DENSITY OF D-STATES IN AMORPHOUS TRANSITION METAL ALLOYS

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DENSITY OF D-STATES IN AMORPHOUS TRANSITION METAL ALLOYS

J. Gaspard

To cite this version:

J. Gaspard. DENSITY OF D-STATES IN AMORPHOUS TRANSITION METAL ALLOYS. Journal

de Physique Colloques, 1980, 41 (C8), pp.C8-414-C8-417. �10.1051/jphyscol:19808102�. �jpa-00220197�

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JOURNAL DE PHYSIQUE CoZZoque C8, suppldrnent au n08, Tome 4 1 , aotit 1980, page C8-414

DENSITY OF D-STATES I N AMORPHOUS T R A N S I T I O N ElETAL ALLOYS

J . P . Gaspard

Groupe des T r a n s i t i o n s de Plzascs, C. N . R. S., B. P. 766, 38042 GrenobZe c l d e x , France.

1

.

I n t r o d u c t i o n

Nearly a l l g l a s s y metals a r e a l l o y s ; t h e most widely s t u d i e d i n fundamental r e s e a r c h a r e binary

(or t e r n a r y ) a l l o y s o f a t r a n s i t i o n metal (TM) o r a noble metal (Ni) w i t h a lnetalloid (P, Si.. .) o r ano- t h e r t r a n s i t i o n metal. The e x i s t e n c e of a t l e a s t two components f a c i l i t a t e s t h e g l a s s formation even if t h e o r i g i n o f t h e mechanism ( d i f f e r e n c e i n a t o - mic s i z e , e l e c t r o n i c e f f e c t ...) i s not f u l l y unders- tood. I t is i n t e r e s t i n g t o analyze t h e e l e c t r o n i c d e n s i t y o f s t a t e s o f amorphous a l l o y s i n o r d e r t o f i n d c o r r e l a t i o n s hetween t h e atomic and t h e e l e c - t r o n i c s t r u c t u r e . I t is indeed obvious t h a t t h e r e i s a r e l a t i o n b e t ~ e e n t h e e l e c t r o n i c s t r u c t u r e -respon- s i b l e o f t h e cohesion- and t h e atomic s t r u c t u r e a s well a s t h e chemical o r d e r .

Considering t h e l i m i t a t i o n s i n t h e determination o f t h c atomic s t r u c t u r e by s t a n d a r d d i f f r a c t i o n tech- niques (X-ray, n e u t r o n s . . .), t h e aim o f t h i s paper is t o i n v e s t i g a t e which p i e c e o f a d d i t i o n a l informa- t i o n can be got from t h e e l e c t r o n i c spectrum, which i s approached experimentally by photoemission spec- t r a (UPS and XPS) / I / .

We performed a s e r i e s o f c a l c u l a t i o n s o f t h e d e l e c t r o n i c spectrum o f t r a n s i t i o n metal a l l o y s and and w e focussed o u r a t t e n t i o n o f t h e e f f e c t o f s h o r t range o r d e r both i n t h e bulk and a t t h e s u r f a - ce.

2. ,Method

The c a l c u l a t i o n o f t h e e l e c t r o n i c spectrum is performed i n two successive s t e p s :

a ) t h e c r e a t i o n o f an amorphous a l l o y by quenching a molten a l l o y and b) t h e c a l c u l a t i o n o f t h e e l e c - t r o n i c d e n s i t y o f s t a t e s (DOS) o f t h e amorphous a l - l o y . This method, based on simple models f o r t h e i n t e r a c t i o n s between atoms in t h e s t r u c t u r e and f o r t h e e l e c t r o n i c i n t e r a c t i o n s (hamiltonian) i s non s e l f c o n s i s t e n t regarding t h e cohesion but i t has t h e advantage t o be very f l e x i b l e . I t i s a b l e t o cover a wide v a r i e t y o f s i t u a t i o n s including bulk and s u r f a - c e s o f systems w i t h various kinds o f d i s o r d e r . This method has been developed by Gaspard /Z/ f o r dege- n e r a t e d bands and it has Seen e x t e n s i v e l y worked o u t by Khanna e t a l . / 3 / and Fujiwara / 1 I I*. They c l e a r l y

