Concept

Bravais lattice

Related notebooks (11)

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"

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)

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

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

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

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

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

Simulating Electron Motion in 2D Materials Using the Drude Model - Basic

Drude model considers electrons small solid particles traveling through lattices as a stationary array of heavier and bigger atoms. The model use "mean free time" as a measure of the frequency an electron gets scattered. This jupyter notebook makes use of this concept and uses stochastic method to simulat electrons traveling through a 2D material of finite width but infinite length."

"#### First we setup the simulation parameters such as the external electric field, number of electrons (default

Simulating Electron Motion in 2D Materials Using the Drude Model - Advanced

Drude model considers electrons small solid particles traveling through lattices as a stationary array of heavier and bigger atoms. The model use "mean free time" as a measure of the frequency an electron gets scattered. This jupyter notebook makes use of this concept and uses stochastic method to simulate electrons traveling through a 2D material of finite width but infinite length."

First we setup the simulation parameters such as the external electric field, number of electrons (default to 1)

Interactive Phonon Band Structure Visualization

In [1]: import numpy as np import matplotlib.pyplot as plt from matplotlib import animation from matplotlib import rc import ipywidgets as ipw from ipywidgets import interact,interactive import ipywidgets as widgets from IPython.display import HTML %matplotlib widget global global_K1 global global_K2 global global_branche global global_selected_k In [2]: def get_closest_point(clic_x,clic_y): # Get the data from the figure ax= plt.gca() # get axis handle acoustic_data = ax.lines[1] op

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Related notebooks (11)

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"

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

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

Powder X-Ray Diffraction Analysis: Exploring Crystal Structures.

\theta

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

Introduction to Reciprocal Lattices with Periodic Boundary Conditions.

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

Ewald Sphere

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

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

Simulating Electron Motion in 2D Materials Using the Drude Model - Basic

Drude model considers electrons small solid particles traveling through lattices as a stationary array of heavier and bigger atoms. The model use "mean free time" as a measure of the frequency an electron gets scattered. This jupyter notebook makes use of this concept and uses stochastic method to simulat electrons traveling through a 2D material of finite width but infinite length."

"#### First we setup the simulation parameters such as the external electric field, number of electrons (default

Simulating Electron Motion in 2D Materials Using the Drude Model - Advanced

Drude model considers electrons small solid particles traveling through lattices as a stationary array of heavier and bigger atoms. The model use "mean free time" as a measure of the frequency an electron gets scattered. This jupyter notebook makes use of this concept and uses stochastic method to simulate electrons traveling through a 2D material of finite width but infinite length."

First we setup the simulation parameters such as the external electric field, number of electrons (default to 1)

Interactive Phonon Band Structure Visualization