How To Determine The Lattice Parameter Of Zinc-Blende

The zinc-blende or sphalerite structure closely resembles the diamond structure. However, zinc-blende differs from diamond in that it consists of two different types of atoms, while diamond structures are associated with single elements. The zinc-blende unit cell is cubic and is described by a lattice parameter or cell side length. The zinc-blende unit cell can be visualized as two overlapping, face-centered unit cells slightly displaced with respect to each other. The atoms in the zinc-blende structure pack tightly together, so you can relate the lattice parameter to the size of the atoms in the unit cell.

Step 1

Look up the atomic radii of the two elements that are crystallized in the zinc-blende structure in a periodic table or chemical handbook. Note that the atomic radii are sometimes labeled as "covalent bond" or "ionic radii" and that the radius for an element may differ when comparing periodic tables because the value of the radius depends on the method used to measure or calculate it. Represent the atomic radius of one of the elements with R1 and the other with R2. For example, if calculating the lattice parameter of GaAs, a zinc-blende structured semiconductor, look up the atomic radius of Ga (R1 = 0.126 nm) and As (0.120 nm).

Step 2

Add the atomic radii to obtain the combined radius: R1 + R2. For example, if determining the lattice parameter of GaAs, add the atomic radii of Ga and As. The combined radius is 0.246 nm = 0.126 nm + 0.120 nm = R1 + R2.

Step 3

Calculate the zinc-blende lattice parameter (a) using the formula: a = (4/3^(1/2)) x (combined radius). For example, the lattice parameter of GaAs is: a = 0.568 nm = (4/3^(1/2)) x (0.126 nm + 0.120 nm) = (4/3^(1/2)) x (R1 + R2).