Q.(a) Analysis shows nickel oxide has the formula Ni0.98O1.00. What fraction of Ni exists as Ni2+ and Ni3+ ions in given oxide ?

A crystal is built by attaching a basis (one or more atoms, ions or molecules) to every point of a lattice -- a purely geometric, periodic arrangement of points in three dimensions -- so that Lattice + Basis = Crystal. Solids first split into crystalline (long-range ordered, sharp melting point, generally anisotropic) and amorphous (short-range order only, gradual softening, isotropic) forms; a single substance existing in more than one crystalline form is polymorphous (allotropic, for elements), while two substances sharing the same crystal structure and atomic ratio are isomorphous. Crystalline solids further split into four bonding-based families: ionic (charged ions, electrostatic bonding, hard/brittle/high-melting, conducts only molten or dissolved), covalent network (atoms in one giant covalently-bonded 3D structure, extremely hard, high-melting, poor conductor), molecular (neutral molecules or atoms held by weak intermolecular forces, soft, low-melting, insulating), and metallic (metal cations in a mobile electron sea, malleable, ductile, good conductor). The smallest repeating 3D block that reconstructs the whole lattice is the unit cell, fully described by three edge lengths (a, b, c) and three interaxial angles (alpha, beta, gamma); it can be primitive (particles at corners only), body …