THE EFFECT OF IMPURITY ELEMENTS ON
CHEMICAL BONDING AT GRAIN BOUNDARIES
C. Briant, R. Messmer
To cite this version:
C. Briant, R. Messmer. THE EFFECT OF IMPURITY ELEMENTS ON CHEMICAL BONDING AT GRAIN BOUNDARIES. Journal de Physique Colloques, 1982, 43 (C6), pp.C6-255C6-269. <10.1051/jphyscol:1982623>. <jpa-00222304>
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Submitted on 1 Jan 1982
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JOURNAL DE PHYSIQUE
Colloque C6, supplément au n° 12, Tome 45, décembre 1982
page C6-255
THE EFFECT OF IMPURITY ELEMENTS ON CHEMICAL BONDING AT GRAIN
BOUNDARIES
C.L. Briant and R.P. Messmer
General Eleotria Company, Corporate Research and Development Center,
Box 8, Soheneotady, New York 12308, U.S.A.
P.O.
Résumé. - Malgré des concentrations totales très basses, les impuretés se ségrègent souvent aux joints de grains des métaux, où elles
s'accumulent. A cause de cette ségrégation, les joints de grains
peuvent être affaiblis. Ainsi ils deviennent les chemins préférés
pour la rupture fragile. Dans cet article on présente les résultats
de calculs d'amas en mécanique quantique qui relèvent de ce problème.
Notre exemple est la fragilisation de nickel par le soufre. Nos
calculs montrent que les éléments fragilisants sont ëlectronégatifs
à l'égard du métal et ils attirent sur eux des charges de ce métal.
Ainsi les charges sont retirées des liaisons métal-métal, qui sont
affaiblies. La fragilisation résulte de cet affaiblissement. On
montre de plus que, bien que ce modèle de fragilisation soit vrai
pour des amas de plusieurs configurations, les degrés de transport
et d'affaiblissement des liaisons ne sont pas les mêmes dans tous
les cas. On conclut que le degré de fragilisation des joints de
grains dépend non seulement de la concentration des impuretés mais
aussi de la structure du joint de grains.
Abstract. Impurity elements, which have very low bulk concentrations in metals, often segregate to grain boundaries where their
concentrations can be greatly enriched. As a results of this segregation, the grain boundaries are often weakened so that they become
preferred paths for brittle fracture.
This paper presents the
results of fully quantum mechanical cluster calculations which have
been applied to this problem. The particular system which we have
considered is the embrittlement of nickel by sulfur. Our results
will show that embrittling elements are electronegative with
respect to their host metal, and draw charge off of the host metal
onto themselves. As a result of this charge transfer, there is
less charge available to participate in metal-metal bonds and they
are weakened.
It is the weakening of these bonds that leads to
embrittlement. The results further show that, although the qualitative model for embrittlement is independent of the cluster
geometry, the degree of charge transfer and hence the amount of
weakening of the metal-metal bonds does depend on geometry. Therefore, grain boundary embrittlement is not strictly a function of
concentration of the impurity but of the structure as well.
1. Introduction. - The chemical composition of grain boundaries is
rarely identical to that of the surrounding matrix.
Instead, as a
result of segregation to these internal interfaces in solids, the concentration of certain elements can become considerably enriched above
their bulk concentrations. Most notably impurity elements which may
have bulk concentrations as low as 10 to 100 ppm may have local
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982623
C6-256
JOURNAL DE PHYSIQUE
concentrations at the grain boundary of 1 to 5 atomic per cent.
The metallurgical interest in grain boundary segregation arises
from the fact that this difference in composition often exerts a great
influence on the properties of the material. For example, impurity
segregation to grain boundaries can make the boundaries particularly
favored paths for fracture (1-11) or corrosion (12-16).
Segregation
can also retard grain boundary motion (17-18) and thus affect the
various stages of recrystallization. Furthermore, segregation can
modify precipitation reactions that occur at grain boundaries (19) and
can also change the atomic structure of the grain boundary (6).
