CsCl primitive cell and basis

[Lemenks]

Homework Statement

CsCl has a BCC unit cell containing 2 atoms, Cs in the origin of the cell and Cl at the centre of the cell. Describe the CsCl unit cell in terms of its primitive cell+basis.

Homework Equations

R = n1a1 + n2a2 + n3a3 ~ R is the vector which relates one point of the lattice to any other.

The Attempt at a Solution

R = n1a1 + n2a2 + n3a3,
Where Cs is at the point (0,0,0) and Cl is at the point (1/2,1/2,1/2)

My issue is mostly with the terminology - I am not really sure what the question is asking. I know that either ion can be described with a SC lattice and together they make a BCC lattice. I don't really know how to answer this.

 

[ehild]

It the Cs and Cl ions were identical spheres, the unit cell would look like as BCC . But they are different, so it is not BCC but a primitive cell with a basis. What kind of cell and what is the basis?

ehild

 

[Lemenks]

Emm, I think its a SC primitive cell with a two point basis, where Cs is at the point (0,0,0) and Cl is at the point (1/2,1/2,1/2).

 

[ehild]

Correct :)

 

[paranormal]

The CsCl unit cell can be described as a primitive cell consisting of a single Cs atom at the origin (0,0,0) and a single Cl atom at the center (1/2,1/2,1/2) of the BCC unit cell. The basis of the primitive cell is the set of vectors (0,0,0) and (1/2,1/2,1/2) which represent the positions of the Cs and Cl atoms, respectively. This primitive cell can be translated and repeated in all three dimensions to create the larger BCC unit cell containing 2 atoms. The vector R represents the translation of one point of the lattice to any other point, and can be expressed as a linear combination of the primitive cell basis vectors (n1, n2, n3) multiplied by the corresponding lattice parameters (a1, a2, a3).