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ATOMIC STRUCTURE OF AN fcc-HEXAGONAL INTERFACE
G. Regheere, J. Penisson
To cite this version:
G. Regheere, J. Penisson. ATOMIC STRUCTURE OF AN fcc-HEXAGONAL INTERFACE. Journal
de Physique Colloques, 1990, 51 (C1), pp.C1-909-C1-914. �10.1051/jphyscol:19901143�. �jpa-00230055�
COLLOQUE DE PHYSIQUE
Colloque CI, supplement au n°l, Tome 51, Janvier 1990
CI-909ATOMIC STRUCTURE OF AN fee-HEXAGONAL INTERFACE
G. REGHEERE a n d J . M . PENISSON
Departement de Recherche Fondamentale, Service de Physique, CFN-G, S5X, F-38041 Grenoble Cedex, France
Résumé - L'interface entre une matrice cubique à faces centrées et des précipités hexagonaux a été étudiée dans un superalliage par microscopie en faisceau faible et par haute résolution. L'alliage contenant une proportion importante de cobalt, la structure de la seconde phase est hexagonale ordonnée. Les précipités ont une forme de plaquettes parallèles aux plans compacts de la matrice. L' interface est elle même située dans ces plans. Le misfit entre les 2 phases est de 2 %. 3 familles de dislocations coins de vecteurs de Burgers 1/6<112> sont présentes. Ce réseau est triangulaire et possède la particularité de présenter des noeuds à 6 segments de dislocations. Les clichés de microscopie à haute résolution montrent que chaque dislocation est associée à une marche haute de 2 plans atomiques 111. Un modèle géométrique simple identique à celui d'un joint de torsion a été élaboré et rend compte de la géométrie observée.
Abstract - The structure of the interface between fee matrix and hexagonal precipitates in a superalloy has been studied using weak beam dark f i e l d and high resolution electron microscopy. An important percentage of cobalt is present in the alloy leading to an ordered hexagonal structure of the precipitates. They are p l a t e - l i k e shaped and the interface is parallel to the compact planes of both phases.
There is a 2 % m i s f i t between matrix and precipitate. The interface is made of 3 sets of 1/6<112> edge dislocations. These dislocations form a triangular net with nodes common to 6 segments of dislocations. Each dislocation is associated with a 2 atomic plane step. A simple geometric model identical to that of a twist boundary is presented.
1 INTRODUCTION
In a two phase alloy, the interface between the different phases play an important role in the different physical properties of the alloy. The knowledge of the structure of these interfaces is then necessary and it represents the first step in the understanding of the deformation process. Many different systems have been investigated on the experimental as well as on the theoretical point of view : Cu-Cr /1,2,/ , Al-Ag /3,4/. A review of the general problem of fcc-bcc interfaces can be found in ref / 5 / . In this kind of interfaces, the two phases have generally different crystallographic structure and different atomic parameters so that the situation is much more difficult than for the grain boundary problem where atomic models have been calculated and compared to experimental structure /6/. In this paper, an interface between fee matrix and ordered hexagonal precipitates is
investigated using weak beam dark field and high resolution electron microscopy.
2 EXPERIMENTAL PROCEDURE
2.1 Composition of the alloy and thermal treatments. The alloy was elaborated from very pure materials and the composition, in atomic percentage, is :
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19901143
COLLOQUE DE PHYSIQUE
so t h a t t h e a l l o y composition i s i n t e r m e d i a t e between Ni and CO based superalloys.
I t was obtained by m e l t i n g t h e components under vacuum. The i n g o t was f i r s t annealed 6 h a t 1250 'C under argon atmosphere. A f t e r t h i s treatment, a l l t h e elements form a sa s o l u t i o n . A second annealing treatment performed between 700 and 850 "C and from 24 120 h leads t o t h e p r e c i p i t a t i o n o f a second phase which i s r e s p o n s i b l e f o r t h e mechani p r o p e r t i e s o f t h e a l l o y .
2.2 E l e c t r o n m i c r o s c o ~ v . A f t e r t h i n n i n g , t h e specimens a r e observed i n a JEOL 4000 EX microscope. The r e s o l v i n g power o f t h i s microscope being around 1.7
A
/7/, t h e 111 ( 2 and 200 (1.8A
) m a t r i x planes are e a s i l y imaged.3 RESULTS
--
3.1 A l l o y m o r ~ h o l o q y . A f t e r a 24 h i n c u b a t i o n period, p r e c i p i t a t e s appear w i t h i n m a t r i x . They a r e p l a t e - l i k e shaped and t h e a n a l y s i s o f t h e d i f f r a c t i o n p a t t e r n s and o f traces show t h a t 4 o r i e n t a t i o n v a r i a n t s a r e present and t h a t t h e broad faces o f p r e c i p i t a t e s a r e p a r a l l e l t o t h e 1 1 1 compact m a t r i x planes.
