Size Broadening (Spherical Harmonics)
The Lorentzian broadening of the reflection is given by the expressions:
Space:
T.O.F. Space:
Energy Space:
but for each
refexion with spherical coordinates
in the reciprocal space,
is calculated by the developement onto the
Spherical Harmonics basis functions as:
Laue class: 2/m
Y00, Y22+, Y22-, Y20, Y44+, Y44-
Y42+, Y42-, Y40
Laue class: -3 m H
Y00, Y20, Y40, Y43-, Y60, Y63-
Y66+
Laue classes: m3, m3m. Cubic harmonics, for m3m K62=0.
K00, K41, K61, K62, K81
Laue class: mmm
Y00, Y20, Y22+, Y40, Y42+, Y44+
Laue classes: 6/m, 6/mmm. For 6/mmm Y66-=0.
Y00, Y20, Y40, Y60, Y66+, Y66-
Laue class: -3 H.
Y00, Y20, Y40, Y43-, Y43+
Laue classes: 4/m, 4/mmm. For 4/mmm Y44-=0 and Y64=0.
Y00, Y20, Y40, Y44+, Y44-, Y60
Y64+, Y64-
Laue class: -1.
Y00, Y20, Y21+, Y21-, Y22+, Y22-