In materials science class, we examined wallpaper patterns for symmetries. Atoms and molecules can pack according to a variety of crystal structures. Mathematics obviously loves patterns too. There are fractal tilings and tessellations. Who doesn’t love Escher? There are probably practical applications to tiling, but more importantly they are great fun that tickles the brain. Recently I took my first stab at pattern making depicting (what else?) water polo.
Months ago, I posted about the collection of crystals and minerals at the Smithsonian Natural History Museum. Well, I went again, this time armed with a nicer (and heavier!) camera, and below are a few of the finds.
Quartz: quartz is a very common type of type of mineral (the second most common after feldspar), made up of silicon and oxygen. This variation is called agate. I used to buy agate slices as a kid, but the Smithsonian’s are slightly fancier.
Another example of quartz. This one arose in a piece of petrified wood. I like this one because it looks like a painting of a setting sun behind a row of pine trees–almost Japanese.
Malachite with azurite: both malachite and azurite are compounds of copper with oxygen, carbon, and hydrogen. The two differ only in the ratios. By geological standards, this rock formed somewhat quickly. We can tell this because the crystals are numerous and small. Single, large crystals form more slowly. This is why you should make ice cream at low temperatures, because when you freeze it quickly, many tiny crystals form, producing a better texture.
Pyrite: As you may see, pyrite, or fool’s gold, has a cubic crystalline structure. Pyrite is composed of iron and sulfur.
Calcite with duftite inclusions: Calcite is known for its optical properties such as birefringence. It was used as a material for gun sights in World War 2. Duftite is a compound of lead, copper, and arsenic. It is the duftite that gives the distinctive green color. I think of this as the kiwi mineral, as it even has the seeds.
I went on a trip to DC last fall. Almost accidentally I ended up in the Natural History Smithsonian Museum. Wow! Especially worthy is the section on minerals. I assume there are other museums with such displays, but I hadn’t been to one. The Hope diamond is displayed also in the minerals section, but fancy jewels I can’t touch are way less interesting than all the minerals and natural crystals.
I find crystals fascinating because they tell you so much about the microscopic structure of the material. Where else in life can you just look at an object and see what it does down to the nanometer? So naturally the camera came out. Below are a few favorites, and some comments about what we can infer from the pictures.
Fluorite (CaF2): As you can see, Fluorite has a cubic crystalline structure. Fluorite can come in basically any color. Color can be due to impurities, exposure to radiation, or defects in the crystalline structure. Fluorite was originally so named due to fluorescent properties; fluorite can fluoresce in a variety of colors depending upon the impurities present.
Beryl (Be3Al2(SiO3)6): You might be more familiar with other names for Beryl, such as aquamarine or emerald or morganite. Beryl is naturally clear, but takes on color in the presence of impurities. Emerald, for example, has chromium or vanadium present. Aquamarine coloration results when the Fe2+ oxidation state is present. Fe3+ results in yellow coloration. You can see in the image above that beryl has a hexagonal crystal structure. You can also see that this is one big hexagonal crystal, unlike the population of cubes in the fluorite picture. This tells us a lot about how the crystal grew. If the crystal grew very fast, there would be a number of columns, because crystallization would be faster than the time for the mineral components to diffuse to one specific column. So this crystal grew pretty slowly.
Wulfenite (PbMoO4): Wulfenite is often found around lead deposits, which makes sense since it contains lead. It has a tetragonal crystal structure, and tends to be yellow or orange or brown in color. You can see that the crystals are much smaller in this picture than the beryl crystal. Clearly these crystals grew quickly from many nucleation sites. The size to which crystals tend to grow is a property of the crystal too; some only form a ton of small crystals, some form a few very large ones. It depends whether it is lower energy to just form another crystal, or if it is lower energy to allow diffusion to an already established crystal. This is related to thermodynamics. Wulfenite seems to favor lots of small crystals. Some wulfenite has a really cool property called piezoelectricity; when there is the right kind of pressure on the crystal, an electric charge accumulates.
Manganese dioxide (MnO2): This manganese dioxide has grown in a dendritic fashion. It might look like frost or snowflakes, which grow in similar ways. These dendrites are very fractal, a favorite topic of mine. Here diffusion was definitely limited, so crystals grew where the materials were present.
Chalcedony (SiO2): Chalcedony is a type of silicon dioxide, which is the chemical composition of most sand. Chalcedony is composed of two different silicon dioxide minerals: quartz and moganite. Quartz and moganite have different crystalline structures which grow together at a fine scale in chalcedony, which is probably why it looks far less geometric than the other crystals I’ve shown. Agate is a type of chalcedony.