# Miller indices, primitive unit cell for fcc and primitive basis vectors for a bcc

Hello experts!

Q#1) Write down the family members of {110} plane in a cubic crystal.

Attempted Answer) According to my study the this family has 6 members. But what are they? Are these the members (110),(101),(011),(-1-10),(-10-1),(0-1-1)?

Q#2) Describe the method to construct the primitive unit cell of an fcc crystal.

Attempted Answer) In this question I think examiner is asking to construct for Wigner Seitz cell for fcc. If it is so, then can you tell me how to construct it for fcc and as well as for bcc. If it is not the meaning of the question then kindly would you elaborate?

Q#3 Write down the primitve basis vectors for a bcc unit cell and show that the volume of primitive unit cell is $\frac{a^{3}}{2}$

Attempted Answer) In question examiner is asking for primitive basis vectors for bcc. I don't know what should it be, may be this R=ra+rb+rc?
And how to show that volume for primitive unit cell is $\frac{a^{3}}{2}$. How to start?

Can you tell me whether my answers are correct or wrong? If wrong the what should be correct one. Please guide me thoroughly.

Thank you. :-)

Hello experts!

Q#1) Write down the family members of {110} plane in a cubic crystal.

Attempted Answer) According to my study the this family has 6 members. But what are they? Are these the members (110),(101),(011),(-1-10),(-10-1),(0-1-1)?

I don't remember the definition of family members but all of those vectors represent the same plane in cubic crystal, by symmetry

Q#2) Describe the method to construct the primitive unit cell of an fcc crystal.

Attempted Answer) In this question I think examiner is asking to construct for Wigner Seitz cell for fcc. If it is so, then can you tell me how to construct it for fcc and as well as for bcc. If it is not the meaning of the question then kindly would you elaborate?

Wigner Seitz cell is one type of primitive unit cell. The primitive unit cell, as opposed to the unit cell, has just one lattice point within it.
http://en.wikipedia.org/wiki/Wigner–Seitz_cell

What is the difference between the (110) plane and the (-1-10) plane? What about the (-110) plane and the (110) plane?

NOTE: This is a question for the OP to think about, not something I actually want other posters to answer!