Type III and IV deformation twins in minerals and metals

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 [Formula: see text] plane produced by the motion of twinning disconnections on a [Formula: see text] 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.