ATOMIC VIBRATIONS AT (100) SURFACES OF FCC AND BCC METALS

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ATOMIC VIBRATIONS AT (100) SURFACES OF FCC

AND BCC METALS

J. Black, D. Campbell, R. Wallis

To cite this version:

J. Black, D. Campbell, R. Wallis.

ATOMIC VIBRATIONS AT (100) SURFACES OF

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JOURNAL DE PHYSIQUE

CoLloque C6, suppl6mnt au n o 12, Tome 42, ddcembre 1981 page ~ 6 - 8 3 7

A T O M I C V I B R A T I O N S A T (100) SURFACES OF

FCC

AND BCC M E T A L S

J.E.

lack*, D.A. Campbell and R.F. Wallis

University of CaZifornia, Irvine, CaZifornia 92717, U.S.A.

Abstract.

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We have studied the dynamics of atom motion at metal (100) surfaces. The interactions between atoms are modelled with central forces and angle bending forces. Results for frequencies and polarizations of surface modes h a v e been obtained for the following metals: body centered C r , Fe, K , M o , Na, V. W; face centered A g , A l , Au, Cu, I r , Ni, P d , P t , Rh. Specific r e s u l t s are presented for Cr and Ni.

1. Introduction.

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In the last few years we have seen the development of experimental techniques which are sensitive to surface phonons. The electron energy loss spectroscopy experiments of Ibach and Bruchmann ( 1 1 and of Andersson [2] have revealed surface phonons o n nickel. H e l i u m scattering experiments by Brusdeylins, D o a k , and Toennies [3] have yielded data on surface vibrations o n LiF. T h i s

latter technique may soon be applied to a study of metal surfaces [ 4 1 . It is clear that there will be a need for a tabulation o f important surface phonon frequencies for a variety of metals. Such a tabulation can serve as a guide to the interpretation of spectral features. In addition, it may serve as a starting point from which to recognize that surface relaxation or reconstruction h a s occurred. It i s the tabulation of important surface phonon frequencies which is the objective of this work.

2. Lattice Dynamical Models.

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We have used several models in calculating the atomic force constants. In the present paper, w e present results for only a single model consisting of first and second neighbor central interactions together with angle bending

interactions. The five force constants a a 2 , $ I , B2, and Y were determined by first calculating y from the elastic constants, and then using the equilibrium condition, along with experimentally determined frequencies at high symmetry points in the bulk dispersion curves.

n n T h e frequencies that gave the best overall fit are vT (?,~,0),

n n n

v(n,O,O) and v(?,~,?). W e measured the goodness of fik by comparing

*present address : Physics Department, Brock University, St. Catherines, Ontario L2S 3 A 1 , Canada

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+ 3 0.24 radians. As we move toward

i,

the SH mode vibrates perpendicular to the

TX

d i r e c t i o n , not perpendicular to the wave vector. Similarly, modes labelled longitudinal vibrate along the

T?

direction, not parallel to the wave vector, at points away from

X.

T h u s the mode marked SV-SH at high frequencies in the center of the

zone edge has components parallel and perpendicular to

r X

in the plane of the surface. All BCC metal results are qualitatively similar to those for Cr.

4. Results for FCC Metals.

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The results are qualitatively very similar to those obtained for the BCC metals. The most striking difference between FCC and BCC metals is the absence of the mode LL at

? .

A typical set of dispersion curves is shown in Fig. 2 for Ni.

'"I I

Fig. 2. Dispersion data along the

M?

direction in the surface Brillouin zone of Ni. Dashed lines indicate s u r f a c e m o d e s , and the cross-hatched

,I

I

areas are those in which the

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M bulk phonons are found.

Note that the mode SV2 at now exists only at il and is no longer a continuation of LL a s i t was in the body centered case. Also the mode of SV-SH character is found near the zone edge center in all cases. Acknowledgements

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This research was supported by grants from the Department of E n e r g y , through Contract No. DE-AT0379-ER1032, from the National Science and Engineering Research Council of Canada, and from the National Science Foundation under Grant No. DMR-7809430.

References

1. H. Ibach and D. Bruchmann, Phys. Rev. Letters

44

(1980) 36. 2. S. Andersson, Surface Sci.

79

(1979) 385.

3. G. Brusdeylins, R. B. Doak and J. P. Toennies, Proceedings of the Fourth Interaction Conference on Solid Surfaces, eds. D. A. Degral and M. Costa, Cannes, 1980, p. 842.

4. J. P. Toennies, private communication.