Homemade Bismuth Crystals

This post is based on the work of Theodore Gray in his blog for Popular Science. Mr. Gray, in addition to designing the UI for Mathematica and creating a literal periodic table… table, also appears to be among the few people who can make perfect bismuth crystals the first time he tries it. See his tutorial here

The principle behind metal crystals is relatively simple: the metals found in most everyday objects were formed by pouring molten metal into an appropriate mold and then rapidly cooling the assembly. This means that the atoms that comprise the liquid metal do not have a lot of time to diffuse through the material and find a location that minimizes their electrical potential relative to the other atoms—they might have time to trade places with their neighbors and form small, ordered regions within the metal structure, but overall the metal solidifies before each atom has had time to try out every possible position in the structure and find the one with the least repulsion from the other charged particles. This means that most metal objects lack global order—under a microscope, small crystalline patches will be visible, but overall the structure is a hodgepodge of various crystal structures and orientations.

This rudimentary explanation suggests that cooling a molten metal slowly will allow larger crystals to form, which provides the logic behind Mr. Gary’s approach, in which molten bismuth is slowly cooled on a stovetop. The idea of metal atoms rearranging themselves also suggests why blacksmiths anneal steel knives by raising them to high temperatures for long periods—at high temperatures, it becomes easier for bonds to break and atoms to trade places and find more energetically favorable positions in the material, thus making the knife more crystalline and thus rigid.

Cubic Bismuth Crystals

Bismuth crystals after cooling.

Bismuth crystals

Bismuth Oxide

Colorful bismuth oxide patterns appear when bismuth is melted and re-cooled.

Bismuth Crystals in Pot

The remainder of the bismuth after the melting process.

Above are some of my efforts to implement Mr. Gray’s approach. The setup is exactly as Mr. Gray and other sources describe–—the bismuth melts at a very low temperature, much like its noxious cousin, lead, and so a steel pot and butane flame are all that are needed to get started. I checked to see how much of the bismuth had re-solidified by blowing on the surface—do not shake the pot, as this will disrupt the formation of larger cubic crystals. Once half or so of the pot has congealed, pour off the remaining liquid bismuth to reveal the crystal structures.

The gorgeous color comes from bismuth oxide, which forms on the surface of the metal almost instantly. I acquired my bismuth from United Nuclear, who have a variety of excellent reagents at reasonable prices. It comes in 5-10 gram pellets like this:

Bismuth pellets

Small pieces of elemental bismuth, purchased from a chemical supplier.

Bismuth can also be found in certain types of game shot (it is often used in lieu of lead)—for more information, see what Scitoys uses bismuth for.

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Laser Microscopy in 20 Minutes

protozoans

Protozoans in a water droplet, projected with a laser pointer beam.

Using a sketchy and cheap Chinese laser pointer, a decent mirror(here provided by an old hard drive platter), and some water from a disgusting aquarium tank, you can create a powerful projection microscope at home. The water droplet itself provides the magnifying optics—using a smaller droplet will increase the magnification, but make focusing the laser a lot more frustrating. The image size can be increased just by increasing the throw distance of the laser. Here’s my setup– I used the straw to make perfectly round droplets by dipping the end in the aquarium, and I used the microfiber cloth to keep smudges off the mirror:

Materials

My materials

Laser Microscope Schematic

My setup of the laser pointer microscope. I used a hard drive platter as my mirror.

With the water from the aquarium, I can easily see amoebas and paramecia swimming around and interacting. Obviously the diffraction limit heavily applies to the quality of the image, but some sub-cellular structures are definitely visible within the amoebas:

A good thing to note is that some of the more geometric bodies that you see moving are actually very small organisms that are Rayleigh and Mie scattering in the laser light—the bodies themselves are too small to see, but they create a geometric interference pattern that appears to move with them through the water.

