ELECTRON MICROSCOPY 



can be noncentral ones. Such problems are 

 discussed in the previously mentioned books 

 on dislocation theory, (8, 9, 25) and the 

 repulsion and attraction of dislocations are 



Slacking Order in Close Packed Structures 



A B C A 



ABA 



Cubic Face Centered 

 . A B CA B C 



Hexagonal Close Packed 

 ...A B A B A S. . 



Fig. 10. Stacking order in close packed struc- 

 tures. 



STACKING SEQUENCES 



Orientation 



(001) 



<110> 



■(112> 

 Cubit: Face Centred 



K C 



K B 



K A 



K C 



K B 



K A 



K C 



K B 



K A 



ABCABCABCAB 



/ \ 



Cubic Sequence [^ ABC/ orCBAv 



/ 

 H!«S9 Sequence [-j BAB\ or ABA 



Hexagonal close packed 



H B 



H A 



H B 



H A 



H B 



H A 



H B 



H A 



H B 



H A 



ABCABCABCAB 





Fig. 11. Stacking sequence in the face-centered 

 cubic and hexagonal close-packed structures. 



H B 



^ -O 



Central Symmetry 





Fig. 12. Symmetry of nearest neighbour atoms 

 in relation to the stacking energy. 



directly observable in the films (G, 10) (Fig. 

 8). 



Stackiiij^ Faults and Partial Dislocations 



As is well known, a cubic face-centered 

 lattice can be understood as a close-packed 

 structure of spheres. On a basic layer in 

 position A a second layer can be placed in 

 two different ways, in position B or C (Fig. 

 10). If the position B is chosen for the sec- 

 ond layer there remain C and A for the 

 third one and so on. A stacking sequence 

 . . . ABCABC . . . builds up a face-centered 

 cubic lattice, a stacking sequence . . . ABAB . . . 

 a hexagonal close-packed lattice. 



The fact that a given material crystallizes 

 in a certain structure, e.g. face centered 

 cubic, shows that once the first two layers 

 A and B are ready, the work to build up the 

 third layer must be lower for position C 

 than for position A, because if there would 

 be no difference the stacking sequence would 

 be random (Fig. 11). Looking at all connec- 

 tions to nearest neighbors of an atom in the 

 second B layer one sees that these connec- 

 tions (directions of binding forces) are of 

 central symmetry in the f.c.c. structure 

 (ABC sequence) and of mirror .symmetry in 

 the hexagonal c.p. structure (ABA sequence). 

 Fig. 12. Thus in a f.c.c. lattice the ABC 

 (CBA, BCA, etc.) sequence with central 

 symmetry marked by K has a lower energy 

 (needs less work to be built up) than the 

 ABA (CAC. BCB, etc.) sequence marked 

 by H. ' 



Different kinds of faults can occur in the 

 stacking sequence; here we consider only 

 the f.c.c. case. A single H inserted into all 

 K means a growth fault (twin boundary; 

 Figs. 13a and b). Two consecutive H mean 

 a so-called "deformation stacking fault" 

 (Figs. 14a and b). 



Thus to a first approximation a deforma- 

 tion stacking fault has twice the energy of a 

 twin boundary (Fig. 12). 



The Burgers vector of a (total) disloca- 

 tion line normally is the shortest connection 



298 



