, Chihara, and Morrison 1 interpreted this rise as the commencement of the formation of thermal vacancies. With graphical methods they evaluated the energy of the vacancy formation, the number of the vacancies, and the portion of the energy of the vacancy formation in Cp. They obtained the volume of the thermal vacancies by a rough evaluation of the rise of the thermal expansion of solid argon 2 above 60 ° K analogous to Cp. On the basis of the anharmonic Einstein model Foreman and Lidiard 3 obtained Cv without vacancy formation and give curves for Co and Cv without vacancy formation as a function of temperature. They showed that the formation of thermal vacancies could be demonstrated by a comparison between volumetric and radiographic measurements of the temperature dependence of the density of solid argon. Dobbs, Figgins, Jones, Piercey, and Riley, 2 however, reported that above 60 ° K the radiographic method is t At present: VEB Werk ffir Femsehelektronik, Berlin, Germany.
168
too inaccurate since recrystallization will commence. To all appearance the formation of thermal vacancies in solid argon can also be proved by particular specific heat measurements. I-0
I
l
I
I
.~ O-9 0.8
I 0'7
Co
,
__
o
c~
0"5I
5o
7o
8'o
9'o
,oo
T ,' (°K) Figure 1. Specific heat of solid argon at constant pressure Cp and constant volume Cv according to Flubacher, Leadbetter, and Morrison) C~ and CO are evaluated specific heats without vacancy formation according to Foreman and Lidiard) The hatched plane shows experimental values for Cp and Cv according to Huebscher TM
CRYOGENICS • JUNE 1966
Up to the present measurements of the specific heat in solid argon were only known 4-9 where the container volume was not completely filled with solid argon. A more or less large part of the container volume was in each case filled with gaseous argon, also just below the melting point where, due to its larger thermal expansion, solid argon occupies the largest part in relation to the container volume. Therefore, the pressure within the samples during the measurements never exceeded the vapour pressure as a function of temperature. This information is backed by a paper on the specific heat of solid argon TM based on experiments in which the measuring container could be completely filled with solid argon. Just below the melting point of solid argon, pressures up to 600 atm could be obtained even in the measuring container. Since the thermal expansions of metal and solid argon differ by the factor of 103, Co and Cv measurements were possible with one and the same sample. Below the temperature at which the measuring container was just completely filled with solid argon the measurements were performed at sufficiently constant pressure during which the argon volume varied continuously, whereas above the temperature the pressure rose rapidly but the volume remained sufficiently constant. Up to the present the constant volume of solid argon has not been measured directly but calculated, for instance, according to the relation
Cv : Cp/(~T'/ + 1)
where ~ is the thermal expansion and ?, the Grfineisen constant. This calculated Cv curve could not be confirmed by the measurements. The experimental values of Cv deviating from the calculated values for Cv are in good agreement with the Cv curve without vacancy formation plotted by Foreman and Lidiard 3 (Figure 1). Therefore, the Cv measurements could be considered as a confirmation of the formation of thermal vacancies in solid argon and for the prevention of the vacancy formation in solid argon by appropriate pressures. REFERENCES 1. BEAUMONT,R. H., CHIHARA, H., and MORR~SON, J. A. Proc. phys. Soc. Lond. 78, 1462 (1961) 2. DOBBS, FIGGINS, JONES, PIERCEY, and RILEY. Nature, Lond. 178, 483 (1956) 3. FOREMAN, A. J. E., and LIDIARD, A. B. Phil. Mag. 8, 97 (1963) 4. EUCKEN, A. Verb. der Deutschen Physikalischen Gesellschaft im Jahre 1916 18, No. 1, p. 4 5. CLUSIUS, K. Z. phys. Chem. B31,459 (1936) 6. HILL, to reference 7 in Thesis, University of Oxford (1952) 7. FIGGINS, B. F. Proc. phys. Soc. Lond. 76, 732 (1960) 8. ANDERSON. to reference 1 in Thesis, University of Oxford (1960) 9. FLUBACHER, P., LEADBETTER, A. J., and MORRISON, J. A. Proc. phys. Soc. Lond. 78, 1449 (1961) 10. HUEBSCHER, H. J. Unpublished diploma thesis (HumboldtUniversitfit zu Berlin, 1963)
