A substance is known to crystallize into a base-centered tetragonal cell as show

Question

A substance is known to crystallize into a base-centered tetragonal cell as shown below. In this cell, a = b = 0.10 nm and c = 0.20 nm. The angles are all 90°. Answer the following: a) How many atoms per unit cell are there? b) Assume the atoms touch along the diagonal directions in the base (the [110] direction for example). What is the atomic radius, R, based on the lattice constants, a, b and c? c) Calculate the Atomic Packing Factor. Calculate the theoretical density Lin a/cm) of this substance given an atomic weight of 70 g/mol. d) (1cm=107nm)

Explanation / Answer

(a) As shown in the picture, there are 8 atoms at the corners of the unit cell, each corner atom can contribute 1/8 th art to the unit cell, thus from 8 corners = 8 x (1/8) = 1 atom

and, there are two atoms at the centers of two opposite faces, each face center atom can contribute 1/2 nd part to the unitcell, thus from two face center atoms = 2 x (1/2) = 1 atom

Therefore total number of atoms present in the given unitcell = 1 + 1 = 2

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