Natural quasicrystal found in a museum specimen

The hallmark of a conventional crystal such as table salt is translational symmetry; a single unit cell repeats at regular intervals. That defining symmetry imposes long-range correlations, but it also greatly restricts the rotational symmetry that crystals can exhibit. Celebrated theorems nearly 200 years old permit only two-, three-, four-, and sixfold symmetry axes.

Quasicrystals do not have the translational symmetry of crystals, but they do have a subtle long-range order. Along any symmetry axis of a quasicrystal, the placement of atoms can be expressed as a sum of two or more periodic functions. But the wavelength ratio for any two of those functions is irrational, and as a result, no single periodic function can represent the atomic positions. The atoms’ quasiperiodicity—indeed, “quasicrystal” is short for quasiperiodic crystal—implies long-range correlations and, as with conventional crystals, allows quasicrystals to display sharp, structure-revealing diffraction patterns. The freedom from translational invariance enables quasicrystals to have a wealth of rotational structures not allowed in crystals; the first quasicrystal to be discovered, for example, displayed fivefold symmetry axes (see reference and Physics Today, February 1985, page 17 ).

To date, more than 100 quasicrystal specimens have been synthesized in the laboratory. Now Luca Bindi of the Natural History Museum of Florence in Italy, Princeton University’s Paul Steinhardt, and colleagues from Princeton and Harvard universities have reported the first observation of a natural version of one of those quasicrystals ² —icosahedral Al₆₃ Cu ₂₄Fe₁₃. The material, a 100-µm grain, is from a mineral assemblage (left figure) now housed in the Florence museum, where it is listed as coming from the Koryak region of far-eastern Russia. The main component in the assemblage is khatyrkite (CuAl₂), but the sample also includes cupalite (CuAl) and other minerals.

The search that led to the natural quasicrystal began about 10 years ago. By that time the International Centre for Diffraction Data (ICDD) had published a catalog of 80 000 x-ray powder diffraction patterns obtained from both synthetic materials and minerals. Because the smashed-up crystals of a powder have random orientations, the sharp diffraction spots that one would obtain with a pure crystal or quasicrystal are smeared into circles. Nonetheless, one might hope that the spacing of the circles would reveal the underlying symmetry of the powdered material. Could the ICDD database be systematically explored and possible quasicrystal candidates identified?

That was the challenge Steinhardt posed a decade ago to Peter J. Lu, then his undergraduate thesis student. Lu rose to the task, and in 2001 he, Steinhardt, and two other Princeton colleagues announced the results of their systematic search through the ICDD catalog, including a list of quasicrystal candidates that merited further study. ³ At the end of the paper, Lu and Steinhardt invited anyone with a plausible quasicrystal candidate to get in touch with them for possible collaboration. Two years ago Bindi took them up on their offer: After a painstaking search through numerous minerals and consultations with his US-based colleagues, he identified the Florence museum’s khatyrkite sample as possibly hosting a quasicrystal. The US team then probed a small piece of it with transmission electron microscopy. Diffraction patterns such as the 10-fold symmetric pattern shown in the right figure identified quasicrystal regions. Subsequent x-ray fluorescence analysis of pure quasicrystal grains determined the material’s chemical formula.

Geologists and physicists have much to learn about the conditions under which quasicrystals form. The study of natural materials can help address that question and may turn up new, never previously contemplated structures.