POWDER DATA III: ADDITIONAL ANISOTROPIC SIZE PARAMETERS
(Optional LINE 36 is read if Size-Model ≠0 on LINE 27)
This specific optional sub-block of the block of lines 26 to 38 (see, loop
over phases) should be given for
each pattern to which the phase contributes (controlled by JCONTR(n_pat)
in line 19. These lines may be
grouped as:
(1) Cylindrical (platelet) shaped crystallites
[If Size-Model =±1]
Comment line:! Platelet-Needle vector (Size)
LINE 36: Sz1, Sz2, Sz3 (3 reals)
(2) User defined selective (hkl) size
broadening due to defects
[If Size-Model<-1]
LINE 36: n1, n2, n3, n4, n5, SZ, CSZ
(5 integers, 2 reals)
Comment line:! Size-Broadening (n1.h + n2.k + n3.l=n n4 +/- n5) Size-par
Code
(3) Spherical harmonics expansion of the
cystallites shape
[Size-Model=15] Laue class: 2/m
LINE 36: Y00, Y22+, Y22-, Y20, Y44+, Y44-
(6 reals)
LINE 36-1: CY00, CY22+, CY22-, CY20, CY44+, CY44- (Codewords 6 reals)
LINE 36-2: Y42+, Y42-, Y40 (3 reals)
LINE 36-3: CY42+, CY42-, CY40 (Codewords 3 reals)
Comment lines are directly the names of the variables as given below.
[Size-Model=16] Laue class: -3 m H
LINE 36: Y00, Y20, Y40, Y43-, Y60, Y63- (6
reals)
LINE 36-1: CY00, CY20, CY40, CY43-, CY60, CY63- (Codewords 6 reals)
LINE 36-2: Y66+ (1 real)
LINE 36-3: CY66+ (Codewords 1 real)
Comment lines are directly the names of the variables as given below.
[Size-Model=17] Laue classes: m3, m3m.
Cubic harmonics, for m3m K62=0.
LINE 36: K00, K41, K61, K62, K81 (5
reals)
LINE 36-1: CK00, CK41, CK61, CK62, CK81 (Codewords 5 reals)
Comment lines are directly the names of the variables as given below.
[Size-Model=18] Laue class: mmm
LINE 36: Y00, Y20, Y22+, Y40, Y42+, Y44+
(6 reals)
LINE 36-1: CY00, CY20, CY22+, CY40, CY42+, CY44+ (Codewords 6 reals)
Comment lines are directly the names of the variables as given below.
[Size-Model=19] Laue classes: 6/m, 6/mmm.
For 6/mmm Y66-=0.
LINE 36: Y00, Y20, Y40, Y60, Y66+, Y66-
(6 reals)
LINE 36-1: CY00, CY20, CY40, CY60, CY66+, CY66- (Codewords 6 reals)
Comment lines are directly the names of the variables as given below.
[Size-Model=20] Laue class: -3 H.
LINE 36: Y00, Y20, Y40, Y43-, Y43+
(5 reals)
LINE 36-1: CY00, CY20, CY40, CY43-, CY43+ (Codewords 5 reals)
Comment lines are directly the names of the variables as given below.
[Size-Model=21] Laue classes: 4/m, 4/mmm.
For 4/mmm Y44-=0 and Y64=0.
LINE 36: Y00, Y20, Y40, Y44+, Y44-, Y60
(6 reals)
LINE 36-1: CY00, CY20, CY40, CY44+, CY44-, CY60 (Codewords 6 reals)
LINE 36-2: Y64+, Y64- (2 reals)
LINE 36-3: CY64+, CY64- (Codewords 2 reals)
Comment lines are directly the names of the variables as given below.
[Size-Model=22] Laue class: -1.
LINE 36: Y00, Y20, Y21+, Y21-, Y22+, Y22-
(6 reals)
LINE 36-1: CY00, CY20, CY21+, CY21-, CY22+, CY22- (Codewords 6 reals)
Comment lines are directly the names of the variables as given below.
[Sz1, Sz2, Sz3] - Vector defining the
platelets
Is the vector defining the platelets. Must be the same for all patterns.
n1, n2, n3, n4, n5, SZ – User-defined rules
for selective hkl size-broadening
Set of ABS(Size-Model) (≤9) lines, defining rules to be satisfied by
reflections undergoing
selective “size-like” broadening due to some kind of defects (anti-phase
domains, … ).
Are set of integers that should be the same for all patterns. If the
Miller indices of the reflection
satisfy the relation:
n1H + n2K + n3L = n4 n + n5
The Lorentzian broadening of the reflection is given by the expressions:
HL = 0.360 SZ λ/cosθ /π2 (2θ space)
HL =(2/π) SZ d5
Dtt1 × 10-3 (T.O.F. space)
HL = SZ/(2d) Dtt1
× 10-3 (Energy space)
Clm±, Klm - SH coefficients
The Lorentzian broadening is calculated as previously, but for each
refexion (hkl) with spherical
coordinates (h, θ, ϕ) in the reciprocal space, SZ is calculatesd by the
developement onto the
Spherical Harmonics basis functions as: