Question

6

1.12 (a) A material is composed of two types of atoms. Atom A has an effective radius of 2.2 Å and atom B has an effective radius of 1.8 Å. The lattice is a bcc with atoms A at the corners and atom B in the center. Determine the lattice constant and the volume den- sities of A atoms and B atoms. (b) Repeat part (a) with atoms B at the corners and atom A in the center. (c) What comparison can be made of the materials in parts (a) and (b)?

Answer 1

0 0 The cross-sectional view of a bec lattice along diagonal is shown in figure- In bec lattice there is one atom at the centre of the cube and there NIN are 8 corner - region quo each corchert contains times of an atom Dk a Let the side of the cube lie lattice constant is a unit. Diagonal of the cube - av3 unit deti ebbechile radius of alom A is and " " " " B is PB ...PG = Boot 20A+PB Viven, - 2/V+Y8) = 2.2 Now, Pg=ave Po = 1.8 Å are = Q(PA + P3) a= 2 ( PA + mo) = 2/8/202+18) 7 since there = 4.62 (188 corner in cubic shell In this unit cell, no of atom A is t no of atom Bis 18848) = 1 : volume density of atom A is where P = (1/30 23x no- of atom a volume of unit cell = a 3 volume of atom 1/30/2.2) 3202 (A is (403) (462) at = 0-4523 - 7 45.23% and volume density of atom B is la Wanyone) uno.of atom B 490.1.8) 3mL = 0.2477 - 72 Lattice constant is 4.62 Å and volume densities of alom A and alom B are 45.23% and 24.8% rospechvely.

A (6) Similarly, assuming a, the lattice constant we get the diagonal of the unit cell arz. PQ = PAT Q BB+ PA = 2 ( PATRB) Now, ar3 = PQ = 2(PA+PB) a= 231 A + B) (20+1-8) ^462 Å Mo of atom A in this unit cell is (8/8) = 1 and No of atom B ist (4162) 3 = 014523 - - 45.23% and P = (48012 ) No. of atom B 4/30/2.83 xt. = 0.2477 4 x 24.8% . In this case also battice constant is 4.62 Å and volume denities of A and B are 45.23% and 24.8% respectively. Now = (W211 13 ) x No of atom a W311 (22) x 1 9 In part @ and ③ we see that the lattice constant and volume densities of atoms are same in both cases . so no comparison can not be dreawn from this point of Lieu.

In (a) I consider atom A is in the centre and in (b), atom B is in centre. Please don't dislike.