LOW TEMPERATURE ELECTRON IRRADIATION OF METALS: EXPERIMENTAL TECHNIQUE P. LUCASSON, A. LUCASSON, and G. LELOGEAIS Laboratoire de Chimie Physique de la Facultd des Sciences de Paris, Orsay, France Received 20 February 1966
E LE C TRO N irradiation is a technique of growing importance for the study of lattice defects in metals. As early as 1957, careful and thorough work on the formation and recovery of Frenkel pairs in copper was performed by Corbett, Walker, and co-workers?,2 However, due to great uncertainties in the theory of point defects, some difficulties in the interpretation of their experimental results still remain today (see, for example, references 3 and 4). This unsatisfactory situation proved useful in the long run, as attempts either to overcome or to get round the theoretical obstacles resulted in the opening of several new and promising directions of research. First of all, theoretical studies were given a strong stimulus. 5-7 CRYOGENICS • JUNE 1966
Next, more sophisticated experimental methods were evolved in order to find a new basis for the understanding of point defect properties of metals. Such experiments included : (1) Electron
bombardment
of
oriented
mono-
crystals ;8-10 (2) Combined quenching-irradiation experiments;l~ (3) Comparison of the behaviour of various electronirradiated metals with that of copper. ~2 A feature common to most of these experiments is that they are performed at low temperatures. In this note we describe a cryostat for electron irradiation of metals at temperatures in the liquid helium range. 169
thermal boundary resistance, by helping to match acoustic impedances at the surface. This work was sponsored in part by the Air Force Office of Scientific Research, Grant AFAFOSR-923-65. REFERENCES I. GOODSTEIN,D. L., McCoRMICK, W. D., and DASH, J. G. Proc. 9th int. Conf. low Temp. Physics, p. 368 (Plenum, New York, 1965) 2. GOODSTEIN,D. L., DASH, J. G., and McCORMICK, W. D. Phys. Rev. Lett. 15, 447 (1965) 3. GOODSXEIN,D. L., and McCoRMICK, W. L. Phys. Rev. Lett. 16, 8 (1966) 4. GOODSTEIN,D. L., and MCCORMICK,W. D. Bull. Am. phys. Soc. U, 125 (1966) 5. N.D.60 Druid Copper; Metals Disintegrating Division, Martin Marietta Corpn, Elizabeth B., New Jersey 6. See, for example, YOUNG, D. M., and CROWELL, A. D. Physical Adsorption of Gases, p. 148 (Butterworths, London, 1962) 7. See, for example, LONG,E., and MEYER,L. Advanc. Phys. 2, 1 (1953)
THE SPECIFIC HEAT OF SOLID ARGON H.-J. H U E B S C H E R Physikalisch-Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Germanyt Received 17 August 1965
THE specific heat of solid argon shows a remarkable rise above 60 ° K. Beaumont, Chihara, and Morrison 1 interpreted this rise as the commencement of the formation of thermal vacancies. With graphical methods they evaluated the energy of the vacancy formation, the number of the vacancies, and the portion of the energy of the vacancy formation in Cp. They obtained the volume of the thermal vacancies by a rough evaluation of the rise of the thermal expansion of solid argon 2 above 60 ° K analogous to Cp. On the basis of the anharmonic Einstein model Foreman and Lidiard 3 obtained Cv without vacancy formation and give curves for Co and Cv without vacancy formation as a function of temperature. They showed that the formation of thermal vacancies could be demonstrated by a comparison between volumetric and radiographic measurements of the temperature dependence of the density of solid argon. Dobbs, Figgins, Jones, Piercey, and Riley, 2 however, reported that above 60 ° K the radiographic method is t At present: VEB Werk ffir Femsehelektronik, Berlin, Germany.
