Abstract
How can a paper on the Green’s function method applied to surface lattice dynamics fit to a workshop on “Ab-initio calculation of phonon spectra”? We think that the answer comes out from the very essence of the method. All what happens at the free surface of a solid, such as the change of force constants, of atomic equilibrium positions, of electronic structure, is due to intrinsic properties of the bulk Hamiltonian manifesting themselves through the symmetry breaking. Thus a full knowledge of the dynamical structure of the bulk, regardless whether obtained ab-initio or in a phenomenological way, should be sufficient to account for all the surface intrinsic dynamical properties. In the Green’s function (GF) method applied to surface problems the bulk dynamical structure is the basic ingredient, whereas the perturbation of an intrinsic surface, induced by the symmetry breaking, turns out to be fully described by the corresponding change in the translational invariance (TI) and rotational invariance (RI) sum rules.
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References
I.M. Lifshitz and L.N. Rosenzweig, Zh. Eksperim. i. Teor. Fiz. 18, 1012 (1948).
A.A. Maradudin and J. Melngailis, Phys. Rev. 133, A1188 (1964).
L. Dobrzynski and G. Leman, J. Phys. (Paris) 30, 116 (1969).
S.W. Musser and K.H. Rieder, Phys. Rev. B2, 3034 (1970).
G. Benedek, Phys. Stat. Sol. (b) 58, 661 (1973).
A.A. Maradudin and L.J. Sham, in “Lattice Dynamics”, ed. M. Balkanski, Flammarion Sciences, Paris (1978), p. 296.
G. Benedek, Surf. Sci. 6l, 603 (1976).
G. Benedek and G.F. Nardelli, Phys. Rev. 155, 1004 (1967).
M.V. Klein, in “Physics of Color Centers”, ed. W. Beali Fowler, Academic Press, New York (1968), p. 430.
I.M. Lifshitz, Nuovo Cimento Suppl. 3, 732 (1956).
A. Messiah, “Mécanique Quantique”, Dunod, Paris (1959).
K.L. Klievew and R. Fuchs, in “Advances in Chemical Physics”, vol. XXVII, eds. I. Prigogine, A. Stuart Rice, J. Wiley & Sons, New York (1974), p. 355.
G. Benedek, in “Dynamics of Gas-Surface Interaction”, eds. G. Benedek, U. Valbusa, Springer Verlag, Berlin (1982).
A.A. Maradudin, E.W. Montroll, G.A. Weiss and I.P. Ipatova, “Lattice Dynamics in Harmonic Approximation”, Solid State Physics Suppl. 3, 2nd ed., Academic Press, New York (1971).
G. Benedek and V. Velasco, Phys.Rev. B23, 6691 (1981).
G. Brusdeylins, R.B. Doak and J.P. Toennies, Phys. Rev. Lett. 44, 1417 (1980) and 16, 437 (1981).
R.B. Doak, M.I.T. Thesis (1981); G. Benedek, G. Brusdeylins, R.B. Doak and J.P. Toennies, in “Proceedings of the International Conference on Phonon Physics, Bloomington, 1981”, ed. W.E. Bron, J. Phys. (Paris), Suppl. (in press) and private communication from G. Brusdeylins, R.B. Doak and J.P. Toennies.
T.S. Chen, F.W. de Wette, G.P. Alldredge, Phys. Rev. B15s, 1167 (1977).
A. Bilz and W. Kress, “Phonon Dispersion Relation in Insulators”, Springer Verlag, Berlin (1979).
U. Schröder, Sol. Stat, Comm. 4, 347 (1966). U. Schröder arid V. Niisslein, Phys. Stat. Sol. 21, 309 (1967).
G. Benedek and N. Garcia, Surface Sci. 103, L143 (1981).
G. Benedek and F. Galimberti, Surface Sci. 71, 87 (1967).
In previous calculations (refs. 5, 7 and 22) the expected degeneracy at the M point between x- and y-polarized surface modes was not verified. The pathological behaviour of a program routine in a small region around M was causing the misfit. An erratum is appearing in Surface Science. We remark that all recent calculations of interface dynamics (Ref. 15) and atom scattering cross sections (refs. 17, 21) are correct. We also note that this inconsistency is not one of the “deficiencies” mentioned by Kliever and Fuchs, ref. 12, which, on the contrary, do not exist.
A.A. Maradudin, R.F. Wallis and L. Dobrzynski, “Handbook of Surfaces and Interfaces”, vol. 3, Garland STPM Press, New York and London (1980).
G.P. Alldredge, Phys. Lett. 41A, 281 (1972).
A.A. Lucas, J. Chem. Phys. 48, 3156 (1968).
F.W. de Wette, in “Lattice Dynamics”, ed. M. Balkanski, Flamma- rion Sciences, Paris (1978), p. 275.
G. Dolling, E.G. Smith, R.M. Nicklow, P.R. Vijayaraghavan and M.K. Wilkinson, Phys. Rev. 168, 970 (1968).
W.J. Buyers, Phys. Rev. 153, 983 (1967).
J.R. Tessman, A.H. Kahn and W. Shockley, Phys. Rev. 92, 890 (1953).
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Benedek, G., Miglio, L. (1983). Green’s Function Calculation of Surface Phonons in Ionic Crystals. In: Devreese, J.T., Van Doren, V.E., Van Camp, P.E. (eds) AB Initio Calculation of Phonon Spectra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3563-4_11
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