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INTERACTION BETWEEN LATTICE
DISLOCATIONS AND GRAIN BOUNDARIES IN FCC METALS AND ORDERED COMPOUNDS
B. Pestman, J. de Hosson, V. Vitek, F. Schapink
To cite this version:
B. Pestman, J. de Hosson, V. Vitek, F. Schapink. INTERACTION BETWEEN LATTICE DISLOCA-
TIONS AND GRAIN BOUNDARIES IN FCC METALS AND ORDERED COMPOUNDS. Journal
de Physique Colloques, 1990, 51 (C1), pp.C1-311-C1-316. �10.1051/jphyscol:1990149�. �jpa-00230308�
COLLOQUE DE PHYSIQUE
Colloque Cl, supplement au nol, Tome 51, janvier 1990
INTERACTION BETWEEN LATTICE DISLOCATIONS AND GRAIN BOUNDARIES IN FCC METALS AND ORDERED COMPOUNDS
B. J. PESTMAN, J.Th.M. DE HOSSON, V. VITEK* and F.W. SCHAPINK**
Department of Applied Physics, Materials Science Centre, University of croningen, Nijenborgh 18, NL-9747 AG Groningen, The Netherlands
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.
" " ~ e p a r t m e n t of Metallurgy, Technological University of Delft, Rotterdamseweg 137, NL-2628 AL Delft, The Netherlands
Abstract - This paper describes a computer simulation study of the interaction between lattice dislocations and tilt grain boundaries. The calculations were camed out using a many-body potential for copper and potentials describing a stable L1, type of structure. Two interaction mechanisms were observed: absorption into the boundary by splittinginto D S c dislocations and splitting into lattice Shockley partial dislocations, one of which was incorporated in the boundary. If the associated step height for the DSC's is small and (one of) the DSC's can glide in the boundary plane, the lattice dislocation dissociates into DSc dislocations in the boundary.
Otherwise, anotherreaction is favourable, like the incorporation of one lattice partial dislocation in the boundary.
l
-
INTRODUCTIONThe interaction between dislocations and grain boundaries is generally believed to be of great importance to the mechanisms of mechanical failure in metals. Especially the difference between ductile and brittle fracture might be explained by variations in the way of interaction between dislocations and grain boundaries. A good example of the importance of this effect can be found in the ordered intermetallic compounds: although some of these alloys with high ordering energy have a large potential for high temperature applications, the brittle fracture occurring in these materials has prohibited their use. In this paper we concentrate on the detailed phenomena, which occur when lattice dislocations impinge on grain boundaries in fcc material and L1, ordered material. The present research is a computer simulation study (lattice statics) of the interaction between 1/2[1 101 screw dislocations and [ l 1 01 symmetric tilt boundaries in fcc and L1, ordered compounds. In the present set-up, the tilt axis of the bicrystal is parallel to the dislocation line, which facilitates the computational procedure. In general, two mechanisms for the interaction between a lattice dislocation and a grain boundary can be discriminated. The first mechanism is referred to as absorption, which can be explained by the dissociation in the grain boundary plane of the lattice dislocation into grain boundary (or D S c [l]) dislocations. The second mechanism for the interaction is referred to as transmission. A lattice dislocation in one grain can create another lattice dislocation in the other grain, usually leaving a residue (the difference between the two Burgers vectors of the two lattice dislocations) in the boundary. The residue is always a D S c dislocation.
2 - METHOD OF CALCULATION
For the description of the interatomic interactions, a Finnis- Sinclair many body potential representing copper [2] was used in the study of the fcc material and in the study of L1, a set of pair potentials representing a stable L1,-structure with high ordering energy was used. See ref 131 (potential set Cl).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990149
Cl-312 COLLOQUE DE PHYSIQUE
First, the grain boundary was relaxed at constant volume using a standard gradient method; details are described elsewhere [4,5]. Secondly, a computational block for the relaxation of the dislocation near the grain boundary had to be constructed. The computational block of the relaxed grain boundary was extended, according to the periodicity of the CSL, to form a block of 40 b X 40 b (b is the magnitude of the Burgers vector of the dislocation) perpendicular to the tilt axis. For the L12-case, different ordering configurations of the grain boundary were considered and the relaxed configuration with lowest energy was chosen as a starting point for the dislocation-grain boundary relaxation.