Of all of these metallurgical problems, perhaps the one that has
received the most extensive experimental study has been intergranular
fracture. It has been well demonstrated that intergranular fracture
is associated with a brittle, low energy fracture process, and in the
absence of an aggressive environment it is always produced by segregation of certain deleterious elements to the grain boundaries. As a
result of experiments which have employed Auger electron spectroscopy,
many of these harmful elements have been identified and some of them
are listed in Table I. It has also been found that some segregated
elements can counteract embrittlement and they are also listed in
Table I.
Certainly, identification of these elements has been a great step
forward in understanding this problem. However, the question has still
remained as to why these elements cause the boundaries to be weakened.
Undoubtedly, they must in some way weaken the chemical bonds at the
grain boundaries, but the question one would like to answer is how
this weakening comes about. In this paper we will describe results of
fully quantum mechanical cluster calculations which address this question. We will specifically consider the embrittlement of nickel by
sulfur. We will show that sulfur is electronegative with respect to
nickel and that it draws charge off of the nickel atoms around it onto
itself. Consequently, less charge is available to participate in
metal-metal bonds and these bonds will be weakened. It is the weakening of these bonds that leads to embrittlement. Our results also show
that grain boundary geometry may affect the degree of embrittlement,
but qualitatively the electronic embrittlement mechanism is independent of the atomic arrangement.
2. Method. The computational method used for these calculations was
the self-consistent-field X-a scattered-wave molecular orbital method.
This method was developed by Slater (20) and Johnson (21) and has been
very sucessfully applied to problems involving transition metals (2224). One of the primary features of the X-ascattered-wave method is
that it is a cluster method. One considers only a finite number of
atoms in a fixed geometry and calculates their molecular orbitals.
From these calculations one can then obtain such information as the
molecular orbital energy levels, contour plots of the orbitals which
correspond to these levels, and contour plots of the charge density.
For the problem being considered here, a cluster method is ideal
because the grain boundary is a defect structure. The problem then
remains to choose a cluster geometry that is similar to the local
atomic arrangement at a grain boundary. Recent work (25-26) has shown
that the structure of grain boundaries can be described as a series of
interlocking clusters which are distorted versions of the Bernal
polyhedra (27). These polyhedra provide cluster geometries which can
be used in these calculations. In this paper we have used four of
M = Metal Atom
I = Impurity
Figure 1: The Bernal polyhedra used in these calculations. (a)
The tetrahedron, (b) the tetragonal dodecahedron, (c) the capped
trigonal prism, and (d) the Archimedian antiprism.
JOURNAL DE PHYSIQUE
these polyhedra for our cluster geometries.
These include the
tetrahedron, the tetragonal dodecahedron, the capped trigonal prism,
and the Archimedian antiprism. These clusters are shown in figures
la, lb, lc, and Id, respectively.
3. Results.
As can be seen from Table I, sulfur is a strong
embrittler of nickel, and boron counteracts this embrittlement.
Furthermore, it has been shown that the beneficial effects of boron
are not a result of site competition with the sulfur (10). Therefore,
to begin our consideration of why certain elements cause grain boundary embrittlement, we consider these two extreme cases. The clusters
which we will examine are the tetrahedra Ni4S and Ni4B. For each of
these calculations the nickel atoms have been placed at the vertices
of the tetrahedron and the impurity atom in the center.
Figure 2 shows the orbital energy levels for these two clusters.
In both Ni S and Ni4B there is a group of closely spaced orbitals near
-5 to -6 $v. These energy levels correspond to orbital's which are
almost entirely located on the metal atoms. However, in both cases
there are four orbitals (la*, la;, lt;, and lt* )which have energies
well below the others. It 1 s these orbitals wgich describe the metal
impurity bond and we wish to consider them in some detail.
Figure 3 shows equi-valued contour plots for the four orbitals.
