Abstract
Nearly one hundred years ago, T. Andrews deduced that for every gas, there should be a “critical temperature” above which the gas cannot be liquefied no matter how much it might be compressed. Further studies revealed that the critical temperature was one coordinate of a point on the P-V-T surface where differences between the intensive properties of the liquid and of the gas disappear (the P-V-T properties near the critical point are schematically diagrammed in Fig. 7.1). Since the time of Andrews, a tremendous body of literature has accumulated on the subject of critical-point phenomena, but progress in characterizing the critical point has been difficult because this point, much like the absolute zero of temperature, is approachable but not attainable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Onsager, Phys. Rev., 65, 117 (1944).
E. Ising, Z. Phys., 31, 253 (1925).
C. N. Yang and T. D. Lee, Phys. Rev., 87, 404 (1952); T. D. Lee and C. N. Yang, ibid, 410.
W. M. Fairbank, M. J. Buckingham, and C. F. Kellers, in Low Temperature Physics and Chemistry, LT-5 (J. R. Dillinger, ed.), p. 50, University of Wisconsin Press (1958); C. F. Kellers, Thesis, Duke University (1960).
M.I. Bagatskii, A. V. Voronel, and V. G. Gusak, Zh. Eksperim. i Teor. Fiz., 43, 728 (1962) [English translation, Soviet Phys.—JETP, 16, 517 (1963)].
A. V. Voronel, Yr. R. Chashkin, V. A. Popov, and V. G. Simkin, Zh. Eksperim. i Teor. Fiz., 45, 828 (1963) [English translation, Soviet Phys.—JETP, 18, 568 (1964)].
G. E. Uhlenbeck, in Critical Phenomena (M.S. Green and J. V. Sengers, eds.), p. 3, NBS Misc. Pub. 273, Washington (1966).
M. E. Fisher, J. Math. Phys., 5, 944 (1964).
M. S. Green, in Critical Phenomena (M. S. Green and J. V. Sengers, eds.), p. ix, NBS Misc. Pub. 273, Washington (1966).
A. B. Pippard, The Elements of Classical Thermodynamics, Cambridge University Press (1960). See especially Chapter 9.
C.E. Chase, E. Maxwell, and W. E. Millett, Physica, 27, 1129 (1961).
M.J. Buckingham and W. M. Fairbank, in Progress in Low Temperature Physics (C. J. Gorter, ed.), Vol. Ill, p. 80, North Holland, Amsterdam (1961).
L. D. Landau and E. M. Lifshitz, Statistical Physics, Chapters 8 and 14, Addison-Wesley, Reading, Mass. (1958).
V. L. Ginzburg, Fiz. Tverd. Tela, 2, 2031 (1960) [English translation, Soviet Phys.— Solid State, 2, 1824(1960)].
V. L. Ginzburg and L. D. Landau, Zh. Eksperim. i Teor. Fiz., 20, 1064 (1950).
V. L. Ginzburg and L. P. Pitaevskii, Zh. Eksperim. i Teor. Fiz., 34, 1240 (1958) [English translation, Soviet Phys.—JETP, 7, 858 (1958)].
L. Tisza, Ann. Phys. (N.Y.), 13, 1 (1961).
C. Domb, in Critical Phenomena (M. S. Green and J. V. Sengers, eds.), p. 29, NBS Misc. Pub. 273, Washington (1966).
L. S. Ornstein and F. Zernike, Proc. Acad. Sci. Amsterdam, 17, 793 (1914);
L. S. Ornstein and F. Zernike, Physik. Z., 19, 134 (1918).
M. E. Fisher, in Critical Phenomena (M. S. Green and J. V. Sengers, eds.), p. 21, NBS Misc. Pub. 273, Washington (1966).
G. S. Rushbrook, J. Chem. Phys. 39, 842 (1963).
J. W. Essam and M. E. Fisher, J. Chem. Phys., 38, 802 (1963).
B. Widom, J. Chem. Phys., 41, 1633 (1964).
B. Widom, J. Chem. Phys., 43, 3898 (1965).
R. B. Griffiths, Phys. Rev. Letters 14, 623 (1965).
J. S. Rowlinson, in Critical Phenomena (M.S. Green and J. V. Sengers, eds.), p. 9, NBS Misc. Pub. 273, Washington (1966).
