0.6 Solid state and superconductors

Solid state structures and superconductors

 Objectives

• Build examples of: simple cubic, body centered cubic and face centered cubic cells.
• Understand and familiarize with three-dimensionality of solid state structures.
• Understand how binary ionic compounds (compounds made up of two different types of ions) pack in a crystal lattice.
• Observe the special electromagnetic characteristics of superconducting materials using 1,2,3-superconductor ${\text{YBa}}_2{\text{Cu}}_3{O}_{8-}$ , discovered in 1986 by Dr. Paul Chu at the University of Houston.

Grading

Your grade will be determined according to the following

• Pre-lab (10%)
• Lab report form. (80%)
• TA points (10%)

Before coming to lab:

• Read introduction and model kits section
• Complete prelab exercise

Introduction

From the three states of matter, the solid state is the one in which matter is highly condensed. In the solid state, when atoms, molecules or ions pack in a regular arrangement which can be repeated "infinitely" in three dimensions, a crystal is formed. A crystalline solid, therefore, possesses long-range order; its atoms, molecules, or ions occupy regular positions which repeat in three dimensions. On the other hand an amorphous solid does not possess any long-range order. Glass is an example of an amorphous solid. And even though amorphous solids have very interesting properties in their own right that differ from those of crystalline materials, we will not consider their structures in this laboratory exercise.

The simplest example of a crystal is table salt, or as we chemists know it, sodium chloride (NaCl). A crystal of sodium chloride is composed of sodium cations ( ${\text{Na}}^{+}$ ) and chlorine anions ( ${\text{Cl}}^{-}$ ) that are arranged in a specific order and extend in three dimensions. The ions pack in a way that maximizes space and provides the right coordination for each atom (ion). Crystals are three dimensional, and in theory, the perfect crystal would be infinite. Therefore instead of having a molecular formula, crystals have an empirical formula based on stoichiometry. Crystalline structures are defined by a unit cell which is the smallest unit that contains the stoichiometry and the“spatial arrangement”of the whole crystal. Therefore a unit cell can be seen as the building block of a crystal.

The crystal lattice

In a crystal, the network of atoms, molecules, or ions is known as a crystal lattice or simply as a lattice. In reality, no crystal extends infinitely in three dimensions and the structure (and also properties) of the solid will vary at the surface (boundaries) of the crystal. However, the number of atoms located at the surface of a crystal is very small compared to the number of atoms in the interior of the crystal, and so, to a first approximation, we can ignore the variations at the surface for much of our discussion of crystals. Any location in a crystal lattice is known as a lattice point. Since the crystal lattice repeats in three dimensions, there will be an entire set of lattice points which are identical. That means that if you were able to make yourself small enough and stand at any such lattice point in the crystal lattice, you would not be able to tell which lattice point of the set you were at–the environment of a lattice point is identical to each correspondent lattice point throughout the crystal. Of course, you could move to a different site (a non-correspondent lattice point) which would look different. This would constitute a different lattice point. For example, when we examine the sodium chloride lattice later, you will notice that the environment of each sodium ion is identical. If you were to stand at any sodium ion and look around, you would see the same thing. If you stood at a chloride ion, you would see a different environment but that environment would be the same at every chloride ion. Thus, the sodium ion locations form one set of lattice points and the chloride ion locations form another set. However, lattice points not only exist in atom positions. We could easily define a set of lattice points at the midpoints between the sodium and chloride ions in the crystal lattice of sodium chloride.