Once we understand how it is that atoms bond together, we can examine what types of matter can be formed. This chapter will give a very brief and obviously crude, but obligatory, overview of some of these types of matter.
Atoms can obviously bond together the form regular crystals. A crys-tal is made of small units reproduced many times and built into a regular array. The macroscopic morphology of a crystal can reflect its under-lying structure (See Fig. 7.1). We will spend much of the remainder of this book studying crystals.
Fig. 7.1: Left: Small units repro-duced periodically to form a crystal.
This particular figure depicts NaCl (ta-ble salt), with the larger spheres being Cl− ions and the smaller spheres be-ing Na+ions. Right: The macroscopic morphology of a crystal often will re-flect the underlying microscopic struc-ture. These are large crystals of salt (also known as halite). Photograph by Piotr Wlodarczyk, used by kind per-mission.
It is also possible that atoms will bind together to form molecules, and the molecules will stick together via weak van der Waals bonds to form so-called molecular crystals (see Fig. 7.2).
Fig. 7.2A molecular crystal. Left: 60 atoms of carbon bind together to form a large molecule known as a buckyball.1 Right: the buckyballs stick together by weak van der Waals bonds to form a molecular crystal.
1The name “buckyball” is a nickname for Buckminsterfullerene, named after Richard Buckminster Fuller, the famed developer of the geodesic dome, which buckyballs are supposed to resemble; although the shape is actually precisely that of a soccer ball. This name was chosen by the discoverers of the buckyball, Harold Kroto, James Heath, and Richard Smalley, who were awarded a Nobel Prize in chemistry for their discovery despite their choice of nomenclature (probably the name “soccerballene”
would have been better).
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Fig. 7.3Cartoon of a liquid. In liquids, molecules are not in an ordered configu-ration and are free to move around (i.e, the liquid can flow). However, the liq-uid molecules do attract each other and at any moment in time you can typi-cally define neighbors.
Another form of matter is liquid. Here, atoms are attracted to each other, but not so strongly that they form permanent bonds (or the tem-perature is high enough to make the bonds unstable). Liquids (and gases)2 are disordered configurations of molecules where the molecules are free to move around into new configurations (see Fig. 7.3).
Fig. 7.4. Molecular structure of an amorphous solid: Silica (SiO2) can ei-ther be a crystal (such as quartz) or it can be amorphous (such as win-dow glass). In this depiction of amor-phous silica, the Si atoms are the lighter shaded atoms, each having four bonds and the O atoms are the dark atoms, each having two bonds. Here the atoms are disordered, but are bonded together and cannot flow.
Somewhere midway between the idea of a crystal and the idea of a liquid is the possibility of amorphous3solids (including glasses). In this
3The word “amorphous” is from Greek, meaning “without form”.
case the atoms are bonded into position in a disordered configuration.
Unlike a liquid, the atoms cannot flow freely (see Fig. 7.4)
Many more possibilities exist. For example, one may have so-called liquid crystals, where the system orders in some ways but remains dis-ordered in other ways. For example, in Fig. 7.5.b the system is
crys-2As we should have learned in our stat-mech and thermo courses, there is no “fundamental” difference between a liquid and a gas. Generally liquids are high density and not very compressible, whereas gases are low density and very compressible.
A single substance (say, water) may have a phase transition between its gas and liquid phase (boiling), but one can also go continuously from the gas to liquid phase without boiling by going to high pressure before raising the temperature and going around the critical point (going “supercritical”).
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talline (ordered) in one direction, but remains disordered within each plane. One can also consider cases where the molecules are always ori-ented the same way but are at completely random positions (known as a “nematic”, see Fig. 7.5.c). There are a huge variety of possible liquid crystal phases of matter. In every case it is the interactions between the molecules (“bonding” of some type, whether it be weak or strong) that dictates the configurations.
Fig. 7.5 Cartoon of liquid crystals.