168
too inaccurate since recrystallization will commence. To all appearance the formation of thermal vacancies in solid argon can also be proved by particular specific heat measurements. I-0
I
l
I
I
.~ O-9 0.8
I 0'7
Co
,
__
o
c~
0"5I
5o
7o
8'o
9'o
,oo
T ,' (°K) Figure 1. Specific heat of solid argon at constant pressure Cp and constant volume Cv according to Flubacher, Leadbetter, and Morrison) C~ and CO are evaluated specific heats without vacancy formation according to Foreman and Lidiard) The hatched plane shows experimental values for Cp and Cv according to Huebscher TM
CRYOGENICS • JUNE 1966
Up to the present measurements of the specific heat in solid argon were only known 4-9 where the container volume was not completely filled with solid argon. A more or less large part of the container volume was in each case filled with gaseous argon, also just below the melting point where, due to its larger thermal expansion, solid argon occupies the largest part in relation to the container volume. Therefore, the pressure within the samples during the measurements never exceeded the vapour pressure as a function of temperature. This information is backed by a paper on the specific heat of solid argon TM based on experiments in which the measuring container could be completely filled with solid argon. Just below the melting point of solid argon, pressures up to 600 atm could be obtained even in the measuring container. Since the thermal expansions of metal and solid argon differ by the factor of 103, Co and Cv measurements were possible with one and the same sample. Below the temperature at which the measuring container was just completely filled with solid argon the measurements were performed at sufficiently constant pressure during which the argon volume varied continuously, whereas above the temperature the pressure rose rapidly but the volume remained sufficiently constant. Up to the present the constant volume of solid argon has not been measured directly but calculated, for instance, according to the relation
Cv : Cp/(~T'/ + 1)
where ~ is the thermal expansion and ?, the Grfineisen constant. This calculated Cv curve could not be confirmed by the measurements. The experimental values of Cv deviating from the calculated values for Cv are in good agreement with the Cv curve without vacancy formation plotted by Foreman and Lidiard 3 (Figure 1). Therefore, the Cv measurements could be considered as a confirmation of the formation of thermal vacancies in solid argon and for the prevention of the vacancy formation in solid argon by appropriate pressures. REFERENCES 1. BEAUMONT,R. H., CHIHARA, H., and MORR~SON, J. A. Proc. phys. Soc. Lond. 78, 1462 (1961) 2. DOBBS, FIGGINS, JONES, PIERCEY, and RILEY. Nature, Lond. 178, 483 (1956) 3. FOREMAN, A. J. E., and LIDIARD, A. B. Phil. Mag. 8, 97 (1963) 4. EUCKEN, A. Verb. der Deutschen Physikalischen Gesellschaft im Jahre 1916 18, No. 1, p. 4 5. CLUSIUS, K. Z. phys. Chem. B31,459 (1936) 6. HILL, to reference 7 in Thesis, University of Oxford (1952) 7. FIGGINS, B. F. Proc. phys. Soc. Lond. 76, 732 (1960) 8. ANDERSON. to reference 1 in Thesis, University of Oxford (1960) 9. FLUBACHER, P., LEADBETTER, A. J., and MORRISON, J. A. Proc. phys. Soc. Lond. 78, 1449 (1961) 10. HUEBSCHER, H. J. Unpublished diploma thesis (HumboldtUniversitfit zu Berlin, 1963)
LOW TEMPERATURE ELECTRON IRRADIATION OF METALS: EXPERIMENTAL TECHNIQUE P. LUCASSON, A. LUCASSON, and G. LELOGEAIS Laboratoire de Chimie Physique de la Facultd des Sciences de Paris, Orsay, France Received 20 February 1966
E LE C TRO N irradiation is a technique of growing importance for the study of lattice defects in metals. As early as 1957, careful and thorough work on the formation and recovery of Frenkel pairs in copper was performed by Corbett, Walker, and co-workers?,2 However, due to great uncertainties in the theory of point defects, some difficulties in the interpretation of their experimental results still remain today (see, for example, references 3 and 4). This unsatisfactory situation proved useful in the long run, as attempts either to overcome or to get round the theoretical obstacles resulted in the opening of several new and promising directions of research. First of all, theoretical studies were given a strong stimulus. 5-7 CRYOGENICS • JUNE 1966
Next, more sophisticated experimental methods were evolved in order to find a new basis for the understanding of point defect properties of metals. Such experiments included : (1) Electron
bombardment
of
oriented
mono-
crystals ;8-10 (2) Combined quenching-irradiation experiments;l~ (3) Comparison of the behaviour of various electronirradiated metals with that of copper. ~2 A feature common to most of these experiments is that they are performed at low temperatures. In this note we describe a cryostat for electron irradiation of metals at temperatures in the liquid helium range. 169