Real-space information

Order and polydispersity are key parameters that characterize many self-assembled systems. However, accurate measurement of particle sizes in concentrated solution-phase systems, and determination of crystallinity for thin-film systems, remain problematic. While inverse methods such as scattering and diffraction provide measures of these properties, often the physical information derived from such data is ambiguous and model dependent. Hence development of improved theory and data analysis methods for extracting real-space information from inverse methods is a priority. 

Glatter O (1979) The interpretation of real-space information from small angle scattering experiments. J Appl Crystallogr 12 166... 

The atomic surface order is described in terms of a simple unit cell and techniques for the preparation of surfaces with defined atomic order are well established. The description of mesoscopic structures is not as straightforward for a single-crystal surface mesoscopic properties can be, e. g., terrace widths and step densities, for dispersed electrodes the size and distribution of particles. Real-space information under in-situ electrochemical conditions is required for the characterization of such mesoscopic properties. This information can only be derived from the application of scanning probe techniques, which were introduced to electrochemistry in the mid-1980s and give high-resolution real-space images of electrode siufaces under in-situ electrochemical conditions. 

However, the real advantage of electron microscopy is the ability to obtain real-space information on the sub-micron scale, coupled with opportunity to probe the molecular organization using diffraction techniques on the same sample. 

To obtain real-space information about the morphology of polymeric materials, various optical microscopic methods such as OM and CLSM are available (cfr. Chp. 5.3). Use of electrons as a light source for microscopy opens other perspectives [124]. Electron microscopy (EM) provides structural information in both the real and reciprocal space. Electron... 

In practice, a diffractometer can only access a finite k-space range with a maximum cutoff value kmax- Provided that sufficiently small k-values can be accessed, a reciprocal-space function such as F(k) will therefore be truncated by a modification function given by M(k) = 1 for k < kmax and M(k) = 0 for k > kmax- lu consequence, the real-space information corresponding to F k) is obtained by the Fourier transform relation... 

The corresponding real space information is given by the total pair correlation function ... 

Biswas P., Atta-Fynn R., Chakraborty S., and Drabold D. A., Real space information from fluctuation electron microscopy applications to amorphous silicon,/. Phys. Condens. Matter, 19,455202 (9 p.) (2007). 

The exact mathematical formalism relating the experimental observable, i.e. the angular distribution of scattering intensity, to the "real-space information, i.e. the distance distribution function p(r), is given by Fourier transformation according to... 

---