STUDY OF LIQUID NICKEL-VANADIUM ALLOYS BY NEUTRON DIFFRACTION AND MODEL SIMULATION

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STUDY OF LIQUID NICKEL-VANADIUM ALLOYS

BY NEUTRON DIFFRACTION AND MODEL

SIMULATION

J. Lemarchand, J. Bletry, P. Desre

To cite this version:

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JOURNAL DE PHYSIQUE CoZZoque C 8 , suppZ6ment au n 0 8 , Tome 41, aoGt 1980, page C8-163

STUDY OF LIQUID NICKEL-VANADIUM ALLOYS BY NEUTRON DIFFRACTION AND MODEL SIMULATION J.L. Lemarchand, J. B l e t r y and P. Desre

Laboratoire de Thermodynamique e t Physico-Chimie Me'taZZurgiques, ENSEEG, B.P. 44, 38401 S a i n t Martin d r H e r e s , France.

1. INTRODUCTION

Structure f a c t o r determination i s one of the main purposes of d i f f r a c t i o n experiments on liquid or amorphous metals. In the case of binary a l l o y s , a combination of three independent measurements i s needed t o obtain the three p a r t i a l s t r u c t u r e fac- t o r s . However, these determinations a r e very d e l i - c a t e and t h e i r accuracy i s often limited.

Nuch more accurate, although l e s s complete, information i s obtained from one single diffraction measurement. In t h a t case, comparison with model c a l c u l a t i o ~ can lead t o a q u a n t i t a t i v e interpretation.

In t h i s paper, neutron d i f f r a c t i o n experiments on vanadium-X alloys a r e presented which allow the p a r t i a l s t r u c t u r e f a c t o r of X-X pairs t o be deter- mined. Nickel -Vanadi um a1 loys a r e studied i n order t o investigate chemical ordering e f f e c t s i n t o t h e liquid phase around the e u t e c t i c comp~sition[~]

.

Experimental r e s u l t s a r e f i n a l l y interpreted with

r21

the aid of geometrical models

.

2 . PRINCIPLE OF THE EXPERIMENTS

The d i f f e r e n t i a l cross-section f o r coherent s c a t t e r i n g by a binary alloy may be written :

or in a normalized form* :

In these expressions, ci and bi a r e respectively t h e atomic concentration and the coherent nuclear s c a t t e r i n g length of element i

,

28 i s the s c a t t e r i n g angle, X the neutron wavelength, Q = 4n t h e modulus of the s c a t t e r i n g vector and the Ashcroft-Langreth p a r t i a l strilcture

[31

.

f a c t o r s a r e defined by

.

where :

.

6i i s the Kronecker 6 function

N

.

p = the number density and

.

P . . ( r ) the normalized d i s t r i b u t i o n func- 1 J

t i o n of i - j pairs.

In the case of nickel-vanadium alloys where t h e s c a t t e r i n g length of nickel : bl=l .03.10-~~cm i s much l a r g e r than the s c a t t e r i n g length of vana-

-12

dium : b2=-0.051.10 cm, a s i n g l e d i f f r a c t i o n ex- periment gives d i r e c t l y t h e nickel-nickel s t r u c t u r e f a c t o r S,,(Q) since coherent cross-section ( 1 )

I I -

reduces t o :

gCoh

= clb: Sll(Q)

Departures from approximation ( 3 ) mainly a r i s e from the term ( c ~ c ~ ) ~ ' ~ ~ ~ ~ ~ s ~ ~ ( Q ) which does n o t exceed 10 % of t h e coherent cross section i f nickel concentration i s greater than 0.50.

3. EXPERIMENTAL CONDITIONS

A1 loys were prepared by induction me1 t i ng from 0.99999 nickel and 0.990 vanadium whose oxygen content was l e s s than 100ppm. The oxygen content of t h e alloys a f t e r 10 hour neutron scans was about 1000ppm. Four alloys were studied with concentra- t i o n s i n nickel : cl=l.OO, 0.887, 0.554 and 0.461 surrounding the e u t e c t i c composition : cy = 0.49.

Neutron d i f f r a c t i o n experiments were carried out a t the D4 spectrometer of t h e I n s t i t u t Laue-

0

Langevin. A 0.693 A wavelength was used in order t o

x which goes t o 1 f o r large Q

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C8- 164 JOURNAL DE PHYSIQUE

reach a maximum Q value of 14.5

2'

which enables a good normalization of experimental scattering patterns.

