3. X-ray diffraction

4. Laue’s and Bragg’s Treatments of X-ray diffraction
The path difference between the two rays reflected from successive planes is
QA2 + A2R = 2d sin θ
Constructive interference is obtained if the path difference is equal to an intergral number of wavelengths (Bragg’s Law)
2d sin θ = nλ

5. X-ray diffraction of N Phases

7. X-ray diffraction of Sm Phases

8. 2D WAXS Pattern of a Tetracatenar SmC Phasenm

9. Polymorphism of Discotic Mesophases
uniaxial
uniaxial
biaxial
Discotic nematic (ND)
uniaxial
Discotic hexagonal columnar Colh or Dh Colho ordered; Colhd disordered
biaxial
Discotic rectangular and tetragonal columnar Colr or Dr; Colt or Dt
(Colh plastic crystal)
Discotic oblique columnar Colob or Dob
Designations Symmetry groups, molecular arrangement within columns
System
Unit-cell symbol(s)
Symmetry at lattice points
Unit-cell edges and angles
Oblique
p (primitive unit cell) 2
a ≠ b, γ ≠ 90º, 120º
Rectangular
p, c (centred unit cell)
2 mm
a ≠ b, γ = 90º
Square p
4 mm
a = b, γ = 90º
Hexagonal
6 mm
a = b, γ = 120º

10. Diffraction Pattern of a Hexagonal Columnar Mesophase
with hk = kh = 10 is set to be 1
An additional peak can appear at which was explained by a periodic electron density distortion (DeGennes, J. Phys. Letters, 1983 (44), L657).

11. Diffraction Pattern of a Hexagonal Columnar Mesophase
with hk = kh = 10 is set to be 1
An additional peak can appear at which was explained by a periodic electron density distortion (DeGennes, J. Phys. Letters, 1983 (44), L657).

12. Diffraction Pattern of a Pseudo-hexagonal Columnar Mesophase
rectangular becomes pseudo-hexagonal if a = sq3 b
So that b2 = a2/3

13. 2D X-ray Diffraction Pattern of a Mechanically Aligned Sample of the ‘Chemical Mixture’ (M = Cu)
Colh
intercolumnar
21.0 Å
X-ray beam
intracolumnar
3.5 Å

14. X-ray diffraction pattern of Cu52 at 90 ºC

15. Temperature dependence of X-ray diffraction pattern