The effect of crystal shape and setting on secondary extinction

The power equations for diffraction from a single crystal of uniform, but arbitrary, cross-section may be solved by numerical procedures to yield secondary extinction coefficients. Calculations are carried out and curves are presented for both absorbing and non-absorbing crystals of circular and rectangular cross-section at several crystal settings and Bragg angles. It is shown that the extinction coefficient for crystals of rectangular cross-section can be quite sensitive to the direction of the incident beam relative to the crystal faces; hence, if extinction is severe, the use of a cylindrical crystal is indicated. In the cylindrical crystal, the extinction coefficient becomes noticeably dependent on the Bragg angle as the extinction becomes more severe. A single-parameter empirical extinction correction of the exponential or linear type commonly used cannot then be valid for groups of reflections which vary widely in Bragg angle. Only if lo/lc > 0.70 is an extinction coefficient of the type exp (--kit) appropriate. An estimate of the mosaic spread parameter may thus be obtained from the less severely extinguished reflections and applied to the more intense reflections. The mosaic-spread parameter may also be conveniently estimated from the limiting intensity if this is experimentally observed.