SURFACE ORDER-DISORDER TRANSITION IN THE SOLID SOLUTION Cu3 Au

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SURFACE ORDER-DISORDER TRANSITION IN THE SOLID SOLUTION Cu3 Au

H. Dosch, J. Peisl

To cite this version:

H. Dosch, J. Peisl. SURFACE ORDER-DISORDER TRANSITION IN THE SOLID SOLUTION Cu3 Au. Journal de Physique Colloques, 1989, 50 (C7), pp.C7-257-C7-265. �10.1051/jphyscol:1989727�.

�jpa-00229894�

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COLLOQUE DE PHYSIQUE

Colloque C7, supplbment au n o l O , Tome 50, octobre 1989

SURFACE ORDER-DISORDER TRANSITION I N TBE SOLID SOLUTION Cu, AU

H. DOSCH and

J.

PEISL

Sektion Physik der U n i v e r s i t d t Miinchen. 0-8000 Miinchen 22, F.R.G.

Resume

-

La c r i t i c a l i t 6 s u p e r f i c i e l l e d'un systgme s e m i - i n f i n i qui

---

s u b i t une transformation des phases de premiere espece e s t considered.

Nous presentons l a d i f f u s i o n des rayons X-Synchrotron sur l a surface (100) de l a superstructure d ' a l l i a g e CusAu ordonne, l a s e n s i t i v i t 6 s u p e r f i c i e l l e 6tant accomplie par l a r e f l e x i o n t o t a l e . La dependance de l ' i n t e n s i t e (0011 6vanescente en f o n c t i o n de l a temperature e t de l a profondeur de d i f f u s i o n e s t analyse4 quantitativement e t on montre que l e parametre d'ordre s u p e r f i c i e l d i s p a r a f t c o n t i n h e n t e t qu'une couche de mouillage d6sordonee e x i s t e prAs de l a temperature de t r a n s i t i o n TO.

Les observations sont en accord avec l a supposition d'une croissance logarithmique de c e t t e region d6sordonn6e de surface en approchant To.

Abstract

-

Surface c r i t i c a l i t y o f s e m i - i n f i n i t e systems which undergo f i r s t order phase t r a n s i t i o n s i s considered. We present Synchrotron-X s u p e r l a t t i c e s c a t t e r i n g i n t e n s i t i e s from the CusAu(100) surface, where the surface s e n s i t i v i t y i s achieved by the scheme o f t o t a l external r e f l e c t i o n . The q u a n t i t a t i v e analysis o f the temperature- and scat- t e r i n g depth-dependence o f the evanescent ( 0 0 1 ) superlattice peak proofs the continous behaviour o f the surface order parameter and the existence o f a disordered " w e t t i n g 7ayer" below the t r a n s i t i o n temperature TO. The observations are consistent w i t h the assumption o f a logarithmic growth o f t h i s surface-induced disordered region when TO i s approached.

For many decades the a l l o y CuaAu has served as a standard f o r s o l i d s o l u t i o n s which display pure order-disorder phase t r a n s i t i o n s /I/.

Consider the p a r t o f the Cu-Au phase diagram ( F i g . l a ) a t the ( f i x e d ) Au- concentration o f 25at%: f o r temperatures T>To=663 K the system i s i n the disordered s t a t e where the so-called Bragg-Wi77iams (BW) long-range order parameter i s zero, whereas below TO one f i n d s a s u p e r l a t t i c e based upon the f c c s t r u c t u r e o f the a l l o y as shown i n Fig.lb. As i n most systems, the formation o f the s u p e r l a t t i c e from the disordered s t a t e i s a discontinuous ( f i r s t order) phase transformation which displays a regime o f nucleation followed by growth and coarsening processes /2/. Since the f c c s t r u c t u r e i s preserved during the t r a n s i t i o n and the i n i t i a l and f i n a l s t a t e s are s i n g l e phased, there i s no need f o r the system t o match the parent and product regions across an i n t e r f a c e , and the ordering process involves only atomic re-arrangements but no long-range d i f f u s i o n .

