Twinning contact point

At the instant of contact between a sphere and a flat specimen there is no strain in the specimen, but the sphere then becomes flattened by the surface tractions which creates forces of reaction which produce strain in the specimen as well as the sphere. The strain consists of both hydrostatic compression and shear. The maximum shear strain is at a point along the axis of contact, lying a distance equal to about half of the radius of the area of contact (both solids having the same elastic properties with Poisson s ratio = 1/3). When this maximum shear strain reaches a critical value, plastic flow begins, or twinning occurs, or a phase transformation begins. Note that the critical value may be very small (e.g., in pure simple metals it is zero) or it may be quite large (e.g., in diamond). 

To illustrate the last point we shall look at a molecule with a center of symmetry. Carbon dioxide, benzene, and ethylene all have this common property, that is, they have a point such that a line, drawn from one atom to this point and extended an equal length beyond, will contact the twin of the first atom. Water (see Fig. 2, B) and most other molecules do not possess such a center of symmetry. If there is molecular symmetry, a vibration may be either symmetric or antisymmetric. For a symmetric vibration, the displacement vector of one atom will be the mirror image of the displacement vector of the opposite atom (see Fig. 2, A, i). Such a vibration obviously leaves the dipole moment unaltered and is thus forbidden in the infrared. On the other hand, the antisymmetric vibration (see Fig. 2, A, ii) does produce a change in the dipole moment. The moment is zero in the equilibrivun position and is some value other than zero at either end of the vibration. This vibration will be active in the infrared. 

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