Suppression of the Secondary Twinning

Arbitrarily oriented (with respect to the crystallographic axes) uniaxial mechanical stress could the twinning initiate (AG 0) or suppress (AG 0). Let us define the coordinate system (Ox x x ) rotated with respect to the crystallographic coordinates 

Ox X2X3. Rotation is described as a subsequent rotation by an angle f about X3 -axis and by an angle f about the previously rotated x j -axis. The uniaxial stress has only one component T in the x -axis direction. An electric field is supposed to be zero. An increment of the Gibbs potential density for the twiiming is ejqtressed as 

The complete rotation matrix for the rotation mentioned above is 

Using the rotation matrix Eq. (7.5) we can transform the elastic constants 2(1) and 522(2) to the rotated coordinate system. The elastic constant components ddfer only in the signs of several terms which are in brackets in Eq. (7.2). Following expressions are obtained 

Value of the function S2(f, f) = cos3c sin cos determines the condition for the twinning. Taking into account 514 0 for quartz the twiiming is suppressed for 0. Value of is a measure of the tendency for twinning under uniaxial stress. If the function Q. reaches its minimum value 

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