Nearly-free electron model

When we talk about nearly-free electron model, we are trying to understand how electrons behave in a material. Think of electrons as tiny particles that orbit around the nucleus of an atom.

Now, let’s imagine we have a piece of metal in front of us. Inside the metal, there are lots of atoms, each of which has some electrons that are orbiting around them. However, these electrons are not bound to any one atom. Instead, they are free to move around the metal and interact with other electrons and atoms.

In the nearly-free electron model, we try to simplify things by assuming that the electrons are not completely free, but are instead influenced more strongly by some atoms than others. We imagine that there are some atoms that have a stronger pull on the electrons, and these atoms help to hold the metal together.

So, in this model, we can think of the metal as being made up of a series of crystal lattices, with each lattice containing a group of atoms that influence the behavior of the electrons. The electrons themselves are quantum particles, which means they can act both like waves and like particles. They exist in energy levels, and they move around by jumping from one level to another.

However, in the nearly-free electron model, we assume that the energy levels are not strictly defined. Instead, we imagine that there is a range of energy values that the electrons can occupy, and that they are free to move within that range.

Now, when an electron moves from one lattice to the next, it can either be scattered or diffused. Scattering occurs when the electron interacts with the atoms in the lattice and changes direction. Diffusion, on the other hand, occurs when the electron moves smoothly through the lattice without being scattered.

Overall, the nearly-free electron model helps us to understand how electrons behave in metal, and how they contribute to the properties of different materials. By simplifying the complex interactions between electrons and atoms, we can get a clearer picture of how electronic properties arise in materials, and how those properties can be manipulated and controlled.