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COINCIDENCE IN HEXAGONAL MATERIALS
J. Antonopoulos, P. Delavignette, Th. Karakostas, Ph. Komninou, E.
Laurent-Pinson, S. Lay, G. Nouet, J. Vicens
To cite this version:
J. Antonopoulos, P. Delavignette, Th. Karakostas, Ph. Komninou, E. Laurent-Pinson, et al.. COIN- CIDENCE IN HEXAGONAL MATERIALS. Journal de Physique Colloques, 1990, 51 (C1), pp.C1- 61-C1-66. �10.1051/jphyscol:1990106�. �jpa-00230002�
COLLOQUE DE PHYSIQUE
Colloque Cl, suppl6ment au n o l , Tome 51, janvier 1990
COINCIDENCE IN HEXAGONAL MATERIALS
J.G. ANTONOPOULOS, P. DELAVIGNETTE*, ~ h . KARAKOSTAS, ~ h . KOMNINOU, E. LAURENT-PINSON* , S. LAY* , G. NOUET" and J. VICENS"
Department of Physics, Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece
Service de Physique des Surfaces, Universite Libre de Bruxelles, C.P.
234, Boulevard du Triomphe, B-1050 Bruxelles, Belgique
* * Laboratoire d l E t u d e s et de Recherches sur les Matkriaux, CNRS UA 1317, Institut des Sciences de la Matiere et du R a y o m e m e n t , Boulevard du Markchal Juin, F-14032 Caen Cedex, France
Resume
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L1analyse de joints de grains a ete realisee sur des metaux a structure hexagonale compacte apres recuit (zirco- nium) ou apres recuit et deformation (zinc, cadmium, magne- sium) et sur des ceramiques (carbure de tungstene-cobalt, carbure de silicium, nitrure de silicium). Dans les metaux hexagonaux, des joints en coincidence ou proches de la coinci- dence sont frequemment observes. Pour les ceramiques : le carbure de tungstene-cobalt, a la difference des deux autres ceramiques, presente une tres forte proportion de joints en coincidence.Abstract
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Grain boundaries have been analyzed in different hexagonal materials : hexagonal close packed metals after annealing (zirconium) or after annealing and deformation (zinc, cadmium, magnesium), hexagonal ceramics (tungsten car- bide-cobalt, silicon carbide, silicon nitride). For the hexa- gonal metals, coincidence or near coincidence grain boundaries are often observed. In the case of ceramics, tungsten carbide- cobalt, unlike silicon carbide and silicon nitride, exhibits a great deal of coincidence grain boundaries.1
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INTRODUCTIONThe characterization of a grain boundary is based on an orientation determination. The existence of grain boundaries in a coincidence site lattice (CSL) orientation in the cubic system is determined by reference to tables of CSL. In hexagonal structures, it is possible to generalise this concept by the determination of tables of CSL for different c/a values. This calculation is based on the approximation of the c/a ratio by a proper fraction of two integers p and v such that p / v = (c/a12
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Methods of calculation of CSLs exist /l-4/. Using these methods, GSLs up to a multiplicity value Z can be determined, for any material, and their conventional unit cell can be also cons- tructed. In this paper we present results concerning the characteri- zation of bicrystals in annealed and deformed structures in hcp metals and in ceramic materials using the C S L model.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990106
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CSLs IN HEXAGONAL CRYSTALScSL tables have been calculated for different p/v ratios. These ratios are chosen in such a way that the deviation with the c/a parametric ratio is of the order of 2%. According to that, the CSLs may be divided in different categories : some, like the twins, have a similar configuration for a large variety of p/v ratios correspon- ding to different multiplicities, Z ; others show a low 2 value only for particular p/v ratios. Practically a grain boundary is charac- terized by the rotation matrix R. The different equivalent descrip- tions are obtained by applying the symmetry element matrices to that rotation matrix. The determination of the closest Z value can be obtained by different methods : comparison of the experimental results with CSL tables or by using a reference triangle of a stereographic projection in which all the 180" rotation axes or the highest angle rotation axes are indicated. Although this approach is straightforward it suffers from a lack of precision. Therefore more sophisticated methods have been developed on the basis of the small angle rotation matrix, of the shift of Kikuchi maps /5/ or splitting of Kikuchi lines. A precision of the order of a few tenths of degree obtained with these last methods allows a good correlation between the observed intrinsic dislocation network and the geometric charac- teristics to be verified.
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C S L BOUNDARIES IN H C P METALS.
Annealing structuresZirconium has been annealed at 1000°C for 30 min followed by an electrolytic polishing up to electron transparency in TEM. The para- metric ratio c/a = 1.595 has been approximated by p.=5 and v=2 such that = 1.581. From the characterization of grain boundaries, different features have been deduced. Rotations around [U v o] by 180" have been found. These coincidences are independent of the c/a value, for instance boundaries to which the following .Z values are attributed have been observed : X 19, 49 and 67. They indicate the possible occurrence of relatively large Z values /6/. Several grains are twinned according to the (1072) or (1122) planes. These twin planes can contain intrinsic and extrinsic dislocation networks
(Fig. la)
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Grains merging into a triple node have been also analysed. The following combinations of triplets have been observed : three low angle boundaries (smallest angle less than loo), two high angle boundaries and one low angle boundary, two twin boundaries and one low angle boundary. In the last case the twins do not correspond to the exact twin orientation relationship and the twin boundaries do not coincide with the twin planes.
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Deformation structuresDeformation twins are commonly observed in hcp metals. In particular the (10x2) twin has been analysed for zinc /7/, cadmium /8/ and magnesium /g/. The different values of p and v integers are given in table 1.
