Specific Heats of Zirconium Alloys at Low Temperatures

G. D. Kneip, Jr; J. O. Betterton, Jr; J. O. Scarbrough

doi:10.1103/PhysRev.131.2425

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Specific Heats of Zirconium Alloys at Low Temperatures

G. D. Kneip, Jr.^*, J. O. Betterton, Jr., and J. O. Scarbrough^†

Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee

^*Present address: SUPERCON, P. O. Box 4209, Houston, Texas.
^†Operated by the Union Carbide Corporation for the U. S. Atomic Energy Commission.

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Phys. Rev. 131, 2425 – Published 15 September, 1963

DOI: https://doi.org/10.1103/PhysRev.131.2425

Abstract

The specific heats of dilute alloys of silver, cadmium, indium, tin, and antimony in hexagonal zirconium have been measured from 1.2 to 4.5°K. For each alloy the specific heat obeys the relation $c = γ T + β T^{3}$ within the experimental error. All of these solutes increase $γ$ linearly with concentration and $\frac{d γ}{dx}$ is linearly related to the chemical valence of the solute. The increase in $γ$ in the tin-zirconium alloys shows that all electrons outside closed shells cannot be treated as equivalent in the rigid band model of alloying. All of these solutes increase the density of states of zirconium, providing evidence for a zone overlap in the zirconium $d$ band and for a small number of electrons in a new band. All of the solutes increase the lattice specific heat and the Debye temperature is a linear function of solute concentration for each of these alloy systems. $\frac{d θ}{dx}$ is not simply related to the solute valence but shows a close correlation with the magnitude of the rate of change of the distance between atoms at (0,0,0) and ( $\frac{1}{3}$ , $\frac{2}{3}$ , ½) of the hexagonal cell. Additions of tin to zirconium do not change the average interaction potential of the BCS theory appreciably.

References (34)

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Omitted endnote
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[c1] N. F. Mott and H. Jones, The Theory and Properties of Metals and Alloys (Clarendon Press, Oxford, 1936), p. 179

[c2] F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), p. 149

[c3] G. V. Raynor, in Reports of Progress in Physics, edited by A. C. Strickland (The Physical Society, London, 1952), Vol. 15, p. 76

[c4] H. Jones, Proc. Phys. Soc. (London) 49, 243 (1937)

[c5] J. Friedel, in Advances in Physics, edited by N. F. Mott (Taylor and Francis, Ltd., London, 1954), Vol. 3, p. 465

[c6] J. A. Rayne, Phys. Rev. 110, 606 (1958)

[c7] J. R. Neighbours and C. S. Smith, Acta Met. 2, 591 (1954)

[c8] R. I. Gayley, Jr., E. A. Lynton, and B. Serin, Phys. Rev. 126, 43 (1962)

[c9] C. H. Cheng, C. T. Wei, and P. A. Beck, Phys. Rev. 120, 426 (1960)

[c10] R. R. Hake, in Proceedings of the Seventh International Conference on Low-Temperature Physics, edited by G. M. Graham and A. C. Hollis Hallet (University of Toronto Press, Toronto, 1961), p. 359

[c11] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)

[c12] Omitted endnote

[c13] G. D. Kneip, Jr., J. O. Betterton, Jr., and J. O. Scarbrough, Phys. Rev. 130, 1687 (1963)

[c14] D. Pines, in Solid State Physics, edited by F. Seitz and D. Turnbull, (Academic Press, Inc., New York, 1955), p. 367

[c15] J. M. Luttinger, Phys. Rev. 119, 1153 (1960)

[c16] J. J. Quinn and R. A. Ferrell, Phys. Rev. 112, 812 (1958)

[c17] D. Bohm and D. Pines, Phys. Rev. 85, 332 (1952)

[c18] P. Nozières and D. Pines, Phys. Rev. 111, 442 (1958)

[c19] M. Gell-Mann and K. A. Brueckner, Phys. Rev. 106, 364 (1957)

[c20] E. P. Wigner, Trans. Faraday Soc. 34, 678 (1938)

[c21] J. G. Fletcher and D. C. Larson, Phys. Rev. 111, 455 (1958)

[c22] H. Jones, Proc. Phys. Soc. (London) A240, 321 (1957)

[c23] S. L. Altmann and C. J. Bradley, Phys. Letters 1, 336 (1962) private communication from S. L. Altmann

[c24] G. W. Lehman and T. G. Berlincourt, Atomics International, AI-1889, 1957 (unpublished)

[c25] J. C. Slater, Phys. Rev. 49, 537 (1936)

[c26] M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939)

[c27] J. O. Betterton, Jr., and D. S. Easton, in Proceedings of the Seventh International Conference on Low-Temperature Physics, edited by G. M. Graham and A. C. Hollis Hallet (University of Toronto Press, Toronto, 1961), p. 270

[c28] C. H. Shaw and E. L. Jossem, Final Report RF Project 471 (1959), Ohio State University Research Foundation (unpublished)

[c29] J. E. Holliday, Bull. Am. Phys. Soc. 7, 416 (1962)

[c30] T. G. Berlincourt, Phys. Rev. 114, 669 (1959)

[c31] F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), p. 38

[c32] J. O. Betterton, Jr., and D. S. Easton, J. Metals 13, 86 (1961)

[c33] D. Pines, Phys. Rev. 109, 208 (1958)

[c34] B. L. Goodman, J. Hillairet, J. J. Veyssié, and L. Weil, in Proceedings of the Seventh International Conference on Low-Temperature Physics, edited by G. M. Graham and A. C. Hollis Hallet (University of Toronto Press, Toronto, 1961), p. 350

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Specific Heats of Zirconium Alloys at Low Temperatures

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