There is nothing superficial about surfaces. While there are many objects that appear smooth, most of what we see is all about nooks and nicks, crannies and pores, pleats and folds, imperfections and inconsistencies, hooks and dips, bumps and craters. We live in a world of beautiful deformations, of breath-taking imperfections, and we should celebrate all of them. Simultaneously. In one globally cavitating “YAWP!” at least once a day.
I first read about close packed structures in high school. I found it fascinating. I can’t explain being fascinated. It is one of those dovetailing moments when your own individual, completely unique brain that is also just like all the other human brains finds something that it likes for whatever impossibly complicated reason and latches onto it. It is a concept with which all of you have more familiarity than you think.
Have you ever shopped for oranges? Not just an orange but a box of oranges. The first layer sits in the box and reveals a uniformity of depressions where each orange touches two (at the corners) or three (at the sawtooth edges) or four (at the straight edges) or six (anywhere besides the places above). Those depressions are an invitation to add another layer of oranges. Or not. You can add that next layer to the enticing curve-edged triangles that have appeared between oranges or you can add them directly above the oranges you’ve already added to your box. If you add them to the dips between oranges, you are making a close packed structure of oranges and they will all sit very comfortably in those dips until you get them home, their imperfect skins pressed against their friends like tiny butts in triangular swing seats.
From this illustration, you see the first, second and third layers and two possible arrangements: hexagonal close-packed (left) and face-centered cubic or cubic close-packed arrangement (right). So orderly! So nice!
The thing is that nature is not orderly and nice. What happens to the stacks of oranges if we add in a grapefruit in one of the layers, right in the middle, and then a couple of divots later we add in a grape or seven? Then we add a variety of apples, plums. and kiwi fruit on top of that? Let’s put a cantaloupe into our lattices, but keep piling up and pushing in the oranges wherever spaces are left. And we do this kind of craziness, not for two or three layers, which would still be a sub-microscopically thin collection of atoms (but a good box of fruit); we go for a trillion cubic layers of atoms (the fruit thing has just become an impossible and fairly useless analogy; let’s put them all back in the grocery already). Atoms don’t always sit in a single layer with other identical atoms. Atoms are paired (or tripled, etc.) with disruptors to these simple lattices (“lattices” is what these formations of atoms are called). Sodium atoms (ions actually, but that is a rat hole I will not go down – yet) are paired with chloride ions (still atoms, just with an additional electron, stolen (perhaps) from the sodium). Sodium and chloride – atom center to atom center – has a lattice constant of 564 picometers (5.64×10-10) meters, a very small but critical distance that helps make those nice cubic crystals you see when you look at a grain of salt with sufficient intent. If you grow your sodium chloride crystals in a vacuum from absolutely pure water that includes nothing but pure sodium and pure chlorine, they will probably be gems of perfection. If they grow in the real world – on a beach or rocky shore at the high tide line or in evaporation ponds used since pre-history to harvest salt, those little crystals will probably include other ions. These are called inclusion impurities or coprecipitates. They may be ions or organic substances that got muscled into the crystallization process in spite of their differences or they may have sufficient affinity with one or another of the primary ions in the substance to bind simply because no energetic reason not to do so. The shape of the crystals will not be so perfectly face-centered cubical and their color might even shift, depending on what is included and to what extent.
In virtually any water you can imagine except the purest water (but we might as well start talking about unicorns now), sodium ion, which has given up an electron to have a single positive charge, a single electron-shaped absence in its uppermost and typically populated energy level, badly wants to fill that hole with almost any substance that comes along with a spare electron in its uppermost and fully populated energy level (we’ll just put the concept of energy levels aside with the notion of ions, although we are now revisiting ions after I promised to delay them). If a fluoride or bromide or iodide atom floats by, they will fill the bill quite nicely but water molecules will do the job by pairing its comparatively electron-rich oxygen (negatively charged) with the momentarily electron-poor sodium ion (positively charged). The water is just lending its cloud of electrons through a process called hydrogen bonding, illustrated forthwith:
Schematic representation of the aqua ion [Na(H2O)6]+.
Instead of this “flat” representation, the sodium ion sits at the center base of two four-sided pyramids defined by the oxygens from the water molecules; this is known as an octahedron. To illustrate, we have the structure on the right, although instead of rubidium ion (Rb+) at the center we have sodium ion (lithium is smaller and only requires four waters for its solvation shell, thus forming tiny floating tetrahedrons all linked to other tetrahedrons through other waters).