Fig. la : A twin boundary in annealed zirconium showing the presence of a parallel array of extrinsic dislocations.
Fig. lb : Parallel array of a set of "twinningm dislocations together with extrinsic dislocations in a twin boundary in deformed cadmium
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TABLE 1:Approximation of the parametric ratio with p and v integers.
For these different descriptions, the (10?2) twin is defined with the following X coincidence indices : 15, 13 and 11.
Usually these twins deviate slightly from the exact coherent confi- guration and often from the exact coincidence orientation calculated for a special value of the p/v ratio. In both cases the deviations are accommodated by sets of parallel dislocations (Fig. lb). The deviation from the exact coincidence orientation can be measured with high precision by studying the shift of Kikuchi maps or the splitting of Kikuchi lines. An analysis of such structures is given in another contribution of this volume.
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C S L BOUNDARIES I N HEXAGONAL CERAMICS.
Tungsten carbide-cobaltIn tungsten carbide-cobalt composites, carbide grain boundaries are often found with coincidence orientations. It is mainly due to the material preparation (liquid cobalt phase sintering process) with a large amount of the cobalt phase which develops low energy facets (1010) and (0001) in the carbide grains. Consequently a high number of grain boundaries has been found parallel to these two densest planes in the hexagonal WC structure (c/a s 1). Generally these grain boundaries can be described by coincidence orientations (2 = 2, 5, 7, ...) calculated with the approximation c = a /10/.
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Silicon carbideHot pressed a-silicon carbide sintered with small amounts of alumi- nium based additives is a more complex material. The densification aids form a glassy phase (aluminosilicate) whichdoesnot wet the Sic grain boundaries but is mainly located in triple junctions of the grain boundaries. Electron diffraction studies have shown that the carbide grains crystallize into the two main hexagonal polytypes 4H and 6H. Interfaces between the same polytype or two different poly- types can be formed in this material. Experimental orientations have been determined for grain boundaries between two 4H grains, two 6H grains or for 4H and 6H grains and compared to theoretical coinci- dence orientations corresponding to the following p/v values 2 1 / 2 , 32/3 (4H) and 24/1 (6H). The results show that the experimental.
orientations deviate greatly from the exact coincidence orienta- tion~. However in many cases the boundary plane is found parallel to the densest plane (0001). A faceting of the grain boundaries is observed in the same specimen after high temperature deformation likely due to the activation of the basal glide plane and the migra- tion of the interfaces at high temperature (Fig. 2a). For the facets corresponding to low energy configurations many grain boundaries
Fig. 2a : Facetted boundary plane between two 6H polytype grains in annealed and deformed Sic sample.
Fig. 2b : Planar boundary observed in as-sintered p - S i 3 N 4 .
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have a high indice plane for the other crystal. However some special configurations have been also observed including the basal plane and relatively dense planes as well as a common plane for the two crys- tals where a bidimensional coincidence can arise. Some configura- tions lead to a good matching of the planes at the interface such as
(0001)~ 8 (10i4) /11/.
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Silicon nitrideSi3N4 powders have been sintered in liquid phase with oxyde addi- tives (MgO, Y203). Sintering is based on a dissolution precipitation mechanisln of the crystals. Two crystallographic forms can exist : a at low temperature and p at high temperature. During sintering a particles are dissolved to precipitate into the p form, a = 0.7606 and c = 0.2907 nm. Such platelets grow along (0001) direction to give a typical microstructure. Adjacent grain boundaries have been orientated by TEM to determine the.ir orientation relationships.
The list of coincidence lattices has been calculated for several ratios p/v (for instance, 1/7, 3/20 and 1/6). The comparison between the experimental orientation and the theoretical data shows that the deviation from the exact coincidence is always greater than the value given by Brandon's criterium except for two cases among the fourteen experimental determinations (Fig. 2b).
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REFERENCES/l/ Bleris, G.L., Nouet, G., Hagege, S. and Delavignette, P., Acta Cryst. A38 (1982) 550.
/2/ Bleris, G.L., Doni, E.G., Karakostas, Th., Antonopoulos, J.G.
and Delavignette, P,, Acta Cryst. A41 (1985) 445.
/3/ Grimmer, H. and Warrington, D.H., Acta Cryst. A43 (1987) 232.
/4/ Hagege, S. and Nouet, G., Acta Cryst. A45 (1989) 217.
/5/ Bary, A., Hagege, S., Ayed, P., Vicens, J., Lay, S., Dela- vignette, P., Polychroniadis, E.K., Komninou, Ph., Karakostas, Th. and Nouet, G., Proc. XIth Int. Cong. on Electron Microsco- py, Kyoto (1986) 1325.
/6/ Karakostas, Th. and Delavignette, P - , Phys. Stat. Sol. (a) 83 (1984) 485.
/7/ Antonopoulos, J.G., Karakostas, Th., Komninou, Ph. and Dela- vignette, P - , Acta Met. 36 (1989) 2493.
/8/ Antonopoulos, J.G., Komninou, Ph., Karakostas, Th. and Dela- vignette, P., Scripta Met. 23 (1989) 417.
/9/ Ayed, P., Thesis, University of Caen (1989).
/10/ Lay, S., Nouet, G., Chermant, J.L., Osterstock, F. and Vicens, J., JIMIS-4 (1985) Minakami Spa, Japan, p. 657.
/11/ Laurent-Pinson, E., Lay, S., Nouet, G. and Vicens, J., 1st European Ceramic Society Conference, Maastricht, The Nether- lands (1989) (to be published).
