X-Ray Crystallography (DP IB Chemistry: HL)

• When visible light waves interact with objects the light is scattered, transmitted and reflected – this gives us information about the macroscopic world
• However, at the scale of atoms, the wavelength of visible light (380-700 nm) is far too large to interact with atoms and molecules in this way
• Inter-atomic distances are in the order of 10^-9m (1nm) which corresponds to the wavelength of X-rays
• The structural technique of single crystal X-ray crystallography can be used to identify the bond lengths and bond angles of crystalline compounds
  
  

The technique of X-ray crystallography forms diffraction patterns which allow the structure of crystals to be deduced

• As X-rays pass through the different layers of a crystal they are refracted and reflected in consecutive planes
• The scattered waves interfere and are at different phases when they hit the detector
• The result is a complex pattern at the detector which can be interpreted to give regions of high and low electron density corresponding to the location of atoms within the crystal structure
  
  
  
  X-ray Scattering

Constructive and destructive interference

• Constructive interference occurs when two waves are in phase with the peaks aligned
• The result is the waves reinforce each other creating a wave with larger amplitude:
  
  

Constructive interference of waves

• Destructive interference occurs when two waves are out of phase by 180^o with one peak aligned with the trough of another
• The result is the waves cancel each other out
• If they have the same amplitude, it is complete cancelling and is called complete destructive interference
  
  
  

Destructive interference of waves

• The diffraction pattern obtained depends on the complex relationship between the angle of incidence, the wavelength and the distance and orientation between the atoms
• A map of electron density can be determined from the diffraction pattern, just as the weave of a fabric can be determined by holding the fabric up to the light
• Early uses of X-ray crystallography were to study the structure of ionic solids, such as sodium chloride
• Contour lines connect points of equal density and show regions where electron density is highest
  
  

   

An electron density contour map for sodium chloride showing the position of sodium and chloride ions. The larger ions are the chloride ions.

• X-ray crystallography can be applied to organic compounds which are able to form solid crystalline structures
• Hydrogen atoms have very low electron density so they barely show up in electron density maps, but the position of other atoms is evident and can be used to measure internuclear distance and bond angle
  
  
  

An electron density map for naphthalene showing the location of the carbon atoms in two adjoining hexagonal rings

• The structure of complex biological molecules such as DNA has been determined by X-ray crystallography