Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Crystallography: Describing Periodic Structures

In course

MSE-305: Introduction to atomic-scale modeling

This course provides an introduction to the modeling of matter at the atomic scale, using interactive Jupyter notebooks to see several of the core concepts of materials science in action. ...

Description

This lecture covers crystallography, focusing on lattice structures, lattice vectors, and lattice planes. It explains how to describe a periodic structure using lattice vectors and discusses the calculation of diffraction patterns from crystals.

Instructor

Michele Ceriotti

Michele Ceriotti received his Ph.D. in Physics from ETH Zürich in 2010. He spent three years in Oxford as a Junior Research Fellow at Merton College. Since 2013 he leads the laboratory for Computational Science and Modeling in the Institute of Materials at EPFL. His research revolves around the atomic-scale modelling of materials, based on the sampling of quantum and thermal fluctuations and on the use of machine learning to predict and rationalize structure-property relations. He has been awarded the IBM Research Forschungspreis in 2010, the Volker Heine Young Investigator Award in 2013, an ERC Starting Grant in 2016, and the IUPAP C10 Young Scientist Prize in 2018.

Official source

Ontological neighbourhood

Earth science

Geology: Mineralogy

Related concepts (32)

Reciprocal lattice

In physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality , where is the momentum vector and is the reduced Planck constant.

Diffraction

Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

Fresnel diffraction

In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, F, of the optical arrangement.

Lattice (group)

In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.

X-ray crystallography

X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.

Related lectures (38)

Electron Diffraction: Basics and Applications

Covers the fundamentals of electron diffraction and its applications in understanding crystal structures and symmetry, including lattice vectors, lattice planes, and dark-field imaging techniques.

Reciprocal lattice: basics and properties MOOC: Transmission Electron Microscopy for Materials Sciences

Covers the basics of the reciprocal lattice in electron diffraction, including diffraction vector geometry and properties of reciprocal lattice unit cell vectors.

Crystal Structures: Reciprocal Lattice and Brillouin Zones

Covers crystallography concepts, including veganicide cells, reciprocal lattices, and Brillouin zones, essential for understanding electron behavior in crystal structures.

Multiple beam scattering in electron diffraction MOOC: Transmission Electron Microscopy for Materials Sciences

Explores multiple beam scattering in electron diffraction, focusing on zone axis diffraction patterns and theoretical approaches.

TEM imaging with diffraction contrast