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. This 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 . They have also been employed in protein crystallography  and to solve inorganic surface structures based on diffraction patterns dominated by surfaces .
 H.F. Fan, Microsc. Res. Tech. 46 (1999) 104.
 D.L. Dorset, C.J. Gilmore, Acta Crystallogr. A 55 (1999) 448.
 C.J. Gilmore, L.D. Marks, D. Grozea, C. Collazo, E. Landree, R.D. Twesten, Surf. Sci. 381 (1997) 77.