Direct Methods
- Practical Electron Microscopy and Database -
- An Online Book -  




Direct methods are numerical techniques for solving the phase problem under single scattering conditions. The methods are based on the assumptions of atomicity and an assumed sign for the scattering potential. Accurate structure factor intensities can be obtained for all reflections from single crystal X-ray diffractions. Determination of crystal structure factor phases can be done through direct methods, Patterson method, charge-flipping algorithm or maximum entropy method, in combination with single crystal X-ray diffraction.

For small crystals, this Direct-Methods technique requires atomic-resolution diffraction data and several strong reflections per atom. The direct method has made it relatively routine to determine structure for molecules of 100 or fewer atoms. However, as molecular size increases, the probability relationships become weaker and the direct method breaks down for molecules larger than about 150 non-hydrogen atoms. Hauptman and Jerome Karle won a Nobel prize in 1985 for their work in the late 1940s and early 1950s on the direct method.

Direct methods have been employed to extend the resolution of high-resolution electron microscope (EM) images, and to solve incommensurate crystal structures [1]. They have also been employed in protein crystallography [2] and to solve inorganic surface structures based on diffraction patterns dominated by surfaces [3].

Example of solving crystal structure by using direct methods is:
         All silicon positions and part of the oxygen positions in high-silica zeolite SSZ-48 (space group P21) were located. [4]










[1] H.F. Fan, Microsc. Res. Tech. 46 (1999) 104.
[2] D.L. Dorset, C.J. Gilmore, Acta Crystallogr. A 55 (1999) 448.
[3] C.J. Gilmore, L.D. Marks, D. Grozea, C. Collazo, E. Landree, R.D. Twesten, Surf. Sci. 381 (1997) 77.
[4] Junliang Sun and Xiaodong Zou, Structure determination of zeolites and ordered mesoporous materials by electron crystallography, DOI: 10.1039/c0dt00666a.