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

International Tables for Crystallography (2006). Vol. C, ch. 5.2, p. 498

Table 5.2.8.1 

W. Parrish,a A. J. C. Wilsonb and J. I. Langfordc

aIBM Almaden Research Center, San Jose, CA, USA,bSt John's College, Cambridge CB2 1TP, England, and cSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England

Table 5.2.8.1| top | pdf |
Some geometrical aberrations in the Debye–Scherrer method [increase in θ = +, decrease = −]

Source of aberrationEffect on θAngle variation of ΔdRemarks
Specimen displacement      
 towards exit [\cos^2\theta] Minimized by accurate construction and centring
 towards entrance + [\cos^2\theta] Extrapolates to zero
 sideways [\sim0] [\sim\theta]  
Beam divergence      
 perpendicular to axis + [\cos \theta\cot\theta] or [\cos^2\theta/2\theta] Minimized by reducing collimator dimensions
 parallel to axis + or − Complex See Langford, Pike & Beu (1964[link])
Film shrinkage + [(\pi-2\theta)\cot\theta] Affects only van Arkel arrangement
Knife-edge calibration + or − [\theta \cot \theta] Affects only Bradley–Jay arrangement. Partly eliminated by usual extrapolation
Specimen absorption + [\cos \theta\cot\theta] or [\cos^2\theta/2\theta] Minimized by reducing specimen diameter or dilution. Extrapolates to zero
For van Arkel and Bradley–Jay arrangements. For Straumanis–Ievins', + or − and [(\pi -2\theta)\cot\theta], respectively.