Some c l a s s i c a l X-ray s c a t t e r i n g concepts l i n k e d w i t h order-disorder trans- i t i o n s , i n p a r t i c u l a r long-range order (LRO) and short range order (SRO) s c a t t e r i n g /3/ o r l i n e broadening caused by antiphase domains / I / , have been conceived i n studying the Cu-Au a l l o y . The LRO parameter and the associated s c a t t e r i n g i n t e n s i t i e s are of special i n t e r e s t i n the surface study decribed here:

L e t t i n g mu be the actual concentration o f Au atoms and pnu(T) the r a t i o which occupies the c o r r e c t s i t e s , then the BW-LRO parameter m(T) which measures the degree of the global order i s defined as

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989727

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I n a s c a t t e r i n g experiment a nonzero v a l u e o f m(T) g i v e s r i s e t o super- l a t t i c e r e f l e c t i o n s which have t h e i n t e g r a t e d i n t e n s i t i e s

la ( T I - ' rnu ( 1 - T A U ) ( f c u - f n u ) 2 m(TI2 (2)

~ A Uand fcu a r e t h e X-ray form f a c t o r s o f t h e Au and Cu atoms. Thus, t h e temperature dependence o f m(T) can be measured d i r e c t l y by m o n i t o r i n g t h e i n t e n s i t y o f a s u p e r l a t t i c e peak. Experiments o f t h i s k i n d reveal an abrupt l o s s o f long-range o r d e r when CusAu i s heated above t h e t r a n s i t i o n temperature To =663K /3/.

W i t h i n mean f i e l d t h e o r y t h i s behaviour f o l l o w s from symmetry arguments, s i n c e t h e expansion o f t h e ( b u l k ) f r e e energy o f t h e system i n terms o f t h e order parameter i s

and a l l o w s f o r a nonzero c o e f f i c i e n t b>O. Consequently, a d i s c o n t i n u o u s phase t r a n s i t i o n takes place when t h e temperature dependent c o e f f i c i e n t a approaches t h e v a l u e 4b2/3g ( F i g . 1 ~ ) .

I I I I

10 20 30 40 50 60 ^I

Atomic percent gold '

F i g . 1

-

The system CusAu: ( a ) P a r t o f t h e phase diagram / 4 / - ( 6 ) u n i t ce7 1 o f t h e s u p e r 7 a t t i c e s t r u c t u r e

-

( c ) f r e e energy near t h e o r d e r - d i s o r d e r

t r a n s i t i o n

Surfaces and i n t e r f a c e s have an e s s e n t i a l i n f l u e n c e on f i r s t order

t r a n s i t i o n s . I t t u r n s o u t t h a t near such a t r a n s i t i o n t h e disordered phase may appear i n t h e surface r e g i o n of t h e systein i n t h e presence o f an o r - dered b u l k . T h i s phenowenon which i e r e l a t e d t o w e t t i n g t r a n s i t i o n s leads t o several c r i t i c a l surface e f f e c t s / 5 / which a r e a c c e s s i b l e t o X-ray and neutron s c a t t e r i n g techniques.

Fi g . 2

-

Order parameter p r o f i l e s near t h e s u r f a c e c l o s e t o a f . i r s t o r d e r phase t r a n s i t i o n : ( a ) onset o f s u r f a c e d i s o r d e r (TKTo); ( b ) o r d e r - d i s o r d e r

i n t e r f a c e (TSTO).

56

i s t h e b u l k c o r r e l a t i o n length.

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I n order t o understand the d r i v i n g mechanism behind surface e f f e c t s , con- s i d e r the surface o f a c r y s t a l which undergoes a f i r s t order phase t r a n s i - t i o n . Since the coordination number o f a given atom a t the surface i s smaller than i n the bulk, we expect t h a t the surface may s t a r t t o disorder a t temperatures below TO. I n f a c t t h i s may occur i f the microscopic i n t e r - actions between the surface atoms are n o t stronger than those i n the bulk.

