STUDY OF LIQUID NICKEL-VANADIUM ALLOYS
BY NEUTRON DIFFRACTION AND MODEL
SIMULATION
J. Lemarchand, J. Bletry, P. Desre
To cite this version:
J. Lemarchand, J. Bletry, P. Desre. STUDY OF LIQUID NICKEL-VANADIUM ALLOYS BY
NEUTRON DIFFRACTION AND MODEL SIMULATION. Journal de Physique Colloques,
1980, 41 (C8), pp.C8-163-C8-166. <10.1051/jphyscol:1980842>. <jpa-00220348>
HAL Id: jpa-00220348
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CoZZoque C8, suppZ6ment au n 0 8 , Tome 41, aoGt 1980, page C8-163
JOURNAL DE PHYSIQUE
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.
38401 S a i n t Martin d r H e r e s , France.
44,
28 i s the scattering angle, X the neutron wave-
1. INTRODUCTION
Structure factor determination i s one of the
the modulus of the scattering
length, Q = 4n
main purposes of diffraction experiments on liquid
vector and the Ashcroft-Langreth partial strilcture
or amorphous metals. In the case of binary alloys,
factors are defined by [31
..
a combination of three independent measurements i s
needed t o obtain the three partial structure fac-
where :
. 6i
i s the Kronecker 6 function
N the number density and
tors. However, these determinations are very deli-
.p
cate and t h e i r accuracy i s often limited.
. P1.J. ( r )
Nuch more accurate, although less complete,
information i s obtained from one single diffraction
=
the normalized distribution func-
tion of i - j pairs.
In the case of nickel-vanadium alloys where
measurement. In t h a t case, comparison with model
the scattering length of nickel : bl=l .03.10-~~cm
c a l c u l a t i o ~can lead to a quantitative interpreta-
i s much larger than the scattering length of vanadium : b2=-0.051.10 -12 cm, a single diffraction ex-
tion.
In t h i s paper, neutron diffraction experiments
periment gives d i r e c t l y the nickel-nickel structure
on vanadium-X alloys are presented which allow the
since coherent cross-section (1)
factor S,,(Q)
II
-
partial structure factor of X-X pairs t o be deter-
reduces to :
mined. Nickel -Vanadi um a1 loys are studied in order
Departures from approximation (3) mainly a r i s e from
t o investigate chemical ordering e f f e c t s into the
the term ( c ~ c ~ ) ~ ' ~ which
~ ~ ~does
~ sn ~
o t ~exceed
( Q )
.
gCoh
clb:
=
Sll(Q)
liquid phase around the eutectic comp~sition[~]
10 % of the coherent cross section i f nickel con-
Experimental r e s u l t s are f i n a l l y interpreted with
centration i s greater than 0.50.
the aid of geometrical models r21
.
2 . PRINCIPLE OF THE EXPERIMENTS
The differential cross-section f o r coherent
scattering by a binary alloy may be written :
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
the alloys a f t e r 10 hour
neutron scans was about
1000ppm. Four alloys were studied with concentra-
or in a normalized form* :
tions in nickel : cl=l.OO, 0.887, 0.554 and 0.461
In these expressions, ci and bi a r e respectively
the atomic concentration and the coherent nuclear
scattering length of element i
,
surrounding the eutectic composition : cy = 0.49.
Neutron diffraction experiments were carried
out a t the D4 spectrometer of the I n s t i t u t Laue0
x which goes t o 1 f o r large Q
Langevin. A 0.693 A wavelength was used in order to
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980842
JOURNAL DE PHYSIQUE
C8- 164
reach a maximum Q value of 14.5
2'
which enables
equal t o : 0.21 barn/sr while the coherent cross
a good normalization of experimental scattering
section calculated from the Ornstein-Zernike rela-
patterns.
tionCgl only amounts t o 0.03 barn/sr. The remaining
The samples were cylindrical, 6 mm in diamet e r and 3 cm high. They were heated between 1300
magnetic cross section : da'g
a
= 0.18 barnlsr i s
800+2000°C was b u i l t using the techniques develop-
thus larger than the ideal paramagnet value :
dopara
An
= 0.08 barn/sr calculated from Halpern and
au
Johnson formula [lo] The difference between doMag
Para
and -""
which has been previcrrsly observed and
ped a t INPG laboratoryL41. For the passage of the
interpreted by ~ e b eL1l1
r
primary beam,windows were cut in the tungsten hea-
relations in the melt. I t i s unfortunately impos-
ting element and in the thermal screens. Sapphire
s i b l e t o obtain the magnetic correlation length
containers were used, resulting in a very low neu-
from an Ornstein-Zernike p l o t Da in the Q inter-
tron background. These sapphi re s i nglecrystal s were
val : 0.3+1.5
and 1600°C under
Torr. For t h i s purpose a
high temperature furnace covering the range
oriented with a molybdenum goniometric table in or-
a r i s e s from magnetic cor-
i-'.
