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Browse materialsMIT 5.069 · Spring 2010

Crystal Structure Analysis

Art: Alembert, Jean Le Rond d', 1717-1783 Diderot,…, Plate xviii chymie cn69m494r dr26xz05s dl full size, 1751 · Public domain

Instructor: Dr. Peter Mueller
Term: Spring 2010
Level: Graduate
What's inside: 1 lecture note · 9 other files · 3 web pages
Materials open: MIT OCW

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Source: MIT OpenCourseWare 5.069 Crystal Structure Analysis, Spring 2010, Dr. Peter Mueller — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Lecture Notes

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MIT OpenCourseWare, Dr. Peter Mueller, 5.069 Crystal Structure Analysis, Spring 2010.

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Crystal Structure Analysis

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Lecture Notes

Lecture 1: Introduction Overview, textbooks, history of crystallography

Lecture 2: Symmetry in 2D Definition of symmetry, introduction of symmetry operators Compatibility of symmetry operators with translation Combining symmetry operations and determination of plane groups

Lecture 3: Symmetry in 3D Extension of the plane groups concept to the third dimension: space groups Introduction of screw axes and glide planes Point groups vs. space groups The unit cell and crystallographic conventions

Lecture 4: X-rays and matter X-ray generation Diffraction experiment with optical grids and laser pointers Convolution theorem and Fourier transformation Introduction of Bragg’s law and Miller indices

Lecture 5: Geometry of diffraction Reciprocal space vs. real space Ewald construction as a geometric interpretation of Bragg’s law

Lecture 6: Structure factors Real atoms are no point atoms (atomic form factors) and show thermal motion (atomic displacement factors) Having more than one atom per unit cell leads to structure factors Fourier transformation gives rise to electron density; crystallographic resolution

Lecture 7: Structure factors II Complex numbers, Euler’s equation and the argand plane Introduction of the phase problem

Lecture 9: Structure refinement Different types of electron density maps (_F_o, _F_c, _F_o-_Fc_, etc.) Introduction of anisotropic displacement parameters Minimization functions: the least-squares approach and different R-factors Crystallographic parameters, constraints and restraints

Lecture 10: Structure refinement II Problems and pitfalls: wrong space group, atom type assignment (all electrons are blue), disorder, twinning What are artifacts (libration, C-C triple bonds, Fourier truncation ripples, etc.)? Finding the hydrogen atoms, “riding model”

Lecture 11: Anomalous scattering Absorption of X-ray photons leads to loss of symmetry in orbital geometry, which results in a violation of Fridel’s law

Lecture 12: Practical aspects and related methods Growing crystals and keeping them alive (never remove the mother liquor!) Mounting crystals onto the diffractometer Short introduction of powder diffraction, neutron diffraction and EXAFS Crystallographic data bases (ICSD, CSD, PDB, reciprocal net)

Lecture 14: Exam You have 50 minutes to answer all questions. You can use pens, a calculator, ruler and compass, as well as a letter sized piece of paper with anything written on it. No books or other material is allowed.