Frozen-Phonon Total-Energy Determination of Structural Surface Phase Transitions: W(001)

C. L. Fu; A. J. Freeman; E. Wimmer; M. Weinert

doi:10.1103/PhysRevLett.54.2261

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Frozen-Phonon Total-Energy Determination of Structural Surface Phase Transitions: W(001)

C. L. Fu, A. J. Freeman, and E. Wimmer^*

M. Weinert

Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60201

Department of Physics, Brookhaven National Laboratory, Upton, New York 11973

^*Present address: Cray Research, Inc., 1440 Northland Dr., Mendota Heights, Minn. 55120.

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Phys. Rev. Lett. 54, 2261 – Published 20 May, 1985

DOI: https://doi.org/10.1103/PhysRevLett.54.2261

Abstract

The prototypical W(001) structural phase transition is investigated by all-electron, frozen-phonon, total-energy calculations. The strong coupling between surface states and the ${\bar{M}}_{5}$ phonons plays a decisive role in favoring the reconstructed $c (2 \times 2)$ structure with a lateral $〈 110 〉$ zig-zag displacement of 0.18±0.01 Å (in excellent agreement with experiment) and no interlayer relaxation. The transition from the (1 × 1) into the $c (2 \times 2)$ phase proceeds over a very flat region of the energy hypersurface and suppresses the relaxation.

References (24)

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([13])
M. Posternak, H. Krakauer, A. J. Freeman, and D. D. Koelling, Phys. Rev. B 21, 5601 (1980) H. Krakauer, 30, 6834 (1984)
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[c1] T. E. Felter, R. A. Baker, and P. J. Estrup, Phys. Rev. Lett. 38, 1138 (1977)

[c2] M. K. Debe and D. A. King, Phys. Rev. Lett. 39, 708 (1977) Surf. Sci. 81, 193 (1979)

[c3] A. J. Melmed et al., Phys. Rev. Lett. 43, 1521 (1979) R. T. Tung, W. R. Graham, and A. J. Melmed, Surf. Sci. 115, 576 (1982)

[c4] I. Stensgaard, L. C. Feldman, and P. J. Silverman, Phys. Rev. Lett. 42, 247 (1979)

[c5] H. Krakauer, M. Posternak, and A. J. Freeman, Phys. Rev. Lett. 17, 1885 (1979)

[c6] I. Terakura, K. Terakura, and N. Hamada, Surf. Sci. 103, 103 (1981)

[c7] A. Fasolino, G. Santora, and E. Tosatti, Phys. Rev. Lett. 44, 1684 (1980) J. Phys. C 6, 846 (1981) E. Tosatti, Solid State Commun. 25, 637 (1978)

[c8] J. E. Inglesfield, J. Phys. C 12, 149 (1979)

[c9] G. Treglia, M.-C. Desjonqueres, and D. Spanjaard, J. Phys. C 16, 2407 (1983) P. C. Stephenson and D. W. Bullett, Surf. Sci. 139, 1 (1984)

[c10] E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 24, 864 (1981)

[c11] M. Weinert, E. Wimmer, and A. J. Freeman, Phys. Rev. B 26, 4571 (1982)

[c12] S. Ohnishi, A. J. Freeman, and E. Wimmer, Phys. Rev. B 29, 5267 (1984)

[c13] C. L. Fu, S. Ohnishi, E. Wimmer, and A. J. Freeman, Phys. Rev. Lett. 53, 675 (1984)

[c14] C. L. Fu, S. Ohnishi, H. J. F. Jansen, and A. J. Freeman, Phys. Rev. B 30, 1168 (1984)

[c15] D. Pines, Elementary Excitations in Solids (Benjamin, New York, 1963)

[c16] H. J. F. Jansen and A. J. Freeman, Phys. Rev. B 30, 561 (1984)

[c17] D. D. Koelling and B. N. Hamron, J. Phys. C 10, 3107 (1977)

[c18] ([13])

[c19] M. Posternak, H. Krakauer, A. J. Freeman, and D. D. Koelling, Phys. Rev. B 21, 5601 (1980) H. Krakauer, 30, 6834 (1984)

[c20] P. Heilmann, K. Heinz, and K. Muller, Surf. Sci. 89, 84 (1979)

[c21] R. A. Barker et al., Solid State Commun. 25, 375 (1978)

[c22] J. A. Walker, M. K. Debe, and D. A. King, Surf. Sci. 104, 405 (1981)

[c23] D. A. King, Phys. Scr. T4, 34 (1983)

[c24] M. Tomasek and S. Pick, Surf. Sci. 140, L279 (1984)

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Frozen-Phonon Total-Energy Determination of Structural Surface Phase Transitions: W(001)

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