Scattering microscopy can also be applied to other transparent materials, such as glass and crystals, to reveal internal structures. A good one to try is a clear marble, preferably one with cracks on the inside. Here is a photograph of the laser through Icelandic spar, a variant of the common calcite crystal that exhibits complex double refracting behavior in standard lighting. The laser reveals the cleavage plane of the crystal quite nicely:

Calcite Interference Pattern

The “Icelandic Spar” variety of Calcite exhibits double refraction when held against a sheet of text; the laser light reveals that this is due to its orderly internal lattice structure.

What is a laser?

Laser light is coherent, meaning that all the photons that comprise it march in phase—they never interfere with one another because they all take the same steps at the same time. This is incredibly useful because it not only means that all the photons have the same frequency—they take the same number of steps per minute—but it also means that they take identical steps (or are in phase).

The reason is matters to the scientists is because, while light is indeed broken up into little particles of energy, these photons happen to act like waves in that they can interfere with one another and overlap, just as ocean waves give rise to complex eddies and lulls. Most light sources like incandescent light bulbs simply toss off photons with whatever phase and frequency happens to be most convenient, but lasers are designed to product barrages of photons that are coherent(have the same phase) and monochromatic(have the same frequency). This allows physicists to start out with no interference at all, and then to introduce various substances into the laser beam to see how they cause interference. Often the interference properties of a substance provide fundamental details about its microscopic structure.

The basic idea of lasers is that an electric field causes many atoms in a gas to reach an excited state, or a state in which their atoms have reconfigured their electronic structure in order to hold additional energy. Most atoms would prefer not to hold this additional energy for long, and so after some time they will decay into their ground(normal) state, releasing the energy that they were hoarding as a photon. The trick to this process is that only certain changes in electron arrangement around the nucleus are physically possible, and so only certain changes in energy are possible. This means that gases are predisposed to emit photons with identical energies because their electrons spontaneously absorb and emit only photons that correspond to the allowed variations in electron distributions. The energy of a photon is directly proportional to its frequency(and thus color) via Plank’s law, which is why we know that the blue part of a candle flame is much hotter than the yellow(low frequency) part. Most elements have characteristic colors that they emit light at, as each element has a unique atomic geometry and thus a unique set of acceptable electronic configurations about their nucleus. The study of the characteristic colors, or spectra, of chemicals is the basis of spectroscopy, which I discuss in my post on incandescence.

So lasers already have the monochromatic issue taken care of—they simply use a mixture of gases that ensures that atoms only spontaneously absorb and emit light at the desired color. But lasers are so powerful because they use stimulated emission— as a photon in a laser passes by an excited atom that has not yet released its energy, it can provoke it to release a photon that is moving perfectly in step with it. So in addition to being monochromatic, the light emitted from a laser is always coherent(in phase).

There’s a reasonable explanation for how this occurs: according to the Pauli Exclusion Principle(or lack thereof for bosons, of which photons are a subclass), it is impossible to tell photons with the same set of properties apart. The basis of this is that photons, unlike objects we encounter in the macroscopic world, are able to overlap like waves. So if I place two photons in the same place, and everything about the two photons is the same, then I can never tell them apart. If a photon in a laser flies by an excited atom and stimulates a photon with a random phase to be released, however, there are two possible ways for the new photon to be in phase, but only one way for them to be out of phase. The reason for this is that there are two axes along which the photons can agree or disagree, but by the Pauli Principle all the disagreements appear to be the exact same, single state. This is rather unintuitive, but minutephysics provides a nice example with a quantum coin flip. The phenomenon is known as the consolidation of eigenstates(eigen is a German prefix that means “terrible algebra”), meaning that there end up being more options for the photons to stay in phase than to go out of phase, resulting in the former being statistically favorable.

As a result, the number of photons in-phase gradually builds up until eventually the laser output is dominated by coherent light. d.

Stargazing with Binoculars

I live in a part of the United States that is relatively far south. As a result, throughout the year I get a chance to see a reasonably large number of constellations, although they are visible for much less time than they would be in the north. On a clear night (and from a high altitude) I can see most of the Argos, although most of its more interesting features and binary systems are unresolvable due to the large amount of atmosphere that scatters the starlight before it reaches me.

