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Crystal Prototypes

June 29, 2017

While we're generally oblivious to the fact, our kitchen tables are hosts to thousands of crystals in the form of sugar and table salt. The crystal habits of these miniature crystal grains can't be seen without a microscope, but the common elementary school science fair project of growing rock candy produces larger crystals of sugar. The growth of rock candy is a good introductory experiment for children, and it will teach them patience as well as a little science, since the process takes several days.

Although great latitude in measurement is tolerated, the precise recipe is to dissolve 476 grams of sucrose (C12H22O11) in 100 mL of water at 100°C. The crystal will grown on a stick, some string, or some yarn, the growth driven by the lower solubility of sucrose at room temperature (200 grams/100 mL). Some instructional videos can be found on YouTube.[1-2]

Since natural processes, such as crystal growth, can proceed over long periods, nature occasionally gives us huge crystals. The so-called Cave of the Crystals in Naica, Chihuahua, Mexico, contains huge crystals of gypsum (calcium sulfate dihydrate, CaSO4·2H2O), one of which is nearly forty feet in length (12 meters), weighing 55 tons. The cave crystals grew to such a huge size over the course of half a million years.

Figure caption
Left image, gypsum crystals in the Naica "Cave of the Crystals." Compare in size with the person shown in the lower right-hand corner. Right image, Title Melencolia I, a 1514 engraving by Albrecht Dürer (1471–1528), now located at the Staatliche Kunsthalle Karlsruhe. Aside from the truncated rhombohedron[3] that looks like a large crystal growing out of the Earth, this engraving also contains a 4x4 magic square based on the number 34. It should have been based on the number 42. (Left image, by Alexander Van Driessche, and right image via Wikimedia Commons, Click for larger image.)

As I wrote in a previous article (Earth's Mineral Wealth, October 19, 2015), a team of mineralogists led by Robert Hazen from the Carnegie Institution for Science (Washington, DC) found that the Earth contains 4,831 known minerals, as sampled from 135,415 locations. Their analysis of the diminishing discovery rate indicates that there are perhaps 1,563 minerals yet to be discovered, for a total of 6,394.[4-5]

Minerals are natural crystals; and, at the dawn of mineralogy, minerals were identified by their crystal habit and other attributes, such as color. Theophrastus (c. 371 - c. 287 BC) wrote a mineralogy book, "On Stones," around 300 BC, but this book primarily describes how minerals are processed and used.[6]

However, Pliny the Elder's Naturalis Historia (77 AD) describes crystal habit, including the octahedral shape of diamond. Book XXXVII of his History is devoted to rock crystals, amber, gemstones, and semi-precious stones. Pliny did have some strange ideas of how some of these form, as the following excerpt shows.[7-8]

Contraria huic causa crystallum facit, gelu vehementiore concreto. Non aliubi certe reperitur quam ubi maxime hibernae nives rigent, glaciemque esse certum est, unde nomen graeci dedere.
Crystal is made by a different process, solidified by forceful gelation. It is not found in great quantity in places other than where the winter snow freezes to the greatest extent, so it is certainly a type of ice, and it is called that in Greek.

The start of Chapter IX, Book XXXVII of Pliny's Naturalis Historia. Here, Pliny describes quartz (called crystal). It's interesting how science has developed beyond using such analogy to describe ontology. (Latin text via the University of Chicago Penelope Web Site. The translation is my own.)

Georgius Agricola (1494-1555) is called the "the father of mineralogy," an honor based on his voluminous "De re metallica," published in 1556. As its title suggests, this book is concerned mostly with metal ores; and, like Theophrastus, the emphasis is on technology rather than science.

At the end of the Middle Ages, about 350 minerals had been described in varying detail in such texts. How does a modern mineralogist deal with the nearly 5,000 minerals discovered to date? The most common types, iron pyrite, for example, are easily identified by their crystal habit and color (see photo), and the rare types are distinguished by a variety of analytical techniques. These include X-ray and electron diffraction, and compositional analysis by X-ray spectroscopy and mass spectrometry. Armed with detailed information, it's time to access the various crystal databases.

Cubical pyrite crystalscubical pyrite crystals from Logroño, Spain, displayed at the Musée cantonal de géologie de Lausanne, Lausanne, Switzerland.

(Photo by "Rama," via Wikimedia Commons.)

In the past, this would mean plowing through Strukturbericht or similar reference books. Today, this means accessing some online databases, one of which was the Crystal Lattice Structures website maintained until 2010 by the US Naval Research Laboratory. This database, still accessible on some mirror sites,[9] contained nearly 300 crystal structures, including a majority of crystal structures with the venerable Strukturbericht designations.

