Reciprocal vectors geometric projection

Note that the soft reciprocal vectors b are expanded in a basis of tangent vectors, and so are manifestly parallel to the constraint surface (as indicated by the use of a tilde), while the hard reciprocal vectors ihi are expanded in normal vectors, and so lie entirely normal to the constraint surface (as indicated by the use of a caret). These basis vectors may be used to construct a geometric projection tensor... 

The inertial and geometrical projection tensors, and associated reciprocal vectors, are identical for models with equal masses for all beads, in which the mass tensor is proportional to the identity. 

In order to determine which lattice planes give rise to Bragg diffraction, a geometrical construct known as an Ewald sphere is used. This is simply an application of the law of conservation of momentum, in which an incident wave, k, impinges on the crystal. The Ewald sphere (or circle in two-dimensional) shows which reciprocal lattice points, (each denoting a set of planes) which satisfy Bragg s Law for diffraction of the incident beam. A specific diffraction pattern is recorded for any k vector and lattice orientation - usually projected onto a two-dimensional film or CCD camera. One may construct an Ewald sphere as follows (Figure 2.44) ... 

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