Regardless, I’ve had a bit of success using a pair of 16x50mm binoculars to pick out constellations. I think that binoculars offer a significant advantage over telescopes, particularly in urban and other light-polluted areas, because they often can offer equivalent resolution at a fraction of the cost and setup. Having a massive Newtonian telescope will only get you so far if the area that you live in doesn’t have fantastic night skies, so binoculars offer an easy way to learn a lot about the night sky. A good thing to keep in mind when choosing binoculars is that magnification does not matter– it can often even be a hindrance, since your eye is better at picking out details than you might think. Instead, a high magnification instrument is going to be extremely sensitive to minor shaking, making prolonged viewing needlessly tedious. Instead, you want binoculars with a ridiculously high resolution, which is a measure of the ability of an optical device to pick up detail. Think of this in terms of the difference between an iPhone display and an old Gameboy Advance: even though the latter had a much larger screen, you can simply see more on the iPhone because it has a much higher pixel density. Telescopes and binoculars are the same way– their resolution increases linearly with the radius of their aperture (ie, the big lens or mirror that collects all the light), so there’s a tremendous advantage to getting binoculars with large lenses.

Some telescopes on the market, particularly the slender refracting (lens-based) telescopes that you see in department stores, have decently large apertures but ruin them by having a very long body. Long bodies increase the magnification, but also increase optical aberrations like diffraction that degrade the image–resulting in a pitiable final resolution. Instead, the best telescopes and binoculars have very low ratios of focal length (the length the light travels before it reaches your eye) to the primary aperture diameter(the size of the lens or mirror that the light first encounters), a quantity known as the focal ratio . Most binoculars already have low f-ratios, but only fat reflecting telescopes (particularly Newtonian types) have decent f-ratios and thus image quality. Regardless, binoculars are clearly the best bet for amateur astronomy, simply because they are simpler to set up and give your brain two copies of the image to process. The ability to simply point them at whatever you are interested in viewing (and to stabilize them by pressing them against your head) is an additional benefit.

The best things to see with binoculars are open clusters and dense nebulae. M42, the gaseous Great Nebula in the sword of Orion, looks fantastic in the winter– even in the magnitude 4 skies around where I live, I can still still see the gaseous blue halo around the central trapezoid of young stars that comprise the sword. The diffuse blue nebula that surrounds the Pleiades is also visible most nights.

Ptolemy’s cluster in Scorpius is naked-eye visible and even more gorgeous in binoculars, and the Beehive Cluster in Cancer is great on Spring nights. There are lots of others, particularly the double cluster near Perseus and the Coathanger Cluster near the summer triangle, that are also well-suited to binocular observing.

Spring is the best time to view galaxies– while the Northern Hemisphere cannot see something quite as astounding as the Large Magellanic Cloud and its smaller sibling, we nonetheless get a great view of the Virgo Supercluster and Coma Berenices, two regions of the sky densely packed with galaxies(which appear as lovely blobs in the binoculars). M31, our neighboring Andromeda Galaxy, is also a great sight early in the year.

There’s tons of things that can be seen with the binoculars– most Messier objects can at least be discerned with binoculars(after all, our present day binocular optics rival the quality that Messier himself used). Good sources for lists of objects are BinoSky and Skymaps, the latter of which are very useful for finding one’s way around in the dark. If you are interested in showing other people objects through the binoculars, I would highly recommend obtaining a cheap and potentially unsafe imported laser— the green wavelength undergoes Rayleigh scattering at night, and so the length of the beam will be visible as it extends into the sky. It’s great to be able to literally point objects out on the celestial sphere, and the end of the beam can be seen through the binoculars(allowing you to guide observers towards Messier objects).

Sodium Metal Isolation: Electrolysis of Sodium Hydroxide

The compound in lye, sodium hydroxide, is among the most easily-accessible corrosive chemicals— a wide range of products ranging from Drano to specialty batteries contain it, despite it being the sort of substance that will happily make short work of your fingertips if you are not careful.

