A NEW HUME-ROTHERY PHASE WITH AN AMORPHOUS STRUCTURE IN NOBLE-METAL / SIMPLE-METAL ALLOYS

(1)

HAL Id: jpa-00225197

https://hal.archives-ouvertes.fr/jpa-00225197

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

A NEW HUME-ROTHERY PHASE WITH AN

AMORPHOUS STRUCTURE IN NOBLE-METAL /

SIMPLE-METAL ALLOYS

P. Häussler

To cite this version:

(2)

Colloque C8, suppl6ment au n012, Tome

46,

d6cembre

1985

page C8-361

A NEW HUME-ROTHERY

PHASE WITH

AN

AMORPHOUS STRUCTURE

IN NOBLE-METAL/

S I M P L E - M E T A L ALLOYS

P. Haussler

Phys.

Inst.,

Univ.

KarZsruhe, P.O.

Box 6380, 0-7500

KarZsrmhe 1,

F.R.G.

REsumE

-

Cet article informe sur les propridtEs structurales d'alliages binaires en d6sordre du type AuISn. Les propridtEs structurales de ces alliages sont domindes fortement par les dlectrols de conduction aux compositions d'un nombre d'6lectrons moyen de Z=1.8 6lectrons par atome (e/aj. Les positions des maxima dans l'espace r et k en fonction de Z montrent un comportement uniforme. C'est pourquoi la phase amorphe se d6crit comme une phase Hume-Rothery nouvelle.

Abstract

-

In this paper we report on the structural properties of disordered binary metallic alloys of the type Au/Sn. Structural properties of these alloys are strongly dominated by the conduction electrons at compositions with a mean electron number Z= 1.8 electrons per atom (ela). Peak positions in r= and in k-space, show a uniform behaviour when plotted versus Z, indicating scaling. The amorphous phase can therefore be described as a new Hume-Rothery phase.

INTRODUCTION

In earlier works we reported on strong similarities between the amorphous and the corresponding liquid phase in binary metallic alloys /I/ and concluded that the amorphous phase can essentially be described as a new Hume-Rgthery (HR) phase 2 Crystalline HR-phases exist approximately between Z=l.O- 1.8e/a 131. The metastable amorphous phase exists for Za1.8eIa and seems to be a limiting case of the crystalline HR-phases. For amorphous alloys at Z=1.8e/a the properties are unique. This is also valid for structural properties. Obviously the conduction electrons have an influence on these.

For crystalline HR-phases different models have been made in order to un- derstand electronic influences on the structure 131. Among others, one is based on the minima of the Friedel-oscillations in r-space which are typical for the effective pair-potential of metals. For certain directions, in these minima the atoms can have energetically preferred positions 141. Other models are based on Brillouin-zone interactions if the Fermi sphere, with radius

2kF, touches the Jones- or Brillouin-zone boundaries in k-space 151.

For liquid metals similar influences have been proposed by different authors 6 Also for amorphous alloys, electronic influences are made re- sponsible for structural properties and their stability 171. A shoulder or peak in the structure factor S(k), close to 2k

,

has been correlated with the above mentioned preferred atomic positions witffin the minima of the Friedel oscillations. We have shown that all the alloy; under consideration have such a shoulder or a second peak near or at zk which shifts with 2kF and exhibits s c a l i ~ g behaviour with respect to z.~'I~ all cases the intersection with 2kF is at Z=1.8e/a 121. For the alloys under consideration the correlation to the Friedel oscillations in r-space was first observed by Leitz and Buckel 181. In the present contribution we substantiate this in a more subtle way in order to refine our arguments about the electronic influence on the structural properties.

The pseudopotential theory gives the bandstructure contribution Ubs to the total energy in terms of the effective pair potential @(r) (or energy-wave- -number characteristic @(k)) and the pair-distribution function g(r) (or

(3)

C8-362

JOURNAL

DE

PHYSIQUE

structure factor S(k)) 191. The bandstructure energy is given by

U

a jr2[g(r)-l]-@(r) dr in r-space and by

ubs

a

IS(^)-@(k)

dk in k-space.

Strictly speakkEg, in binary alloys three contributions due to three partial correlations should be used. Experimentally, these functions are hard to ob- tain. In this paper we focus on total functions 1111 which also clearly show influences of the electron system. According to Friedel, the screening behaviour, due to the influence of the conduction electrons, results to a medium- and long-ranged oscillatory behaviour in @(r), which can be described asymp- totically with @(r) a cos(2kFr)/r3 191. The oscillations can extend under the repulsive core and may be exposed by a variation of its radius /lo/. The wavelength of the Friedel-oscillations is X;=2n/2kF. The pair-distribution function itself is oscillatory according to g(r) a l+sin(k r)/r, where k is

P

a large peak in S(k). A coincidence of the maxima in g(r) and the minimaP in @(r) results in a large bandstructure term :n the total energy. The bandstructure term itself is negative and therefore, a reduced total energy will result. Such a matching between a sin- and a cos-function only occurs in an optimal manner if k p equals 2kF, that means, if the wavelengths of both oscillations are identical and if the Friedel minima are additionally shifted -1/4*X;. Such a shifting can occur under special conditions 1 0 The (+)cos-function will then transform to a (-)sin-function. Peak positions would then be given by rFn= (n+1/4)-X; with n=1,2,3,4,-*a.

A good way to study the influences of the conduction electrons on structural properties is to look on the structure of different disordered alloys for which the diameter of the Fermi sphere can be changed by alloying. We com- pare experimental structure data with rFn=(n+l/4)*X; in r-space and with kFn

= (n+1/4)*4/5*2kF in k-space. 2kF is calculated within the free-electron model, assuming liquid mass densities for the pure elements and constant atomic volumes of both components within the alloys.

