Natural Quasicrystals: The Solar System's Hidden Secrets. By Luca Bindi. Springer Briefs in Crystallography, Vol. 1, Springer, 2020, x+89 pp. Softcover. Price EUR 51.99. ISBN 978‐3‐030‐45676‐4

Crack open a geode, or pick up a shiny rock near a natural water stream, and there is a good chance you will see crystals. But the chances that these will be quasicrystals are close to nil. Why is it that quasicrystalline minerals appear to be so rare? Is it surprising, or should we be surprised that they exit at all? Natural Quasicrystals: The Solar System’s Hidden Secrets, by Luca Bindi, tells the story of the search for quasicrystals that occur naturally as minerals, and proposes a plausible explanation for how, and surprisingly where, they may have formed. Allow me to begin with a quick recap of post-Shechtman terminology. A crystal is a structure possessing long-range order in the positions of its atoms, indicated by the presence of Bragg peaks in its diffraction diagram (p. 928 in IUCr, 1992; Lifshitz, 2007). Crystals may or may not be periodic. Quasicrystals are quasiperiodic crystals (Levine & Steinhardt, 1986) that are explicitly aperiodic (Lifshitz, 2003). They lack periodicity, but they are crystals nevertheless. Icosahedral or decagonal crystals cannot be periodic. Cubic crystals, on the other hand, may or may not be periodic. The simplest icosahedral crystals, those whose Bragg peaks are indexed by six integers, are classified into three Bravais classes (Rokhsar et al., 1987): simple (or primitive) icosahedral (si), bodycentered icosahedral (bci), and face-centered icosahedral (fci). How surprising is the existence of quasicrystals in general? When Dan Shechtman discovered the first quasicrystal (Shechtman et al., 1984) it shattered the prevailing paradigm that all crystals were periodic, and ushered a bona fide Kuhnian scientific revolution (Kuhn, 1962). Today, almost four decades later, aperiodic crystals are found almost everywhere, and while their realization in new contexts and novel physical systems is exciting as ever, and often provides important insight, it is hardly surprising. It is in this context that one should consider the search for quasicrystalline minerals. Years ago, a group of scientists led by Paul Steinhardt, who would eventually become the author’s collaborators, embarked on a quest to find such minerals, by searching through scientific databases and issuing a public call to curators of mineral collections worldwide. The search eventually led to a 4 mm rock in the collection of Bindi’s home institute, the Museo di Storia Naturale of the Università degli Studi di Firenze (in Italy). The sample originated from the Khatyrka region of the Kamchatka peninsula in Russia. It consisted of light-colored material on its exterior, surrounding a dark substance, consisting mainly of khatyrkite and cupalite (metallic alloys of copper and aluminium), with tiny granules of the sought-after quasicrystal, which was given the mineral name ‘icosahedrite’ for its icosahedral point-group symmetry. Ensuing analysis established that the granules were face-centered icosahedral (fci) crystals with the familiar composition of Al63Cu24Fe13 – the first thermodynamically stable quasicrystal ever discovered (Tsai et al., 1987, Calvayrac et al., 1990). Further analysis of the sample showed traces of stishovite, a polymorph of SiO2 that usually forms at very high pressures and temperatures, as well as a distribution of oxygen isotopes that indicated that the sample might be of extraterrestrial origin. These and other details led to the hypothesis that the quasicrystalline mineral was formed through a high-pressure and high-temperature shock, generated by a hypervelocity impact of asteroids in outer space – a truly spectacular event that may have taken place as early as when the solar system itself was forming, around 4.5 billion years ago, hence the title of the book. ISSN 2052-5206