P1 Conduction?

So conduction only occurs in solids (metals) because they delocalised electrons and a fixed shape/arrangement of atoms. Therefore, when they get heated up, the atoms (or particles?) gain energy, and *bump* into their neighboring atom(particle?)? What's the scientific word for this 'bump' process and how does that transfer the energy? Like, imagine it was a 3 mark exam question asking the process of conduction etc. Please help this is really confusing! :?

collisions i think

When metals are heated, the free electrons gain kinetic energy and move through the metal faster. When they collide with other free electrons, the kinetic energy is transferred.

When non-metals are heated, the particles gain more kinetic energy and vibrate more. They collide more with neighbouring particles so the kinetic energy is transferred to neighbouring partcles.