3.2 C r v s t a l l o q r a ~ h i c s t r u c t u r e o f t h e second phase. Chemical m i c r o a n a l y s i s o f p r e c i p i t a t e s leads t o t h e formula /8/:
T h e i r s t r u c t u r e i s deduced from t h e a n a l y s i s o f t h e d i f f r a c t i o n p a t t e r n s and o f t h e
b
r e s o l u t i o n images taken on e x t r a c t e d p r e c i p i t a t e s . This s t r u c t u r e i s ordered hexagonal type. T h i s p a r t i c u l a r s t r u c t u r e i s due t o t h e presence o f c o b a l t i n l a r g e proport w i t h i n t h e p r e c i p i t a t e s . I n a l l o y s c o n t a i n i n g o n l y N i , C r and Nb, t h e p r e c i p i t a t e s have orthorhombic s t r u c t u r e ( p Ni,Nb ) / g / . These 2 s t r u c t u r e s are very s i m i l a r , t h e c d i f f e r e n c e being t h e d i s t r i b u t i o n o f Nb atoms i n t h e compact planes: i n t h e DO,,struct i t i s t r i a n g u l a r w h i l e i n t h e orthorhombic i t i s r e c t a n g u l a r . This phase change car explained i n terms o f conduction e l e c t r o n d e n s i t y /8/.
The m a t r i x - p r e c i p i t a t e o r i e n t a t i o n r e l a t i o n s h i p i s :
This o r i e n t a t i o n r e l a t i o n s h i p i s a common one i n d i c a t i n g t h a t t h e compact planes compact d i r e c t i o n s o f b o t h phases are r e s p e c t i v e l y p a r a l l e l .
3.3 S t r u c t u r e o f t h e i n t e r f a c e . F i g 1 shows a weak beam d a r k f i e l d image o f a s i r i n t e r f a c e observed n e a r l y perpendicular t o t h e i n t e r f a c e plane. The d i f f r a c t i o n vectot
<422> and 3 sets o f d i s l o c a t i o n s are present; they form a t r i a n g u l a r l a t t i c e and p e r i o d i c i t y o f t h i s l a t t i c e i s 100
h .
Contrast a n a l y s i s u s i n g d i f f e r e n t d i f f r a c t vectors showed t h a t t h e d i s l o c a t i o n s are pure edge w i t h a/6 <112> Burgers vectors v r e f e r r e d t o t h e m a t r i x .When t h e m a t r i x has a toll> o r i e n t a t i o n 2 s e t s o f p r e c i p i t a t e s a r e seen edge-on. 1 o r i e n t a t i o n i s the b e s t one f o r h i g h r e s o l u t i o n observations because t h e compact plane:
both s t r u c t u r e s and t h e i n t e r f a c e a r e i n t h e edge-on p o s i t i o n . I f defocus c o n d i t i o n s s u i t a b l y choosen, t h e s t a c k i n g sequence o f f c c and hexagonal l a t t i c e s are c o r r e c t l y i m z so t h a t t h e i n t e r f a c e p o s i t i o n can be a c c u r a t e l y determined. The weak beam images shc t h a t t h e i n t e r f a c e s t r u c t u r e c o n s i s t s i n a t r i a n g u l a r n e t o f edge d i s l o c a t i o n s . Tt d i s l o c a t i o n s l i n e s are p a r a l l e l t o t h e t h r e e <011> d i r e c t i o n s l y i n g i n t h e i n t e r 1 p1 ane.
F i g 1 : Weak beam dark f i e l d image o f a s i n g l e i n t e r f a c e n e a r l y perpendicular t o the i n c i d e n t beam. The d i s l o c a t i o n network has a t r i a n g u l a r d i s t r i b u t i o n ; 6 d i s l o c a t i o n segments meet a t t h e nodes. The Burgers v e c t o r s are 1/6 <112> ( when r e f e r r e d t o the m a t r i x ) .
F i g 2 : High r e s o l u t i o n image o f t h e i n t e r f a c e . I n t h i s o r i e n t a t i o n , t h e s t a c k i n g sequence o f both phases are imaged. The p o s i t i o n o f the i n t e r f a c e i s arrowed on b o t h sides o f an i n t e r f a c i a l d i s l o c a t i o n
Cl-912 COLLOQUE DE PHYSIQUE
With the orientation used for high resolution images, only one set of dislocation:
parallel to the incident beam, the 2 other ones being inclined. This is not a
\convenient situation but in thin parts of the specimen
(the thickness must be less
t 100A
),images of interfacial dislocations have been obtained (fig
2).The Burc vectors and the interface position can be determined from these images. Two differ Burgers vectors were found. The first one corresponds to the edge a/6 [ll?] vector wt is parallel to the image plane; in this case
2extra half atomic planes perpendicular the interface are present. The second Burgers vector is equal to a/12
[ll?]anc corresponds to the projection on the observation plane of the inclined a/6
[ i 2 i ]Burc vector(fig
3)so that the high resolution images are in agreement with the previous
hbeam dark field images. This inclined Burgers vector is only observed in extremely t parts of the specimen where the effects of the inclined dislocation line on the image be neglected. All the dislocations are associated to a step in the interface plane
:2. The step height is 2 d,,, matrix planes but in some cases, mainly near the end of precipitates it can be larger.
Fig
3 :Schematic diagramm showing the distribution of the different Burgers vectors wi respect to the incident electron beam. The 111 interface plane is parallel to the plane of the diagram.