L. P. Kadanoff, Physics, 2, 263 (1966).
R. B. Griffiths, Phys. Rev., 158, 176 (1967).
L. P. Kadanoff, W. Götze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, J. Swift, D. Aspnes, and J. Kane, Rev. Mod. Phys., 39, 395 (1967).
M. S. Green, M. Vincentini-Missoni, and J. M. H. Levelt Sengers, Phys. Rev. Letters, 18,1113(1967).
R. A. Ferrell, N. Menyhárd, H. Schmidt, F. Schwabl, and P. Szépfalusy, Phys. Rev. Letters, 18, 891 (1967);
R. A. Ferrell, N. Menyhárd, H. Schmidt, F. Schwabl, and P. Szépfalusy, Ann. Phys. (N.Y.), 47, 565 (1968).
B. I. Halperin and P. C. Hohenberg, Phys. Rev. Letters, 19, 700, 940 (1967).
D. R. Johnston, G. J. Oudemans, and R. H. Cole, J. Chem. Phys., 33, 1310 (1960).
R. H. Sherman and E. C. Kerr, Proc. of LT-10, Vol. I, p. 325, Moscow (1967). Private communication.
C. N. Yang and C. P. Yang, Phys. Rev. Letters, 13, 303 (1964).
M. H. Edwards and W. C. Woodbury, Phys. Rev., 129, 1911 (1963).
L. A. Landau and E. M. Lifshitz, Statistical Physics, Addison-Wesley, Reading, Mass. (1958), Sections 79–81.
L. Tisza and C. E. Chase, Phys. Rev. Letters, 15, 4 (1965).
C. E. Chase, R. C. Williamson, and L. Tisza, Phys. Rev. Letters, 13, 467 (1964);
C. E. Chase and R. C. Williamson, in Critical Phenomena (M.S. Green and J. V. Sengers, eds.), p. 197, NBS Misc. Pub. 273, Washington (1966).
L. Mistura and D. Sette, Phys. Rev. Letters, 16, 268 (1966).
M. J. Buckingham, in Critical Phenomena (M. S. Green and J. V. Sengers, eds.), p. 95, NBS Misc. Pub. 273, Washington (1966).
M. H. Edwards, Phys. Rev. Letters, 15, 348 (1965).
P. R. Roach and D. H. Douglas, Jr., Phys. Rev. Letters, 17, 1083 (1966).
M. H. Edwards, Proc. of LT-10, Vol. I, p. 592, Moscow (1967).
P. R. Roach and D. H. Douglas, Jr., Phys. Rev. Letters, 19, 287 (1967);
P. R. Roach, Phys. Rev., 170, 213 (1968).
R. H. Sherman, Phys. Rev. Letters, 15, 141 (1965).
C. E. Chase and G. O. Zimmerman. Phys. Rev. Letters, 15, 483 (1965).
R. H. Sherman and E. F. Hammel, Phys. Rev. Letters, 15, 9 (1965).
M. E. Fisher, Phys. Rev. Letters, 16, 11 (1966).
J. de Boer, Physica, 14, 139 (1948);
J. de Boer and B. S. Blaisse, Physica, 14, 149 (1948);
J. de Boer and R. J. Lunbeck, Physica, 14, 510, 520 (1948).
G. O. Zimmerman and C. E. Chase, Phys. Rev. Letters, 19, 151 (1967).
M. R. Moldover and W. A. Little, Phys. Rev. Letters, 15, 54 (1965); M. R. Moldover, Thesis, Stanford University (1966).
L. P. Kadanoff and J. Swift, Phys. Rev., 166, 89 (1968).
J. F. Kerrisk and W. E. Keller (to be published) ; J. F. Kerrisk, Thesis, U. of N.M., 1968.
A. Michels, J. V. Sengers, and P. S. Van der Gulik, Physica, 28, 1201, 1216 (1962);
A. Michels and J. V. Sengers, Physica, 28, 1238 (1962).
J. V. Sengers, in Critical Phenomena (M. S. Green and J. V. Sengers, eds.), p. 165, NBS Misc. Pub. 273, Washington (1966).
K. R. Atkins and M. H. Edwards, Phys. Rev. 97, 1429 (1955).
M. H. Edwards, Can. J. Phys., 36, 884 (1958).
E. C. Kerr and R. D. Taylor, Ann. Phys. (N.Y.), 26, 292 (1964).
V. P. Peshkov and A. P. Borovikov, Zh. Eksperim. i Teor. Fiz., 50, 852 (1966) [English translation, Soviet Phys.-JETP, 23, 559 (1966)].