Next, the displacement field of the dislocation was imposed (in the upper grain). In the L1, material, the displacement field of a 1/2[1 1 O] superpartial was imposed near the grain boundary. It was connected by a ribbon of APB (antiphase boundary) on the (1
1
1) plane to another superpartial that was imposed with its elastic center outside the computational block, at equilibrium distance according to lineair isotropic elastic theory. Along the dislocation line, periodic boundary conditions were applied; the anisotxopic elastic solution (as if there was only one grain present) was used for the boundary conditions perpendicular to the dislocation line. The dislocation-grain boundary relaxation was carried out in the usual way for dislocation relaxation [6].3 - RESULTS
A number of boundaries in the misorientation range 31.59' to 50.48" were relaxed: the Z=27
(1
1 5) (0=31.59'); the Z=57 (Z 2 7) (0=44.0") and the C=11 (1 1 3) (0=50.48"). For fcc a periodic pattern of structural units was found:Z=27: A.A; 2=57: ABBB; C=l l: B.B, where the
.
indicates a translation of 1/4[1 1 O] along the tilt axis. For the L1,-structure a similar pattern was found: C=27: A,A,.A,A2; 2=57: A2B,B,Bl.A,B,B2B,; Z=11: B,B,.B,B,, where the.
indicates a translation of 1/2[1 1 01 and the subscripts,
and,
indicate topologically similar units with different distributions of atom types. ~ b r both materials, the C=27 and the Z=11 boundaries are favoured boundaries [4], i.e.the boundaries in the intermediate misorientation range are composed of the structural units of these boundaries.
For the two favoured boundaries, the C=27 and the Z=11, and for the long period boundary, the Z=57, an extensive study of the dislocation-grain boundary interaction in both materials was performed. The relaxations were carried out with the initial position of the dislocation at different locations along the grain boundary period, at a few lattice parameters away from the grain boundary plane.
All low-energy configurations that have been found are represented in a figure showing the relaxed boundary structure (the symbols indicating the atom positions are drawn as if there was no dislocation present). Some examples of dislocation structures are depicted using the differential displacement method [7]. This method indicates the relative displacement of each atom with respect to its neighbours in the direction of the Burgers vector. If the absolute value of the relative displacement exceeds half of the periodicity of the lattice in that direction, an integer number times the period is added or subtracted. In the case of the L1, structure, the periodicity of the fcc structure was used to facilitate the comparison. The relative displacements are indicated by arrows drawn between the atoms. In the figures, the regions where the differential displacements have a size between 0.30 a, and 0.354 a, (half the periodicity along the tilt axis;
a, is the lattice constant) are indicated by lines; the regions where the differential displacements are between 0.15 a, and 0.30 a, are indicated by lobes (two lines parallel).
fcc (Cu)
For the 2=27 boundary, four low energy configurations were found, all showing splitting into two Shockley partial dislocations, on different ( 1 1 1 ] planes. See fig. la. One of the Shockley partials always was attracted to the boundary.
Some local relaxation effects could be observed, as indicated in fig. lb.
Fig. l a - (Left) The configurations found for the L 2 7 boundary in fcc. In this and the following figures, the different symbols indicate different heights. Following order 0 + X A
.
Fig. l b
-
(Right) Configuration nr.1 from fig. la. The heights indicated by the symbols indicate heights before the dislocation was imposed. The local relaxations are indicated by circles.The =l1 boundary showed only one low energy configuration: the screw dislocation was absorbed in the boundary and split into two D S c dislocations, the 1122[4 7
i]
and the 1122[7 4 I].
See fig. 2. The cores of the D S c dislocations moved about 3.5 a,, apart. The two dislocations cause a step in the boundary plane of + l and -1 interplanar distance, respectively. This result compares well to experimental results [g].Fig. 2
-
The configuration found in the 5 1 1 boundary in fcc.The configurations for the &S7 boundary are very similar to the configurations of the two delimiting favoured boundaries. See fig. 3. In the parts of the boundary that can be described by %l l units, the mechanism of absorption in the boundary is observed again. The splitting was never beyond the two 2=27 units on both sides of the Z=11 region.
For the E 2 7 units, three of the four configurations that have been found for the E 2 7 boundary are found here again.
More details can be found in a previous paper on fcc [g].
COLLOQUE. DE PHYSIQUE
Fig. 3
-
The configurations found for the S 5 7 boundary in fcc.The G 2 7 boundary showed two different types of interaction, with little differences in the energies of the final configurations. In the first case, the superpartial was attracted to the boundary, but with no or very little splitting into Shockley partials. See fig. 4a. Strong local relaxations and spreading of the core in the boundary plane could be observed. In the second case, the superpartial was absorbed in the boundary and split into two D S c dislocations of the fcc (or disordered) S 2 7 grain boundary: the 1154[16 11 l] and the 1154[11 16
3 .
See fig. 4b.Fig. 4a
-
(Left) The configurations found for the S 2 7 boundary in L1, (except the case of absorption, see fig. 4b).The B-atoms are indicated by thicker lines. In this and the following figures, the different positions of the APB, attached to a configuration are indicated by broken lines and the number of the configuration.
