Дефекти решітки

When I was getting engaged, I went diamond shopping. The salesperson told me the four C's of diamonds. I recall that one of the four C's is color. A clear diamond was better. A diamond with color was of lower quality. She pulled out an expensive diamond. It looked clear and sparkled beautifully. It also cost more than my car! Next, she showed me the inexpensive diamonds. They were still beautiful. Yet, they had a slightly yellowed look. But, what caused the yellow color?

As we learned about solids, we discovered crystals. Crystalline solids have a repeating structure. In ionic crystals, we call their geometry a unit cell. Covalent networks are repeating VSEPR molecular geometries. The strength of the ionic and covalent bonds gives crystals unique physical properties. For example, they are strong and have high melting temperatures. But what happens if their repeating geometry gets disrupted?

Lattice Defects

What caused the inexpensive diamonds to yellow? Defects in the crystal lattice. No substance is 100% pure. Even 99.9% is one defect per one thousand atoms! The cheaper the diamond, the more defects it had. The lattice defects affected the light's diffraction. Let's look at the three broad defect classifications.

Point Defects: Point defects are local. Only one atom is missing or replaced. So, the defect only affects a handful of unit cells.
Line Defects: Line defects are a series of errors from atom misalignment or removal. The repeating defects happen along a line.
Surface Defects: Surface defects affect the whole side of a crystal.

More Detail on Point Defects

Substitutional: In substitution, one atom replaces another. The replacing atom is a different element with a different atomic radius. The size change affects the electrostatic interactions. Sometimes, the element has a different number of valence electrons. So, the ionic charge could be different. These also affect the electrostatic interactions.
Vacancy: A vacancy is a blank space in the lattice. An atom should be filling the empty space. Because an atom is missing, the charge isn't balanced. So, locally the energy is higher and less stable. But, overall the crystal is still stable because neighboring unit cells are intact.
Interstitial: In interstitial defects, an atom inserts itself into an unexpected area. The new atom changes the unit cell geometry. For example, we may transition from a simple cubic to a body-centered cubic.
Schottky Defect: Ionic crystals need to maintain their neutral charge. Let's say we have a cation vacancy. Then somewhere in the crystal, there is a corresponding anion vacancy. We call the two vacancies a Schottky pair (pronounced: shot-key).
Frankle Pair Defect: A Frankle pair is the combination of a vacancy and interstitial defect. The atom from the vacancy moves into the interstitial area.

More Detail on Line Defects

Edge Dislocations: An edge defect is a series of vacancies or interstitial defects that happen in a straight line. Imagine that we remove a whole line of atoms from the center of a crystal. A series of unit cells would change and distort the geometry. We could do the same thing by adding atoms.
Screw Dislocations: A screw dislocation is like an edge dislocation. But, screw dislocations occur in a cylindrical shape. You can imagine a sheet of atoms. Indent the center of the sheet to look like a snowboarding half-pipe. The defects pushed the atoms downward. As we move away from the defects, the atoms slope upward.

More Detail on Surface Defects

Imagine a sodium chloride ( $NaCl$ ) lattice. Sodium chloride is a face-centered cubic. Each face of the unit cell has a sodium ion. Each face of the next unit cell will have a chlorine ion. So, the chlorines surround the sodium. But, on the outside of the crystal, the sodium is not surrounded on one side. Surface defects happen when the crystal stops growing. In our example, the surface sodium atoms have fewer bonds than the inner sodium atoms.

A lot more could be said about surface defects. However, it starts to become really complicated. If you want to know more, study inorganic chemistry.

How Do Crystals get Defects?

A while ago, my wife and I celebrated our 5th wedding anniversary. To celebrate, we went to Wind Caves National Park in South Dakota. In the caves, there is a remarkable geological formation. It's called box-work because it looks like 1800s pulp boxes. The park is unique because it contains 99% of the world's box-work. It formed millions of years ago when the caves flooded. The flood waters dissolved the calcite (calcium carbonate). The remaining rock was insoluble.

In nature, most crystals grow from chemical processes. Often, crystals form in the earth's crust. The mantle's magma is an unbelievably hot liquid solution. It's filled with atoms and ions. As it rises to the crust, it cools. The atoms and ions lose kinetic energy and begin to bond. But, there are so many different atoms that it's easy to get a substitution. For example, magnesium and silicon are very abundant. So, in quartz, a silicon atom could get replaced by magnesium. But what about line defects? They occur when the cooling is very rapid. That atoms and molecules don't have time to arrange themselves. So, they don't line up in the proper orientation.