Concept

Reciprocal lattice

Related notebooks (13)

Ewald Sphere

Constructing Brillouin Zones of the 2D Square Lattice

Brillouin zones of the two-dimensional square lattice¶{.anchor-link} {#Brillouin-zones-of-the-two-dimensional-square-lattice}

This notebook demonstrates construction of the first three Brillouin zones of square lattice

Constrution of the first Brillouin zone¶{.anchor-link} {#Constrution-of-the-first-Brillouin-zone}

The first Brillouin zone is the Wigner-Seitz cell of the reciprocal lattice. Hence

Introduction to Reciprocal Lattices with Periodic Boundary Conditions.

Real vs. Reciprocal Space in 2D[1]¶ Introduction[2]¶ In this short notebook, we will introduce the lattice with periodic(Born- von Karman) boundary condition. Following the boundary condition, there is a transformation from real lattice to the reciprocal lattice. In the code below, we define a1 and a2 through cartesian vectors. Hence, the reciprocal vectors will be the original rotated by 90 degrees multiplied by 2pi and divided by the area of the unit cell (|a1xa2|) In [1]: i

Interactive Wave Visualization: Transverse and Longitudinal Modes.

"First, we define a 2D lattice as follow:"

"Next, we define a function that updates the atomic positions in the lattice at each call"

Powder X-Ray Diffraction Analysis: Exploring Crystal Structures.

XRay Diffraction[1]¶ The purpose of this notebook is to study the powder XRay diffraction spectra of some systems. When the crystal is hit with an XRay wave, the wave is diffracted only for specific case where the Bragg condition is satisfied for one of the lattice planes in the material. For single crystal diffraction, the condition is satisfied only for specific orientation of the crystal, such that the incident ray has the correct

\theta

value for the plane. In powder XRay data, however, any plane ori

Tight-Binding Approximation for 2D Lattices: Square, Triangular, Lieb, and Honeycomb

In [1]: import numpy as np import matplotlib.pyplot as plt

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib inline In [2]: def band(nkl,kpoints,ham): :param k: wave number nk=32 # Define the position of the original lattice #klines=np.zeros((nkl-1,nk)) n=0 d=np.size(ham([0.0,0.0]),1) evk=np.zeros((nknkl-nk-1,d)) lenk=np.zeros((nknkl-nk-1,d)) for i in range(0,nkl-1)

Wavepacket construction and propagation in 1D tight-binding model

"# Wavepacket construction and propagation along the 1D chain \n", "\n", "## Introduction\n", "In this notebook, we demonstrate the wavepacket construction and propagation, which is at the heart of the semiclassical approximation. For simplicty, we will consider the familiar 1D chain described using the tight-binding Hamiltonian. We will have to take a sufficiently large number of sites

N

and impose periodic boundary conditions. For simplicity, in the code below we assume lattice constant $a =

Ewald Sphere

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Ewald Sphere¶{.anchor-link} {#Ewald-Sphere}

Play with the Ewald Sphere This schematics represent the Ewald sphere for a typical high

Illustrating Band Structures in Solids: Free Electrons and Atomic Orbitals

In [1]: import numpy as np from numpy import linalg as LA import matplotlib.pyplot as plt

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib widget The emergence of band structures[1]¶ If you have questions about this notebook, e-mail Oleg Malanyuk (oleg.malanyuk@epfl.ch) This jupyter notebook is intended to provide a illustration of the band structures in solides, starting from the points of v

Band Structure Investigation of Monolayer and Bilayer Graphene Using the Tight Binding Model

In [1]: import matplotlib.pyplot as plt import numpy as np from mpl_toolkits import mplot3d import itertools %matplotlib widget Band Structure of Mono and Bilayer Graphene[1]¶ If you have questions about this notebook, e-mail Oleg Malanyuk (oleg.malanyuk@epfl.ch) The purpose of this notebook is to investigate the band model of Mono and Bilayer graphene modeled with tight binding model. Tight binding model for monolayer graphene[2]¶ Monolayer graphene is a sheet of carbons aranged in a he

Digital Simulation of Guitar Feedback in I Feel Fine by The Beatles

I Feel Fine, Digitally[1]¶ This notebook is a little musing inspired by the "internal mechanics" of a very famous audio snippet, namely the guitar sound at the beginning of the song "I Feel Fine", written and recorded by the Beatles in 1964. The historical significance of the record lies in the following claim by John Lennon:

 "I defy anybody to find a record... unless it is some old blues
 record from 1922... that uses feedback that way. So I claim it for
 the Beatles. Before H

Calculation and plotting of some important quantities relative to the electron s properties in a conventional TEM

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Related notebooks (13)

Ewald Sphere

Constructing Brillouin Zones of the 2D Square Lattice

Brillouin zones of the two-dimensional square lattice¶{.anchor-link} {#Brillouin-zones-of-the-two-dimensional-square-lattice}

This notebook demonstrates construction of the first three Brillouin zones of square lattice

Constrution of the first Brillouin zone¶{.anchor-link} {#Constrution-of-the-first-Brillouin-zone}

The first Brillouin zone is the Wigner-Seitz cell of the reciprocal lattice. Hence

Introduction to Reciprocal Lattices with Periodic Boundary Conditions.

Interactive Wave Visualization: Transverse and Longitudinal Modes.

"First, we define a 2D lattice as follow:"

"Next, we define a function that updates the atomic positions in the lattice at each call"

Powder X-Ray Diffraction Analysis: Exploring Crystal Structures.

\theta

value for the plane. In powder XRay data, however, any plane ori

Tight-Binding Approximation for 2D Lattices: Square, Triangular, Lieb, and Honeycomb

In [1]: import numpy as np import matplotlib.pyplot as plt

from future import print_function

Wavepacket construction and propagation in 1D tight-binding model

N

and impose periodic boundary conditions. For simplicity, in the code below we assume lattice constant $a =

Ewald Sphere

Ewald Sphere¶{.anchor-link} {#Ewald-Sphere}

Play with the Ewald Sphere This schematics represent the Ewald sphere for a typical high

Illustrating Band Structures in Solids: Free Electrons and Atomic Orbitals

In [1]: import numpy as np from numpy import linalg as LA import matplotlib.pyplot as plt

from future import print_function

Band Structure Investigation of Monolayer and Bilayer Graphene Using the Tight Binding Model

Digital Simulation of Guitar Feedback in I Feel Fine by The Beatles

 "I defy anybody to find a record... unless it is some old blues
 record from 1922... that uses feedback that way. So I claim it for
 the Beatles. Before H

Calculation and plotting of some important quantities relative to the electron s properties in a conventional TEM