Crystallography Course

Lesson 1 • Crystal Chemistry Basics

Links atomic radii, bonding type, and coordination number to crystal structure. Prepares students to predict and rationalise structural choices.

Lesson 2 • Miller Indices and Crystallographic Planes

Teaches indexing of planes and directions using Miller notation. Enables students to describe and communicate crystal geometry precisely.

Lesson 3 • Crystal Systems and Symmetry Elements

Covers the seven crystal systems and fundamental symmetry operations. Students classify crystals by symmetry before advancing to space groups.

Lesson 4 • Nature of Crystalline Solids

Defines long-range order, periodicity, and anisotropy in solids. Anchors the chapter by contrasting crystals with amorphous and polycrystalline materials.

Lesson 1 • The 230 Space Groups

Surveys the complete set of space groups and their derivation. Students learn to identify space group symbols and extract symmetry information.

Lesson 2 • Subgroups and Supergroups

Explains group-subgroup relationships and their role in phase transitions. Prepares students for advanced topics in structural distortions.

Lesson 3 • Symmetry Operations on Atomic Positions

Applies space group operators to generate all atoms in a unit cell. Reinforces abstract symmetry concepts through concrete coordinate transformations.

Lesson 4 • Point Groups and Crystal Classes

Derives the 32 crystallographic point groups from symmetry operations. Connects point group symmetry to macroscopic crystal morphology.

Lesson 1 • Systematic Absences and Space Group Identification

Links translational symmetry to missing reflections in diffraction data. Enables space group determination from raw diffraction patterns.

Lesson 2 • X-Ray Generation and Properties

Covers X-ray production in sealed tubes and synchrotron sources. Establishes wavelength, intensity, and monochromatisation as key experimental variables.

Lesson 3 • Scattering Theory Fundamentals

Introduces atomic scattering factors and structure factors. Connects electron density distribution to measured diffraction intensities.

Lesson 4 • Powder vs. Single-Crystal Diffraction

Compares experimental geometries and information content of both methods. Guides students in selecting the appropriate technique for a given problem.

Lesson 1 • Diffractometer Instrumentation

Describes components of modern powder and single-crystal diffractometers. Grounds students in hardware before software-driven data collection.

Lesson 2 • Powder Diffraction Data Collection

Addresses sample preparation, instrument alignment, and scan parameters for powder methods. Directly enables phase identification and Rietveld refinement.

Lesson 3 • Single-Crystal Data Collection Strategy

Covers crystal selection, mounting, and scan strategy optimisation. Ensures completeness and redundancy needed for reliable structure solution.

Lesson 4 • Reciprocal Space and Reflection Files

Explains reciprocal lattice geometry and standard reflection file formats. Prepares students to interface data with structure-solution software.

Lesson 1 • Charge Flipping and Dual-Space Methods

Covers iterative real-space and reciprocal-space methods for ab initio solution. Extends solution capability to larger and more complex structures.

Lesson 2 • The Phase Problem in Crystallography

Explains why diffraction measures amplitudes but not phases, and why this prevents direct Fourier inversion. Motivates all structure-solution strategies.

Lesson 3 • Molecular Replacement

Uses a known structural model to solve phases for a related structure. Particularly powerful for macromolecular and related organic structures.

Lesson 4 • Direct Methods

Introduces probabilistic phase relationships used in direct methods. Enables ab initio structure solution for small molecules.

Lesson 1 • Least-Squares Refinement Principles

Derives the least-squares minimisation function and its application to crystallographic parameters. Establishes the mathematical basis for all refinement methods.

Lesson 2 • Constraints and Restraints

Distinguishes hard constraints from soft restraints and their use in underdetermined refinements. Enables stable refinement of disordered or data-limited structures.

Lesson 3 • Rietveld Refinement for Powder Data

Applies full-profile fitting to powder diffraction data for structure refinement. Extends refinement skills to polycrystalline and multiphase samples.

Lesson 4 • Atomic Displacement Parameters

Covers isotropic and anisotropic displacement parameters and their physical meaning. Correct modelling of thermal motion is essential for accurate structures.

Lesson 1 • Geometric Analysis of Structures

Extracts bond lengths, angles, torsion angles, and non-bonded contacts from refined coordinates. Connects structural geometry to chemical and physical properties.

Lesson 2 • Crystal Structure Databases

Introduces the Cambridge Structural Database, ICSD, and related repositories. Teaches search, retrieval, and comparative analysis of deposited structures.

Lesson 3 • Crystallographic Figures of Merit

Defines R1, wR2, GooF, and other quality indicators used to assess refinement quality. Provides benchmarks for acceptable structure quality.

Lesson 4 • Automated Validation Tools

Uses PLATON, checkCIF, and related tools to detect errors and alert flags. Ensures structures meet publication and deposition standards.

Lesson 1 • Twinning in Crystals

Defines twinning types, their effect on diffraction data, and refinement strategies. Equips students to recognise and handle twinned datasets.

Lesson 2 • High-Pressure and In Situ Crystallography

Addresses diamond anvil cell techniques and time-resolved in situ experiments. Prepares students for structure determination under non-ambient conditions.

Lesson 3 • Neutron Diffraction

Explains neutron scattering lengths and the complementary role of neutron diffraction. Enables location of light atoms and magnetic structure determination.

Lesson 4 • Modulated and Aperiodic Structures

Introduces superspace formalism for incommensurately modulated crystals. Expands structural understanding beyond conventional periodic models.