The reason the sodium hydroxide is so unreasonably caustic is not because it is acidic, but rather because it is so anti-acidic, or basic. While acids do have their fair share of malevolent uses—most notably to melt Coke cans—they only represent half of the story. Acids corrode things like metal because they love to toss protons at things they encounter, allowing them to provoke strange reactions in a wide variety of compounds. But bases are guilty of just the opposite; they steal protons from anything they come in contact with. Different materials will be more susceptible to acids or bases depending on their properties: while a metal might readily dissolve when exposed to an acid(usually because the acid’s protons encourage the metal to oxidize extra quickly), it might remain relatively inert when a base is applied to it. Likewise, organic compounds like cellular membranes are particularly susceptible to bases, making bases the reagents of choice for products like drain cleaner, which are used to break up the greasy globs of proteins that inhabit your kitchen sink after dinner. The susceptibility of organic tissue to bases is part of the reason why bases can be so dangerous.

As demonstrated by the familiar vinegar and baking soda volcanoes that annually discolor the floors of school gymnasiums nationwide, reactions between acids and bases are particularly vigorous. This makes sense, since one reagent is eager to steal a proton and another is eager to relinquish one. The products of acid/base reactions tend to be inert gases and water, making them extremely useful in bodily metabolic processes like digesting food.

A chemistry teacher once told me that half of all chemistry is simply keeping track of electrical charges. Acid/base reactions certainly seem to fall in this half. Thus it would seem natural that there are certain types of reactions that will only occur in the presence of an electric field, as not all compounds have the proclivity to exchange protons and electrons as acids and bases. Electrolysis reactions represent those charge exchanges that will not occur spontaneously unless abetted by an external electric field. These reactions generally only occur between metals within a conducting solution(like saltwater), because metals and ionic solutions are generally the best at conducting the DC currents necessary to sustain such reactions. Electrolysis and its variants are used in industry to plate metals with other metals, to etch designs without the need for a laser, and occasionally to isolate pure elements that tend to not exist in pure forms in nature—because the electric field puts so much energy into the reaction vessel, it allows otherwise unstable elements to be isolated.

The latter usage is quite beneficial to the home chemist—there are many great tutorials out there for making pure hydrogen and oxygen gases by running a battery through salt water. The reason I mention this usage of electrolysis in the context of acid base chemistry is because, one fine day in high school, I decided that it would be a prudent idea to heat sodium hydroxide to its melting point and then perform electrolysis with a high-current power supply. I wanted to isolate pure sodium metal, which has a variety of useful properties, and for this reason I was oblivious to the risks of running high power electrical current through boiling hot caustic lye. Here is the result, complete with Hollywood production values:

Here is what was supposed to happen: By running a cheap tube from a cooler filled with dry ice, I could pipe cold carbon dioxide into the melting crucible and displace any oxygen inside the chamber. This would supposedly suppress any fires from starting and keep side reactions in check. Supposedly, if I had done this perfectly, the molten sodium hydroxide would have reacted happily with the DC current and liberated a small amount of molten elemental sodium at one of the electrodes, which would have formed a shiny metallic pool at the top of the molten base.

Sadly, I seem to have undervalued the awesome power of bases. The molten sodium hydroxide will react with almost anything it can find, and so it begins to react with the metal sides of my melting vessel to yield samples of an intricate group of molecules known as “complex ions.” These are the sickening black substances that accrue inside my crucible—the molten sodium hydroxide normally should have remained transparent. The carbon dioxide seems to have done its job, as I still have all of my fingers, but the reaction nonetheless failed to yield an appreciable amount of sodium due to the complex ions’ interloping.

You can hear some sodium metal hissing as I drop the cathode into the pool of water at the end of the video, leading me to believe that a small amount of sodium was indeed liberated (and yes, I did wait for the cathode to cool before I dropped it in). The hissing is the sound of the elemental sodium aggressively recombining with water to form sodium hydroxide and hydrogen gas, the latter of which loudly deflagrates due to the heat of the reaction.

