Lattice points | Fourier analysis | Neutron-related techniques
In physics, the reciprocal lattice represents the Fourier transform of another lattice (group) (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is a periodic spatial function in real space known as the direct lattice. While the direct lattice exists in real space and is commonly understood to be a physical lattice (such as the lattice of a crystal), the reciprocal lattice exists in the 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 Planck constant. The reciprocal lattice of a reciprocal lattice is equivalent to the original direct lattice, because the defining equations are symmetrical with respect to the vectors in real and reciprocal space. Mathematically, direct and reciprocal lattice vectors represent covariant and contravariant vectors, respectively. The reciprocal lattice is the set of all vectors , that are wavevectors of plane waves in the Fourier series of a spatial function whose periodicity is the same as that of a direct lattice . Each plane wave in this Fourier series has the same phase or phases that are differed by multiples of at each direct lattice point (so essentially same phase at all the direct lattice points). The reciprocal lattice plays a fundamental role in most analytic studies of periodic structures, particularly in the theory of diffraction. In neutron, helium and X-ray diffraction, due to the Laue conditions, the momentum difference between incoming and diffracted X-rays of a crystal is a reciprocal lattice vector. The diffraction pattern of a crystal can be used to determine the reciprocal vectors of the lattice. Using this process, one can infer the atomic arrangement of a crystal. The Brillouin zone is a Wigner-Seitz cell of the reciprocal lattice. (Wikipedia).
Mod-01 Lec-5ex Diffraction Methods For Crystal Structures - Worked Examples
Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course
Algebra 1 2.08b - Using Reciprocals
From the Algebra 1 course by Derek Owens. Distance learning courses for homeschool students (and others) are available at http://www.derekowens.com
From playlist Algebra 1 Chapter 2 (Selected Videos)
Powered by https://www.numerise.com/ Reciprocal graphs 1
From playlist Important graphs
Reciprocal Graphs | Graphs | Maths | FuseSchool
Reciprocal functions are actually extremely important. Isaac Newton deduced that the forces needed to hold planets in orbits is a reciprocal relationship with the squares of their distances. Radioactive isotopes decay reciprocally, and trees lose their leaves reciprocally. The graph appe
From playlist MATHS
Lattice Structures in Ionic Solids
We've learned a lot about covalent compounds, but we haven't talked quite as much about ionic compounds in their solid state. These will adopt a highly ordered and repeating lattice structure, but the geometry of the lattice depends entirely on the types of ions and their ratio in the chem
From playlist General Chemistry
From playlist Pre-Algebra/Introductory Algebra
From the Algebra 1 course by Derek Owens. Distance learning courses for homeschool students (and others) are available at http://www.derekowens.com
From playlist Algebra 1 Chapter 2 (Selected Videos)
Introduction to Solid State Physics, Lecture 8: Reciprocal Lattice
Upper-level undergraduate course taught at the University of Pittsburgh in the Fall 2015 semester by Sergey Frolov. The course is based on Steven Simon's "Oxford Solid State Basics" textbook. Lectures recorded using Panopto, to see them in Panopto viewer follow this link: https://pitt.host
From playlist Introduction to Solid State Physics
Student Video: 2D Brillouin Zones
MIT RES.3-004 Visualizing Materials Science, Fall 2017 Speaker: Jurgis Ruza View the complete course: https://ocw.mit.edu/RES-3-004F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62EJXwSgoVRfh1tEiSc01bh A short introduction into reciprocal space and the construction
From playlist MIT RES.3-004 Visualizing Materials Science, Fall 2017
Student Video: Real and Reciprocal Space in 2D and 3D
MIT RES.3-004 Visualizing Materials Science, Fall 2017 Speaker: Maya Berlinger View the complete course: https://ocw.mit.edu/RES-3-004F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62EJXwSgoVRfh1tEiSc01bh This video shows a visualization of crystals in 2 dimensions
From playlist MIT RES.3-004 Visualizing Materials Science, Fall 2017
Lecture 29 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the general stretch theorem and begins covering medical imaging. The Fourier transform is a tool for solving physical p
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Huajie Chen - Convergence of the Planewave Approximations for Quantum Incommensurate Systems
Recorded 04 May 2022. Huajie Chen of Beijing Normal University, School of Mathematical Sciences, presents "Convergence of the Planewave Approximations for Quantum Incommensurate Systems" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: We study the
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Introduction to Solid State Physics, Lecture 9: Scattering Experiments (X-ray Diffraction)
Upper-level undergraduate course taught at the University of Pittsburgh in the Fall 2015 semester by Sergey Frolov. The course is based on Steven Simon's "Oxford Solid State Basics" textbook. Lectures recorded using Panopto, to see them in Panopto viewer follow this link: https://pitt.host
From playlist Introduction to Solid State Physics
Introduction to Solid State Physics, Lecture 5: One-dimensional models of vibrations in solids
Upper-level undergraduate course taught at the University of Pittsburgh in the Fall 2015 semester by Sergey Frolov. The course is based on Steven Simon's "Oxford Solid State Basics" textbook. Lectures recorded using Panopto, to see them in Panopto viewer follow this link: https://pitt.host
From playlist Introduction to Solid State Physics
6. Crystal Bonding & Electronic Energy Levels in Crystals
MIT 2.57 Nano-to-Micro Transport Processes, Spring 2012 View the complete course: http://ocw.mit.edu/2-57S12 Instructor: Gang Chen License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 2.57 Nano-to-Micro Transport Processes, Spring 2012
Ross Harder - Bragg Coherent Diffraction Imaging at the Advanced Photon Source 34-ID Beamline
Recorded 12 October 2022. Ross Harder of the Argonne National Laboratory presents "Bragg Coherent Diffraction Imaging at the Advanced Photon Source 34-ID Beamline" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: The 34-ID-C beamline at the APS is dedicated to Bragg C
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Cubic and Reciprocal Graphs: Find Cubic Equation From Sketch (3 Solutions) (Grade 9) - Maths
Topic: Cubic and Reciprocal Graphs: Find Cubic Equation From Sketch (3 Solutions) Do this paper online for free: https://www.onmaths.com/cubic-and-reciprocal-graphs/ Grade: 9 This question appears on calculator and non-calculator higher GCSE papers. Practise and revise with OnMaths. Go to
From playlist Cubic and Reciprocal Graphs