The discussion focuses on the slip systems in face-centered cubic (FCC) crystals, specifically addressing the number of {111} planes and <110> directions. Participants explore the geometric and symmetrical properties of the cube that contribute to these slip systems.
Participants express differing views on the uniqueness of the {111} planes and <110> directions, indicating that there is no consensus on the interpretation of symmetry and its implications for the number of slip systems.
Some assumptions about the definitions of unique planes and directions, as well as the implications of symmetry, remain unresolved. The discussion does not clarify the mathematical basis for the claims made regarding the number of slip systems.
This discussion may be of interest to students and professionals in materials science, crystallography, and solid mechanics, particularly those exploring the mechanical properties of crystalline materials.
In a cube, you'll find you can draw 8 {1,1,1} planes. However, you'll also see that only 4 of these are unique - the other 4 being parallel to these and separated from them by distance of a/sqrt(3), where 'a' is the cube edge.asdf1 said:what i don't understand is why are there 4{111} planes instead of 1?
Doesn't this argue that there is only one relevant <110> direction? After all, I can generate the other 5 face diagonals from any one, using a combination of symmetry preserving rotations.Astronuc said:Rotational symmetry - rotate the cube 90° about the normal to the face plane, and one face diagonal transforms to the other (perpendicular) diagonal.
Or rotate the cube 180° about the normal to the base and the <110> becomes <1\bar10>.