final
Chemistry 125: Lecture 5Sept. 11, 2009
X-Ray Diffraction SPM techniques are not quite good enough yet to study how electrons are distributed in bonds. Because light is scattered by charged particles of small mass, the electron distribution in molecules can be determined by x-ray diffraction. The roles of molecular pattern and crystal lattice repetition can be illustrated by shining a visible laser through diffraction masks to generate scattering patterns reminiscent of those encountered in X-ray studies of ordered solids.
For copyright notice see final page of this file
Motivation for the Trajectory of Coulomb’s Work with his Torsion Balance:
Devises an improved suspension for a compass needle.
Studies wire torsion “in order to determine the laws of cohesion and elasticity in metals and in all solid bodies.”
(Engineering; Newton’s “Business of Experimental Philosophy”)
Confirms Hooke’s Law for torsion.
1784
1777
1785-9 Determines 1/r2 Laws for E&M.
Cu
Pentacene on Cu Scanned with a Single-Atom Tip at 5K
L. Gross, et al., Science, Aug. 28, 2009
2.5v1010 v/m!
Scanning Probe Microscopies(AFM, STM, SNOM)are really powerful.
Sharp points can resolve
individual moleculesand individual atoms
and even bonds (almost)
MicrographiaRobert Hooke (1665)
“But Nature is not to be limited by our narrow comprehension; future improvements of glasses may yet further enlighten our understanding, and ocular inspection may demonstrate that which as yet we may think too extravagant either to feign or suppose.”
Water
Oil“Thickness” ~ 200 nm
Path Difference = 400 nm
= 0.5
Strong400 nm
Scattering
No800 nm
Scattering
= 1
Interference upon Scattering
Hooke: Observ. IX. Of the Colours observable in
Muscovy Glass,and other thin Bodies.
Confus’d Pulses of Light
ChargedParticle
In What Way is Light a Wave?F
orce
at
Diff
eren
t P
ositi
ons
- O
neT
ime Up
Down
0
Position
Accelerated Electrons “Scatter” Light
Why don’t protons or other nuclei scatter light?Too heavy!
direct beam
Interference of Ripples
AngularIntensity
Distribution at
great distancedepends onScatterer
Distribution at
the origin
By refocussing, a lenscan reassemble the information
from the scattered wave into an image of the scatterers.
But a lens for x-rays is hard to come by.
Be sure to read the webpage on x-ray diffraction.
Blurring Problem
Blurring Problem from Motion and Defects
Time Averaging
Space Averaging in Diffraction(Cooperative Scattering)
Advantage for SPM(Operates in Real Space)
In 1895 RöntgenDiscovers X-Rays
Shadow ofFrau Röentgen’s
hand (1896)
In 1912 LaueInventsX-Ray
DiffractionCuSO4 Diffraction
(1912)
Wm. Lawrence Bragg(1890-1971)
Determined structure of ZnS from Laue'sX-ray diffraction
pattern (1912)
Youngest Nobel Laureate(1915)
Cou
rtes
y D
r. S
teph
en B
ragg
What can X-ray diffraction show?
How does diffraction work?
Like all light, X-rays are waves.
Atoms?Molecules? Bonds?
by permission, Konstantin Lukin
Bragg Machinehttp://www.eserc.stonybrook.edu/ProjectJava/Bragg/
Breaks?in & out
same phase
Direct
Two Scattering Directions are Always Exactly in Phase
“scattering vector”
Specular perpendicular to scattering vector
All electrons on a planeperpendicular to
the scattering vectorscatter in-phase at
the specular angle !
Specular
10
scattering vector 3
+2
+4
+1
324 1
12
3
Net in-phasescattering
TotalElectrons
Suppose &angle such that:
Electrons-on-Evenly-Spaced-Planes Trick
10
scattering vector 3
+2
+4
+1
3
+2
-4
-1
0324 1
Suppose first path difference is half a wavelength,because of change in (or angle)
Net in-phasescattering
TotalElectrons
0.5
11.5
Electrons-on-Evenly-Spaced-Planes Trick
View fromCeiling
10.6
m
633 nm
DIFFRACTION MASK
(courtesy T. R. Welberry, Canberra)
…………………..spot spacing = 10.8 cm
Q. What is the line spacing?
End of Lecture 5Sept 11, 2009
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