Gardner, W.R.

Hoffer, J.K.

Phillips, N.E.

Waterfield, C.G.

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Lawrence Berkeley National LaboratoryRecent WorkTitleTHERMODYNAMIC PROPERTIES OF bcc He4Permalinkhttps://escholarship.org/uc/item/8zw8f7j6AuthorsHoffer, J.K.Gardner, W.R.Waterfield, C.G.et al.Publication Date1968-08-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaRECEIVED LAWRENCE RADIATION LABORATORY NOV 20 1968 LIBRARY AND DOCUMENTS SECTION University of California Ernest O. Radiation Lawrence Laboratory THERMODYNAMIC PROPERTIES OF bee He 4 J. K. Hoffer, W. R. Gardner, C. G. Waterfield and N. E. Phillips August 1968 TWO-WEEK LOAN COPY This is a Library Circulating Copy which may be borrowed for two weeks. For a personal retention copy, call Tech. Info. Diuision, Ext. 5545 tserKeley, California UCRL-18384 .., ~ ~ ~ r-I ~ ....... . ~ }f~ --- .....c: DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. Talk to be presented at the 11th International Conference on Low Temperature Physics in St. Andrews, Scotland, August 22-29, 1968. UNIVERSITY OF CALIFOhNIA Lawrence Radiation Laboratory Berkeley, California AEC ~ontract I;Jo. W-7405-eng-48 4 THERMODYNAMIC PROPERTIES OF bee He .. J. K. Hoffer, W. R. Gardner, C. G. Waterfield and N. E. Phillips August 1968 \ UCRL-18384 Preprint ... -2- UCRL-18384 0.3°K and the entropy was evaluated. In the two-phase regions the S-V isotherms (see Fig. 2) are straight lines and their slopes give the temperature derivative of the equilibrium pres-sure. The values of P-PO in the vicinity of the bcc phase are compared with direct measurements(2,5,6) in Fig. 3. (The data of Ref. 2 have been adjusted by 0.2 atm to correspond to Po = 25·00 atm.) The relatively large scatter in the direct measurements of the bcc-hcp equilibrium pressure and their poor agreement with the values calculated thermodynamically presumably reflect the difficulty in measuring the equilibrium pressure ina solid-solid mixture. As Fig. 3 shows, the shape of the bcc phase in the P-T diagram obtained in this work differs substantially from that given by the direct measurements. As a consequence, the thermal expansion determined from Figs. 1 and 3; i.e. t:N/6T at constant P, is everywhere positive whereas the direct measurements gave 21.21 - \ l 21.0L .! 0 E 20.8~ ,-,.., E ! 0 ':-" i I > 20.6f-20.4 f-1 j '--____ ---'I _ 1.20 1.30 ~ ! ~ i I I i , l i -J i i I ,,~, I __~I ______ ~I ______ -LI ______ -LI ______ -LI ______ ~I~ 1.40 1.50 1.60 1.70 1.80 1.90 T (oK) . Fig. 1. The V-T diagram of He4 in the vicinity of the bcc phase. /, f-I , . . ,' • . 1 -3- UCRL-18384 regions of negative value.(3,5) The bee-phase measurements for eleven of the sixteen runs that passed through this ph~se are presented in Fig. 4 and show that (dCV/dV)~ > O. Furthermore, (OS/OV)T has normal values (between 2.07 and 2.70 atm/oK) showing that the suggested anomalies do not occur. The expected discontinuous increase of Cv at the melting temperature of the bcc phase is preceded (and at the higher molar volumes obscured) by a rapid but smooth increase beginning 0.02°K lower, which is accompanied by an increase in the thermal relaxation time of the sample. This behavior is independent of the thermal history of the sample and was even observed when the heat capacity points were taken with decreasing temperature (by balancing a negative heat leak witn a power input that was interrupted to produce a decrease in sample temperature). There is some theoretical basis(7) for expecting 4 Fig •. 2. The S-V diagram of He • 6 hcp e·G,illy 9 Mill, .... Vj~"O, 8 Faj,b(l"~ I o~1 ~''---Ti-' ---t.;'---;J'>;----L--1 1.4 1.5 1,6 1.7 1.8 T ('K I Fig. 3. The P-T diagram • -4- UCRL-18384 anomalous thermal properties very close to the melting point and also for expecting them to be more conspicuous in He, and particularly in bcc He, than in most solids. III ~ o , I Q) 0 E ....... 'I-:> -.; 'It ~ ....... > 0 0. 30r--- ---- -- ----, r-0.26 0.22 1.4 () - 21,096 • - Z I,09.d 6-21.013 • - 21.0~7 et - ZI.O'~ • - 2'.013 e - 20.984 • - 20.9€-0 D-20.921 ~ ~f.: 1 ~ ....... t4·:'''~ .. c i J AA·1Y~ • • a: j 0 __ Jt __ ~I __________ -LI _______ : ___ p._~~,_·_·_~~~-·----i 1.5 1.6 1.7 T ( oK) 1.8 4 Fig. 4. The heat capa.city of bcc He. The vertical bars indicate stability limits of the phase. 1. L. Goldstein, Phys. Rev. 122, 726(1961). 2. J. H. Vignos and H. A. Fairbank, Phys. Rev. Letters ~, 265(1961); Phys. Rev. 147, 185(1966). 3· G. Ahlers, Phys. Rev. 135, A 10 (1964). 4. D. O. Edwards and, R. C. Pandorf, Phys. Rev. 144, 143(1966). 5. E. R. Gri1ly and R. L. Mills, Ann. Phys. (NY) 18, 250(1962). 6. Go A. Swenson, Phys. Rev. §,2, 538(1953). 7. B. J A1d'er {private communication). 4-'" , .. r \ This report was prepared as an account of Government sponsored work. Neither the United States, nor the Com-mission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, appa-ratus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any infor-mation, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Com-mission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor . 

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THERMODYNAMIC PROPERTIES OF bcc He4

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THERMODYNAMIC PROPERTIES OF bcc He4

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