Liquid crystals have some of the erties of a solid and some of the prop-erties of a liquid. (a) The far left is a crystal of molecules—all the molecules are positionally ordered and all are ori-ented in the same direction. (b) In the middle left picture the molecules re-tain their orientation, and rere-tain some of their positional order—they group into discrete layers—thus being “crys-talline” in the vertical direction. But within each layer, they are disordered and even can flow within the layer (this is known as a smectic-C phase). (c) In this figure, the positional order is lost, the positions of the molecules are ran-dom, but the molecules all retain their orientations (this is known as a nematic phase). (d) On the far right, the sys-tem is a true liquid, there is no posi-tional order or orientaposi-tional order.
One can also have so-called quasi-crystals which are ordered but non-periodic arrangements. In a quasi-crystal, such as the one shown in Fig. 7.6, component units are assembled together with a set of regu-lar rules which appears to make a periodic structure, but in fact the pattern is non-repeating.4 Although quasicrystals made of atoms are
extremely rare in nature,5 many man-made quasicrystalline materials 5The first naturally occuring quasicrys-tal was found in 2009. It is believed to be part of a meteorite.
are now known.
Fig. 7.6This quasicrystal, known as Penrose tiling, can be assembled by fol-lowing a simple set of rules. While the pattern looks regular it is actually non-periodic as it never repeats.
4The fact that chemical compounds can have regular but non-repeating structures was extremely controversial at first. After discovering this phenomenon in 1982, Dan Shechtman’s claims were initially rejected by the scientific community. The great Linus Pauling was particularly critical of the idea (see margin note 5 in Chapter 6) Eventually, Shechtman was proven right and was awarded the Nobel Prize in chemistry in 2011.
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One should also be aware of polymers,6which are long chains of atoms.
Examples include DNA, collagen (see Fig. 7.7), polypropylene, etc.
Fig. 7.7Cartoon of a polymer. A poly-mer is a long chain of atoms. Shown here is the biological polymer collagen.
And there are many more types of condensed matter systems that we simply do not have time to discuss.7 One can even engineer artificial
7Particularly interesting are forms such as superfluids, where quantum mechan-ics dominates the physmechan-ics. But alas, we must save discussion of this for another book.
types of order which do not occur naturally. Each one of these types of matter has its own interesting properties and if we had more time we would discuss them all in depth! Given that there are so many types of matter, it may seem odd that we are going to spend essentially the entire remainder of this book focused on simple crystalline solids. There are very good reasons for this however. First of all, the study of solids is one of the most successful branches of physics—both in terms of how completely we understand them and also in terms of what we have been able to do practically with this understanding. (For example, the entire modern semiconductor industry is a testament to how successful our understanding of solids is!) More importantly, however, the physics that we learn by studying solids forms an excellent starting point for trying to understand the many more complex forms of matter that exist.
References
• Dove, chapter 2 gives discussion of many types of matter.
• Chaikin and Lubensky gives a much broader discussion of types of matter.
6Here is a really cool experiment to do in your kitchen. Cornstarch is a polymer—a long chain of atoms. Take a box of cornstarch and make a mixture of roughly half cornstarch and half water (you may have to play with the proportions). The concoction should still be able to flow. If you put your hand into it, it will feel like a liquid and be gooey. But if you take a tub of this and hit it with a hammer very quickly, it will feel as hard as a brick, and it will even crack (then it turns back to goo). In fact, you can make a deep tub of this stuff and although it feels completely like a fluid, you can run across the top of it. (If you are too lazy to do this, try Googling “Ellen cornstarch” to see a YouTube video of the experiment. You might also Google “cornstarch, speaker” to see what happens when you put this mess on top of an acoustic speaker.) This mixture, sometimes known as “Oobleck” in a nod to Dr. Seuss, is an example of a “non-Newtonian” fluid—its effective viscosity depends on how fast the force is applied to the material. The reason that polymers have this property is that the long polymer strands get tangled with each other. If a force is applied slowly the strands can unentangle and flow past each other. But if the force is applied quickly they cannot unentangle fast enough and the material acts just like a solid.