SURFACE PHONONS AND THE INCOMMENSURATE RECONSTRUCT1 ON OF CLEAN Mo (100)

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SURFACE PHONONS AND THE

INCOMMENSURATE RECONSTRUCT1 ON OF

CLEAN Mo (100)

A. Fasolino, G. Santoro, E. Tosatti

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C6, suppldment au no 12, Tome 42, dgcembre 1981 page C6-846

SURFACE PHONONS AND THE INCOMMENSURATE RECONSTRUCT

ION OF CLEAN Mo

(100)

A . ~asolino*, G. ~antoro** and E. ~osatti*'

*GNSM-CNR and SISSA, Istituto di Fisica Teorica, Universitd di Trieste, 34014 Miramare-Grignano, Trieste, Italy

**

_{Istituto di Pisica and}_GNSM-CNR,_{Universitd di Modena, 41100 Modena, Italy} '~nternutiona~ Centre for Theoretical Physics, 34014 Miramare-G~~ignano, Trieste,

I t a l y

Abstract.- We present a model lattice dynamical study of the Mo(100) incommensurate reconstruction. We find that both the predicted periodicity and polari- zation of the incmensurate distortion agree with experiment. Interesting changes of the periodicity are predicted in presence of an electric field of magnitudes such as those used in Field-Ion-Microscopy.

1. Introduction.- The Mo(100) displacive reconstruction is peculiar, because it is incommensurate, with a temperature independent periodicity, roughly given by k=(0.44, 0.44)2a/a(l). It was earlier supposed that the incommensurability could be due to intra-surface long-range forces, connected with a partly filled surface state band and related 2-dimensional Fermi surface(2'. In a subsequent model study of the lattice-dynamical aspects of the connnensurate (/2x/2)~45' reconstruction of W(100), it was found, however, that incommensurate surface phonon instabilities may also occur with strictly short-ranqe surface forces. In this work we pursue the idea that incommensurability of Mo(100) could be due to this latter elastic reason. We still envisa- ge the chemically unbounded surface electrons and 2-dimensional Fermi surface, to be the driving force of this phenomenon(3). However, the actual surface distortion and its periodicity will be finally determined by a compromise between the driving force and the deformation energies involved. In the present approach one assumes a simple mcdel for the driving forces (simulated by a first neighbor intra-surface repulsion) and one determines the distorted state by a careful study of the lattice energies, via a surface phonon calculation. We follow here the conventional soft-mode approach to structural phase transitions, whose basic ingredients are: a) the hannonic vibra- tion spectrum of the ideal surface and its instabilities, b) t2.e a n h a m n i c forces that intervene to stabilize the surface once the distortion is introduced by freezing- in the soft mode.

2. Mo(100) surface instabilities.- Our model is the same introduced earlier for the W(100) ~urface'~). We have an n-layer slab (n>lS) with bulk-like intratomic forces,

1

au

a2u

except for the outher surface layer. The force constants a =

-(-I

and Bs=

s R aR. R=a

between two surface first neighbors (distance a) are adjustable to represent the extra surface forces. By looking for imaginary surface phonon modes we can construct a "phase diagram" as a function of a and

Bs.

The result is shown in Fig.1. Beside the stable region and the regions MI, M and L where the corresponding zone-border

5 2

modes are unstable, we find two regisns I 1 and I2 where the instability occurs first

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at an incommensurate wavevector. However in the I2 region, the inst5 bility occurs along the A-line (qA=

(4,4-6)2~/a). This disagrees with experiment, that shows a 1-type distortion (q -(i-6,f-6)2n/a) with _1- 6=0.06. In the region TI, on the other hand, two instabilities occurs almost simultaneously along the A-line and along the C-line. we have previously argued(')

,

however, that in this circumstance one should expect a 1-distortion, because the anharmonic restoring forces are weaker for 1 than for

A.

We are thus led to assume that the Fig. 1 : T=O phase diagram as a function

of the surface force constants of Mo(100). Mo(1OO) incommensurate distortion corresponds to the I phase. We now

1

consider some of the consequences of this model.

3. Surface lattice d'istortion.- The nature of the expected surface lattice distortion is best understood by considering in detail the mechanisms through which the incommensurability occurs. Fig.2 shows how an absolute minimum in w can occur slightly off the M point, whenever an M5 (in-plane) and an M1 (vertical) soft modes happens to come sufficiently close in energy. At the M point itself, MI and M5 are orthogonal by symmetry. Away from M, however, they interact producing a minimum in the lowest

Z1

or

A1

branch, while the

Z2

and

A2

branches remains higher. Therefore the incommensurate distortion is predicted to have

Z1

symmetry. This mode consists of an admixtu- re of in-plane longitudinal (110) motion and of vertical (0011 motion. This is preci-

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sely the symmetry found by careful analysis of LEED data by Barker and Estrup

.

The present mechanism bear several analogies with that invoked in incommensurate ferroelectrics(')

,

with a noticeable difference: the twofold degeneracy is here bro- ken quadratically rather than linearly, by moving away from the high symmetry point. The implications of this fact on the presence of discommensurations as well as on the behaviour of the distortion periodicity with temperature are presently under

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investigation and will be reported elsewhere

.

4. Effects of electic fields.- A possible test of the present model could consist in trying to change artificially the periodicity of the surface distortion. This could be done, for example, by applying a very strong surface electric field such as one finds in FIM experiments. We have evaluated how the surface phonon modes are altered

'+ -+

-

by the field by supposing the first layer atom to acquire a charge p=al ( u - u ~ ~ ) - Z

-+ -r

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JOURNAL DE P H Y S I Q U E

Fig. 2 : Surface phonon branches of Mo(100) along the C and I\ directions in the second layer-Webelieve thata is positive, so that a raised atom becomes po- sitively charged, but the same reasoning would apply for a<O with a reversed electric field. In the new phonon spectrum all modes involving a vertical displacement are softened by the field. The new phase diagram is drawn (dashed line) in Fig.1 for a

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sufficiently strong field whose absolute magnitude is E=3x10 V/cm if we take a=l e/A

-+

For increasing field we expect the reconstruction q-vector to shift, the distortion acquiring more and more z component, until at some critical field E the distortion should become M -like (couunensurate c(2x2)), with strictly vertical displacements.

1

This is made clear in Fig.1 if one supposes the point P to represent the actual Mo(100) surface. Once the field is applied P falls inside the M1 region. The new commensurate field-induced phase should become particularly evident e-g. by fieldetchins. An observation in this direction has actually been reported (9) for W ( 100) where, howg ver the reconstruction is commensurate even at zero field.

References

1. T E Felter, R A Barker and P J Estrup, Phys.Rev.Lett. 33, 1138 (1977) 2. E Tosatti, solid.st.Connnun.

21,

881 (1978)

3. An alternative explanation is given in: J E Inglesfield, ~.Phys. C

12,

149 (1979) 4. A Fasolino, G Santoro and E Tosatti, Phys.Rev.Lett.

44,

1684 (1980)

5. A Fasolino, G Santoro and E Tosatti, La vide, Le couches minces (suppl.)

201,

679 (1980)

6. R A Barker, S Semancik and P J Estrup, Surf. Sci. 94, ~ 1 6 2 (1980)

7. V Dvor*, in "Modern trends in the theory of condensed matter", ed.by A Pekalski and J Przystawa, Springer (Berlin), p.447 (1980)

8. A Fasolino and E Tosatti, to be published