Nitrocellulose

A few weeks ago I tried to make nitrocellulose, with mixed results:

A large portion of common explosives— including TNT (trinitrotoluene) and dynamite (nitroglycerin)—have the key prefix “nitro” in them. This is not a coincidence; nitrogen groups, when added to benign organic compounds, tend to suddenly make them more reactive. The full chemistry behind this is complex, but a good thing to keep in mind is that nitrogen, when added to a compound consisting predominantly of carbon, has the net effect of destabilizing the electronic structure of the molecules. Carbon has four electrons, and so it likes to form four bonds with neighboring molecules—either in the form of four single bonds, two doubles, or a triple and a single. In the chemical theory of Lewis structures, this property is the basis of the “octet rule”: if we count each single bond as two electrons “paired together” with a covalent bond(with one electron coming from the carbon, and the other from whatever it bonds to), then carbon is content when it has eight electrons around it—four from itself, and four from the various things to which it bonds. Nitrogen, on the other hand, has five electrons when it is not bonded to any other atoms. But rather than always forming five bonds, nitrogen and most other atoms prefer to stick to the octet rule, and so two of nitrogen’s electrons form an internal bond within the molecule(called a lone pair), the members of which don’t bond to anyone outside the molecule. As a result, nitrogen usually ends up forming three single bonds or a single and a double bond, with its lone pair of electrons allowing it to still have eight total electrons. While there are some great exceptions to this covalent bonding scheme(much to the dismay of high schoolers everywhere), the Lewis octet rule for drawing covalent molecules provides great insight into the relative stability of chemical compounds.

While the Lewis structure rules give us excellent insight into how organic molecules bond, they don’t actually tell us what the molecule looks like at the atomic level. As quantum mechanics has predicted(and modern molecular imaging routines like NMR have verified), the structure of an organic molecule is heavily influenced by the addition strange atoms like nitrogen. Nitrogen has relatively high electronegativity, which means that it tends to attract electrons to itself. The derivation of why nitrogen and other gases(particularly diatomic gases like halogens, which tend to covalently bond in pairs to form compounds like O2 and N2) is rather complex(see Linus Pauling’s derivation, or consult Wikipedia’s summary of it), but it essentially involves the idea that certain atoms just accept electrons in bonds much more readily—the reasons involve nuclear shielding, dissociation energy, and a litany of other complex quantum effects. But the relevant result is that, even in large organic molecules the electrons tend to be slightly delocalized—they like to move into parts of the molecule beyond their bonding pair, where they traditionally would be expected to stay. The electronegative nitrogen atom tends to pull all of them very slightly towards itself, ensuring that every electron pair has slight asymmetry due to the pull of the nitrogen group. While this pull varies based in distance in the molecule, it has the net effect of destabilizing bonds throughout the molecule. This allows the organic molecule to fall apart much more easily, making the decomposition reaction explosively exothermic.

Thus nitration of organic compounds with nitric acid is a powerful way of making normal compounds become explosive. The reaction itself is often carried out in an ice bath with nitric acid, and it usually must be carefully monitored to prevent the nitrogen groups from substituting in for too many carbons in the compound(an effect known as “runaway nitration,” which either creates a more dangerous product or merely an inert product), as well as to ensure that the compound does not detonate prematurely. The above video shows the combustion of “guncotton,” which is the result of nitrating the cellulose polymers that comprise ordinary household cotton. For obvious reasons, this compound is known as “nitrocellulose.”

A key thing to notice is that the guncotton dissolves in acetone—ordinary cotton does not do this quite so readily. This is because the electronegative nitrogen succeeds in making parts of the cellulose molecules polar—because they attract some of the electrons towards themselves, the molecules are left with a positive and a negative end that was not present before they had nitrogen attachments. This polarity allows the highly polar acetone molecules to easily pick apart the polymer chains and dissolve the cotton. If the acetone is then allowed to evaporate, the polar molecules recombine into solid nitrocellulose in a manner similar to when sugar water evaporates and leaves behind rock candy.