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Chemistry 125: Lecture 5
Sept. 10, 2010
X-Ray Diffraction
In the last 25 years various manifestations of Scanning Probe Microscopy, such as AFM,
STM, and SNOM, have enabled chemists to “feel” individual molecules and atoms. SPM
techniques are not quite good enough yet to study how electrons are distributed in bonds.
Because light is scattered predominantly by the charged particles with the smallest 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
Despite Earnshaw,
might there still be
shared-pair bonds
and lone pairs?
Only
one of these five cantilevers
is
used
Atomic
Gold
in any one experiment. They differ in
Force
coated
stiffness and ability to twist.
Microscopy
Hair
Si Chip
1.4 mm
The smallest scale
division is 20 mm
Scanning Electron Micrographs of
AFM Cantilever
Tip
Radius of
curvature
~20 nm
1mm
©The IN-VSEE Project; Arizona State University 1999
http://invsee.asu.edu/Invsee/listmod.htm
Tips
Cantilever/Chip Holder
Cantilever/Chip Holder
Sensitive to
< 1 molecule
change in
height !
AFM traces at 1 min
intervals of part of
the surface of a
benzoin crystal
dissolving in
95% water /
5% n-propanol.
The larger pit
is 5.1 nm deep.
Each ledge
is one “unit cell”
(1.7 nm) high.
fast
Ledge
Dissolution
Rate
slower
slow
fast
5 mm
(~600 molecules)
Scanning Tunneling Microscopy (1999)
Br(CH2)11COOH
on graphite
O
Br
Geo. Flynn
D. Yablon
(Columbia Univ)
Quantum corral
Permission limited by IBM
Click to link to copyright webpage
http://www.almaden.ibm.com:80/vis/stm/corral.html
STM
Image
of Fe
atoms
on Cu
(1993)
Reprint Courtesy of International Business Machines Corporation, copyright 1993 © International Business Machines Corporation
High Resolution Requires Small Probe
No Barriers
Horizontal Line
Close Barriers
One Broad Hump
Distant Barriers
Distorted Humps
Rolling Wheel with Chalk on Axle to Trace Chalk-Trough Profile
Pentacene on Cu Scanned with a
Single-Atom Tip at 5K
10 v/m!
10
2.5v
Cu
L. Gross, et al., Science, Aug. 28, 2009
SNOM
Light
Scanning Near-Field
Optical Microscope
Glass Fiber
Aluminum Coating
100 nm Aperture
Sample (scanned)
Emitted Light
Lens
Detector
mm
scale
W. Brocklesby www.orc.soton.ac.uk by permission
red wavelength
SNOM image of nanofabricated material
Scanning Probe Microscopies
(AFM, STM, SNOM)
are really powerful.
Sharp points can resolve
individual molecules
and even atoms
but not bonds
Lux
A lonely
architectural
curiosity on
Sterling
Chemistry
Laboratory
at Yale
University
(1923)
Micrographia
Robert 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.”
Strong
400 nm
Scattering
No
800 nm
Scattering
“Thickness” ~ 200 nm
Oil
Path Difference = 400 nm
=1l
= 0.5 l
Interference upon Scattering
Water
Hooke: Observ. IX.
Confus’d Pulses of Light
Of the Colours observable
in Muscovy Glass,
and other thin Bodies.
Chris Incarvito’s New Toys
User Operated - CCD Detector
~$200K
X-Ray
Tube
~$350K
Image Plate
"Seeing" Individual
Molecules, Atoms,
and Bonds?
Problem:
l
What IS light?
In What Way is Light a Wave?
Force on Charge at One Position
Up
Charged
Particle
0
Down
Time
Force at Different Positions - OneTime
In What Way is Light a Wave?
Up
Charged
Particle
0
Down
Position
Accelerated Electrons “Scatter” Light
direct beam
Why don’t protons or other nuclei scatter light?
Too heavy!
Interference of Ripples
Angular
Intensity
Distribution
at
great distance
depends on
Scatterer
Distribution
at
the origin
By refocussing, a lens
can 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.
"Seeing"
Molecules, Atoms, Bonds
Collectively
by X-Ray Crystallography
SPM “feels” them
Individually
Blurring Problem from Motion and Defects
Blurring Problem
Time Averaging
Space Averaging in Diffraction
(Cooperative Scattering)
Advantage for SPM
(Operates in Real Space)
Shadow of
Frau Röentgen’s
hand (1896)
In 1895 Röntgen
Discovers X-Rays
In 1912 Laue
Invents
X-Ray
Diffraction
CuSO4 Diffraction
(1912)
Wm. Lawrence Bragg
(1890-1971)
Determined structure of
ZnS from Laue's
X-ray diffraction
pattern (1912)
(1915)
Courtesy Dr. Stephen Bragg
Youngest Nobel Laureate
B-DNA
R. Franklin
(1952)
Science, 11 August 2000
>100,000 atoms
+ hydrogens!
25 nm (250 Å)
What can X-ray diffraction show?
Molecules? Atoms? Bonds?
How does diffraction work?
Like all light, X-rays are waves.
Wave
Machines
Bragg Machine
http://www.eserc.stonybrook.edu/ProjectJava/Bragg/
in & out
same phase
Breaks?
by permission, Konstantin Lukin
Two Scattering Directions are Always Exactly in Phase
Specular
perpendicular to
scattering vector
Specular
All electrons on a plane
perpendicular
to
Direct
the scattering vector
scatter in-phase at
the specular angle !
Electrons-on-Evenly-Spaced-Planes Trick
3
4
2
1
Electrons-on-Evenly-Spaced-Planes Trick
Total
Electrons
Suppose l &
angle such that:
3
+4
1l
+2
2l
3l
3
4
2
1
+1
10
Net in-phase
scattering
Electrons-on-Evenly-Spaced-Planes Trick
Total
Electrons
3 3
+4 -4
0.5l
+2 +2
1l
1.5l
3
4
2
1
Suppose first path difference is half a wavelength,
because of change in l (or angle)
+1 -1
10 0
Net in-phase
scattering
spot spacing = 10.8 cm
…………………..
Q. What is the line spacing?
DIFFRACTION
MASK
(courtesy T. R. Welberry, Canberra)
10.6 m
View from
Ceiling
633 nm
To see and understand these
diffraction images, study the
course X-ray website:
https://webspace.yale.edu/chem125/125/xray/diffract.html
and particularly the section:
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
End of Lecture 5
Sept 11, 2009
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J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0