🌊 First: normal X-ray scattering (no anomalous effect)

When X-rays hit atoms in a crystal:

• Electrons oscillate
• They re-emit X-rays → scattering

This scattering creates the diffraction pattern.

Normally we assume:

Scattering is purely elastic → no energy is absorbed.

Mathematically:

F_ = F_{-h-k-l}

This means:

• Friedel pairs have identical intensity

So:

👉 No extra information about phase can be obtained.

⚡ What is anomalous scattering (intuitive idea)

Anomalous scattering happens when:

The atom absorbs some of the X-ray energy and then re-emits it with a small phase shift.

So scattering is no longer perfectly elastic.

This only happens strongly for heavy atoms and only at specific X-ray energies.

🧠 Think of it like this

Normal atom:

• behaves like a simple mirror → reflects light cleanly

Anomalous atom:

• behaves like a mirror + sponge
• it absorbs some energy
• re-emits with delay and changed amplitude

This “delay” = phase change

That tiny change is what crystallographers exploit.

📊 Mathematical view (simplified)

Normal scattering factor:

f

With anomalous scattering:

f = f_0 + f' + if''

Where:

• ( f_0 ) → normal scattering
• ( f' ) → real correction (dispersion)
• ( f'' ) → imaginary correction (absorption-related)

These extra terms:

👉 change reflection intensities 👉 break Friedel’s law.

🎯 Why is this useful?

Because now:

I(hkl) eq I(-h-k-l)

This intensity difference allows us to:

• locate heavy atoms
• estimate phases
• solve structure.

This is the basis of SAD/MAD phasing.

🔥 What is the absorption edge?

Now the REALLY key idea.

Atoms have core electrons:

• K-shell
• L-shell
• etc.

Each shell has a specific binding energy.

Absorption edge = threshold energy

If X-ray energy becomes high enough to:

eject a core electron

Then absorption suddenly increases.

This sharp increase in absorption vs energy is called:

Absorption edge

It looks like a step in an absorption spectrum.

Why is anomalous scattering strongest there?

At the absorption edge:

• Atom strongly interacts with X-rays
• Electron excitation becomes very efficient
• ( f' ) and ( f'' ) change rapidly

This produces:

• maximum anomalous signal
• biggest intensity differences.

So crystallographers:

👉 tune synchrotron wavelength exactly to that edge.

📡 Example (from your lecture)

They used tungsten.

Procedure:

1. Measure absorption spectrum
2. Find edge position
3. Collect diffraction data at:

• Peak wavelength
• Inflection wavelength
• Remote wavelength

This is MAD phasing.

🧠 Super important intuition

Normal diffraction:

• all atoms scatter similarly
• symmetry preserved
• no phase info.

Anomalous diffraction:

• heavy atoms scatter “weirdly”
• symmetry slightly broken
• tiny intensity differences appear
• these differences encode phase information.

⭐ VERY short exam definition

Anomalous scattering: Deviation from normal elastic X-ray scattering that occurs near an atom’s absorption edge, causing changes in scattering amplitude and phase, which lead to intensity differences between Friedel pairs and allow phase determination.

Absorption edge: The X-ray energy at which core electrons of an atom can be excited or ejected, causing a sharp increase in absorption and strong anomalous scattering effects.