Fig. 4b
-
(Right) Absorption of the superpartial in the S 2 7 boundary in Ll,. The double cirkels indicate anti-site defects.These D S c dislocations cause a step in the grain boundary plane of resp. +4 and -4 interplanar distances. It can be seen that some shuffling of atoms occurred, corresponding to the motion of the DSc's and the migration of the boundary plane in the upward direction. A new structural unit can be found between the cores of the two DSc dislocations. As the two DSc dislocations do not belong to the D S c lattice of the L1, ordered boundary, this unit belongs to a different ordering configuration of the E=27 boundary with energy higher by about 8%. In the region where the shuffling of atoms took place, anti-site defects have been created. See fig. 4b.
For the %l l boundary, a similar configuration as in fcc was found again, showing absorption of the superpartial in the boundary and splitting into two D S c dislocations of the fcc S 1 1 boundary, the 1122[4 7
i]
and the 1/22[7 4 l].
The part of the new boundary between the two D S c dislocations corresponds to a different ordering configuration of the C=l l boundary with 3% higher energy. The separation between the two D S c dislocations was 7 q. An other configuration with slightly higher energy showed absorption of the superpartial in the boundary with splitting into two dislocations, each with Burgers vector 11411 1 0]
.
These two dislocations have moved apart in the boundary plane in a zig-zag way. The small edge component of the D S c dislocations of the first configuration was not present in this case. See fig. 5.Fig. 5
-
The configurations found for the Ell boundary in Ll,.Most of the configurations that were found for the 2=57 boundary are very similar to the configurations found for the two delimiting favoured boundaries. See fig. 6. In the part that can be described as consisting of E11 structural units, absorption in the boundary and splitting into the two X=11 D S c dislocations as well as the splitting in a zig-zag way can be observed. The splitting was never beyond the E 2 7 units on both sides of a &l1 region. Some of the configurations of the L 2 7 unit in the 5 5 7 boundary show a clear splitting into Shockley partials with one partial in the lattice away from the boundary and one partial merged in the boundary. Some configurations were found that showed interference between the different units. In many cases strong local relaxations occurred.
Fig. 6
-
The configurations found for the &57 boundary in Ll,.Cl-316 COLLOQUE DE PHYSIQUE
4 - DISCUSSION AND CONCLUSIONS
In all the examples studied sofar, there was an attractive force between boundary and (partial) dislocation core. We will now discuss the results of the relaxations of each grain boundary and make a comparison between the results obtained for fcc and Ll,.
For the 2=11 boundary, the absorption in the boundary and splitting into the two D S c dislocations can be understood, using: the b2 criterion, the fact that both are glissile in the boundary plane, the small step height associated with these D S c dislocations and the conservation of step height [10]. The boundary that is formed beween the DSC's is topo- logically the same as the original boundary for fcc; for L1, it has only a slightly higher energy. Especially the DSC's in the fcc structure would be expected to move as far apart as possible. An explanation of the limited splitting might be found in a possibly high "frictional" force occuring in the density dependent desciption of interatomic forces.
In the E 2 7 case the attraction without splitting into DSC's in the boundary plane shows that the (partial) dislocation core can lower its energy by merging into the boundary core. In the L1, structure little splitting into Shockley partials occurred because of the high CSFenergy. Absorption in the boundary and splitting into DSC dislocations, as occurred in the L1, structure, causes a larger step in the grain boundary plane than in the %l l boundary and glide of the two D S c dislocations will be associated with shuffling of atoms. Also, depending on the way the shuffling takes place, anti-site defects can be created in the shuffled region (i.e. the region between the positions of the boundary plane before and after migration). This will limit the separation of D S c dislocations. Also for other boundaries in ordered structures, shuffeling of atoms can cause anti-site defects to be created and thus limit the splitting of D S c dislocations. Again, thereason why the splitting in the boundary plane did not occur in fcc might be foundin the differences in the interatomic forces compared to Ll,.
The structural unit model may help us to predict the interaction between the (superpartial) screw dislocation and a long period boundary, if we know the interaction between the dislocation and the delimiting favoured boundaries. However, there are two considerations that have to be kept in mind: first, in the case of absorption in the boundary and splitting into DSC dislocations, the width of splitting is limited; secondly, the minority units can be thought to contain a dislocation core and there can be elastic interaction. The latter consideration may be a goodexplanation of thedifferences between conf. 1 and 2 of the 2=57 boundary and conf. l of the L 2 7 boundary in the L1, case: the 2/22[2 2 6] D S c dislocation describing the misorientation of the 2=57 boundary with respect to the C=l l boundary has its core located at the Z=27 unit. This D S c dislocation will have elastic interaction with the Shockley partials of the 1/2[1 101 superpartial; the 1/6[2 1
i]
will be attracted to the boundary, but the 1/6[1 2 l] will be repelled. In this way a CSF can be created more easily.ACKNOWLEDGEMENTS
This work is part of the research program of the Foundation for Fundamental Research on Matter (F.0.M.-Utrecht) and has been made possible by financial support from the Netherlands Organization for Research (N.W.0.-The Hague).
A support ofthe National Science Foundation, MRL Program under Grant no. DMR88-19885 (VV) is acknowledged.
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