X-ray Diffraction
Introduction
3.1 X-Ray Diffraction
X-rays have a wavelength in the range of Angstroms – much smaller than the microwaves you previously used. As such, X-rays can probe much smaller distance scales than the ”crystal” you used in the lab. The physics is entirely the same: The sample and detector are rotated and peaks in the diffraction pattern correspond to angles where the Bragg condition is met:
(1) 
where 
is the diffraction order, 
is the wavelength, 
is the lattice spacing, and 
is the angle of the incoming wave.
The sample is rotated in three dimensions, leading to many two-dimensional images of the reciprocal space. These images are often mapped onto a surface called Ewald’s Sphere. The 2-D images can be put together to generate the three-dimensional reciprocal space. The spacing of this reciprocal space indicates the spacing and symmetries of the crystal.
3.2 High Tc Cuprate Superconductors
Lanthanum barium copper oxide (LBCO) was the first high-temperature superconductor, discovered in 1986 (and winning the Nobel prize in 1987). LBCO belongs to the family of ‘cuprate’ superconductors, which are characterized by planes of copper oxide and irregularly high superconducting temperatures. An image of the crystal is shown in Figure 1. LBCO can be hard to Google-search for since most people are searching for the LCBO. Make sure you add ‘crystal’ or ‘diffraction’ or ‘superconductor’ to your search query. In this experiment, you will be studying a ‘trendier’ material in Nd-LSCO [1].
Figure 1: Crystal structure of LBCO. Red=copper, green=oxygen, blue=lanthanum, barium. An image of
Nd-LSCO can be found in reference [1]. Figure from Wikipedia
3.3 Important Concepts
Here are some Wikipedia links that you may find helpful. During your time in the X-ray facility, these terms WILL come up in discussions about your data and how it’s collected.
Reciprical Space (AKA 
space), Miller Indices
face-centered, orthorhombic, tetragonal