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X-ray diffraction - PowerPoint PPT Presentation


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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 QA 2 + A 2 R = 2d sin θ

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slide4

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

slide9

Polymorphism of Discotic Mesophases

uniaxial

uniaxial

biaxial

Discotic nematic (ND)

uniaxial

Discotic hexagonal columnarColh or DhColho ordered;Colhddisordered

biaxial

Discotic rectangular and tetragonal columnarColr or Dr; Coltor Dt

(Colh plastic crystal)

Discotic oblique columnarColob or Dob

slide10

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).

slide11

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).

slide12

Diffraction Pattern of a Pseudo-hexagonal Columnar Mesophase

rectangular becomes pseudo-hexagonal if a = sq3 b

So that b2 = a2/3

slide13

2D X-ray Diffraction Pattern of a Mechanically Aligned Sample of the ‘Chemical Mixture’ (M = Cu)

sample

Colh

intercolumnar

21.0 Å

X-ray beam

intracolumnar

3.5 Å