Due t o the surface induced break i n t h e t r a n s l a t i o n a l symmetry, the order parameter m(T) becomes inhomogenous near the surface and has t o be w r i t t e n as m(T,z), where z measures the distance from the surface. The order parameter p r o f i l e m(z) a t a f i x e d temperature can be deduced w i t h i n mean f i e l d theory by minimizing the f r e e energy o f the gg!.i_17,nf7&j& system /5/

r e s u l t i n g i n the general behaviour as shown i n Fig.2: When the system i s close enough t o T O , an i n t e r f a c e develops a t a p o s i t i o n L separated from t h e surface. As To i s approached, L diverges as

Lo l n ( t ) , f o r short range

L ( t )

=

i n t e r a c t i o n s

L* t- 1 13

,

f o r longe range

w i t h t=(To-T)/To. Simultaneously, the surface order Parameter mi(t)%m(z=O,t) disappears continuously w i t h a power law

This scheme has now been studied i n d e t a i l , t a k i n g i n t o account i n t e r f a c e f l u c t u a t i o n s and surface segregation phenomena by renormalization group (RG) techniques and Monte Carlo c a l c u l a t i o n s / 6 / . Even though there are s t i l l some open questions about the r 6 l e o f f l u c t u a t i o n s , these studies show t h a t the c r i t i c a l surface exponent B i , which appears as a universal number i n the one-density Landau-Ginzburg (LO) theory, a c t u a l l y depends among else on the range o f the i n t e r a c t i o n s and the c r y s t a l l o g r a p h i c o r i e n t a t i o n o f the surface under consideration. For the CusAu(100) surface which w i l l be discussed below the p r e d i c t i o n f o r Br i s

0.5

-

1.0 w i t h i n the LG theory / 7 / D l

= {

_2.2

_-

_2.8 w i t h i n the RG theory /6/

The continuous behaviour o f the surface order parameter m i has already been observed experimentally by LEED /8/ and SPLEED /9/ measurements, though the q u a n t i t a t i v e analysis o f these data lead t o r a t h e r contro- v e r s i a l values f o r R i ranging from 0.33 t o 0.8.

The challenge f o r surface s e n s i t i v e X-ray s c a t t e r i n g experiments on t h i s system i s t o reconfirm the continuous surface t r a n s i t i o n , t o provide the experimental evidence f o r the existence of a disordered surface l a y e r and t o determine the growth law o f t h i s " d i s o r d e r wetting" as w e l l as t o shed some l i g h t on the c r i t i c a l surface exponents R i .

X-rays and neutrons can be rendered surface s e n s i t i v e by the scheme o f t o t a l external r e f l e c t i o n . The observed d i f f r a c t i o n ("Grazing Inci-dence D i f f r a c t i o n " , GID) i n t e n s i t i e s u s u a l l y provide a somewhat averaged information about a surface region as i l l u m i n a t e d by the evanescent wave f i e l d i n s i d e the c r y s t a l . Recently i t has been demonstrated experimentally t h a t the depth o f t h i s probe can be enhanced considerably and c o n t r o l l e d i n an elegant way by an extension o f t h i s scheme /10,11/.

