Diffraction simulation

Knupp, C., and Squire, J. M. (2004). HELIX A helical diffraction simulation program. / Appl. Cryst. 37, 832-835. 

Meng YS, Ceder G, Grey CP, Yoon W-S, Shao-Hom Y (2004) Understanding the crystal structure of layered LiNio.5Mno.5O2 by electron diffraction and powder diffraction simulation. Eiectrochem Solid State Lett 7(6) A155-A158... 

Steinmann P. 1997. DIFFRACT vl.O - a Fraunhofer diffraction simulation program www.physics. gla.ac.uk/ awatt/Physics2/P2Lab/diffract/doc/ difcont. htm. 

Simulations of that kind result in a wide variety of A-scans and wavefront snapshots. The first screening of this material reveals, that the simulations in which the transducer is coupling partly to the V-butt weld and partly to the steel exhibit quite a number of pulses in the A-scans because the coupling at the interface of the weld results — due to the anisotropic behavior of the weld — in a complicated splitting of the transmitted wavefront. The different parts of the splitted wavefront are reflected and diffracted by the backwall, the interface, and — if present — by the notch and, therefore, many small signals are received by the transducer, which can only be separated and interpreted with great difficultie.s. 

Only the simulations in which the transducer is coupling either to the V-butt weld or to the surrounding steel can be analyzed in a simple and intuitive way, which means that the different pulses in the A-scan signals can be related uniquely to the reflection or diffraction of the wavefront at the weld, the backwall, and/or the notch. 

Since the development of grazing incidence x-ray diffraction, much of the convincing evidence for long-range positional order in layers has come from this technique. Structural relaxations from distorted hexagonal structure toward a relaxed array have been seen in heneicosanol [215]. Rice and co-workers combine grazing incidence x-ray diffraction with molecular dynamics simulations to understand several ordering transitions [178,215-219]. 

Bartell and co-workers have made significant progress by combining electron diffraction studies from beams of molecular clusters with molecular dynamics simulations [14, 51, 52]. Due to their small volumes, deep supercoolings can be attained in cluster beams however, the temperature is not easily controlled. The rapid nucleation that ensues can produce new phases not observed in the bulk [14]. Despite the concern about the appropriateness of the classic model for small clusters, its application appears to be valid in several cases [51]. 

With XRD applied to bulk materials, a detailed structural analysis of atomic positions is rather straightforward and routine for structures that can be quite complex (see chapter B 1.9) direct methods in many cases give good results in a single step, while the resulting atomic positions may be refined by iterative fitting procedures based on simulation of the diffraction process. 

Table 81.21.1. Surface stmctural detemiination methods. The second colunni indicates whether a technique can be considered a diffraction method, in the sense of relying on wave interference. Also shown are statistics of surface stmctural detemiinations, extracted from the Surface Stmcture Database [14], up to 1997. Counted here are only detailed and complete stmctural determinations, in which typically the experiment is simulated computationally and atomic positions are fitted to experiment. (Some stmctural detemiinations are perfomied by combining two or more methods those are counted more than once in this table, so that the colunnis add up to more than the actual 1113 stmctural detemiinations included in the database.)...

The first analytical tool to assess tire quality of a zeolite is powder x-ray diffraction. A collection of simulated powder XRD patterns of zeolites and some disordered intergrowths togetlier witli crystallographic data is available from tlie IZA [4o]. Phase purity and x-ray crystallinity, which is arbitrarily defined as tlie ratio of tlie intensity of... 

The structure of the metallocene cation energy minimised with the Car-Parrinello method agrees well with the experimentally obtained crystal structures of related complexes. Typical features of the structure as obtained from X-ray diffraction on crystals of very similar neutral complexes (e.g., the dichlorides), such as small differences in distances between C atoms within a cyclopentadienyl (Cp) ring, as well as differences in distances between the C atoms of the Cp ring and the Zr atom, were revealed from the simulations. 

Idistribution functions can be measured experimentally using X-ray diffraction. The regular arrangement of the atoms in a crystal gives the characteristic X-ray diffraction pattern with bright, sharp spots. For liquids, the diffraction pattern has regions of high and low intensity but no sharp spots. The X-ray diffraction pattern can be analysed to calculate an experimental distribution function, which can then be compared with that obtained from the simulation. 

Gdanitz, R J 1992. Prediction of Molecular Crystal Stluctures by Monte Carlo Simulated Annealing Without Reference to Diffraction Data. Chemical Physics Letters 190 391-396. 

Molecular dynamics simulations of proteins often begin with a known structure (such as an X-ray diffraction structure) that you want to maintain during equilibration. Since the solvent may contain high energy hot spots, equilibration of the protein and solvent at the same time can change the protein conformation. To avoid this, select only the water molecules and run a molecular dynamics equilibration. This relaxes the water while fixing the protein structure. Then deselect the water and equilibrate the whole system. 

J.S. Wark, R.R. Whitlock, G. Kiehn, R. Smith, and Z. Lin, Simulation of Transient X-Ray Diffraction from Shocked Crystals, in Shock Compression of Condensed Matter—1989 (edited by S.C. Schmidt, J.N. Johnson, and L.W. Davison), Elsevier Science, Amsterdam, 1990, pp. 901-904. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Figure 18.14 The diffraction pattern of helices in fiber crystallites can be simulated by the diffraction pattern of a single slit with the shape of a sine curve (representing the projection of a helix). Two such simulations are given in (a) and (b), with the helix shown to the left of its diffraction pattern. The spacing between the layer lines is inversely related to the helix pitch, P and the angle of the cross arms in the diffraction pattern is related to the angle of climb of the helix, 6. The helix in (b) has a smaller pitch and angle of climb than the helix in (a). (Courtesy of W. Fuller.)...

To measure the goodness of fit, and to quantify the structural determination, a reliability (i -factor) comparison is used. In comparing the data and simulation of the experiment for many trial structures, a minimum R factor can be found corresponding to the optimal structure. In this way atomic positions can be determined in favorable cases to within a few hundredths of an A, comparable to the accuracy achieved in Low-Energy Electron Diffraction (LEED). 

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