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STUDENT: Hello, everyone. Today, I'm going to talk about a very important model, analyze the energy band of a crystal, that is the tight binding model. Before I talk about tight binding model, let's now take a look at free electron model. The potential energy of free electron can be considered as zero, so the Hamiltonian of the free electron system is without the potential term. And the waveform function can be simply written as a plane wave. By substituting the wave function into Schrodinger equation, we can gather energy dispersion relation, which is a parabola in one dimension case. And we usually form the parabola into the first Brillouin zone. And this is the reduced Brillouin zone. And in this figure, we can see that the first band is at the bottom of the parabola. And the second band and third band, fourth, and so on. Similar to one dimension case, the energy of three dimension case is proportional to kx squared plus ky squared plus kz squared. For a given ...

STUDENT: Rainbows-- while we may not notice them, there are rainbows all around us as we go about our daily lives. They are hidden in the reflection of soap bubbles, the shine on a CD, and even in oily puddles on the street. In this video, we'll explore the phenomenon of light wave interference and how it creates the colors we see on the surfaces of thin films. Since soap and oil are usually colorless, why do they have iridescence? Let's start with the laws of light reflection and refraction, then peruse through some visual simulations of these fundamental principles. When waves travel through space and hit an interface or a surface, some of the wave reflects off the surface and the rest refracts, continuing through the new medium at a different angle. When the refracted wave hits another surface, part of it reflects back out of the medium and combines with the first wave or interferes with the first wave. Since the first and second reflected waves travel differen...

STUDENT: So you're probably all familiar with the field measured in this paper here by Shrodinger, which is a quantum theory. And you surely also know that the students have a lot of problems visualizing it, and understanding its behavior in some intuitive way. For example, you know the tunneling effect. And you won't expect a classical cat to just tunnel through potential wall. What I am going to show you in this presentation is an algorithm called the split operator Fourier transform algorithm, which can be used to describe quantum tunnel evolution, and therefore, for example, the tunneling effect. And I think that it also might be interesting for you as material scientists, on the one hand, because you might be interested in time evolution of your properties, especially for nanosystems, quantum systems. But on the other hand, I will show you iteration of this algorithm which can also be used to derive other algorithms, like the [INAUDIBLE] algorithm. And you al...

STUDENT: Let's talk about the Mohr's Circle, an important tool in materials science and mechanical engineering. What is Mohr's Circle, and what does it do? Assume you have a rod, and you want to break it with your hands. What can you do about it? You can pull it, compress it, or twist it. Each of these will induce a stress in the rod in a different way. And the Mohr's Circle helps you analyze this. Mohr's Circle is a graphical tool, a visual way to see how to go from one state of stress to another. Usually you are given a state of stress that you calculated from using stress equations. Then you want to find a state of stress at a new angle of orientation, or principal stresses at that orientation, or the maximum in-plane shear stresses. And Mohr's Circle allows you to draw this representative element to visualize the calculations for you. Now, let's derive the Mohr's Circle. So now we take a look at the piece of material that we cut from th...

STUDENT: Today we're going to look at Hooke's Law in Cubic Solids. Hooke's law describes behavior of springs. What we're going to do is we're going to model the solid as a collection of springs connecting a whole bunch of atoms in a cubic lattice. Now, disclaimer-- I'm probably going to do this all wrong. But what's science if we don't make a few mistakes, right? Let's get started. The potential that describes fairly well the behavior of the interaction between two atoms is the Lennard-Jones potential. It describes the van der Waals interaction, and it looks something like this. It's a potential with a term which goes 1 over r to the 12th, and one term which goes 1 over r to the 6th. And as you can see, as the atoms get very close, they repel greatly, and then they have a sweet spot here, which is the distance they prefer to be at. As they get farther away, they start to repel more again. The atom like to sit right there in that lit...

STUDENT: Materials are often classified as crystalline, semi-crystalline, or amorphous. Most polymers are semi-crystalline. This means a fraction of the material is amorphous and lacks order in arrangements of polymer chains, while the remainder of the material exhibits parallel, well-ordered chains that define crystalline regions. There are several methods for determining the degree of crystallinity in a polymer. X-ray diffraction can be used to determine degree of crystallinity, because intensity of X-ray diffraction reflection is proportional to the material density. An X-ray diffraction pattern displays both sharp Bragg's peaks, arising from the crystalline portion, and a broad diffraction peak caused by scattering from the amorphous portion of the polymer. The degree of crystallinity can be determined using this formula, where the total integrated intensities, all of the sharp peaks, are divided by the integrated intensities of all peaks, including that of the am...