These experiments have been sparked by the t h e o r e t i c a l work o f D i e t r i c h and Wagner /12/ who r e v i s i t e d GID i n conceiving experiments t o t e s t surfaces f o r c r i t i c a l behaviour. The schematic setup o f t h i s depth c o n t r o l l e d G I D i s shown i n Fig.3. The X-ray beam of wavelength A grazes the sample surface a t an angle ai below the c r i t i c a l angle ^{a c =}( r ~ r e / r ) l / ~ (r.=classical e l e c t r o n radius, ro=mean e l e c t r o n density) and creates the specularly r e f l e c t e d beam (which i s n o t considered here) as well as the evanescent wave f i e l d ( " d i s t o r t e d wave")

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~ r o d g Planes

Fig.3

-

Schematic setup f o r depth c o n t r o l 7ed g r a z i n g incidence d i f f r a c t ion. ks , r

=

incoming and d i f f r a c t e d beam ;

i n s i d e the c r y s t a l which can be r e f l e c t e d from Bragg planes l y i n g perpen- d i c u l a r t o the surface. The (e.g. Bragg) s c a t t e r i n g i s observed w i t h i n a range o f glancing angles ar=O

-

4ac by a p o s i t i o n s e n s i t i v e detector.

I n the f o l l o w i n g we w i l l discuss some properties o f t h i s d i f f r a c t e d beam w i t h i n the " d i s t o r t e d wave Born approximation" (DWBA) which t r e a t s the s c a t t e r i n g by a kinematic St6rungsansatz, but takes a l l o p t i c a l e f f e c t s properly i n t o account. A s t r a i g h t f o r w a r d c a l c u l a t i o n then gives

/ l o /

w i t h the geometry f a c t o r

which includes the p o l a r i z a t i o n vector e o f the X-ray and appropriate combinations o f the Fresnel transmlssion c o e f f i c i e n t s T i n f (R=Q/Q) f o r a r b i t r a r y s c a t t e r i n g geometries. S ( Q l ,Qz) i s the kinematic s t r u c t u r e f a c t o r f o r a given momentum t r a n s f e r g=(Ql

1

^,Qz⁾w i t h

Q1

para1 l e l and QZ perpendicular t o the surface. Dosch and co-workers

/ l o , I

^1/ have shown t h a t DWBA gives a c o r r e c t d e s c r i p t i o n o f the observed i n t e n s i t i e s when the given c r y s t a l e x h i b i t s no dynamical s c a t t e r i n g e f f e c t s . However, i f per- f e c t c r y s t a l s are considered the e f f e c t s caused by the dispersion surface

Fig.4

-

The s c a t t e r i n g depth p r o f i l e s provided by t h e p o s i t i o n s e n s i t i v e d e t e c t o r ( F i g . 3 ) f o r d i f f e r e n t incidence angles ai (calcu7ated f o r a t y p i c a l sample). For comparison t h e associated p e n e t r a t i o n depth o f t h e specular beam i s shown ( l o g a r i t h m i c s c a l e ) .

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can no longer be neglected /13,14/. I n the f o l l o w i n g we consider the case where the X-ray i s polarized perpendicular t o the plane o f incidence and where the angles ai and ar are o f the order o f the c r i t i c a l angle ar

(Fig.21, then ( 7 ) and ( 8 ) y i e l d /11/

The momentum t r a n s f e r Q r perpendicular t o the surface, which reads i n s i d e the c r y s t a l

/ l o /

( w i t h

ae=~n/A),

plays the c r u c i a l r61e f o r the depth information. The imaginary p a r t

Im(Q=)

induces an e f f e c t i v e damping of the scattered beam i n the z- d i r e c t i o n . The very useful p r o p e r t i e s o f the associated s c a t t e r i n g depth (Fig.4)

are e x p l o i t e d i n depth c o n t r o l l e d G I D experiments

/ l o / .

Inspection o f Fig.4 shows t h a t the p o s i t i o n s e n s i t i v e detector records depth p r o f i l e s o f the surface region i l l u m i n a t e d by the evanescent wave f i e l d .

