"has just one lattice point in the unit cell" wrt 'primitive unit cell' ?Watch
Atkins Inorganic Chemistry
A primitive unit cell (denoted by the symbol P) has just one lattice point in the unit cell (Fig. 3.3) and the translational symmetry present is just that on the repeating unit cell. More complex lattice types are body-centred
A primitive cubic unit cell has 8 lattice points - does he mean that 7 of those points are from the neighboring unit cells? What does he mean by
and the translational symmetry present is just that on the repeating unit cell.
You left/right/up/down shift and replicate the ENTIRE unit cell to build the 3D structure which means.. there will be overlap on the 7-lattice points since they belong to neighbor-cells - is that what he's trying to say?
He goes on to say
More complex lattice types are body-centred (I, from the German word innenzentriet, referring to the lattice point at the unit cell centre) and face-centred (F) with two and four lattice points in each unit cell, respectively, and additional translational symmetry beyond that of the unit cell.
for the body-centered I get the 2 lattice points since 1 point is from the cubic unit cell and +1 for the atom at the center of the cube. But.. for the face centered.. 1+3.. out of 6 faces to a cube - how did he get that result?
A cube is composed off 8 lattice points so why does he write: 'has just one lattice point in the unit cell'. How does a face-centered cube contain 'four lattice points in each unit cell, respectively'
Anyway I read further and he says
1. A lattice point in the body of, that is fully inside, a cell belongs entirely to that cell and counts as 1.
2. A lattice point on a face is shared by two cells and contributes 1/2
to the cell.
3. A lattice point on an edge is shared by four cells and hence contributes 1/4.
4. A lattice point at a corner is shared by eight cells that share the corner, and so contributes 1/8.
So that accounts for it.