A sinusoidal twin boundary harmonizes with the elastic anisotropy of quartz

Abstract Minerals are crystalline solids manifesting various symmetries in their ordered structures despite high-energy defects seated in their atomic templates. Twin boundaries are imperfections affording energy reduction through reflection, rotation, or inversion of the crystal lattice, forming symmetrical intergrowths. Quartz is one of many minerals that twins as a rule, yet its most common twin is rarely seen without destructive analysis. Disguised as one crystal, this penetrative twin abides by the Dauphiné Law, appearing in 2D as patchworks of irregular domains to roughly triangular sectors. The physical basis for such diverse morphologies remains inconclusive. However, because twins are related by a rotational symmetry that disrupts quartz’s piezoelectric property, their enigma and ubiquity have plagued quartz’s profound technological role in society for over a century. Here we noninvasively map twins and find their boundaries ideally manifest as a 3D waveform oscillating in harmony with α-quartz’s elastic anisotropy. While maximizing elastic strain energy, the sinusoid minimizes internal energy by equipoising twins’ softer and stiffer parts that are transposed in r- and z-rhombohedra, such that oscillations correspond to the threefold c-axis symmetry mirrored in Young’s modulus. This helps explain twin diversity and invites new appraisals of quartz’s microstructural behavior from geological and engineering perspectives.