Due t o the a c t i o n o f the s c a t t e r i n g depth

h ,

the experimental setup described above provides the Laplace transform o f the order paremeter p r o f i l e m(z,t) /10,15/:

iii(h,t)

= I.'

e-zlh m(z,t)dz ^{( 1 4 )}

Since the i n t e n s i t y o f the evanescent s u p e r l a t t i c e s c a t t e r i n g i s analogous t o ( 2 ) given by

we f i n d f o r the order parameter p r o f i l e s shown i n Fig.2 t h e f o l l o w i n g associated s u p e r l a t t i c e i n t e n s i t i e s (neglecting t r i v i a l p r e f a c t o r s ) :

1

-

(25bCl-ml ( t ) ] ) / h f o r TSTO (Fig.2a)

I.( A , t ) - 10- (16)

l e - ~ t / ~ -l / p ( j b / h ) e - ' t / j b

l2

f o r TSTo (Fig.2b)

I n d e r i v i n g (16) we used the f a c t t h a t the corre'lation lengthJb-O(ao) (ao=3.705A l a t t i c e constant o f u n i t c e l l ( F i g . l b ) ) remains f i n i t e on a microscopic scale ( f i r s t order phase t r a n s i t i o n ) . The expression I.(A,t) f o r TsTo becomes p a r t i c u l a r l y simple when, i n a f i r s t approximation, the termsjb/A and exp(-Lt/jb) are neglected. Then, 1 ~ ( A l t ) ~ e x p ( - 2 L t / A ) , O r w i t h ( 4 )

h ( A , t ) ^@t 2 f h w i t h RA=Lo//\ (17)

f o r a l n ( t ) divergence o f L t .

The Synchrotron-X-ray experiments have been performed a t a Cu~Au(100) surface. The sample was mechanically polished u n t i l i t showed a m i r r o r l i k e surface /16/ and was subsequently t r a n s f e r r e d i n t o the UHV preparation chamber o f the FLIPPER I s t a t i o n a t HASYLAB (DESY, Hamburg), where i t was sputtered w i t h A r ions and annealed i n a standard way. LEEO and Auger measurements showed t h a t a clean and w e l l ordered s i n g l e c r y s t a l surface was present before the sample was mounted w i t h i n a p o r t a b l e UHV chamber onto the D4 surface spectrometer o f HASYLAB (Fig.5).

The experimental s t a t i o n D4 i s supplied w i t h a white X-ray beam from a bending magnet. While a t o t a l r e f l e c t i o n Au-mirror eliminates unwanted high energy photons, the downstream Ge(l11) monchromator selected t h e

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actual wavelength X=1.5A f o r t h e experiment. Various s l i t systems before

Position Sensitive Detector Horizontal

w r

I ^'

i

^sompr ^~peculor

I---,- -L Born Monitor

Fig.5

-

Experimental d e t a i l s o f t h e depth c o n t r o l l e d G I D (For explana- t i o n s see t e x t )

and a f t e r t h e sample were used t o determine t h e s i z e o f t h e incoming beam (2mm hor.xO.07mm v e r t . ) and t h e s i z e o f t h e e f f e c t i v e sample surface area (see i n s e t o f F i g . 5 ) as w e l l as t o d e f i n e t h e p a r a l l e l momentum t r a n s f e r . The glancing angle ar/ac was s e t t o 0.5, 1.0 and 1.5 i n order t o g i v e depth p r o f i l e s i n t h e PSD between less than 20A and approximately 400A.

(a~=7.8mrad in our c a s e ) . We measured t h e temperature dependence o f these depth p r o f i l e s o f t h e ( 0 0 2 ) fundamental and t h e ( 0 0 1 ) s u p e r l a t t i c e

r e l e c t i o n between T=473K and T=673K. Fig.6a shows some PSD s p e c t r a o f t h e ( 0 0 2 ) r e f l e c t i o n a t 3 d i f f e r e n t temperatures. I n p r i n c i p l e , such d a t a can be used t o determine near s u r f a c e Debye-Waller f a c t o r s o r s u r f a c e