showedthat t h e a v e r a g e d e n s i t y o f s t a t e s i s f a i r l y s i m i - l a r t o t h a t o f c r y s t a l l i n e c o m p a c t phases (FCCorHCP) f o r an energy r e s o l u t i o n of about - 5 eV, corresponding t o XPS masurements and compatible w i t h t h e approximation o f t h e t h e o r e t i c a l models. However s t r o n g de- v i a t i o n s occur i n t h e l o c a l d e n s i t i e s o f s t a t e s depending on t h e c o o r d i n a t i o n number and on t h e l o c a l arrangement o f t h e f i r s t s h e l l o f atoms in a way d i f - f i c u l t t o analyse.

I n t h i s work, we obtained t h e amorphous a l l o y s t r u c t u r e by a molecular dynamic c a l c u l a t i o n (see e.g. V e r l e t / 4 / ) o f atoms i n t e r a c t i o n v i a Lennard- Jones p o t e n t i a l s . The r e l e v a n t parameters a r e t h e d e n s i t y p, t h e atomic s i z e s rA, rg, t h e temperature

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808102

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T, the energy prefactors of the Lennard-Jones poten- 'AA+€BB + R ) . R i s t h e t i a l s ( ~ ~ ~ ( ' 1 1 , ^E~~ and eAB =

---

regular solution parameter, thc value of which i s varied between 0 and 5 : a p o s i t i v e value of R corresponds t o a tendancy t o heteroatomic bond forma- t i o n . The f i n a l configuration i s obtained s t a r t i n g from a FCC configuration melted a t a temperature kT = 2 ( i n E~ u n i t s ; the melting temperature i s kT = .7) and subsequently cooled down.

The e l e c t r o n i c d density of s t a t e s is obtained i n a t i g h t binding description taking f u l l account of the d degeneracy. The dda, ddq, dd6 parameters a r e those given i n / 5 / . Nearest neighbor i n t e r a c t i o n i n the l i q u i d a r e taken up t o the f i r s t minimum i n the p a i r c o r r e l a t i o n function. Only diagonal disorder is taken i n t o account, i . e . depending on the type of atoms, o r the atomic l e v e l is EA o r EB. The den- s i t y of s t a t e s i s obtained by a continued f r a c t i o n technique described i n /6/.

Twelve c o e f f i c i e n t s of the f r a c t i o n a r e c a l c u l a - ted ; t h i s corresponds t o an energy resolution o f

. 3 eV.

3. Characterization of the local atomic s t r u c t u r e Various attempts have been made t o characterize the l o c a l order i n amorphous and l i q u i d s t r u c t u r e s . The Voroni polyhedra s t a t i s t i c s 171 provide a cha- r a c t e r i z a t i o n of the l o c a l environment and is per- haps in r e l a t i o n with the l o c a l e l e c t r o n i c proper- t i e s o f mono o r divalent metals, but it has no r e - l a t i o n with the e l e c t r o n i c spectra of t r a n s i t i o n metals /3/. For the l a t t e r , we propose a characte- r i z a t i o n based on closed c i r c u i t s t a t i s t i c s , ^j.e.

t h e number of nearest neighbors ( c i r c u i t s of length 2) and the number of c i r c u i t s of length 3 (v3).

~ i g ' . 1 shows the d i s t r i b u t i o n of c i r c u i t s of length 3 in a pure l i q u i d . As an icosahedral s t r u c - t u r e corresponds t o v3 = 30 and a FCC o r HCP s t r u c -

t u r e t o v3 = 2 4 , one observes t h a t - a t l e a s t a t t h i s l e v e l of a n a l y s i s - t h e environments s i m i l a r t o t h a t of the compact c r y s t a l l i n e phases a r e i n grea- t e r number than the (deformed) icosahedral environment.

This shows t h a t the icosahedron is not an impor- t a n t s t r u c t u r a l u n i t of the amorphous s t r u c t u r e .

F C C

I 1 1 1 1 I I I I

2 2 2 4

26

2

Fig. I ^:D A M b L L t i o n

06

CihCcLit6 06 Length 3 .

