Abstract
Experiments to measure the kinetic coefficients of the helium crystal surface, which have been criticized by Grabinski and Liu,1 are analyzed to determine the effect of heat flow through the surface and the effect of nonhydrostatic crystal strain. The experiments studied are the low-temperature measurements of the damping of melting-freezing waves in4He, the high-temperature relaxation of the4He crystal surface after an electrostatic disturbance, the relaxation in shape of a3He crystal, and the measurement of the Onsager cross-coefficient using a heat current in4He. After a review of the theory, in which the dependence of the growth coefficient on the thermal conditions of the experiment is discussed, the corrections to published results due to heat flow are shown to be small and within the experimental errors. The effect of nonhydrostatic strain is shown to be second order and consequently negligible in most existing measurements of kinetic or static properties. However, if sufficiently large, nonhydrostatic strain produces an instability of the surface that was predicted by Grinfeld.7 This effect may explain a corrugation of the surface observed by Bodensohn et al.9 during rapid cooling. The threshold for the Grinfeld instability and the frequency and damping of melting-freezing waves below the threshold is discussed. We propose a new experiment to study the instability and to measure the elastic and plastic properties of the crystal.
Similar content being viewed by others
References
M. Grabinski and M. Liu,J. Low Temp. Phys. 75, 271 (1989).
B. Castaing and P. Nozieres,J. Phys. (Paris)41, 701 (1980).
R. M. Bowley and D. O. Edwards,J. Phys. (Paris)44, 723 (1983).
P. E. Wolf, D. O. Edwards, and S. Balibar,J. Low Temp. Phys. 51, 489 (1983).
D. O. Edwards, S. Balibar, and P. E. Wolf,75th Jubilee Conference on Helium-4, J. G. M. Armitage, ed. (World Scientific, [Singapore 1983), p. 70.
S. E. Korshunov,Zh. Eksp. Teor. Phys. 92, 1320 (1987) (Sov. Phys. JETP 65, 741 (1987)).
M. A. Grinfeld,Dokl. Akad. Nauk SSSR 290, 1358 (1986) [Sov. Phys. Dokl. 31, 831 (1986)].
P. Nozieres, Lectures given at the Beg-Rohu (Brittany) Summer School, 1989 (to be published).
J. Bodensohn, K. Nicolai, and P. Leiderer,Z. Phys. B 64, 55 (1986).
L. D. Landau and I. M. Lifshitz,Statistical Physics, Third Edition, Part 1 (Pergamon Press, London, 1980), p. 368.
H. J. Maris and T. E. Huber,J. Low Temp. Phys. 48, 99 (1982).
V. I. Marchenko and A. Ya. Parshin,Pis'ma Zh. Eksp. Teor. Fiz. 31, 767 (1980) [Sov. Phys. JETP Lett. 31, 724 (1980)].
E. R. Grilly,J. Low Temp. Phys. 11, 33 (1973).
P. Nozieres and M. Uwaha,J. Phys. (Paris)48, 389 (1987).
T. H. Huber and H. J. Maris,Phys. Rev. Lett. 47, 1907 (1981);J. Low Temp. Phys. 48, 463 (1982).
B. Castaing, G. Bonfait, and D. Thoulouze,Physica B 109–110, 2093 (1982); L. Puech, B. Hebral, D. Thoulouze, and B. Castaing,J. Phys. Lett. (Paris)43, L809 (1982).