The plane of these plots is the shaded plane in figure la. If we compare these plots orbital by orbital we see that there are definite but
consistent differences between the two clusters. For any given orbital
there is clearly more content on the nickel atoms in Ni B than in
Ni4S.
Since these plots must reflect the location of charge in a
given orbital, this result means that charge is drawn off the nickel
atoms onto the sulfur, whereas in the cluster containing boron this
charge transfer does not occur. In Ni S these orbitals are largely
concentrated on the sulfur and are driwn rather tightly around it,
having little content in the region between the nickel and sulfur. In
Ni B the orbitals do have some content on the boron but they are not
pufled in as tightly and there is considerable content in the region
between the boron and the nickel atoms. Therefore, it would appear
that the bond between the sulfur and the nickel atoms is heteropolar
with charge concentrated on the sulfur whereas the bond between the
boron and the nickel atoms is homopolar with charge shared between
them.
Based on these results we can suggest the following mechanism for
embrittlement. Sulfur, which embrittles nickel, is electronegative
with respect to nickel in that it draws charge off of the nickel atoms
around it onto itself. As a result of this charge transfer, there
will be less charge available to participate in the nickel-nickel
bonds and they will be weakened. The weakening of these bonds will
lead to the observed embrittlement. In contrast, a cohesive enhancer
such as boron in nickel is not electronegative with respect to the
host metal and forms a rather homopolar bond with it. Consequently,
charge will not be drawn out of the metal-metal bonds and they will
not be weakened. The homopolar bond formed between this type of
impurity and the metal will provide an additional increment of bonding
at the grain boundary.
Clearly, to test these ideas we should examine larger clusters
where we can directly observe the effect of an embrittling element on
the metal-metal bonds. Therefore, we have performed calculations on
the eight atom tetragonal dodecahedron (figure lb), the nine atom
TABLE I
GRAIN BOUNDARY EMBRITTLERS AND COHESIVE
ENHANCERS OF TRANSITION METALS
(References to Work in Parentheses)
Transition Metal
Grain Boundary Embrittler
Cu
Te (1),Bi (2)
Fe
S(3) ,N(4) ,Sn(5) ,Te(6) ,Se(7)
w
P(8)
Mo
o(9)
C(9)
Ni
S(10,ll)
B(10)
0-
Cohesive Enhancer
0
Ni4S
NiqB
-
-2.0SPIN UP
-4.0
-
-2.0-
SPIN DOWN
SPIN UP
-
SPIN DOWN
-
-4.0412
912-
-2
20!
212
-8.0-
-
-t
-
-
s -8.0-
>
a
0
12-
12
-
Y
a
Y
W
Z
112-
--
112
-
-100 -
-
-10.0lo(--
-
-12.0-
-
A
--
101
-12.0-
-
- 14.0
ol-,
b
Figure 2: The orbital energy levels for (a) Ni4S and (b) Ni4B.
JOURNAL DE PHYSIQUE
Figure 3: Contour plots of the four molecular orbitals that contribute to the metal-impurity bond.(a) Ni4S and (b) Ni4B.
capped trigonal prism (figure lc) and the ten atom Archimedian
antiprism (figure Id). In all cases we have first performed calculations for the cluster with nickel atoms at the vertices of the
polyhedron and no embrittling atom present in cluster. We have then
repeated the calculation, again with the nickel atoms at the vertices
but also with a sulfur atom in the center of the cluster.
In order to determine the effect of the presence of sulfur on the
metal-metal bonds in the cluster we have examined the total valence
charge density for each of these clusters. They are shown in figures
4, 5, and 6. Let us first consider the results for Ni8 and Ni8S shown
in figures 4 a and b, respectively. The plane of these plots is such
that it includes nickel atoms 1, 4, 7, and 8 in Ni8 and these same
nickel atoms plus the sulfur atom in Ni8S.
Particular attention
should be paid in this figure to the darkened contour. In Ni this
contour clearly contributes to a bond between nickel atoms 1 an8 7, 4
and 8, and 7 and 8. In Ni S this contour has been changed. It no
longer contributes to a bondsbetween atoms 1 and 7 and 4 and 8 and its
contribution to a bond between atoms 7 and 8 has been greatly reduced.
Instead it now contributes to a bond between the sulfur atom and
nickel atoms 1 and 4. Therefore, we see that the same basic mechanism
is holding in this larger cluster. When sulfur is added to the nickel
cluster, it forms a strong heteropolar bond with the nickel atoms
nearest to it. Charge is localized in this bond and is primarily centered on the sulfur atom. Less charge is then available to participate in the metal-metal bonds and they are weakened. This last fact
is demonstrated by the change in the darkened contour in the figure.
The results for Ni
and Ni S, shown in figures 5 a and b,
respectively, are quite gmilar tJ0those for the eight atom cluster.
The plane of these plots include nickel atoms 1, 2, 3, and 4 (see figure Id for identificati0n)in Ni
and these same atoms plus the sulfur
atom in Ni S.
the darigned contour clearly contributes to a
bond betwela
yi&l(d I and 2 and 3. However, when sulfur is added
the contour is changed so that it no longer contributes to these bonds
but to a bond between the sulfur atom and nickel atoms 1 and 2. The
metal-metal bonds between atoms 1 and 3 and 2 and 3 are weakened. However, it would appear that the embrittling effect of sulfur may be
less in this cluster because, although the contour is broken into two
parts, the part enclosing only atom 3 is still practically touching
that part surrounding the sulfur atom and nickel atoms 1 and 2. This
result is in contrast to the clear separation observed in Ni8S between
that part of the contour surrounding nickel atoms 7 and 8 and that
part surrounding nickel atoms 1 and 4 and the sulfur.
ate::
Finally, we consider the results for Nig and NigS shown in figures 6 a and b, respectively. The plane of these plots is one which
includes nickel atoms 1, 2, and 3 in both clusters. Coutours on atom
4 are also observed but they are not in the plane of the plot.
Although the change caused by adding sulfur is not nearly as great,
close examination of these two figures reveals that the same mechanism
is operative. Again we see that the darkened contour contributes to a
bond between atoms 1 and 3 and 2 and 3 in Ni
In Ni S the contour is
still continuous around all three nickel Ztbms, but between nickel
atoms 1 and 3 and 2 and 3 it has been pulled in to form a tighter
neck. This pulling in is a much milder form of the charge depletion
which caused the complete break off of the contour observed in the
eight and ten atom clusters. Therefore, the embrittling effect of
sulfur is not as strong in this cluster, but the same qualitative
effect of the addition of sulfur to a cluster of nickel atoms, i.e.
less charge available to participate in nickel-nickel bonds, can still
JOURNAL DE PHYSIQUE
Figure 4: Contour plots of the total valence charge density for
(a) Ni8 and (b) Ni8S.
Figure 5: Contour plots of the total valence charge density for
(a) N i l B and (b) NilflS.
Figure 6: Contour plots of the total valence charge density for
(a) Nig and (b) Ni9S.
Figure 7: Contour plots of the total valence charge density for
(a) Ni
and (b) Ni @S. In these cluster nickel atoms 3 and 4
have b&gn brought id closer to the center of the cluster than
they are in the clusters shown in Figure 5.
JOURNAL DE PHYSIQUE
be observed.
4. Discussion. The results presented above have provided us with a
general explanation of why certain impurity elements should cause
grain boundary weakening. Those elements are electronegative with
repect to their host metal and draw charge off of the metal onto themselves. There is then less charge available to participate in the
metal-metal bonds and they are weakened. It is the weakening of these
bonds that leads to grain boundary embrittlement. The results also
show that the ease with which a grain boundary is embrittled will
depend on its atomic structure. This result is quite consistent with
experimental observations made in our laboratory which show that in an
embrittled sample, even though one may achieve completely intergranular fracture, the amount of plastic tearing associated with individual
grain boundaries can vary. This result is also consistent with our
experimental observations that the boundaries most prone to fracture
in a sample are not necessarily those with the highest concentration
of segregant
.