4 INTERPRETATION OF
THERESULTS
The interfacial dislocation structure is governed by the symmetry of the system and by misfit between the atomic parameters of both phases.
The misfit is defined by
:where d, and dp are respectively the atomic parameters of the matrix and the precipitat It can be mecsured directly on the electron diffraction patterns and the value is
:Using the Bollmann's formalism /10/, a coincidence site lattice
(CSL
)can
constructed. The compact planes of both phases have a
3fold symmetry and the dense at01
rows are parallel so that the CSL has the same geometry
:fig 4a. Its parameter depends
the misfit; with the previously
bcalculated value this parameter is
130 Awhich is larl
than t h e experimental d i s t a n c e between d i s l o c a t i o n s . The s i m p l e s t p o s s i b l e d i s l o c a t i o n s t r u c t u r e i s shown on f i g 4b. Each d i s l o c a t i o n segment l i e s between two adjacent good f i t areas. The r e s u l t i s an hexagonal network o f a/2 <110> edge d i s l o c a t i o n s which i s n o t i n agreement w i t h t h e experimental images. T h i s s t r u c t u r e has however been observed i n some Ni base s u p e r a l l o y s /ll/. I t a l s o corresponds t o t h e s t r u c t u r e o f t w i s t g r a i n boundaries i n metals /10/. From t h i s analogy w i t h a t w i s t boundary, o t h e r geometrical models can be constructed i f some d i s l o c a t i o n nodes are allowed t o d i s s o c i a t e . T h i s procedure has been described i n d e t a i l by H i r t h and Lothe /12/. The d i s l o c a t i o n nodes can be separated i n t o 2 d i f f e r e n t classes: K and P and i n each c l a s s t h e nodes can be symmetrical o r unsymmetrical
.
I f o n l y t h e P nodes d i s s o c i a t e , t h e s t r u c t u r e shown i n f i g 4c r e s u l t s . The d i s l o c a t i o n s a r e now p a r t i a l edge d i s l o c a t i o n s ( b = a/6<112> ) . T h e i r d i s t r i b u t i o n i s t r i a n g u l a r and 6 d i s l o c a t i o n segments meet a t each node. The spacing between d i s l o c a t i o n i s 110 A. I t should be remarked t h a t i n t h e case o f a t w i s t boundary, t h e d i s s o c i a t e d nodes correspond t o an i n t r i n s i c s t a c k i n g f a u l t and t h e d i s s o c i a t i o n amplitude i s governed by t h e s t a c k i n g f a u l t energy.F i g 4 a - coincidence s i t e l a t t i c e . The dots represent t h e centers o f t h e good f i t areas. The l a t t i c e has t h e same 3 - f o l d symmetry as t h e compact planes o f b o t h phases. I t s parameter i s g i v e n by t h e m i s f i t .
b - d i s l o c a t i o n network deduced from t h e CSL.
c - d i s l o c a t i o n network deduced from b when h a l f t h e d i s l o c a t i o n nodes are d i s s o c i a t e d
d
-
same as c b u t a l l t h e nodes are d i s s o c i a t e d .I n t h e interphase boundary, t h e s t a c k i n g f a u l t has no p h y s i c a l meaning b u t an e q u i v a l e n t s i t u a t i o n e x i s t s i f t h e i n t e r f a c e plane moves towards a new good f i t area which l i e s a t a d i f f e r e n t l e v e l . T h i s i s why a two atomic step i s associated t o each p a r t i a l d i s l o c a t i o n . The n e c e s s i t y o f such steps has already p o i n t e d out by King and Smith /13/ i n r a t h e r s i m i l a r examples. F i n a l l y , i f both t h e P and K nodes can d i s s o c i a t e another s t r u c t u r e i s
Cl-914 COLLOQUE DE PHYSIQUE
p o s s i b l e which c o n s i s t s i n an hexagonal network o f p a r t i a l d i s l o c a t i o n s . The spa between d i s l o c a t i o n s i s now 75
A
: f i g 4d. The comparison o f t h e experimental image t h e i n t e r f a c e boundary t o these geometrical models shows t h a t o n l y t h e s t r u c t u r e descr on f i g 4c i s p o s s i b l e .5 CONCLUSION
Using weak beam d a r k f i e l d and h i g h r e s o l u t i o n e l e c t r o n microscopy, t h e s t r u c t u r e o f i n t e r f a c e between an f c c m a t r i x and hexagonal p r e c i p i t a t e s has been determined.
geometrical m i s f i t i s r e l a x e d by t h e presence o f a t r i a n g u l a r network o f p a r d i s l o c a t i o n s . This r a t h e r unusual d i s t r i b u t i o n can be described on t h e b a s i s I geometrical model u s i n g t h e CSL concept. The choice between t h e t h r e e d i f f e r e n t poss models i s o n l y made by comparison w i t h experimental r e s u l t s and t h e f i n a l e x p l a n a t i o ~ t h i s p a r t i c u l a r s t r u c t u r e w i l l need t h e c a l c u l a t i o n o f t h e energy o f these c o n f i g u r a t i ~ REFERENCES
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