Відео

We continue our discussion of Rietveld refinements with more details and a practical guide to guide you through a successful Rietveld refinement.

The Rietveld method is used to refine the structures of crystals from powder diffraction data. Unlike single crystal methods, where the crystal structure is determined from structure factors extracted from a diffraction experiment, in the Rietveld method the entire powder diffraction pattern is fit. In this lecture we examine the general principles of the Rietveld method.

In the second half of this lecture on structure factors we explore the reasons behind the systematic absences associated with screw axes and glide planes, and see how the structure factors for centrosymmetric and noncentrosymmetric space groups differ. The latter part of the lecture covers Friedel's Law and Laue Groups.

The structure factor F(hkl) arises from interference effects between X-rays scattered off of different atoms in the unit cell. All of the information about where the atoms are located in the unit cell is contained in the structure factor. In this lecture we look at the origins of the structure factor and see how they are calculated. We finish with some illustrative examples.

As X-rays pass through a sample they are absorbed and this affects the intensities of various diffraction peaks. In this lecture we learn how to calculate the linear absorption coefficient for any substance from it's composition, density and the wavelength of the X-rays. Then we consider how to use this information when designing experiments and analyzing diffraction data.

This is the first of several lectures that examine the factors that determine the intensities of diffraction peaks. Here we focus is mainly on effects other than the structure factor, including the polarization and Lorentz factors, multiplicities, and absorption effects.

In this lecture we see that for most space groups certain classes of diffraction peaks are systematically absent. Those peaks that are allowed are are said to follow specific reflection conditions. For example in a body centered space group only the reflection indices (hkl) where h k l is an even number are seen. We can use this information to dramatically narrow down the choice of space group.

In this lecture we discuss the use of computer programs for indexing powder diffraction patterns. The focus is primarily on the indexing routines in the software package Topas, but other programs are discussed as well.

This is a continuation of lecture 17, where the procedure for indexing an X-ray powder diffraction pattern of a cubic material was illustrated. In this lecture we extend the technique to tetragonal and hexagonal crystal systems.

In this lecture we look at the X-ray powder diffraction pattern of a cubic material and see how to calculate the 2-theta values of the diffraction peaks. We see that the positions of each and every diffraction peak is determined by the length of the unit cell edge and the X-ray wavelength. We finish by manually indexing the diffraction pattern of MgO.

In this lecture we see how the Bragg concept of diffraction (reflecting from parallel lattice planes) and the Laue concept of diffraction (scattering from atoms, typically in transmission) relate to one another. We review how to assign Miller Indices to lattice planes and calculate the spacing between families of parallel planes.

In this lecture we examine the relationship between the real space lattice that defines a crystal structure and its reciprocal space lattice. We then see the connection between the reciprocal space lattice and points of constructive interference that give rise to the diffraction pattern of the crystal.

In this lecture we explore the conditions that lead to diffraction from two- and three-dimensional crystals.

In this lecture we examine the geometric conditions that lead to diffraction of X-rays by crystals. First, we derive Bragg's Law, which gives the angle at which the scattered X-rays constructively interfere if the X-rays are partially reflected from parallel planes in a crystal. Next, we consider scattering in the forward direction (transmission) of an incoming beam of X-rays by a one-dimension...

Diffraction Lecture 12: Elastic Scattering of X-rays

Diffraction Lecture 11: Crystallographic Symmetry and Physical Properties

Diffraction Lecture 10: Space Group Symmetry and the Structures of Molecular Crystals

Diffraction Lecture 9: Space Groups and the Structures of Metallic and Ionic Crystals

Diffraction Lecture 8: Space Group Symmetry Part 2

Diffraction Lecture 7: Space Group Symmetry Part 1

Diffraction Lecture 6: 2D Plane Group Symmetry

Diffraction Lecture 5: Point Groups

Diffraction Lecture 4: Travel Symmetry Operations

Diffraction Lecture 3: Point Symmetry Operations

Diffraction Lecture 2: Translational Symmetry in Three Dimensions

Diffraction Lecture 1: Translational Symmetry in Two Dimensions

Lecture 40 Conductivity of Transition Metal Compounds

Lecture 39 Semiconductors

Lecture 38 Conductivity and the Free Electron Model