RESULTS AND DISCUSSION

Fig. 1 shows measured structure S ' k ' data of Au/Sb alloys. In both lo figures vertical lines are drawn in order to mark k and r

.

In k-space the firgp peakFnis split into two components. The first peak at k p decreases and the second one a t k increases with decreasing Z. P e ~ h e latter is very close to k =2k and be- comes equal to 2kFFAt 86 at% Sb or Z=1.8e/a. For other compositions this peak changes its position parallel with 2k 121. In r-space the ideal matchEng is obviously fulfilled in the me- 3 dium range

.

The shifting of -1/4*Xr for the positions of the FriedeE minima has been assumed. The atomic peak positions change very drastically in order to match ideally. The first peak 0

position can match only for the (nm.'~ [nml

alloy with Z=1.8e/a. In fig. 2

the correlation of the second Fig. 1

-

Total structure factors S(k) and peak at kpe with k =2k and the total pair distribution functions g(r) of correlation of theF#irsF nearest amorphous AuISb-allo~s 181-

neighbour distance rl with a

(4)

a s p e c i a l s t a t e : The f i r s t p e a k i n k - s p a c e i s g i v e n e x a c t l y by 2kF a n d t h e f i r s t n e a r e s t n e i g h b o u r d i s t a n c e r l e x a c t l y by a s h i f t e d F r i e d e l minimum. T h e F r i e d e l minima s e e m t o b e e x t e n d e d c l o s e t o t h e c o r e .

h

1

a) amorphous

1

a)amorphous b) liquid

I

F i g . 2

-

a ) D i f f e r e n c e s b e t w e e n k a n d 2k 1 2 1 , b ) n e a r e s t n e i g h b o u r d i s - t a n c e s r l / 1 1 / i n u n i t s of ~ ; ? ' ~ f o r d i H f e r e n t - A U - a n d C u - a l l o y s i n t h e a m o r p h o u s a n d c o r r e s p o n d i n g l i q u l d s t a t e v e r s u s Z. E x p l a n a t i o n of t h e s y m b o l s i s g i v e n o n t o p o f t h e f i g u r e s . A s m e n t i o n e d a b o v e a p e a k i n S ( k ) n e a r 2kF i s c o r r e l a t e d w i t h t h e p e a k s i n r - s p a c e i n t h e medium-range o r d e r 7 I n f i g . 3 t h i s c a n b e s e e n f o r d i f f e r e n t a l l o y s . The f u l l s y m b o l s r e p r e s e n t m e a s u r e d p e a k p o s i t i o n s of a m o r p h o u s a l l o y s , w h e r e a s t h e o p e n s y m b o l s h a v e b e e n o b t a i n e d on t h e c o r r e - s p o n d i n g l i q u i d p h a s e . The t h i n c u r v e s g i v e t h e - 1 1 4 . ~ ~ s h i f t e d p o s i t i o n s of

s e v e r a l F r i e d e l minima. The t h i n v e r t i c a l l i n e s mark c o m p o s i t i o n s w i t h

Z = 1 . 8 e / a . O b v i o u s l y t h e i d e a l m a t c h i n g b e t w e e n a l l p e a k - p o s i t i o n s a n d t h e s h i f t e d F r i e d e l minima i s a l w a y s g i v e n a t t h i s s p e c i a l 2 - v a l u e . ( l ) C h a n g i n g 2k by a l l o y i n g , t h e a t o m i c p o s i t i o n s , - e s p e c i a l l y i n A u - a l l o y s , c l o s e l y f o f l o w t h e c h a n g i n g F r i e d e l minima a t Z > 1 . 8 e / a . The f i r s t p e a k c a n o n l y d o t h i s i n a p o o r m a n n e r b u t i t s e e m s t o f o l l o w 2k a s c l o s e l y a s p o s s i b l e . We w a n t t o e m p h a s i z e t h a t r l d o e s n o t c h a n g e I f n e a r l y w i t h c o m p o s i t i o n . Ob- v i o u s l y i t b e h a v e s

i p

s u c h a way t h a t t h e i n t e r s e c t i o n w i t h t h e F r i e d e l m i n i - mum i s e x a c t l y a t Z = 1 . 8 e / a . I n Au/Sb n e a r 60 a t % Sb a n d Cu/A1 a t 8 0 a t % A 1

---

(5)

(6)

t h e i d e a l d i s t a n c e of p e a k s i n k - s p a c e would be X = 4 / 5 - 2 k F

.

I n f i g . 4 t h e t h i n c u r v e s r e p r e s e n t t h e s e v a l u e s a n d i n d e e d , atF:=1.8e/a t h i s c o n d i t i o n i s f u l f i l l e d f o r a l l p e a k s i n k - s p a ~ e . ~ T h e p e a k a t k p e i s l o c a t e d a t 2kF a n d a l l A = 4 / 5 - 2 k F . . t h e n e x t a t s u c c e s s i v e l y a d d e d A c c o r d i n g l y , a l l p e a k s a r e e x a c t l y s i t u a t e d o n p o s i t i o n s d e s c r i b e d a g a l n by a ( + ) s i n - f u n c t i o n . A t h i g h e r Z - v a l u e s , a c c o r d i n g t o t h e d i f f e r e n c e b e t w e e n r , a n d 5 1 4 . ~ 5 i n r - s p a c e , t h e d i s t a n c e b e t w e e n d i f f e r e n t p e a k s i n k - s p a c e a n d t h e c a l c u l a t e d t h i n c u r v e s d e v i a t e more a n d more f r o m t h e i d e a l b e h a v i o u r a n d i n a d d i t i o n a

p e a k a p p e a r s a t a k p much s m a l l e r t h a n 2kF. The n o n l i n e a r c o n c e n t r a t i o n de-