To further illustrate, here is a stripped-down diagram of six waters binding to an ionized metal (M) at the inner center of the octahedron. The diagram also shows how this hydrogen bonding continues by oxygens in the next sphere out from the metal binding through the hydrogens in the waters affiliated with the metal ion.
But again I have digressed! Water – pure, unadulterated by absolutely anything water – will dissolve anything onto which it can place its tiny hydrogen bonding mittens. If no sodium ion (or any of the other group 1 alkali metals) is available, a group 2 alkali earth metal – or almost any ionizable metal from the transition metals or lanthanides or real-world actinides will suffice, thank you. And we haven’t even touched on all of the polyatomic ions that water will cluster about like electronically ambiguous fanatics looking to rub shoulders with their i(c)ons. Water will grab anything with an electron or more missing and will grab anything with extra electrons as well. If there is soluble lead in a water pipe, the lead is grabbed by water and whisked along to your tap. It will grab organic compounds (table sugar, vitamin C, short-chain alcohols and acids, for instance), charged or not, to the extent that they are mixable (miscible) with water; if the organic compounds aren’t miscible, they will form a very tight interface. You have probably seen this interface in oil-vinegar salad dressing, although that is an imperfect example. If you have some mineral oil in the medicine cabinet, remind yourself what an immiscible interface looks like.
To provide a visual example, the following is a photograph of air bubbles in foam. Notice the irregularity of the bubbles. This is not exactly like imperfections in crystals or dissolved substances, but will suffice as an analogy to the irregularity of materials dissolved in water. All water-metal solvation does not form octahedrons and not all waters surround positively-charged ions; they also surround negatively-charged ions, neutral materials, and are surrounded by other waters as well. It’s messy.
Order and chaos of air-bubbles in a foam: from order to chaos or from chaos to order? Hexagonal packing of spheres due to regularly sized spheres, transitioning to disorder due to spheres of differing size.
If water has a difficult time being pure, what about the rest of the world? The rest of the world is more like the composition of minerals than it is about absolute purity and pristine structures. What do I mean? Here is a mineral, or rather here is a photograph of at least three minerals (Uvarovite, Malachite, Azurite) sharing space.
Uvarovite has the chemical formula Ca3Cr2(SiO4)3. Malachite’s formula is Cu2CO3(OH)2. Azurite goes by the alias Cu3(CO3)2(OH)2. When they are blended together as they are in this formation, bits of each stick into the lattices of the other – a copper (Cu) infiltrating the chromium (Cr), a silicate ion ([SiO4]4−) latched onto a copper, an hydroxide (OH–) here, a carbonate (CO32-) there, an intrusion of calcium (Ca2+) toying with the affections of a carbonate, although there may be patches that are as pure as nature allows. And there is always the promiscuous water molecule and its tendency to complicate matters with its waters of hydration to consider. See the wave-like shapes in the chunk of history above? There’s a really good chance that this occurred because the various minerals were once suspended in water and somewhat slowly, for whatever reason, the water dried out or the minerals were in a sufficiently concentrated solution that they precipitated out. The blue stuff in the middle? See the little bumps? Those are tiny crystals. This is where all the stuff about water solvating various ions of various sizes and the solid surfaces of rocks kind of come together.
And this is the sort of world that surrounds us. A world of appearances that are far more complicated than they seem. Surfaces that are even more complicated than diligent study reveals. Scientists, after all, are looking for rules, patterns, predictability (however chaotic at first blush the predictability may seem) at the heart of the messiness. It would not make sense to take an item like the pictured jumble of minerals and break it down – the only unique “it” that “it” is – and determine EXACTLY how all of the minerals fit together and where the inconvenient atom that is “none of the above” has interloped into something already impossibly complex. The scientist studying any facet of the universe looks for the through-line that links the messy with its fundamental characteristics and helps us understand what a predictable, impossible universe surrounds us.
(Updated, extended, clarified, polished, and propagated afresh: 12:21PM EDT Aug 12, 2016).
(Further updated with the addition of the following videos 7:15PM EDT Aug 12, 2016).
Hydrogen bond rearrangement dynamics in liquid water by molecular dynamics simulation. 1 second in the movie corresponds to 1 picosecond in reality. The blue spheres represent oxygen, aqua spheres represent hydrogen and the yellow connectors represent hydrogen bonds.
Featured Image: https://commons.wikimedia.org/wiki/File:Ductile_Iron.png