On the Martin Boundary for Markov Chains.

wide compared with the length of the specimen, and so is the angle between the lateral edge of the kink band and the axis of extension, E = [sin xo/sin (xi + so) ] 1. (2) For narrow kink bands and deformation bands, (a) an approximate relation is s = cot (900 w); (b) a more precise relation where a and ,3 are the respective angles between the kink-band boundary and the active glide plane in the band and in the unstrained ends, s = cot a + cot fi. The validity of these equations has been tested against rotational and strain data for experimentally deformed crystals of calcite and dolomite. The above relations are based on the assumption that throughout progressive strain the boundary surface of a kink or deformation band is occupied by the same material particles and serves as a datum with reference to which the crystal lattice of the band may be considered to rotate about the intersection of the kink-band boundary surface and the glide plane T. By making a similar assumption with regard to a twin-lamella boundary in calcite, it is possible to explain complex rotational effects leading to simple geometric relations previously observed between a completely twinned crystal lattice and the completely twinned lattice of an enclosed rotated lamella.