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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.

Despite Earnshaw, might there still be shared-pair bonds

and lone pairs?

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)

Lux

A lonelyarchitecturalcuriosity on

SterlingChemistryLaboratory

at YaleUniversity

(1923)

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

Chris Incarvito’s New Toys

User Operated - CCD Detector

X-RayTube

~$200K

Image Plate~$350K

"Seeing" IndividualMolecules, Atoms,

and Bonds?

Problem:

What IS light?

In What Way is Light a Wave?F

orce

on

Cha

rge

at O

ne P

ositi

on

Up

Down

0

Time

ChargedParticle

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.

"Seeing" Molecules, Atoms, Bonds

Collectivelyby X-Ray Crystallography

SPM “feels” themIndividually

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

B-DNAR. Franklin

(1952)

Science, 11 August 2000

25 nm (250 Å)

>100,000 atoms+ hydrogens!

What can X-ray diffraction show?

How does diffraction work?

Like all light, X-rays are waves.

Atoms?Molecules? Bonds?

WaveMachines

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

scattering vector

324 1

Electrons-on-Evenly-Spaced-Planes Trick

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

Copyright © J. M. McBride 2009. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).

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