D. Elwell and H. Meyer, Phys. Rev., 164, 245 (1967).
A. van Itterbeek and G. Forrez, Physica, 20, 133 (1954).
C. E. Chase, Phys. Fluids, 1, 193 (1958).
I. Rudnick and K. A. Shapiro, Phys. Rev. Letters, 15, 386 (1965).
M. B. Barmatz and I. Rudnick, Proc. of LT-10, Vol. I, p. 512, Moscow (1967); M. B. Barmatz, Thesis, UCLA (1966); M. Barmatz and I. Rudnick, Phys. Rev., 170, 224 (1968).
J. R. Clow and J. D. Reppy, Phys. Rev. Letters, 16, 887 (1966).
B. D. Josephson, Physics Letters, 21, 608 (1966).
J. A. Tyson and D. H. Douglass, Jr., Phys. Rev. Letters, 17, 472, 622 (1966);
J. A. Tyson, Phys. Rev. 166, 166 (1968).
O. V. Lounasmaa and L. Kaunisto, Ann. Acad. Sci. Fennicae, Ser. AVI, No. 59 (1960).
H. A. Kierstead, Phys. Rev., 162, 153 (1967).
O. V. Lounasmaa and E. Kojo, Ann. Acad. Sci. Fennicae, Ser. AVI, No. 36 (1959).
E. R. Grilly, Phys. Rev., 149, 97 (1966).
E. R. Grilly and R. L. Mills, Ann. Phys. (N.Y.), 18, 250 (1962).
W. H. Keesom and A. P. Keesom, Physica, 1, 128 (1934); Leiden Communications Suppl.No.7b(1933).
O. V. Lounasmaa, Phys. Rev., 130, 847 (1963).
H. A. Kierstead, Phys. Rev., 138, A1594 (1965).
H. A. Kierstead, Phys. Rev., 153, 258 (1967).
K. R. Atkins and R. A. Stasior, Can. J. Phys., 31, 1156 (1953).
R. D. Taylor and J. G. Dash, Phys. Rev., 106, 398 (1957).
J. Kerrisk and W. E. Keller, Bull. Amer. Phys. Soc, Ser. II, 12, 555 (1967).
L. Goldstein, Phys. Rev., 135, A1471 (1964);
L. Goldstein, Phys. Rev., 140, A1547 (1965).
R. Brout, Phys. Rev., 131, 899 (1963).
F. London, Superfluids, Vol. II, p. 55, John Wiley, New York (1954).
J. L. De Coen and H. Tompa, Physica, 32, 995 (1966).
P. Sikora and F. Mohling, Los Alamos Sci. Lab. Report LA-DC 8333 (1967).
A. Z. Patashinskii and V. L. Pokrovskii, Zh. Eksperim. i Teor. Fiz., 46, 994 (1964) [English translation, Soviet Phys.-JETP, 19, 677 (1964)].
W. M. Fairbank and C. F. Kellers, in Critical Phenomena (M. S. Green and J. V. Sengers, eds.), p. 71, NBS Misc. Pub. 273, Washington (1966).
K. C. Lee and R. D. Puff, Phys. Rev., 158, 170 (1967).
D. F. Brewer, in Superfluid Helium (J. F. Allen, ed.), p. 159, Academic Press, London (1966); Proc. of LT-10, Vol. I, p. 145, Moscow (1967).
F. D. Manchester, Rev. Mod. Phys., 39, 383 (1967).
I. Rudnick, E. Guyon, K. A. Shapiro, and S. A. Scott, Phys. Rev. Letters, 19, 488 (1967);
D. F. Brewer, G. W. Leppelmeier, C. C. Lim, D. O. Edwards, and J. Landau, Phys. Rev. Letters, 19, 491 (1967).
D. F. Goble and L. E. H. Trainor, Can. J. Phys., 44, 27 (1966).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1969 Springer Science+Business Media New York
About this chapter
Cite this chapter
Keller, W.E. (1969). Critical Phenomena in He3 and He4 . In: Helium-3 and Helium-4. The International Cryogenics Monograph Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6485-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4899-6485-4_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-6232-4
Online ISBN: 978-1-4899-6485-4
eBook Packages: Springer Book Archive