final Chemistry 125: Lecture 5 Sept. 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 Determines 1/r 2 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, v10 10 v/m!

Scanning Probe Microscopies (AFM, STM, SNOM) are really powerful. Sharp points can resolve individual molecules and individual atoms and even bonds (almost)

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.”

Water Oil “Thickness” ~ 200 nm Path Difference = 400 nm = 0.5 Strong 400 nm Scattering No 800 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-Ray Tube ~$200K

Image Plate ~$350K

"Seeing" Individual Molecules, Atoms, and Bonds? Problem:

What IS light?

In What Way is Light a Wave? Force on Charge at One Position Up Down 0 Time Charged Particle

Charged Particle In What Way is Light a Wave? Force at Different Positions - OneTime Up Down 0 Position

Accelerated Electrons “Scatter” Light Why don’t protons or other nuclei scatter light? Too heavy! direct beam

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 Blurring Problem from Motion and Defects Time Averaging Space Averaging in Diffraction (Cooperative Scattering) Advantage for SPM (Operates in Real Space)

In 1895 Röntgen Discovers X-Rays Shadow of Frau R ö entgen ’ s hand (1896) In 1912 Laue Invents X-Ray Diffraction CuSO 4 Diffraction (1912)

Wm. Lawrence Bragg ( ) Determined structure of ZnS from Laue's X-ray diffraction pattern (1912) Youngest Nobel Laureate (1915) Courtesy Dr. Stephen Bragg

B-DNA R. 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?

Wave Machines

by permission, Konstantin Lukin Bragg Machine 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 plane perpendicular to the scattering vector scatter in-phase at the specular angle ! Specular

scattering vector Electrons-on-Evenly-Spaced-Planes Trick

10 scattering vector Net in-phase scattering Total Electrons Suppose & angle such that: Electrons-on-Evenly-Spaced-Planes Trick

10 scattering vector Suppose first path difference is half a wavelength, because of change in (or angle) Net in-phase scattering Total Electrons Electrons-on-Evenly-Spaced-Planes Trick

View from Ceiling 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 5 Sept 11, 2009 Copyright © J. M. McBride 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).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0