Crystals have long been among the most fascinating shapes in the world of nature, art and industry. When you think of the word, you may picture an elegant ballroom chandelier, a piece of quartz you found yourself or pieces of salt.

Even without the use of a microscope to examine the finer structure of crystal materials, you are probably struck most by their regular angles, and the sense that they obey strict rules while manifesting a fantastic array of shapes.

In chemistry, a crystal is matter that assumes a crystalline form, almost always a solid. The hallmark of this kind of structure is a repeating subunit of sorts, which is usually an atomic nucleus at the center of a geometric cube and ions carrying a different charge placed at the cube's corners or in the centers of its sides.

One popular DIY crystal in chemistry labs the world over is alum. Working with this material, which you can easily obtain in most supermarkets, is a great way to become familiar with the behavior of certain solutions and the formation of crystals generally.

Before you can fully appreciate crystals, it's a good idea to take a step back and review how chemists and physicists classify states of matter. A change in state of matter is not a change in the chemical composition of a substance (that is, its molecules don't change) but instead a change in the physical arrangement of the matter.

The three standard states of matter are, in order of increasing molecular kinetic energy, solid, liquid and gas.

When molecules are in the form of a solid, that means that their molecules have lower total and average kinetic energy (KE) than the same amount of that substance do in the liquid state, which in turn features a lower KE than the gaseous state for that substance.

Often, molecules in the form of a solid, the nuclei of which have virtually no freedom to move about in relation to each other, form regular, repeating patterns called lattices.

While these small (conceptual, not actual) lattices span only a molecule or two, their properties extend largely to the "macro" world. Quartz, on inspection, is quite evidently a "regular" sort of rock, with eye-pleasing geometric angles and lines; other crystals, many of them synthetic, capture, reflect and refract light in visually appealing ways and are popular in jewelry, architecture and elsewhere.

• Some crystals exist in the liquid state at room temperature, such as the liquid crystal diode (LCD) used in some modern display systems.

When a solid with molecules that consist of bonded ions (charged atoms or molecules) is placed in a liquid, the bonds of the solid may be broken, and the constituent atoms or molecules of the solid substance may become evenly dispersed throughout the liquid. When this is the case, the result is called a solution; when water is the liquid, is is called an aqueous solution,

• In this context, the liquid is a solvent, and the solid is a solute.

The amount of a solute than can be dissolved in a given amount of water or other solvent is, as you should expect, finite; in many cases, the solubility of a given substance in a given solvent also depends on the temperature at which this chemical reaction is occurring.

In general, as temperature rises, solubility increases, and as temperature drops, solubility decreases. This means that for a given amount of solute, a solution may form at one temperature, but solid my be present at a lower temperature.

At the point at which no more solute can be dissolved in solution, the solution is called saturated, and conditions are in place for crystal formation to occur. If more solution is added (or, in some cases, if the solution is cooled), more solute accumulates as the solution is now supersaturated. Crystals now begin to form as a result of favorable collisions between solute molecules in the ever-more-crowded solution.

Alum is a useful crystal for learning about how these solids form, as the appearance and growth of alum crystals can be easily produced, controlled and observed. Alum can refer to either a substance with a specific chemical formula or a class of chemicals that includes this "flagship" compound. The chemical that goes by the name "alum" most commonly is actually potassium alum.

The formula for potassium alum is KAl(SO₄)₂⋅12 H₂O. This means that a molecule of potassium aluminum sulfate, KAl(SO₄)₂, is surrounded by twelve water molecules to generate one unit of the crystalline lattice structure. But because the metal in the formula may be something other than potassium, the first part of the alum chemical formula may be KCr(SO₄)₂, KAl(SO₄)₂ or something else.

Alum has a molecular weight (MW) of 477.4 grams (g). It has a melting point of 93 °C, close to water's boiling point of 100 °C. This means it will reliably remain a solid at room temperature, which is normally in the range of 20 to 22 °C. It produces white to colorless crystals. It is not soluble in ethyl alcohol as it is in water and the polyhydroxyl alcohol glycerol.

Materials: You can find alum in the spice section of most supermarkets. Other than that, everything you need is easy to maintain. Make sure the water you use is in fact distilled, i.e., "pure" and free of ions that could contaminate the process. You should have at your disposal these items:

• Distilled water
• Several small bowls or saucers
• A pan for boiling water
• A stirring spoon

Making alum crystals via evaporation: Based on the preceding material, you should expect that to begin with, you want conditions to be maximally favorable for the alum you add to the water to dissolve. After all, the more quickly you can saturate and supersaturate a solution, the sooner you can start the process of crystal-growing in earnest.

Start by boiling a small amount of water (about 2 fluid ounces to 4 fluid ounces, or about 100 milliliters, is enough) and then letting it cool a little. Start adding alum by the spoonful and carefully stirring in between additions until it dissolves. Keep doing this in small gradations until no more alum can dissolve. The solution is now supersaturated.

Next, pour off some of the water, being cautious to not include the undissolved alum at the bottom of the pan. Allow this to cool on its own for a couple of minutes and then put what remains in the pan into the bowls or dishes, and place them in the refrigerator.

This will maximize the surface area of the mixture in relation to its volume, promoting the faster evaporation of water and the accelerated growth of alum crystals.

Follow-up and questions for study: You will begin to see crystals form within an hour or two, but be patient; after a day, you will see real crystals, and within two days you will have a crystal display.

Why is it that you see crystals of different sizes in the same bowl or between bowls? What conditions other than temperature and concentration might promote the attachment of alum molecules to each other? Would you describe any of these as random?