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Principles

What is X-ray crystallography?

X-ray crystallography is an experimental technique that uses the fact that X-rays are diffracted by crystals. It is not an imaging technique. X-rays have the correct wavelength to be scattered by the electron cloud of an atom of comparable size. Based on the diffraction pattern obtained from the regular assembly of molecules or atoms in the crystal, the electron density can be reconstructed. Additional phase information extracted either from the data, or from extra experiments, must be supplied to complete the reconstruction.

Why Crystallography?

The knowledge of accurate molecular structures is a prerequisite for drug design and for structure based functional studies to aid the development of effective therapeutic agents and drugs. Crystallography can reliably provide the answer to many structure related questions, from global folds to atomic details of bonding. In contrast to NMR, which is an indirect spectroscopic method, no size limitation exists for the molecule or complex to be studied. The price for the high accuracy of crystallographic structures is that a good crystal must be found.

The stages of crystal structure determination

  • Grow some crystals (hours/days) - Crystal growing guide
  • Select a suitable crystal and mount it on a glass fibre (minutes)
  • Collect a few data sets - check quality of data and obtain unit cell (mintues/hours)
  • Collect whole set of data (hours/days)
  • Integrate data (minutes)
  • Solve the structure (minutes/hours/days)
  • Refine the structure (minutes/hours/days)

    A few minutes of time invested in selecting a decent crystal for study will save days or even weeks of work during the latter stages.

     

    Somehow, the x-rays have to be produced and recorded. This is done using a diffractometer. Many designs of diffractometer are in use, but essentially they are all the same in how they work.

  • Source - x-ray tube producing a very high intensity beam of x-rays. (Such high intensity that severe tissue damage will be sustained if exposed to direct beam, but all diffractometers have numerous safety mechanisms.)

  • Sample - A small crystal of 0.1 - 0.5 mm in length is used and carefully positioned in the centre of the x-ray beam.

  • Detector - measures the intensity of the scattered radiation

     


    The x-ray diffractometer at Bristol University

     


    A typcial x-ray diffractometer

     

    In order to solve the structure the unit cell and space group must be determined. Crystals are three dimensional ordered structures than can be described as a repetition of identical unit cells. The unit cell is made up of the smallest possible volume that when repeated, is representative of the entire crystal. The dimensions of a unit cell can be described with 3 edge lengths (a,b,c) and 3 angles (alpha, beta, gamma). The 3D location of atoms within a unit cell can be listed as their x, y, z Cartesian Coordinates. Space groups describe the symmetry of a unit cell, of which there are exactly 230 variations. The unit cell is determined from the diffraction of the x-rays using the Bragg equation.


    Reflection of x-rays from two planes of atoms in a solid.

    The path difference between two waves:

    2 x wavelength= 2dsin(theta)

    For constructive interference between these waves, the path difference must be an integer number of wavelengths:

    n x wavelength= 2x

    This leads to the Bragg equation:

    n x wavelength = 2dsin(theta)

    Forutunately a computer can do all this for us! The rest of the data is collected by the computer once the unit cell has been determined. The computer then performs what can be regarded as 'black box' calculations on the data to convert the diffraction pattern back into a map of electron density. It is then down to the user to interpret the data and to use their chemical knowledge to assign a structure. Refinements are then made for intensity and absorption correction. This all sounds so easy, but in practice it requires patience, chemical knowledge, some logical thinking and a certain amount of luck!

     

    X-RAYS  - HISTORY  - MAX VON LAUE  - WILLIAM H. BRAGG  - WILLIAM L. BRAGG  - PRINCIPLES

     

     

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