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Quasicrystals

August 10, 2012

Recent news stories have mentioned the discovery of naturally-occurring quasicrystals. The discovery of man-made quasicrystals was enough to garner a Nobel Prize for Dan Schechtman. What is the big deal?

Truth be told, I hadn’t been paying attention to quasicrystals.  I’m more interested in the structure of melts, glasses, and more mundane crystals found in igneous rocks. But the picture of a man-made quasicrystal stopped me in my tracks.

This doesn’t happen very often. I heard Duane Allman playing slide guitar live when I was kid, not old enough to get into the concert … What is that sound?  In some of the first results from the Mars rover, years ago, a Martian rock was found to be an andesite. What? Andesites on Earth are associated with active orogenic arcs. They are there because of plate tectonics, but on Mars?  I stopped at the rock on the Olivia Raney Library Building on the corner of the Fayetteville Street Mall and West Morgan Street. Wait, that’s not right… The rock is a rapikivi granite (also known as the countertop material Baltic Brown), formed in unusual circumstances with rounded feldspars mantled by plagioclase, the reverse of what is usually found. I’m not the first geologist to be brought up short by rapikivi granite.

Now, the pictures of a quasicrystal were not right.  Very not right.  The crystal faces have 5 sides.  That is fairly uncommon in nature, especially in a crystal as nice as that one.  So I went to the original article and found something  impossible:  fivefold symmetry. There is twofold, four-, six- , eight-, and twelvefold symmetry. There is threefold symmetry, but not fivefold symmetry. This is not a new idea. The mathematics of crystal symmetry were worked out in the 19th Century, and still form the basis for a lot of crystallography and spectroscopy.

Research on the atomic arrangements of quasicrystals showed that the kind of order we expect in natural crystals wasn’t there. It was almost there, but not quite. You couldn’t perfectly stack layers of the quasicrystal on top of each other.  They would almost fit, but not quite. It may not seem like a big deal, but this line of research lead to the Nobel Prize. First, there’s figuring out what Mother Nature did, then there’s figuring out ways to fool Mother Nature into doing what she may not want to do.

This highlights the importance of museum collections. The natural quasicrystal was found in the collection of the Museo di Storia Naturale of the Università degli Studi di Firenze in Florence, Italy, leading to a search that resulted in one and a half tons of materials being panned by hand.  Minerals and rocks in museum collections present a huge number of combinations of chemical elements fit (or misfit) into a large number of crystal structures. Why should a materials scientist kill themselves trying to make some of these when nature has already grown them? People who are interested in storing radioactive waste want to know what happens to the material after thousands or millions of years of radiation exposure. Metamict minerals contain radioactive elements. Radioactive decay produced radiation over the eons, which totally disrupted the crystalline structure of the mineral. Why expose yourself to radiation when nature has already conducted the experiment for a lot longer than you can? The minerals are there in the collections.

I work on apatite minerals, a calcium phosphate mineral akin to your teeth and bones but also of interest in radioactive waste disposal, fertilizer, biomaterials engineering, industrial phosphors and fast ion conductors.  A lot of early spectroscopy on the apatites yielded uncertain results because the powders precipitated from water at low temperature didn’t make nice crystals. When I started with apatite spectroscopy, I went to Dr. Carl Francis at the Harvard Mineralogical Museum to get the biggest crystals I could find.  I grow my own now.

Growing crystals forms the backbone of much of what we know about igneous rocks. I do nothing special by the standards of the science, but I can grow minerals at pressures up to those of the upper mantle, and at temperatures up to 1500°C.  In my lab at the Museum of Natural Sciences, I have equipment that allows temperatures to 900°C and pressures about 2000 times atmospheric pressure.

The paper on the natural quasicrystals shows that the associated minerals come from a meteorite, most likely the very rare CV3 meteorites. One quasicrystal was found in a grain of stishovite, which is a quartz polymorph that only forms at very high pressures. So the quest to grow quasicrystals starts again. What is the secret of the meteoritic environment that makes a quasicrystal?  High temperature plus vacuum? Transient high temperature and very high pressure from shock metamorphism caused by asteroid collision, plus vacuum?  How does one build that?  And where do we find some more of those?

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2 Comments leave one →
  1. Lysa Chizmadia permalink
    August 10, 2012 6:36 pm

    Greetings Dr. Tacker,

    You are correct in that there has never been any 5-fold rotational symmetry observed in inorganic crystals. However, your crystallographic analysis of the pyritohedron in the picture is flawed. Pyritohedrons, like other crystallographic forms do indeed have five-sided faces (many crystals with pyramid terminations often show five-sided faces, with c-parallel faces longer than the other three, e.g. {1bar100} in quartz). Nevertheless, the pentagonal faces in pyritohedra are not regular; their dimensions are more similar to home plate in a baseball diamond. Pyritohedrons (named after the mineral pyrite) do not have any five-fold rotational symmetry; they have 3 mirror planes, 3 2-fold rotational axes (on the three a-axes) and 4 3-fold rotoinversions. The point group is 2/m(bar3), indicating that there is in fact no five-fold symmetry. In fact, this point group has the lowest symmetry content in the isometric crystal system.

    Hope this helps.

    Sincerely,
    Dr. Lysa Chizmadia
    University of Puerto Rico
    Department of Geology

    • August 13, 2012 2:19 pm

      I revised the blog to make it clearer: the five-sided crystals were unusual enough that they caught my eye, and so I went to the original paper, where they demonstrated five-fold symmetry, something forbidden by classical crystallography.

      I’ll post a picture of pyrite with five sided faces in hopes that it will clarify the rest of Dr. Chizmadia’s comment for everyone else.

      Cheers,
      Chris

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