L. Puech, G. Bonfait, and B. Castaing,J. Low Temp. Phys. 62, 315 (1986).
F. Graner, S. Balibar, and E. Rolley,J. Low Temp. Phys. 75, 69 (1989).
A. F. Andreev and A. Ya Parshin,Zh. Eksp. Teor. Fiz. 75, 1511 (1978) [Sov. Phys. JETP 48, 763 (1978)].
A. F. Andreev and V. G. Knizhnik,Zh. Eksp. Teor. Fiz. 83, 416 (1982) [Sov. Phys. JETP 56, 226 (1982)].
K. O. Keshishev, A. Ya. Parshin, and A. B. Babkin,Zh. Eksp. Teor. Fiz. 80, 716 (1981) [Sov. Phys. JETP 53, 362 (1981)].
G. Agnolet,Jpn. J. Appl. Phys. 26, A79 (1987);
S. V. Iordanskii and S. E. Korshunov,Zh. Eksp. Teor. Phys. 87, 927 (1984) [Sov. Phys. JETP 60, 528 (1984)].
L. Puech and B. Castaing,J. Phys. Lett. (Paris)43, 601 (1982).
S. Mukherjee and D. O. Edwards,Jpn. J. Appl. Phys. 26, A113 (1987); D. O. Edwards, S. Mukherjee, and M. S. Pettersen,Phys. Rev. Lett. 64, 902 (1990).
R. J. Donnelly and P. H. Roberts,J. Low Temp. Phys. 27, 687 (1977).
B. M. Abraham, Y. Eckstein, J. B. Ketterson, M. Kuchnir, and P. R. Roach,Phys. Rev. A 1, 250 (1970).
W. R. Gardner, J. K. Hoffer, and N. E. Phillips,Phys. Rev. A 7, 1029 (1973).
R. M. Bowley and D. O. Edwards, unpublished.
F. Graner, R. M. Bowley, and P. Nozieres,J. Low Temp. Phys. 80, 113 (1990).
G. Armstrong and A. S. Greenberg,J. Phys. (Paris)39-C6, 135 (1978).
E. R. Grilly,J. Low Temp. Phys. 4, 615 (1971).
A. C. Anderson, J. I. Connolly, O. E. Vilches, and J. C. Wheatley,Phys. Rev. 147, 90 (1966).
S. Balibar, D. O. Edwards, and C. Laroche,Phys. Rev. Lett. 42, 782 (1979).
J. Landau, S. G. Lipson, L. M. Maatanen, L. S. Balfour, and D. O. Edwards,Phys. Rev. Lett. 45, 31 (1980).
F. Gallet, P. E. Wolf, and S. Balibar,Phys. Rev. Lett. 52, 2253 (1984).
P. E. Wolf, F. Gallet, S. Balibar, E. Rolley, and P. Nozieres,J. Phys. (Paris)46, 1987 (1985).
F. Gallet, S. Balibar, and E. Rolley,J. Phys. (Paris)48, 369 (1987).
J. W. Gibbs,The Scientific Papers of J. Willard Gibbs (Dover, New York 1961), p. 195.
L. D. Landau and I. M. Lifshitz,Theory of Elasticity (Pergamon Press, London, 1970), chapter 1, sections 1–7.
L. D. Landau and I. M. Lifshitz,Statistical Physics, Third Edition, Part 1 (Pergamon Press, London, 1980), chapter 12 and particularly the footnote on p. 368.
P. Nozieres and D. E. Wolf,Z. Phys. B 70, 399 (1988);70, 507 (1988).
M. Uwaha and G. Baym,Phys. Rev. B 26, 4928 (1982).
A. F. Andreev,Progress in Low Temperature Physics, Vol. 8, D. F. Brewer, ed. (North-Holland, Amsterdam, 1982).
S. Balibar and B. Castaing,Surf. Sci. Rep. 5, 87 (1985).
P. R. Granfors, B. A. Fraass, and R. O. Simmons,J. Low Temp. Phys. 67, 353 (1987).
Author information
Authors and Affiliations
Additional information
This laboratory is associated with the CNRS and the Universite Pierre et Marie Curie.
Rights and permissions
About this article
Cite this article
Balibar, S., Edwards, D.O. & Saam, W.F. The effect of heat flow and nonhydrostatic strain on the surface of helium crystals. J Low Temp Phys 82, 119–143 (1991). https://doi.org/10.1007/BF00681525
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00681525