HOW MUCH INFORMATION CAN LOW ENERGY ION SCATTERING GIVE ABOUT SURFACE PHONONS ?

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HOW MUCH INFORMATION CAN LOW ENERGY

ION SCATTERING GIVE ABOUT SURFACE

PHONONS ?

D. Martin, R. Walker

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C6, supple'ment a u n o 12, Tome 42, de'cembre 1981 page C6-807

HOW MUCH INFORMATION CAN LOW ENERGY I O N SCATTERING G I V E ABOUT SURFACE PHONONS

?

D.J.

Martin and R.P. walker*

Department o f Pure and A p p l i e d P h y s i c s , U n i v e r s i t y o f S a l f o r d , SaZford, Im?cashire M5 4WT, U.K.

*

_{Dmesbury Laboratory, SERC, Warrington WA4 4AD, U.K.}

Abstract

-

von-Kbrm'an scattering on surface

Using correlation coefficients calculated i p the Born model, the temperature variation of low energy ion spectra is shown to be capable of giving information Debye temperatures but not on detailed aspects of surface phonons.

1. Introduction.

-

Low energy ion scattering

[

I

]

can be exploited to give information on surface phonons _[2]

.

We have shown,[3] using the Debye model, that correlations between atomic yibrations have a significant influence on these results and now extend these studies by using the Born von-Khrmln model for the phonons. The results for the ion scattering using this model, differ from the Debye case and it should be possible to obtain information on the correlations. However, the technique cannot readily give information on details such as the force constant ratios.

2. Mean square atomic displacements and correlations.- On the basis of an earlier study [4] we have developed a Born von-KQrmSn calcul- ation for <u2(~) > and the correlation coefficients f(u,,,ug) in a simple model of

bulk

monatomic FCC and BCC crystals. Only the next- nearest neighbour and nearest neighbour force constants, of ratio R , are used. This model is crude for surface phonons but it allows US

to examine the influence of the two major parameters T/eD

(eD

set to agree with the Debye result for < u 2 ( T + w ) > ) and R.

The results for <u2(T/e )>are insensitive to R ; they deviate only

D

a few percent from the Debye result. In general the correlations are, as expected, much more sensitive to R and dlffer markedly from the Debye result, as shown in figure (1). However, the particular correlation coefficient which is important for ion scattering is that for displacements perpendicular to the atomic row and, as shown in

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C6-808 JOURNAL DE PHYSIQUE

figure (I), this is particularly insensitive to change in R. Studies in other directions and a l s o in FCC crystals reveal a similar pattern: for orthogonal displacements ? i s % 6 0 2 of the D e b y e value and changing R f r o m 0.1 to 1.0 changes Q by only % 202.

3. Quasi-double and

quasi-triple

ion scattering.- It is possible to characterize peaks in the intensity against energy measurements of ion scattering spectra as quasi-double (QD) and quasi-triple (QT)

[

I

]

.

O n the basis of a s i m p l e two-atom model [3] the QD peak height is found to

1

vary as A / <~~'>'(l-~~) w h e r e A is an (inaccurately known)constant. related to the n e u t r a l i z a t i o n probability and s c a t t e r i n g cross-section,

<u 2 > refers to displacements perpendicular to the chain and

el

is the correlation coefficient for nearest neighbour displacements perpendicular to the chain. Provided the measurements are extended to T<<eD it should be possible to measure s u r f a c e D e b y e temperatures. Figure 2 shows a plot o f the QD peak height f o r K r + s c a t t e r i n g f r o m C u <LOO> row, as obtained f r o m "chain" simulation [,]3 against

l / ~ ~ ( l - ~ ) . h e solid circles are the results for the correct

9 ' the open circles are the results i f

eD

is 20% too high. I n D *

practice

eD

would be adjusted to give the best straight line through the origin. U n f o r t u n a t e l y , i t is d i f f i c u l t to extract s e p a r a t e information o n 8 and

e

f r o m QD r e s u l t s and lack of k n o w l e d g e o n

e

P

leads to errors ln 8 D'

A s i m p l e three atom model _1.3'3 gives for the Q T peak height:

06.

_{______--_---}

R = 0 1

,c'

p-

,,..--- 6' ,ox /' // " / ,

**,*'/**

01' , , , _ _

.

. . . 'Dcbye / -

.

,

_ _ _ _ _

---

_--_1.0 1 0 0 1 0 0 0 0 0 5 10 1 5 2 0 T 'Q,

Fig'.l:The correlation c o e f f i c i e n t s F i g . 2 : QD peak height f r o m a+comp- as a function of T / B D for a t o m s of uter s i m u l a t i o n for lOkeV Kr

scattered f o r a <loo> r o w of C u separation <Ill> i n a B C C monatomicatoms for a s c a t t e r i n g a n g l e + = 3 0 0 , crystals with R=0.1 and 1.0. The

1

dotted curve is the D e b y e result. plotted a g a i n s t l/<uZ> (1-e,)

1

The broken curves are f o r displace-

for the correct value o f e D = 3 0 0 K ments in the <Ill> direction.The

(solid circles) and for eD=360K solid c u r v e s a r e f o r < l T 0 >

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where <vZ2>=<u 2>mk QD/n2 and a=62mk/h2

D

is a constant related to the scattering cross section and neutraliz-

ation probabLlity,e2 the correlation coefficient for displacements of second nearest neighbours in the row a n d 6 the depth of the "thermal pit" giving QT scattering. For T"QD a plot of In( QT peak height)+ ln(T) against 1/T will have slope &i2mk@;/3fb2 (3-4el+

e2,.

Again separate information on 8 a n d e c a n n o t be obtained. However, by

D

choosing the scattering conditions to give QT scattering for T<<8 _D it is in principle possible to see evidence of the correlations and to measure them as shown in figure (3) where the predictions of equation (1) are compared with simulation results. Unfortunately, because the relevant correlation coefficients are insensitive to R , this information is of limited value.

If these results are true in general it follows that low energy ion scattering is only intrinsically capable of giving information on surface Debye temperatures and that QD peak measurements, extended to T<<BD, may be superior to QT measurements.

We are grateful to Drs G J Keeler, D G Armour, S A Cruz and

E V Alonso for discussions and the SERC for grant support.

Fig.3.QT peak height for 4KeV ~ r + scattered from a o 4 1 D row of Na

atoms for-8139.7 and E =2.93 to

f

3.0lkeV. The curves show the predictions of equation (l),the points are simulation results. Solid curve and solid circles:uncorrelated Debye model eDuc=51K. Chain curve:

correlated Born von-Karman model. same BD.Broken curve and open circles

correlated Born von-Karman model 9 =

0,s 1:o. ? :5 2'0 D

References

4 4 . 4 K . u simulations diverge for T+O due to change of

e

with T

1. Boers, A.L., Surface Sci.

63

(1977) 475.

2. Poelsema, B., Verheij, L.K. and Boers, A.L., Nuclear Instr.

Methods, 132, (1976)623.

3 . Martin, D . K Surface Sci.

97

(1980) 586 and Walker, R.P,, and

Martin, D.J. paper submitted to Surface Sci.