(materials science) slip system

[asdf1]

for the FCC cubic, there are 12 slip systems: 4 {111} planes and 3 <110> directions...
what i don't understand is why are there 4{111} planes instead of 1?

 

[Astronuc]

How many corners to a cube? How many major diagonals?

 

[Gokul43201]

what i don't understand is why are there 4{111} planes instead of 1?

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.

What I don't understand is why there are only 3 <110> directions when it looks to me like there should be 6 (2 face diagonals on each of the 3 faces).

 

[Astronuc]

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>.

 

[asdf1]

ok~ thank you!

 

[Gokul43201]

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>.

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.

Yikes! I've completely lost touch with basic crystallography - time to hit the books.