The samples were c y l i n d r i c a l , 6 mm i n diame- t e r and 3 cm high. They were heated between 1300 and 1600°C under Torr. For t h i s purpose a high temperature furnace covering the range 800+2000°C was b u i l t using the techniques develop- ped a t INPG laboratoryL41. For the passage of t h e primary beam,windows were cut i n the tungsten hea- ting element and i n the thermal screens. Sapphire containers were used, resulting in a very low neutron background. These sapphi r e s i nglecrystal s were oriented with a molybdenum goniometric t a b l e i n order t o l i m i t the number of Bragg reflexions super- posed on the liquid a l l o y pattern. The temperature was measured t o f 5°C with an optical pyrometer. 4. DATA TREATMENT

do

Cross section

a

was derived from d i f f r a c - tion measurements a f t e r a data treatment process which can be divided i n t o two steps[51,[o

.

The number of neutrons C(Q) scattered by the a l l o y i s f i r s t derived from experimental countings with the aid of background, container s c a t t e r i n g and a b s o r p tion ccrrections

'.

From C(Q) ane' then c a l c z l a t e r

o r i t s normalized f o r m ( ~ h i c h goes t o 1 f o r l a r do 2

ge Q ) : S ( Q ) =

a

/

c

cibi

1 (4)

This second s t e p involves calculating a normal iza- tion constant

'51

and correcting for nu1 tiplef-73, incoherent and i n e l a s t i c s c a t t e r i n g

C81.

The f i n a l

do

cross section

a

i s the sum of t h e desired coherent cross section and a magnetic s c a t t e r i n g term :

5. MAGNETIC SCATTERING 5.1

-

LJQLJID-JICKEL

In t h e case of pure nickel and f o r small Q values ( i .e. around 0.3 ;-I),% was found

equal t o : 0.21 barn/sr while the coherent cross section calculated from the Ornstein-Zernike rela- tionCgl only amounts t o 0.03 barn/sr. The remaining magnetic cross section : d'ag

_a

= 0.18 barnlsr i s thus larger than the ideal paramagnet value :

dopara

-

A n = 0.08 barn/sr calculated from Halpern and

au

doMag Johnson formula [lo] The difference between

Para

and which has been previcrrsly observed and

-""

interpreted by ~ e b e r L1l1 a r i s e s from magnetic cor- r e l a t i o n s in the melt. I t i s unfortunately impos- s i b l e t o obtain the magnetic correlation length from an Ornstein-Zernike p l o t

Da

in the Q i n t e r - val : 0.3+1.5

i-'.

On the other hand the magnetic cross section decreases with Q and becomes negligible with res- pect t o the nuclear coherent cross section

2

"

1

(= bl) beyond Q = 1.5 A-

.

5.2

-

NICKLLzVANADIUM-ALLO_YS In lili-V a1 1 oys, the magnetic contributionto cross section (5) very 1 i kely decreases with vanadium concentration but s t i l l explains why in the 8&.7at% nicitel alloy experimental valcles of S(Q) a r e larger than calculated valuzs of S(Q) f o r Q4.5 (see figures 1 and 2 ).

6. PARTIAL NICKEL-NICKEL STRUCTURE FACTOR

For Q>1.5 A"-' three main changes may be no- ticed on Sll(Q) ( & f ( ~ ) ) as nickel concentration decreases (see figure 1) :

i ) a s l i g h t s h i f t of t h e position Q : ~ of Sll(Q) f i r s t peak towards small Q,arising from s i z e effects i i ) an overall decrease of Sll(Q) o s c i l l a t i o n s which i s due t o the decrease of t h e p a r t i a l number density of nickel : pl=clp

(4)

5 Fig. 1

-

Experimental S(Q).

~ = 1 5 0 0 ' ~

,

el=i.

( a ) , 0.887 ( b ) , 0.554 ( c ) . In t h e next section a l l these r e s u l t s a r e quantitatively interpreted.

7. MODEL INTERPRETATION AND CONCLUSIONS 7.1

SIZE-UEFECT

If one neglects the coupling between

0 5 10

Fig. 2

-

Calculated S(Q). T=1500°C,

'T=150G°C, Cl=l. ( a ' ) , 0.887 ( b ' ) , 0.554(c1) dl and d2 the Goldschmidt diameters of Ni and V :

"

dl = 2.50 and d2 = 2.72 A. Therefore atomic diameters of nickel and vanadium seem t o be addi- t i v e and almost i n s e n s i t i v e t o alloying.