It is interesting to consider in more detail why sulfur has a
less demonstrable embrittling effect on the nine atom capped trigonal
prism than on the eight or ten atom clusters and also why the ten atom
cluster appears to be slightly less embrittled by sulfur that the
eight atom cluster. Several factors appear to contribute to these
differences and they are all related to the spatial arrangement of
atoms in the cluster. In Ni8S there are two distinct sets of atoms.
Four of the atoms (numbers 1, 2, 3, and 4) are located near the sulfur
and the other four are located at some distance from it. Ni S also
has two distinct sets of atoms. Eight form the antiprisml!nd
are
located near the sulfur while the two atoms that cap the antiprism are
farther away. In Ni S one set of six atoms forms the trigonal prism
while three others 2orm the caps. However, the arrangement of all
nine atoms is such that they are all approximately equidistant from
the sulfur. Therefore, as we proceed in the order Ni8S, Ni OS, and
Ni S, the sulfur has an increasing number of nearest neighbbrs from
wh?ch to draw charge. Therefore, one would expect less charge to be
drawn off any one atom as this number increases which in turn means
that the metal-metal bonds would be weakened less. This idea is quite
consistent with the results. The second point concerns the difference
between Ni S and the other two clusters. In both NiSS and Ni 0S there
are two sets of nickel atoms, one set near the sulfur atom an4 one set
removed from it. In these clusters we can directly observe the effect
of sulfur on the bonds between these two sets of atoms. In Ni S,
although we do have two sets of atoms, one is not distinctly fartaer
away from the sulfur than the other. Therefore, any changes in metalmetal bonds caused by the charge transfer would primarily affect bonding between the nine atoms in this cluster and the next shell of
neighbors. Finally, we have found that changes in the bond lengths in
any given cluster can affect the results. Generally, as the cluster
is contracted the embrittling effect of an element is decreased. This
fact can be seen by comparing the results in figures 7 a and b with
those in figures 5 a and b. Figures 7 a and b are plots for Ni
and
Ni S but in this case atoms 3 and 4 (see figure Id for identi%icati&[)
have been brought in closer to the center of the cluster. When
cluster, the effect on the
sulfur is added to this contracted Ni
bonds between atoms 1 and 3 and 2 and 3
l
!
s
much less. The only signs
of weakening of these bonds are the small trapezoidal holes which form
between the two pairs of atoms. These represent a decrease in charge
in the bonds.
Previously reported results (28-29) have also shown that this
model holds up well for systems other than sulfur in nickel. An examination of the embrittling systems listed in Table I shows that the
embrittling elements tend to come from groups IV to VI in the periodic
table and thus would generally be electronegative with respect to the
embrittled metals. It would be tempting to try to correlate embrittling potency with values from an electronegativity scale such as
Pauling's (30). However, our work (29) has shown that the Pauling
scale, which was based on chemical data, is not always reliable for
metallurgical problems such as this one and that naive use of such a
scale could lead to erroneous conclusions.
Finally, we should point out the implications that our results
have concerning the fracture path in the solid. Our model tells us
that the fracture should occur by the breaking of metal-metal bonds.
At first thought, this result might seem to imply that the fracture
would occur at some distance from the boundary. However, it can
easily be shown (31-32) that the crack can propogate within one atom
layer of the center of the boundary and break only metal-metal bonds.
Furthermore, the crack can cut back and forth across the center of the
grain boundary by this same bond breaking mechanism.
5. conclusions. The conclusions of this work are the following:
1.
Impurity elements which cause embrittlement are electronegative
with respect to the host metal atoms. They draw charge off of
the surrounding atoms which leaves less charge available to participate in the metal-metal bonds.
2.
