The reciprocal of resistivity (ρ) of a material is called its conductivity (σ), i.e.,
With rise of temperature, the collision of electrons with fixed lattice ions/atoms increases so that relaxation time (τ) decreases. Consequently, the conductivity of metals decreases with rise of temperature. Figure represents the variation of conductivity of metal with temperature. Initially the variation of conductivity with temperature is linear and then it is non-linear.
(ii) Conductivity of ionic conductor increases with increase of temperature because with increase of temperature, the ionic bonds break releasing positive and negative ions which are charge carriers