TABLE I

chemical order and s i z e e f f e c t s and i f atomic diameters a r e additive Q:' i s related t o atomic dia-

t21 meters dl and d2 by : 11 1 Zf Ql

=.a;

[7.55

-

4.3 (T

-

111 ₍₆₎ 'I I L

where

7

= cldl + c2d2 i s t h e average atomic diame-

x These values a r e obtained from a l i n e a r interpo- t e r of t h e a1 loy. Experimental Q t l values agree l a t i o n between measured d e n s i t i e s of liquid nickel

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C8-166 JOURNAL DE PHYSIQUE

7.2

CI4EMICfiLCG-CDER

Measured 3 ( Q ) can be f i t t e d w i t h a good accuracy (see f i g u r e s 1 and 2) b y c a l c u l a t e d S(Q) u s i n g r e l a t i o n :

HS

S.

.

(Q) = bi t e x p ( - 0 2 ~ 2 ) 2 [Si (9)-6. 1

1 J

Pm

1 J

L e t us consider t h e d i f f e r e n t terms o f t h i s equation. The Debye-Waller f a c t o r which i s i n t r o d u c e d i n ( 7 ) t o f i t t h e damping o f

S(Q)

o s c i l - l a t i o n s i s r e l a t e d t o some mean v i b r a t i o n frequen-

where h i s the Planck constant, kB t h e Boltzmann constant and m t h e mean atomic mass o f t h e a l l o y . I t t u r n s o u t t h a t v equals 5.10 S-I i .e. roughly 2/3 o f t h e mean Debye frequency of t h e correspon- ding c r y s t a l l i n e phases, i n agreement w i t h o u r pre-

D

53 vious model f o r l i q u i d metals

.

HS

P a r t i a l s t r u c t u r e f a c t o r s S. . ( Q ) are c a l - l J

c u l a t e d from our geometrical model

K21

.

I f one again n e g l e c t s t h e coup1 i n g between chemi c a l o r d e r and s i z e e f f e c t s t h i s model depends on t h r e e parameters: i ) i t s number d e n s i t y

om

which i s i n t r o d u c e d i n t o equation ( 7 ) t o t a k e i n t o account t h e d i f f e r e n c e between model and experimental d e n s i t i e s .

i i ) some diameter dm whose value l i e s between dl and

a

i i i ) and t h e f i r s t neighbour o r d e r parameter :

where rl i s t h e t o t a l c o o r d i n a t i o n number and n12 the number o f 2 atoms surrounding a 1 atom. Numeri- c a l values of these f i t parameters a r e r e p o r t e d on t a b l e 1.

The negative value o f 6 expresses a chemi c a l o r d e r i n g phenomenon which i s due t o a p r e f e - r e n t i a1 a t t r a c t i o n between n i c k e l and vanadi um

*

V(Q) prepeak. I t should be i n t e r e s t i n g t o compare these values w i t h thermodynami ca1 p r e d i c t i o n s b u t t h i s i s u n f o r t u n a t e l y impossible because t h e e n t h a l - py o f m i x i n g o f l i q u i d Ni-V a l l o y s has n o t y e t been measured.

Although such an o r d e r i n g phenomenon between two metals belonging t o t h e beginning and t o t h e end o f t h e 3d t r a n s i t i o n s e r i e s may l o o k s u r p r i s i n g i t has a l s o been observed by Sakata e t a1 [I6] i n amorphous Cu-Ti a l l o y s whose e l e c t r o n i c s t r u c t u r e i s s i m i l a r . I n b o t h systems, s t r u c t u r a l s t u d i e s have thus opened t h e t r a c k t o d i f f i c u l t thermodyna- m i c a l o r e l e c t r o n i c p r o p e r t i e s measurements. REFERENCES

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-

f

Such a prepeak cannot be e x p l a i n e d by t h e presence o f oxygen i m p u r i t i e s s i n c e even i f t h e 1000 ppm oxygen atoms were ( v e r y u n l i k e l y ) only surrounded by n i c k e l atoms (maximum order), t h a t could o n l y a f f e c t 10-3 x 10 ( f i r s t neighbours) = 1 a t % i n n i c k e l

.