Q.A two dimensional solid pattern formed by two different atoms X and Y is shown below. The black and white squares represent atoms X and Y respectively. The simplest formula for the compound based on the unit cell from the pattern is

There are exactly seven primitive crystal systems, distinguished by how their three edge lengths and three angles relate: cubic (a=b=c, all angles 90 deg), tetragonal (a=b not-eq c, all 90 deg), orthorhombic (a not-eq b not-eq c, all 90 deg), hexagonal (a=b not-eq c, alpha=beta=90 deg, gamma=120 deg), rhombohedral (a=b=c, all angles equal but not 90 deg), monoclinic (a not-eq b not-eq c, alpha=gamma=90 deg, beta not-eq 90 deg), and triclinic (a not-eq b not-eq c, no angle equal to 90 deg or to another). Once possible centrings (body-centred, face-centred, base-centred) of these seven are also counted, Bravais showed only 14 distinct lattices are geometrically possible -- the 14 Bravais lattices (Table 6.2): 3 cubic + 2 tetragonal + 1 hexagonal + 4 orthorhombic + 2 monoclinic + 1 trigonal + 1 triclinic = 14.

For the three cubic unit cells, the number of atoms belonging to one cell is found by weighting each shared lattice position: a corner atom (shared by 8 cells) contributes 1/8; a face-centred atom (shared by 2 cells) contributes 1/2; a body-centred atom (unshared) contributes a full 1.

• Simple cubic (SC): atoms at 8 corners only. Atoms/cell = 8x(1/8) = 1. Coordination number 6 (touch along edges only, a = 2r). …