Changes of resistance with temperature in metallic conductors and NTC thermistors

The atoms in most solids are arranged in a crystal lattice structure as shown in the diagram below:

This lattice structure provides a medium for vibration of the atoms about their equilibrium position. As the temperature of the solid increases, the intensity of the vibration of its atoms also increases.

The more intense that the lattice vibrations of atoms in a material are, the more difficult it is for free electrons to pass through it. This is because the electrons will be more likely to collide with the vibrating atoms if they are oscillating more intensely, causing them to slow down. (Intensity here refers to the speed and amplitude of oscillations). This in turn increases the resistance of the material.

As the temperature of a metal or semiconductor increases, its atoms gain energy, and once they gain enough energy they begin to release electrons (this is known as thermionic emission). This increases the number of charge carriers available in the conductor, which decreases its resistance.

Negative temperature coefficient thermistors are designed in such a way that as their temperature increases, their resistance decreases. This occurs because they release a large amount of charge carriers as their temperature increases (outweighing the effects of lattice vibrations). Below is a graph temperature-resistance of an NTC thermistor:

As for metallic conductors, as their temperature increases, their resistance also increases due to lattice vibrations in the conductor becoming more intense. More electrons are also released but not quickly enough to counter the disruptive effect of the lattice vibrations. Below is a graph temperature-resistance of a metallic conductor: