Neutron scattering - determing the magnetic moment for MnO

[peripatein]

I'm told that the MnO crystal resembles in structure that of NaCl (FCC) with lattice constant a, and am first asked to write a general expression for the position vector R_j of the ion j in the unit cell of MnO. I am then asked to find the vector K for MnO in order to use the relation μ_j=μ₀e^(iK⋅R_j) to determine the magnetic moment of an ion at the position R_j.

I initially wrote down the unit cell vectors for one of the two atoms, and added to these a basis (due to the second atom): a₁=a/2(x^+y^),a₂=a/2(x^+z^),a₃=a/2(y^+z^), with basis: d₁=0,d₂=a/2(x^+y^+z^).
How am I to formulate the expression for the general position vector R_j? Would it simply be a linear combination of all these vectors? Next, for determining the value of the vector K, need I to first find the reciprocal lattice?
I'd appreciate some explicit assistance/guidance.

 

[BigJDubs]

For the position vector Rj of the ion j in the unit cell of MnO, it can be expressed as:Rj = n1a1 + n2a2 + n3a3 + d1d1 + d2d2 where n1, n2 and n3 are integers representing the number of unit cells along each of the lattice vectors (a1, a2 and a3). To find the vector K for MnO, you need to first calculate the reciprocal lattice vectors. The reciprocal lattice is defined as a set of vectors that are perpendicular to the lattice vectors and have a length such that the dot product between two reciprocal lattice vectors is equal to 2π. The reciprocal lattice vectors for MnO are then given by:K1 = 2π/a (y^-z^)K2 = 2π/a (z^-x^)K3 = 2π/a (x^-y^)Using these reciprocal lattice vectors, you can then calculate the vector K for MnO using the relation μj=μ0e(iK⋅Rj).