On the other hand the magnetic cross section
der t o l i m i t the number of Bragg reflexions super-
decreases with Q and becomes negligible with res-
posed on the liquid alloy pattern. The temperature
pect t o the nuclear coherent cross section
2
" 1
(= bl) beyond Q = 1.5 A-
was measured t o f 5°C with an optical pyrometer.
4. DATA TREATMENT
Cross section do was derived from diffrac-
a
tion measurements a f t e r a data treatment process
which can be divided into two steps[51,[o
.
The
.
5.2
-
NICKLLzVANADIUM-ALLO_YS In lili-V a1 1oys,
the magnetic contributionto cross section (5) very
1i kely decreases with vanadium concentration but
s t i l l explains why in the 8&.7at%nicitel alloy expe-
number of neutrons C(Q) scattered by the alloy i s
rimental valcles of S(Q) are larger than calculated
f i r s t derived from experimental countings with the
valuzs of S(Q) f o r Q4.5
aid of background, container scattering and absorp
tion ccrrections .'
From C(Q) ane' then calczlater
o r i t s normalized form(~hichgoes to 1 f o r l a r
do
2
ge Q ) : S ( Q ) =
/ c cibi
(4)
a
1
This second step involves calculating a normal ization constant 5'1 and correcting for nu1tiplef-73,
incoherent and i n e l a s t i c scattering C81. The final
cross section do i s the sum of the desired coherent
a
cross section and a magnetic scattering term :
(see figures
1 and 2 ).
6. PARTIAL NICKEL-NICKEL STRUCTURE FACTOR
For Q>1.5 A"-' three main changes may be noticed 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 the 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 the partial number
density of nickel : pl=clp
i i i ) the progressive appearance of a prepeak around
5. MAGNETIC SCATTERING
5.1
-
Q = 1.9
arising from a chemical order e f f e c t .
LJQLJID-JICKEL
This prepeak which i s reduced t o a shoulder in the
In the case of pure nickel and f o r
88.7 a t % nickel alloy transforms i n t o a well re-
small Q values ( i .e. around 0.3 ;-I),%
was found
solved peak i n 55.4 and 46.1 a t % nickel alloys.
0
Fig. 2
5
Fig. 1
-
Experimental S(Q).
-
,
~ = 1 5 0 0 ' ~el=i. ( a ) , 0.887 ( b ) , 0.554 ( c ) .
In the next section a l l these r e s u l t s a r e
5
10
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 :
"
quantitatively interpreted.
dl
7. MODEL INTERPRETATION AND CONCLUSIONS
7.1
=
2.50 and d2
=
2.72 A. Therefore atomic
diameters of nickel and vanadium seem t o be addi-
SIZE-UEFECT
t i v e and almost insensitive to alloying.
If one neglects the coupling between
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-
meters dl and d2 by t21 :
Zf - 111
Ql11 1 [7.55 - 4.3 (T
=.a;
I
where
'I
(6)
L
7 = cldl + c2d2 i s the average atomic diame-
t e r of the a1 loy. Experimental Q t l values agree
with relation (6) t o a 1 % accuracy i f we take f o r
x These values are obtained from a linear interpolation between measured densities of liquid nickel
and vanadium.
JOURNAL DE PHYSIQUE
C8-166
7.2
CI4EMICfiLCG-CDER
Measured 3 ( Q ) can be f i t t e d w i t h a good
*
V(Q) prepeak.
I t should be i n t e r e s t i n g t o compare
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)
these values w i t h thermodynami ca1 p r e d i c t i o n s b u t
using r e l a t i o n
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 -
:
HS
.
S. (Q) = bi t e x p ( - 0 2 ~ 2 ) 2 [Si (9)-6. 1
1J
Pm
1J
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-
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
where h i s the Planck constant, kB t h e Boltzmann
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
constant and m t h e mean atomic mass o f t h e a l l o y .
have thus opened t h e t r a c k t o d i f f i c u l t thermodyna-
I t t u r n s o u t t h a t v equals 5.10
S-I
i.e. roughly
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.
2/3 o f t h e mean Debye frequency of t h e correspon-
REFERENCES
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[lj J.L LEMARCHAND, These I n g e n i e u r Docteur, INP
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D53 .
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 lJ
.
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 introduced 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-
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-
156;
I--
17,
55,
c a l values of these f i t parameters a r e r e p o r t e d on
table
1.
The negative value o f 6 expresses a che-
mi 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
atoms and i s responsible f o r t h e appearance o f the.
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 nickel
.