What is the interaction between x-rays and electrons Since x-rays are electromagnetic radiation they interact with atoms like any other radiation. Transmission—pass through Absorption—are absorbed %Absorbed=100-%transmitted These are the two principal interactions and are of little interest

Secondary Interactions Scattering—elastic scattering (wavelength of scattered radiation is the same as incident radiation)—Raleigh scattering Absorption followed by emission— florescence.—anomalous scattering

A General Rule Any effect which adds a degree of randomness (disorder) will cause the intensity of the diffracted x-rays to fall off faster as a function of theta.

Diffracting Power of Atoms

Why does scattering decrease Thompson theory of scattering by a free electron If the plane of polarization unchanged then no angular dependency. It the plane of polarization changes 90 degrees than falls off by cos 2 (2  )] Since any direction is average of two then fall off (1+ cos 2 (2  ))/2

Fall off in atoms The atomic falloff is greater than for free electrons!! Bad reason—interference between scattering from electrons in the atom—this fails to explain why hydrogen falls off greatest!

Think of Hydrogen Imagine a perfect crystal of hydrogen atoms. Assume no motion in atoms Because of the very short wavelength of x-rays the time scale is very fast. The electrons are not ordered By the general rule there will be a fall off with theta!

How can we estimate the average deviation of the electrons from the nuclear position? If the electron travels in a very small region than the deviation will be small. Thus the number of electrons/volume is a good estimate of the electron deviation. This is the electron density.

Does this work? Hydrogen has the lowest electron density and therefore has the largest falloff with theta. Heavy metals have very similar volumes and thus have high electron densities and have low falloff with theta.

Atomic Motion Atoms are not stationary in a crystal. Even at 0K they vibrate. This adds even more disorder f’=f exp(-B/4 2sin 2 (  )/  ) B is called the Debeye Isotropic Temperature Factor B=8  2 where is the mean- square amplitude of vibration

ADP’s The u and B factors were referred to as temperature factors. This is a terrible name. Today called atomic displacement parameters (adp’s) For a carbon typically B=4.0 at room temperature u=0.05 For a heavy atom B=2.5 at room temperature or u=0.03

No Vibration

Room Temperature

Low Temperature

Advantages of Low Temp The high angle data intensity is increased. The crystal is not likely to lose solvent Inside the nitrogen beam the crystal is not likely to react Can mount crystals with grease and not glue—much quicker

Room Temp

150 K

Absorption

Other Problems Decay—crystal decomposes over time Collect some reflections every so often to check for decay Mis-centering—crystal moves in and out of beam Recenter some reflections every so often to see if crystal has moved. If so recenter and recalculate the orientation matrix

Eulerian Cradle

Kappa Geometry

Data Collection