4 . Density of s t a t e s of disordered a l l o y s

We performed c a l c u l a t i o n s of t h e a l l o y d density of s t a t e s f o r a s e r i e s of parameters corresponding t o d i f f e r e n t l o c a l environments and d i f f e r e n t d a t o - mic l e v e l spacings 6 = (EA - EB)/W W( = band width).

The concentration 20 % A (80 % B) is r e p r e s e n t a t i - ve of many e u t c c t i c concentrations around which a - morphous phases forms. The parameters EM and €33 a r e i d e n t i c a l .

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JOURNAL DE PHYSIQUE

C8-416

4.1. Completely disordered a l l o y s

Fig. 2 and 3 show the r e s u l t s f o r 6 = 0.2 and 6 = 0.4 and R = 0. For the l a r g e s t value of 6, one observes a s p l i t t i n g o f the d band i n a A-type mino- r i t y and a B-type majority band a s observed experimentally by Oelhafen e t al. / 8 / . Very close r e s u l t s

-even i n t h e minority band- a r e obtained by a s i n - g l e s i t e CPA c a l c u l a t i o n (dotted

-.-

l i n e ) based on the pure amorphous density of s t a t e s . This shows t h e v a l i d i t y of the CPA c a l c u l a t i o n s i n the case of complete chemical disorder (R = O), and f o r a high coordination ( Z ^2.11), a s already observed i n FCC s t r u c t u r e s /9/.

Fig. 2 : DeMni.44

0 6

b-tatw 06 an &oy A . 2 B e g 6 0 h

6 = . 2 .

4.2. Alloys with s h o r t range order

In most of the amorphous a l l o y s , it is generally admitted -and t h e r e a r e p a r t i a l experimental eviden- ces- t h a t the l o c a l order resembles t o t h a t of the corresponding c r y s t a l s . When short range order is present, the s i n g l e s i t e CPA approximation i s by e s - sence no longer v a l i d and n m r i c a l c a l c u l a t i o n s have t h e i r f u l l i n t e r e s t .

!Ve performed c a l c u l a t i o n s on quenched l i q u i d s t r u c t u r e s f o r various values of the regular s o l u - t i o n parameter. The l a r g e r Q, t h e stronger the t e n - dency t o form heteroatomic p a i r s . Figs. 2 and 3 show t h e q u a n t i t a t i v e evolution of the spectra when

The minority band . presents . v a r i a t i o n s due t o R ; the bigger R , the narrower the bandwidth. Howe- ver the magnitude of the v a r i a t i o n s o f the spectrum f o r r e a l i s t i c R values i s presumably not l a r g e enough t o be seen i n the photoemission spectrum.

-

N(E 1

-

^{0 - 0}

---

II

-

¹

- -

o m 5

r\

Fig. 3 : De~niAg 0 6 6 . t a t e h 0 6 an a l l o y A . 2 B.g j ~ h 6 = .4

4.3. Surfaces of a l l o y s

I t i s well established t h a t the surface concen- t r a t i o n of an a l l o y can be very d i f f e r e n t from the bulk concentration, a t the thermodynamic e q u i l i - brium. In Fig. 4, we represent t h e l o c a l d e n s i t i e s

of s t a t e s a t the surface of an a l l o y without ( f u l l l i n e ) and with (dotted l i n e ) surface segregation e f f e c t . We observe an important e f f e c t on the l o c a l DOS, which can be observed experimentally i n the UPS spectrum. In TI4 a l l o y s , it i s possible t o e s t i - mate the surface concentration a t equilibrium from the s p e c t r a l v a r i a t i o n s / l o / . The surface DOS could a l s o be r e l a t e d t o the i n t e r e s t i n g anticorrosive properties o f amorphous a l l o y s , i n p a r t i c u l a r with C r

.

n

is increased from 0 t o 5 ( i n E~~ u n i t s ) .

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Fig. 4 : Swl6ace dennitg

06

b - i i z t u 06 an a o g .

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3077 (1973).

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36,

C o l l . C2, 1 (1975).

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.

^OELHAFEN, E. HAUSER a n d H. J.

G ~ E R O D T ,

t o be p u b l i s h e d .

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10,

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/ 1 1 / . T . FUJIWARA, J . Phys. F.,

2

(1979) 2011

h he

latter shows a characteristic difference between the liquid and amorphous densities of

states.