X-ray diffraction

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

X-ray diffraction of N Phases

X-ray diffraction of Sm Phases

2D WAXS Pattern of a Tetracatenar SmC Phase 0.7-0.75 nm

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

Diffraction Pattern of a Hexagonal Columnar Mesophase with hk = kh = 10 is set to be 1 An additional peak can appear at 1.323 which was explained by a periodic electron density distortion (DeGennes, J. Phys. Letters, 1983 (44), L657).

Diffraction Pattern of a Hexagonal Columnar Mesophase with hk = kh = 10 is set to be 1 An additional peak can appear at 1.323 which was explained by a periodic electron density distortion (DeGennes, J. Phys. Letters, 1983 (44), L657).

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

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

X-ray diffraction pattern of Cu52 at 90 ºC

Temperature dependence of X-ray diffraction pattern