roughness parameters. I n t h i s study. however, we focused o n t o t h e

temperature dependence o f t h e ( 0 0 1 ) r e f l e c t i o n : some r e p r e s e n t a t i v e depth s p e c t r a a r e shown i n Fig.6b f o r a i / a c = l f o r v a r i o u s temperatures near T O . Note t h a t f o r a r / a o < l , thus f o r s c a t t e r i n g depths A<30A, t h e associated ( 0 0 1 ) i n t e n s i t i e s disappear s t e a d i l y w i t h increasing temperature, whereas f o r a i / a ~ > l . 5 o r A > l 5 0 A t h e r e i s a sudden drop i n t h e s u p e r l a t t i c e

i n t e n s i t y c l o s e t o T O . T h i s d i s t i n c t depth dependence o f t h e near s u r f a c e order parameter i s shown more c l e a r l y i n Fig.7a f o r two d i f f e r e n t

s c a t t e r i n g depths 30A and 300h, c o n f i r m i n g t h a t c l o s e t o t h e f r e e s u r f a c e o f CuaAU t h e order parameter vanishes c o n t i n u o u s l y , w h i l e deeper i n t h e bulk t h e expected f i r s t order phase t r a n s i t i o n s occurs. According t o Fig.7a t h e bulk and s u r f a c e order parameters disappear a t t h e same tempera-ture. I n order t o demonstrate t h e loss o f depth s e n s i t i v i t y by only c o n t r o l l i n g t h e incidence angle ai we a l s o show i n Fig.7b t h e depth

i n f o r m a t i o n which one

Fig.6

-

Surface Bragg s c a t t e r i n g from CusAu observed a t at

/a

= I : ( a ) (002) fundamental r e f l e c t i o n a t t h r e e d i f f e r e n t temperatures.

( b ) (001) s u p e r l a t t i c e r e f l e c t i o n c l o s e t o T O .

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o b t a i n s from a r - i n t e g r a t e d s c a t t e r i n g f o r two d i f f e r e n t incidence angles below and above a=: i n t h e l a t t e r case t h e d i f f e r e n c e between t h e surface- induced continuous and t h e ( b u l k ) discontinuous order parameter i s c l e a r l y much l e s s pronounced.

I n t h e f o l l o w i n g we consider t h e temperature dependence o f t h e super- l a t t i c e i n t e n s i t y I m ( h , t ) a t a given s c a t t e r i n g depth A . The general behaviour of these i n t e n s i t i e s i s summarized i n Fig.8 on a double

l o g a r i t h m i c s c a l e , where t h e pronounced i n f l u e n c e of t h e s c a t t e r i n g depth can be examined by eye. Apparently two temperature regions can be

d i s t i n g u i s h e d :

For t>t* t h e r e i s only a s u b t l e temperature dependence which can be r e f e r - red t o t h e onset o f s u r f a c e disorder ( F i g . 2 a ) . Consequently, t h e observed s u p e r l a t t i c e s c a t t e r i n g should be describable by t h e r e l a t i o n ( 1 6 a ) . Thus, a p l o t of ( 1

-

I m ( h , t ) / I o ) versus)\-1 should r e s u l t i n l i n e a r r e l a t i o n s which have t h e slopes 2 j b [ l - m i ( t ) ] .

Fi g. 7

-

Order-disorder t r a n s i t ion a t v a r i o u s depths

( a ) Observed behaviour a t two d i f f e r e n t s c a t t e r i n g depths obtained from u p -reso 1 ved (00 1 ) s p e c t r a

( b ) Corresponding r e s u l t from a r - i n t e g r a t e d (001) i n t e n s i t i e s

-

^lnt

Fig.8

-

Depth-resolved (001) i n t e n s i t i e s as a f u n c t i o n o f t h e reduced temperature on a double- l o g a r i t h m i c sca l e (see t e x t ) .

T h i s i s shown i n Fig.9a f o r t h r e e temperatures. The slopes o f these r e l a t i o n s provide t h e temperature dependence o f t h e t o p - l a y e r order

parameter m l ( t ) . From a more d e t a i l e d experimental study of such r e l a t i o n s i n t h i s temperature range we expect t o e x t r a c t t h e c r i t i c a l surface

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exponent 81 .

A

[A1 -

Fig.9 - Experimenta7 test of the predicted relations for near surface super lattice scattering observed with tota

1

externa 7 reflect ion:

(a) T<To (t>t* 1.- re 7at ion

(

16a):onset of surface- induced disorder

( b )

**TsTo (t<t*): relation**

( 1 7 ) :

growth of a disorder-wetting layer

The temperature regime TSTO (t<t* in Fig.8) has been discussed recently by Dosch et a1./15/. The superlattice intensities I.(A,t) decay in a very good approximation according to a power law with an exponent

28,

which depends sensitively upon the scattering depthh. The evidence for a

logarithmic growth of the thickness Lt of the wetting layer follows from Fig.9b which shows that

13,

is proportional to

A - '

as predicted

by

the relation (17). The amplitude LO of the logarithmic growth is determined to be 3ao or approximately 1OA.

In conclusion we have applied the recently proposed "depth-controlled GID"

/lo/ to measure the temperature dependence of the Bragg-Williams order parameter close at the Cu~Au(100) surface. The observed superlattice reflection shows the discontinous bulk and the continous near surface behavior depending on the actual scattering depth. By analyzing the scattering depth dependence of the (001) reflection quantitatively we could demonstrate that the continuous loss of long range order at the (100) surface is mediated

by

a disordered surface layer which grows logarithmicly with reduced temperature.

The pleasant collaboration with L.Mailander (Munich) and R.L.Johnson (Hamburg) is gratefully acknowledged. This work was supported by the Bundesminister fur Forschung und Technologie (BMFT, Bonn).

REFERENCES

/1/ Warren,B.E., X-Ray Diffraction, Addison-Wesley Pub.Comp.(l968) /2/ Nagler,S.E., Shannon,R.F., Harkless,C.R., Singh,M.A.,

Phys.Rev.Lett.6J (1988) 718

/3/ Cowley,J.M., Phys.Rev.BjQ (1950) 24

Oshima,K., Harada,J., Moss.,S.C., J.Appl.Cryst.12 (1986) 276

/4/ Hansen and Anderko, Constitution of Binary A??oys, McGraw-Hill Book Comp .

/5/

Lipowsky,R., Phys.Rev.Lett.43 (1982) 1575 Lipowsky,R., Speth,W., Phys.Rev.B2,8 (1983) 3983

/6/

Gompper,G., Kroll,D., Phys.Rev.BS (1988) 459 C7/ Lipowsky,R., Ferroelectrics

7-3

(1986) 69

/8/ Sundaram,V.S., Farrell,B., Alben,R.S., Robertson,W.D., Phys.Rev.Lett.a (1973) 1136;

McRae,E.G., Malic,R.A., Surf.Sci.,l-48 (1984) 551 /9/ Alvarado,S.F., Campagna,M., Fattah,A., Uelhoff,W.,

Z.Phys.B@ (1987) 103

(10)

/lo/ Dosch,H., Batterman,B.W., Wack,D.C., Phys.Rev.Lett.s (1986) 1144 /11/ Dosch,H., Phys.Rev.B35 (1987) 2137

/12/ Dietrich,S., Wagner,H., Z.Phys.BB (1984) 207

/13/ Afanas'ev,A.M., Melkonyan,~.~., Acta.Cryst.Aa9 (1983) 207

/14/ Bernhard,N., Burkel,E., Gompper,G., Metzger,H., Peisl,J., Wagner,H., Wallner,G., Z.Phys.Bm (1987) 303

/ 1 5 /

Dosch,H., Mailander,L., Lied,A., Peisl,J., Grey,F., Johnson,R.L., Krummacher,S., Phys.Rev.Lett.B (1988) 2382

/ 1 6 /

The sample has kindly been provided by S.Krummacher (KfA Julich)