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-

 

 

 

Colour notes