a quasicrystal
/ KWAH-zee-cry-stal /
Imagine tiling a bathroom floor and being told you may only use tiles that never quite repeat — yet the whole floor still has a strict, beautiful, long-range pattern, and photographing it from far away gives crisp, sharp spots of light. That sounds impossible: order without repetition. A quasicrystal is exactly this made real in atoms. It has long-range order — atoms sit in fixed, predictable relationships across the whole solid — but it has NO periodicity: there is no unit cell you can copy-and-paste to build the crystal. It is ordered but not repeating.
How can we be sure it is ordered rather than random? Because it diffracts. Shine X-rays or electrons at a quasicrystal and you get a diffraction pattern of sharp, discrete spots (Bragg-like peaks), the fingerprint of long-range order — a truly random or glassy solid gives only diffuse haloes. But the spots are arranged with symmetries that a periodic crystal is FORBIDDEN to have: a clean ten-fold or five-fold star, or eight- or twelve-fold. The first, found by Dan Shechtman in 1982 in a rapidly cooled aluminium-manganese alloy, showed a ten-fold electron-diffraction pattern so shocking that it took years to be believed; it won the 2011 Nobel Prize in Chemistry. The atoms fill three-dimensional space following a rule like the Penrose tiling: two or more building blocks packed in a fixed but non-repeating sequence governed by an irrational ratio, the golden mean tau = (1 + sqrt 5) / 2 = 1.618... .
Why does this matter beyond being a curiosity? Because it forced science to redraw the definition of a crystal. For two centuries a crystal MEANT a periodic array; quasicrystals proved order and periodicity are not the same thing, and the International Union of Crystallography rewrote the definition to be any solid with an essentially discrete diffraction pattern. Real icosahedral quasicrystals (Al-Cu-Fe, Al-Pd-Mn) are hard, slippery, poor conductors of heat and electricity despite being metals, and a natural quasicrystal has even been found in a meteorite. They are the clearest proof that nature's order is richer than the 230 space groups allow.
Shechtman's original electron-diffraction pattern of Al-Mn shows ten bright spots arranged in a perfect decagon, with more spots nested inside at ratios of tau = 1.618. The spots are sharp — proof of long-range order — yet no periodic lattice on Earth can produce ten-fold symmetry. That single photograph broke a 200-year-old rule.
A quasicrystal: sharp diffraction (long-range order) with a forbidden ten-fold symmetry (no periodicity).
A quasicrystal is NOT a glass and NOT a defective ordinary crystal. Its diffraction spots are genuinely sharp (long-range order), it simply has no unit cell. 'Ordered' and 'periodic' turned out to be two different things.