Simulation Testing

Learning Physics with Interactive Simulations

This particular page is maintained by Thushari Jayasekera, as a part of her ongoing educational project, "Physics and FUN with Clicks",

This particular page is aimed at learning Solid State Physics and Materials Science with Interactive Simulations. Pl. Note that this is only a sample lecture (first version) from Undergraduate Solid State Physics Class. All notes will be uploaded as time permits. This particular lecture contains one interactive simulations to understand the properties of phonons.....)

       - Please do not only play with the simulation. Work through the Math and use the simulation only to visualize the concept

       - As of now, when you click on the simulation title, it will be re-directed to a different page. This will be fixed eventually. 

Solid State Physics Lecture 10 - Understanding Phonons

Phonons are quantized Lattice Vibrations. Understanding the properties of phonons is important, as phonons govern the thermal properties of semiconductor materials. In this lecture, we will discuss the concept of phonons via atomic vibrations of the simplest possible solid: One-Dimensional (1D) Monoatomic Chain, using the first order model; Hooke's Law.

One-Dimensional Atomic Chain

The system is in equilibrium for a given atomic positions. That we have a set of equilibrium coordinates for the atomic configuration. The total energy of system is a function of equilibrium coordinates, $u_{i}$.

$\epsilon =\epsilon (u_{1},u_{2},u_{3},........,u_{N})$

The total energy of the system is a function of atomic coordinates. The equilibrium energy is the minimum energy configuration. We can expand the total energy in terms of the atomic displacements.

$\epsilon =\epsilon _{\alpha ,l}{\frac {\partial \epsilon }{\partial u_{\alpha }}}du_{\alpha }$