Mechanical & Materials Engineering, Department of


Date of this Version



PNAS 2022 Vol. 119 No. 13 e2118253119


Copyright © 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).


Type IV twins are defined and shown to exist in triclinic crystal systems, as well as in some monoclinic and trigonal systems. Here, we focus on Pericline twins in triclinic plagioclase as an example. Type IV twins are associated with the irrationality of one of the twinning elements that is rational for a type II twin. The formation of type IV twins is accomplished through the shear on a K2 plane produced by the motion of twinning disconnections on a K1 plane, followed by rotational partitioning. The same systems where type IV twins are present also have type III twins instead of type I. Without using the correct type IV analysis, one would deduce the wrong magnitude and direction of shear associated with the twinning process, the magnitude of which would increase with greater triclinicity. Types I and II twins form if and only if there are rational lattice translation vectors lying in the plane of distortion/shear. Otherwise, the twins are types III and IV.

Historically, two types of twins (I and II) have been categorized for twinning in minerals and metals. When analyzed by the topological model, a crystallographic construction used to define the defect structure of interfaces, triclinic and some other lowsymmetry crystals do not fall into either category and instead form two new twinning types, namely, III and IV. Aside from accurately describing twin structures, these concepts are important for understanding the deformation of minerals such as plagioclase and for deriving constitutive models for the deformation.