Question

4.) Given that the ionic radii of cesium and bromine are 0.165 and 0.196 nm respectively, and their atomic weights are 132.91 g/mol and 79.90 g/mol, respectively, a.) find the theoretical lattice parameter for CsBr b.) describe a Schottky defect in this structure, c.) find the ionic packing factor. Although this is not a bcc structure, your result is similar to that found for the atomic packing factor for a bce structure. Why is this So? d.) describe Schottky defects in this system. (How many vacancies, interstitials are there and what type of defects are these?) 5.)What crystallographic direction is shown in the figure below? 1/2 1/4

Answer 1

For the question 4.a, see below attached picFor 4.b., see below pic

4.a) For this structure, body diagonal= 2x rat 2 × rBr 3 x a 2x0.165+2 x 0.196. a-length of the cube Br a-0.42 nm Cs The lattice parameter: a= 0.42 nm The CsBr is a simple cubic structure, where Br atoms form the Cube structure by sitting at the corners and Cs atom is placed at the centre.

4.b) Br Cs A Schottky defect occurs when cation and Anion sides are vacant to maintain the Charge balance.
For 4.c,d and 5 .a, see the below attached pic
-n(rc,4rBr3) volume occupied by ions volume of the unit cell 4.c) Theoritical ionic packing factor (0.16540.1967 volume occupied by ions volume of the unit cell Theoritical ionic packing factor- -30.679 0.423 The structure of the CsBr is Simple Cubic. The Cs atoms are placed at the corner of cube forming a Simple Cubic Structure. One Cs atom is placed at centre of the Cube. As Cs atom is placed at the centre, the ionic packing (0.679) is similar to that of BCC (0.68) 4.d) The number of defects can be calculated using the formula where temperature is needed. But here temperature is not Provide 5.a) Direction Final coordinate-initial coordinate 1/2 1/4 [-2 0-3] [20 3]