The atomic arrangement at the boundary does not affect the general model for embrittlement. However, it does affect the amount
of charge transfer and hence the degree of embrittlement. Therefore, certain arrangements of atoms at the grain boundaries would
be more easily embrittled than others. Generally, an increase in
the number of nearest neighbors around the impurity and a
decrease in the lattice spacing tends to decrease the embrittling
potency of the impurity.
6. s
i
h
T
-Naval Research.
work was partially sponsored by the Office of
1.
MARCUS, H. L. and PATON, N. E., Metall. Trans. 5 (1974) 2135.
2.
HONDROS, E. D. and McLEAN, D., Phil. Mag. 29 (1974) 771.
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TAUBER, G. and GRABKE, H. J., Berichte del Bunsen Gesell. fur
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4.
HOPKINS, B. E. and TIPLER, H. R., J. Iron and Steel Institute 127
(1954) 110.
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SEAH, M. P. and HONDROS, E. D., Proc. Roy. Soc. A 3 3 (1973) 191.
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RELLICK, J. R. McMAHON, C. J., Jr., MARCUS, H. L. and PALMBERG,
P. W., Metall. Trans. 2 (1971) 1492.
PICHARD, C., RIEU, J. and GOUX, C., Mem. Scient. Revue Metall. I0
(1976) 13.
JOSHI, A. and STEIN, D., Metall. Trans.
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ARMIJO, J. S., Corrosion,
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G.,
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published (1982).
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MESSMER, R. P. and SALAHUB, D. R., Phys. Rev. B 1_6 (1977) 3415.
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BRIANT, C. L. and MESSMER, R. P., Proceedings of a Conference on
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DISCUSSION
F. CABANE-BBCUJTY : You explain the embrittlement of nickel by sulfur; we observe
that Cu-S
and Ag-S
high purity solid solutions are not brittle :
could you explain the reason for this difference of behaviour
between Ni on one hand and Cu and silver on the other hand?
C.L. BRIANT :
Without performing calculations on the Cu-S and Ag-S system, I
cannot explain your experimental observations. However, both experiment and theory have shown that the embrittling potency
of an impurity element depends greatly on the transition metal
that is being embrittled, (see reference 29).Therefore, one cannot
extrapolate either experimental or theoretical results on Ni to
these other metals and expect the same effects.
P. LESBATS :
a) To begin some metallurgical comment, you told grain boundary
brittleness is caused by impurity : we have experimental evidences
that the grain boundaries can be brittle on pure b.c.c. metals.
Concerning the role of phosphorous, even in steels, if they are
very pure without sulfur or nitrogen, the embrittlement by phosphorous only is not very strong. Michel Biscondi will come back
to these points in the last paper.
b)The X-a scattered wave technique is a very nice method. However
I am wondering if in this case a cluster method is very appropriate
because an isolated impurity generates a long range interaction
which is important and which is not taken into account by such
a method.
c) Are your calculations fully self-consistent, because the charge
transfer is very sensitive to the degree of self consistency?
JOURNAL DE PHYSIQUE
C.L.
BRIANT :
a) Dr. Biscondi's results are very interesting, but at this point
it is very difficult for me to comment on then in any detail.
b) The X-a scattered wave calculations seem to be quite appropriate for this type of problem. Examination of the literature will
show its great successin problems of chemisorption and magnetism.
In these problems one is also interested in a type of impurity
interacting with a transition metal. Because of the excellent
agreement between theory and experiment in these cases, it would
appear that these should be no problem in applying the X-a scattered wave method to the problem of grain boundary embrittlement,
The calculations are fully self-consistent.
M. AUCOUTURIER :Did you obtain results on "non electronegative" embrittlers like
Gallium in Aluminium or Hydrogen in Iron or Nickel? Could it also
be possible to show the influence of Hydrogen in Ni-S system?
C.L. BRIANT :
We have only very recently begun to examine the effect of Ga on
Al, but our preliminary results would suggest that an electronegativity argument might still hold. We have examined H in Ni and
found very little change transfer.This
result suggests that the
mechanism for hydrogen embrittlement is different from that of the
other embrittling elements.
