Crystallographic shear vector

Crystallographic shear planes (CS planes) are planar faults in a crystal that separate two parts of the crystal which are displaced with respect to each other. The vector describing the displacement is called the crystallographic shear vector (CS vector). Each CS plane causes the composition of the crystal to change by a small increment because the sequence of crystal planes that produces the crystal matrix is changed at the CS plane. (From this it follows that the CS vector must be at an angle to the CS plane. If it were parallel to the plane, the succession of crystal planes would not be altered and no composition change would result. A planar boundary where the displacement vector is parallel to the plane is more properly called an antiphase boundary.)... 

It is sometimes important to specify a vector with a definite length perhaps to indicate the displacement of one part of a crystal with respect to another part, as in an antiphase boimdary or crystallographic shear plane. In such a case, the direction of the vector is written as above, and a prefix is added to give the length. The prefix is usually expressed in terms of the unit cell dimensions. For example, in a cubic crystal, a displacement of two unit cell lengths parallel to the b axis would be written 2ao[0 1 0]-... 

Fig. 24. Anderson and Hyde model for forming a crystallographic shear plane in WO3. The perfect structure consists of WOg octahedra stacked as shown. In the Anderson and Hyde model anion vacancies are imagined to collect as shown on the left-hand side of the figure and then collapse to give the structure shown on the right. Along the fault the stacking arrangement of the WOj tetrahedra is not the same as in good material and also the structure is sheared along the fault plane by the vector 5cj[TT0]. From Hyde and Bursill. ...

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