X-ray diffraction
16
description
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 - PowerPoint PPT Presentation
Transcript of X-ray diffraction
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 magneticfield of 11.7 T
SmC layers
53o
120 ºCO
O
H15C7O
H15C7O
O
O
OC7H15
OC7H15
S
N N
Polymorphism of Discotic Mesophases
Discotic nematic (ND)
Discotic hexagonal columnarColh or Dh
Colho ordered;Colhd disordered
Discotic rectangular and tetragonal columnarColr or Dr; Colt or Dt
Discotic oblique columnarColob or Dob
uniaxial uniaxial
biaxial
biaxial
uniaxial
(Colh plastic crystal)
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 p 6 mm a = b, γ = 120º
Diffraction Pattern of a Hexagonal Columnar Mesophase
7:4:3:1
hkkh
adhk
22
3
4
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).
(10)
(11)
a
Diffraction Pattern of a Hexagonal Columnar Mesophase
7:4:3:1
hkkh
adhk
22
3
4
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).
(10)
(01)
(11)
a
Diffraction Pattern of a Pseudo-hexagonal Columnar Mesophase
2
2
2
2
1
b
k
a
hdhk
22 3kh
adhk
rectangular becomes pseudo-hexagonal if a = sq3 bSo that b2 = a2/3
2D X-ray Diffraction Pattern of a Mechanically Aligned Sample of the ‘Chemical Mixture’ (M = Cu)
sample
X-ray beam
intercolumnar21.0 Å
intracolumnar3.5 Å
Colh
X-ray diffraction pattern of Cu52 at 90 ºC
10 200
20000
40000
Inte
nsit
y (
coun
ts)
2 (°)
0 10 20 30
1000
1500
2000d100
d210
d200
d110
Inte
nsit
y (
coun
ts)
2 (°)
60 90 120 150
17.8
17.9
18.0
d 100
(Å)
T (°C)60 90 120 150
364
368
372
S (
Å2 )
T (°C)
Temperature dependence of X-ray diffraction pattern