V. VITEK :
Il
a) How much are the results affected by the symmetry and free
surfaces" of the clusters? Perhaps you get similar effects of
charge redistribution if asymmetric clusters are used.
b) If this is not so and electronegativity is the principal
reason for charge redistribution then the effect is independant
upon whether the impurity is in the grain boundary or not and the
grain boundary effect is simply that it is a region of higher
concentration of impurities.
c) However, in boundaries a large variety of clusters and their
orientations exist and thus it seems that, in average, the
same number of sitronger and weaker bonds will be formed.
C.L. BRIANT :
a) In the text we have presented results for a number of different
cluster geometries and, as pointed out there, we always see the
same qualitative effects, & the embrittling impurity draws charge off of the metal atoms and weakens the metal-metal bonds. We
f u r t h e r showed t h a t t h e d e g r e e of c h a r g e t r a n s f e r would depend on
t h e number of n e a r e s t n e i g h b o u r s t h a t t h e i m p u r i t y atom h a s a t
t h e g r a i n boundary. Any asymmetry of t h e c l u s t e r would be r e f l e c t e d i n t h i s manner. Asymmetry a l o n e would n o t cause a charge red i s t r i b u t i o n i n pure N i c l u s t e r s of t h e t y p e s e e n h e r e .
b) I b e l i e v e t h a t you a r e c o r r e c t i n assuming t h a t one o f t h e
major f u n c t i o n s o f t h e g r a i n b o u n d a r i e s i s t o c o n c e n t r a t e i m p u r i t y
atoms. It a l s o impedes d i s l o c a t i o n motion which a l l o w s a s t r e s s t o
be b u i l t up t h e r e .
c ) Our c a l c u l a t i o n s would s u g g e s t t h a t e m b r i t t l i n g elements would
c a u s e t h e f o r m a t i o n of b o t h s t r o n g and weak
b o u n d a r i e s . It i s t h e p r e s e n c e
bonds a t t h e g r a i n
o f t h e weak bonds and t h e f a c t
t h a t a c r a c k can p r o p a g a t e a l o n g t h e b o u n d a r i e s by b r e a k i n g o n l y
t h e s e weak bonds t h a t c a u s e s e m b r i t t l e m e n t . This f i n a l p o i n t
i s i l l u s t r a t e d i n some d e t a i l s i n r e f e r e n c e 31.
L. HOBBS :
One of t h e t h i n g s t h a t one l e a r n s from s t u d y i n g d e f e c t a g g r e g a t i o n ,
i n c l u d i n g i m p u r i t i e s , i s t h a t atomic arrangements i n d e f e c t aggreg a t e s o f t e n m i m i c t h o s e found i n compounds of t h e elements i n v o l ved. With t h e e x c e p t i o n of t h e capped t r i g o n a l prism c o n f i g u r a t i o n
of NiOS, w h i c h a l o n e r e s e m b l e s t h e atom c o n f i g u r a t i o n s i n t h e NiAs
s t r u c t u r e of NiS o r FeS, your c l u s t e r c o n f i g u r a t i o n s appear r a t h e r
arbitrary.
I n f a c t , t h e NigS c o n f i g u a t i o n p r e d i c t s t h e l e a s t em-
b r i t t l e m e n t on your model.
C.L.
BRIANT :
These c l u s t e r s were chosen because t h e y should r e p r e s e n t t h e a r r a n gement of atoms a t t h e g r a i n boundaries. Although c e r t a i n l y a s e g r e g a t e d atom w i l l a f f e c t t h e arrangement of m e t a l atoms around i t ,
i t seems u n l i k e l y t h a t t h e atomic arrangement a t a l l g r a i n boun-
d a r i e s would t a k e on a g a l l i u m a r s e n i d e (Ni3S2) s t r u c t u r e . We d i d
s e e t h e s m a l l e s t e f f e c t f o r Ni2S and t h e r e a s o n s f o r t h i s a r e
discussed i n the text.