Abstract
The generalized susceptibility, X( →q ), of both NbC and TaC determined from APW energy band calculations show large maxima to occur at precisely those DDmax values at which soft phonon modes were observed by Smith. Maxima in X( →q ) are predicted for other directions. The locus of these →q max values can be represented by a warped cube of dimension ~1.2(2π/a) in momentum space — in striking agreement with the soft mode surface proposed phenomenologically by Weber. In sharp contrast, the X( →q ) calculated for both ZrC and HfC — for which no phonon anomalies have been observed — fall off in all symmetry directions away from the zone center. We thus interpret the phonon anomalies in the transition metal carbides as due to an “overscreening” effect resulting from an anomalous increase of the response function of the conduction electrons.
Supported by the Air Force Office of Scientific Research (Grant No. 76-2948), the National Science Foundation (Grant Nos. DMR-72-03101-A02 and DMR-72-03019) and the Energy Research and Development Administration.
On leave from the University of Paris-Sud, 91405 Orsay, France and Le Centre de Mécanique Ondulatoire Appliquée du Centre National de la Recherche Scientifique, 23 rue du Maroc, 75019 Paris.
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References
H.G. Smith and W. Glaser, Phys. Rev. Lett. 25, 1611 (1970).
H.G. Smith in Superconductivity in d and f Band Metals, ed. by D.H. Douglass ( AIP, New York, 1972 ).
B.M. Powell, P. Martel and A.D.B. Woods, Phys. Rev. 171, 727 (1968).
B.W. Batterman and C.S. Barret, Phys. Rev. Lett. 13, 390 (1964); L.R. Testardi in Physical Acoustics, Vol. X, 193 (W.P. Mason and R.N. Thurston, Eds., Academic Press, New York, 1973 ); M.Weger and I.B. Goldberg in Solid State Physics, Vol. 28, 1 ( F. Seitz and D. Turnbull, Eds. Academic Press, New York, 1973 ).
L.R. Testardi, Comments Sol. State Phys. 6, 131 (1975).
W.L. McMillan, Phys. Rev. 167, 331 (1968),
W. Weber, Phys. Rev. B 8, 5093 (1973).
B.M. Klein, D. Papaconstantopoulos, Phys. Rev. Lett. 32, 1193 (1974).
G.D. Gaspari and B.L. Gyorffy, Phys. Rev. Lett. 28, 801 (1972).
C.M. Varma and R.C. Dynes, Bull. Am. Phys. Soc., 259 (March 1976).
W. Weber, H. Bilz and U. Schroder, Phys. Rev. Lett. 28, 600 (1972).
W. Weber, Phys. Rev. B 8, 5082 (1973).
H.G. Smith, Phys. Rev. Lett. 29, 353 (1972).
D.J. Chadi and M.L. Cohen, Phys. Rev. B 10, 496 (1974).
M. Mostoller, Phys. Rev. B 5, 1260 (1972).
M.P. Verma and B.R.K. Gupta, Phys. Rev. B 12, 1314 (1975).
S.K. Sinha and B.H. Harmon, Phys. Rev. Lett. 35, 1515 (1975).
W. Hanke, J. Hafner and H. Bilz International Conference of Low Lying Vibrational Modes and their Relationship to Superconductivity and Ferroelectricity, San Juan, Puerto Rico 1975 (to be published).
J.C. Phillips, Phys. Rev. Lett. 26, 543 (1971).
Michele Gupta and A.J. Freeman, Bull. Am. Phys. Soc., 21, 258 (1976); Phys. Rev. Lett. 1976 submitted; Phys. Lett. 1976 (in press).
J.C. Slater, Phys. Rev. 81, 385 (1951).
L. Ramqvist, B. Ekstig, E. Källne, E. Noreland and R. Manne, J. Chem. Phys. Solids 32, 149 (1971).
E. Källne and M. Pessa, J. Phys. C 8, 1985 (1975).
R.W. Simpson, Ms. Sc. Thesis, University of Florida, Gainesville (1969).
Michele Gupta, V.A. Gubanov and D.E. Ellis (to be published).
L.F. Mattheiss, Phys. Rev. B 5, 315 (1972).
G. Lehmann, P. Rennert, M. Taut and H. Wonn, Phys. Status Solidi 37, K27 (1970); G. Lehmann and M. Taut, ibid. 54, 469 (1972).
O. Jepsen and O.K. Andersen, Solid State Comm. 9, 1763 (1971).
L.E. Toth, Transition Metal Carbides and Nitrides ( Academic, New York, 1971 ).
T.H. Geballe, B.T. Matthias, J.P. Remeika, A.M. Clogston, V.H. Compton, J.P. Maita and H.J. Williams, Phys. 2, 293 (1966).
N. Elyashar and D.D. Koelling, Bull. Am. Phys. Soc., 21, 309 (1976).
L.F. Mattheiss, Phys. Rev. B 1, 373 (1970).
W.E. Evenson, G.S. Fleming and S.H. Liu, Phys. Rev. 178, 930 (1969).
J. Rath and A.J. Freeman, Phys. Rev. B 11, 2109 (1975).
G. Gilat and L.J. Raubenheimer, Phys. Rev. 144, 390 (1966).
W.R. Fehlner and P.D. Lolly, Sol. State Comm. 14, 653 (1974).
S.K. Sinha, Naval Research Laboratory Colloquium, January 18 (1976).
B. Klein, D. Papaconstantopoulos and L. Boyer (in this Proceedings).
R.P. Gupta and S.K. Sinha, Phys. Rev. B 3, 2401 (1971).
J.F. Cooke, H.L. Davis and Mark Mostoller, Phys. Rev. B 9, 2485 (1974).
R.P. Gupta and A.J. Freeman, Bull. Am. Phys. Soc. 20, 364 (1975) and Phys. Rev. B May 15 (1976).
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Gupta, M., Freeman, A.J. (1976). Direct Correlation of Observed Phonon Anomalies and Maxima in the Generalized Susceptibilities of Transition Metal Carbides. In: Douglass, D.H. (eds) Superconductivity in d- and f-Band Metals. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8795-8_17
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