International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 6.4, pp. 609-610

Section 6.4.3. Primary and secondary extinction

T. M. Sabinea

aANSTO, Private Mail Bag 1, Menai, NSW 2234, Australia

6.4.3. Primary and secondary extinction

| top | pdf |

It is customary in the literature to distinguish between primary extinction, which is extinction within a single mosaic block, and secondary extinction, which occurs when a ray reflected by one mosaic block is subsequently reflected by another block with the same orientation. In the correlated block model, no distinction is made between the two types, and the problem reduces to that of primary extinction in the crystal as a whole. The angular distribution of blocks is an indicator of the extent of diffraction coupling between blocks during the passage of a single ray through the crystal.

In the uncorrelated block model, the problem must be separated into two regimes, with the input to the secondary-extinction system being the intensities from each mosaic block after allowance for primary extinction within each mosaic block.

In all theories, it is assumed that the primary-extinction parameter (the block size) and the secondary-extinction parameter (the mosaic spread) are physically independent quantities. If the dislocations in the crystal are concentrated in the small-angle boundaries, the two parameters can be combined to give the dislocation density. Qualitatively, the lower the dislocation density the larger the block size and the smaller the mosaic spread. Cottrell (1953[link]) has given the relationship [ \rho ={ \Theta \over b(D\ell)^{1/2}}, \eqno (6.4.3.1)]where ρ is the dislocation density, [\Theta ] is the total mosaic spread in radians, b is the Burgers vector of the dislocations, [\ell] is the block size and D is the size of the irradiated region.

References

Cottrell, A. H. (1953). Dislocations and plastic flow in crystals. Oxford University Press.








































to end of page
to top of page