Education

Chemical Crystallography 613

is a course offered every odd-numbered year by the University of Wisconsin-Madison Chemistry Department. Students gain experience by solving and refining a number of structures with a progressive degree of difficulty.

Instructors

John Berry (berry@chem.wisc.edu)
Ilia A. Guzei (iguzei@chem.wisc.edu)

About the course

The course is designed for individuals who desire to acquire basic crystallographic knowledge, mathematical foundations of diffraction principles, and hands-on experience in operation of diffractometers, computer software, and crystal structure determination.  The course provides the concepts of crystallographic analysis including point/space group symmetry, the use of reciprocal lattice to understand diffraction by crystals, and crystallographic experiment design.

Modern single-crystal X-ray diffraction is the most powerful and unambiguous analytical method for the absolute structural elucidation of solids.  The chemistry department is equipped with two state-of-the-art area-detector CCD diffractometers, which  allow complete stereochemical characterizations of over 90% of non-macromolecular compounds within 1-2 days.  This analytical tool enables researchers to ascertain both stoichiometeries and absolute configurations of small-to-large size compounds.  This course is particularly important for a student interested in comprehending and evaluating the countless structure determinations given in the literature.  In addition, it provides an excellent foundation for the determination and/or interpretation of protein structures and would be extremely valuable as an introduction to protein crystallography.

A large portion of the second part of the course will take place in the departmental computer laboratory for the students to learn the practical aspects of crystal structure analysis.  An additional session will be include a hands-on practicum at the X-ray diffraction facility. These sessions will cover: (1) selection and mounting of single crystals on a diffractometer; (2) use of diffractometers for data-collection; (3) use of SHELXTL/OLEX2 computer program packages for processing X-ray data, structural solution and refinement, and preparation of publication quality reports; (4) important topics such as establishing absolute structure (e.g., molecular chirality) for non-centrosymmetric space groups, interpretation of inter-/intramolecular hydrogen bonding interactions, and analysis of molecular conformations; (5) use of the Cambridge Structural Database, which contains over 10⁶ structures.

During the course each student will solve a number of crystal structures (at least one research sample may be submitted by the student) and will give a brief presentation on an individually assigned crystallographic study.

The course provides minor Chemistry credit of 3 hours for all disciplines within Chemistry (analytical, chemical biology, inorganic, materials, organic, physical) and for outside departments (Biochemistry, Engineering, Food Science, Geology, Materials Science, and Physics).  Undergraduate and non-dissertator graduate students will have to register for the course.

Symmetry @ Otterbein – wonderful interactive web site, especially the Symmetry Gallery.

Excellent Symmetry and Space Group Tutorial by Bruce Foxman.

Symmetry video – 11 minutes, 64 MB. This “psychedelic” movie from the 1960s illustrates symmetry with proper music.

Site with resources on structures containing several independent molecules in the asymmetric unit.

Crystallographic space group diagrams and tables

Space Group Diagrams and Tables

Escher Web Sketch

Program EwaldSphere is excellent for visualization of the reciprocal lattice and diffraction geometry by crystals. The program, its manual, open-access paper discussing it can be downloaded from the Barbour Laboratory web site. The program is written by Len Barbour.

Program XRayView: a virtual X-ray crystallography laboratory is available from  George Phillips‘s download site.

Kevin Cowtans’s Book for Fourier Transform – explanation of the phase problem and X-ray diffraction.

Fourier Transform/Diffraction Simulation, Fourier Transform Tutorial, n-Dimensional Fourier Transform, Introduction to Fourier Transform for Image Processing

An interactive guide to Fourier Transform by Kalid Azad.

An Intuitive Explanation of Fourier Theory by Steven Lehar

Single Crystal Diffractometry using the Apex2 Software: A Tutorial by Bruce Foxman.

Instructions for crystal alignment by Daniel Kratzert.

Single Crystal X-ray Diffraction Experiment through the eyes of Dr. Maik Tretbar (Schomaker Laboratory) – a PowerPoint presentation.

Tips for crystal growing by Martin Lutz

Crystal Growth, Evaluation and Handling by Alexander J. Blake

Crystal growing guides by Paul Boyle

Crystal Growing Tips by Martin Dinger and Jerzy Klosin

Roger D. Sommer’s article “How to grow crystals for X-ray crystallography“.

How do crystals form?

It’s a very interesting question, considering that crystals are everywhere – they cool our beverages, run our digital clocks, adorn crowns of the kings. In fact the entire earth crust is made of crystals.

A crystal is an anisotropic, homogeneous solid consisting of a three-dimensional periodic ordering of atoms, molecules, or ions.

Crystal form by a dynamic process called crystallization that signifies transition from chaos to perfection. Unlike living organisms, crystal do not draw nourishment from within, but rather they grow by deposition of like material from the outside to the crystal surface.  Crystals grow in one of three major ways: from a vapor, from a solution, or from a melt. In all cases the crystal growth is a three-stage process.

It begins with nucleation, in which a few molecules or ions approached each other in an appropriate orientation to form a stable submicroscopic aggregate.

The second stage is growth, which is an orderly addition of further molecules of ions in a regular manner.  The crystal owes its shape to the orderly array of the atoms which compose it.  The symmetry of the crystal shapes is their most recognizable feature.

In the final stage, termination, growth stops. At this stage the appearance of a crystal grown under specific conditions (known as habit) can be evaluated.  The habit is evident in the relative development of the different faces of a crystal for a given material.

It is instructive to estimate how rapidly molecules must order themselves at the surface of a growing crystal.  Even when the crystal growth rate is as slow as 1/10 of an inch per day, about a hundred layers of molecules must be laid down per second on the crystal surface.

There is no limit to how large a crystal one can grow – there is only limit to our patience and material supply. The largest crystal ever found is believed to be a beryl from Malakialina, Madagascar. It measures 59 feet long and 11 feet across, and weighs 380 tons.

The text above cites or based on the following sources: “Crystallography” by Walter Borchardt-Ott, “Crystals and crystal growing” by Alan Holden and Phylis Morrison, “Crystals and light” by Elizabeth Wood, and “X-ray crystallography” by Gregory Girolami.

My recommended books on crystallography

The UW-Madison Chemistry Library has a good spectrum of links for X-ray Crystallography.

Links to books and references are available from the Chemistry Library Page.

The Royal Society of Chemistry’s “Maths for Chemists” booklet

Introductory lectures on crystallography – theory and practice by Charles Campana . Lecture 1. Lecture 2.

Structure Determination by X-ray Crystallography by Patrick J. Carroll (University of Pennsylvania).

Single-crystal X-ray diffraction, an on-line course by Joe Reibenspies (Texas A&M).

Powder X-ray diffraction, an on-line course by Joe Reibenspies (Texas A&M).

Courses in single-crystal and powder X-ray diffraction by Joe Reibenspies (Texas A&M).

Interpretation of crystal structure determinations by Huub Kooijman

OLEX2 has a YouTube channel with curated playlists, including “Modeling Disorder” and “Twinning”

These models were created by Bob Shanks based on the classic wooden 3D models. Feel free to download and print them locally. You may want to use an STL viewer.

Structure Solution and Refinement with OLEX2 by Dr. Carla Slebodnick, Virginia Tech. A dataset to go with the manual example.

Structure Solution and Refinement with Olex2 by Charlotte Stern, Northwestern University.

OLEX2 cheat sheet.