Now, a team of scientists from the Naval Research Laboratory (Washington DC), Duke University (Durham, North Carolina), NRCN (Beer-Sheva, Israel), St. Olaf College (Northfield, Minnesota), and Brigham Young University (Provo, Utah) have published an updated version of the database that now included 288 standardized structures in 92 space groups.[10-12] There is a companion website for the database, which provides a complete description of each structure, formulas for their primitive vectors, and all of their basis vectors. The website, located at http://aflow.org/CrystalDatabase, also contains tutorials on crystal systems, space groups, primitive and conventional lattices, Wyckoff positions, Pearson symbols and Strukturbericht designations.

The original NRL Crystal Lattice Structures web site was launched in 1995 by Michael Mehl, a scientist at the U.S. Naval Research Laboratory, as a resource for his colleagues.[11] As Mehl, now at the United States Naval Academy, explains, "The library showed how crystallography relates to crystals in the real world... It also gave a broad overview of structures seen experimentally, which is always a good place to start looking for something new."[11] The NRL web site was removed after security upgrades to the NRL Internet, and its growth over the decades had made it unnecessarily complicated.[11]

Figure captionThe Strukturbericht A15 crystal structure, with Cr3Si as an example.

An important superconductor, Nb3Sn, discovered in 1954, has the A15 structure.

(Via AFLOW Crystal Database. Click for larger image,)

With Mehl's help, Stefano Curtarolo, a professor of mechanical engineering and materials science at Duke University, and other scientists decided to put all the information together into a paper and relaunch an improved open-source version of the website.[11] The published paper, subtitled, "Part I," contains the information of the original website in an improved format.[10] This paper has 288 entries for various crystalline structures, it contains generic mathematical equations describing the placement of atoms in the crystal, and it's 833 pages long.[11]

says Cormac Toher, an assistant research professor of mechanical engineering and materials science at Duke University,
"Having the equations for the atomic placements written out gives more flexibility to include slight variations and to specifically tune each structure... We're also going to have a 3D viewer of the structures at the top of each entry so that people can see the structures at different angles."[11]

Each entry in the database is linked to the AFLOW library of the Duke Center for Materials Genomics, an online database that lets users predict the properties of hypothetical binary and ternary materials.[11] Online visitors can populate a particular crystal structure with atoms of selected elements, and the program will compute the likely material properties.[11] This research was funded by the Office of Naval Research, and the Department of Energy.[11]


  1. Homemade Maple Rock Candy (Sugar Sticks), YouTube Video by Mr Eastcoastman, December 20, 2013.
  2. How to Make Rock Candy (No Bake Recipe), YouTube Video by Cookies Cupcakes and Cardio, November 26, 2014.
  3. Hans Weitzel, "A further hypothesis on the polyhedron of A. Dürer's engraving Melencolia I," Historia Mathematica, vol. 31, no. 1 (February, 2004), pp. 11-14, https://doi.org/10.1016/S0315-0860(03)00029-6.
  4. Robert M. Hazen, Grethe Hystad, Robert T. Downs, Joshua Golden, Alex J. Pires, and Edward S. Grew, "Earth's “missing” minerals," American Mineralogist, vol. 100, no. 10 (October, 2015), DOI: 10.2138/am-2015-5417. A PDF version can be found here.
  5. Earth's mineralogy unique in the cosmos , Carnegie Institution Press Release, August 26, 2015.
  6. Earle Radcliffe Caley and John F. C. Richards, Eds., "Theophrastus on Stones: Introduction, Greek Text, English Translation, and Commentary," Ohio State University Press (Columbus, 1956), PDF file.
  7. Pliny the Elder: the Natural History, Chapter XXXVII, Latin text at the University of Chicago Penelope Web Site.
  8. Pliny the Elder, The Natural History, Book 37, John Bostock and H.T. Riley, Trans., Taylor and Francis (London:1855) at the Tufts University Project Perseus Web Site.
  9. Mirror of NRL Crystal Lattice*Structures Web Site.
  10. Michael J. Mehl, David Hicks, Cormac Toher, Ohad Levy, Robert M. Hanson, Gus Hart, Stefano Curtarolo, "The AFLOW Library of Crystallographic Prototypes: Part 1," Computational Materials Science (In Press, May 22, 2017), DOI: 10.1016/j.commatsci.2017.01.017. Also available on arXiv.
  11. Ken Kingery, "D.I.Y. Crystal-Makers Get Refurbished Online Cookbook," Duke University Press Release, June 2, 2017.
  12. Library of Crystallographic Prototypes on the AFLOW Web Site.

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