A brief history of the new evolution of the powder diffraction method is described in this chapter. The advent of the Rietveld method gave a great impact on the traditional powder diffraction method. It was just a small step, according to Dr, H.M. Rietveld, to refrain from the integrated intensity and to use a profile intensity as an observation. Since then, however, the Rietveld method has been used to refine a number of crystal structures by using powder diffraction data, and it is now an indispensable technique in materials research. It also stimulated a development of the method such as the Pawley method, and induced interactions with other techniques such as the individual profile fitting. A rush of conferences held in a recent few years indicates an increasing interest of the people in powder diffraction.
Synchrotron radiation sources have sufficient brightness to permit the construction of aberration free diffractometers with perfectly symmetric instrument resolution functions. This paper outlines the development of one such general purpose instrument. It combines X-ray optical and mechanical simplicity with versatility, high speed and adequate resolution for general purpose measurements in both angle scanning and energy scanning data collection modes of operation. These ideas were developed as part of a long term collaboration with W. Parrish of I.B.M. San Jose at the Stanford Synchrotron Radiation Facility and an instrument with identical X-ray optics has been avairable for users at Daresbury Laboratory for several years.
Characteristics of the High Resolution Powder Diffractometer (HRPD) recently installed at JRR-3M are described. The machine is composed of 64 detectors equally spaced at every 2.5 degrees in diffraction angle. The obtained resolution of the machine is 0.2% in Δd/d at best. It is also described that the Wide Angle Neutron Diffractometer (WAND) at HFIR is particularly suited for studing kinetics of the phase transitions in various materials. Some experiments performed with the dif fractometers are reviewed briefly.
A method of time-of-flight (TOF) neutron powder diffraction based on the pulsed neutron source is described. When the source flux is sufficiently high, a high-resolution machine is easily realized by adopting a long flight path and back-scattering geometry. A high-resolution powder diffractometer HRP is in operation at the KENS pulsed neutron source in KEK, and achieves a resolution of Δd/d-3×10-3. An example of structure refinement by HRP is shown. Application of TOF neutron diffraction to structure analysis at high pressure is also presented.
The outline of the Rietveld method is described where structure and lattice parameters are directly refined from powder diffraction data. Several functions such as extinction correction, preferred-orientation function, and profile-shape function, which are contained in the model function, have been improved to give physical meanings to parameters contained in them. Structure-refinement strategy is introduced which may be useful for beginners. Combined refinement of X-ray and neutron diffraction data is now being used more and more widely to extract structural information from powder patterns as much as possible.
The first half of this chapter is devoted for describing: 1) a brief history of profile functions in both neutron and X-ray powder diffractions, 2) the relation between the Voigt and pseudo-Voigt functions and that between the pseudo-Voigt and Pearson VII functions, 3) the methods of asymmetrizing the symmetric profile function, and 4) the effect of profile-function truncation in powder pattern fitting. In the latter half of this chapter, the theory and application of the pattern decomposition method are described. Examples are pattern decompositions by using the individual profile fitting method and the Pawley method, The use of convolution function in pattern fitting derives the physically meaningful information from the profile shape. A sophisticated example of whole-powder-pattern fitting using a lattice-direction-dependent profile-width-model is given.
A recent progress of the Maximum Entropy Method to obtain a precise electron density distribution from X-ray powder diffraction data is reviewed. Results for rutile (TiO2), fcc metal Al and hcp metal Mg are given. In rutile case, apical and equatorial bonds of TiO6 octahedra are visible in the MEM density map, which is the electron density map obtained by the Maximum Entropy Method. The nuclear density distribution of rutile is also shown, in which it is seen that the nuclear is localized only on the atomic site. The MEM map of Al looks to be well described by the nearly free electron model. On the other hand, in the case of Mg, the small electron density peaks are seen between three Mg atoms on the basal plane, on which electronic layers are formed in this subsatnce.
The application of the X-ray powder diffraction technique for the characterization of thin films is descussed. The conventional powder diffraction method can be used for the microstructure analysis, and the specular reflection method for the layer-structure analysis of thin films. Results on the characterization of selected single- and multiple-layer thin films are presented to illustrate the types of information that can be obtained with the methods.
Fundamentals of powder diffractometry are presented, which are 1) the angle dispersive method, 2) problems in the measurements by the X-ray powder diffractometer, 3) errors from particle size and corrections for the preferred orientation, 4) energy dispersive method and 5) corrections for the anomalous dispersion.
In currently used structure analysis based on powder diffraction data, the TDS correction which is well established in the accurate structure analysis by using a single crystal has so far been ignored except early studies for cubic crystal (i.e. Warren; X-ray Diffraction (1969) ) . It is pointed out that such correction is also necessary for the powder diffraction data, if the aim of structure analysis is in obtaining the accurate thermal parameters of the constituent atoms of a crystal.
Time-resolved observations of phase transitions and solid reactions have been undertaken by angular dispersive powder diffraction at high temperature and pressure using the curved position sensitive detector (PSD) . The PSD streamer mode has a great advantage for the in situ observations of the structure changes within a few seconds because of high photon count efficiency of more than 70% and high angular resolution of 0.06° in 2θ. A Computer Aided Measurement And Control (CAMAC) System was applied to the time-resolved measurement of the diffraction intensities. An ADC having a 450MHz fast converter and histogram memory were installed in the system. The in situ observation of the pressure-induced amorphization of GeO2 using diamond anvil pressure cell and kinetic studies of dehydration of alkaline earth hydroxides at high temperature are presented in this paper.
Recent high-pressure powder diffraction techniques using diamond-anvil cell/multi-anvil apparatus incorporated with synchrotron radiation X-rays and advanced detector system have made it possible to reliably determine atomic positions in a pressure range near 1 Mbar. We have presented such techniques and several experimental results mainly obtained at Photon Factory.
A method of structure determination in quasi-periodic structures by the Rietveld method is shown with special emphasis on difficulties encountered in the powder method and their solutions. Features of recently developed Rictveld programs for quasi-periodic structures are reported.
Nowadays high angular resolution powder diffraction data are available from specially designed diffractometers and cameras employing synchrotron radiation and/or conventional X-ray sources, Several unknown structures have been determined from the powder diffraction data. The structure analysis is performed in the following sequence of steps; 1) data collection, 2) indexing and lattice parameter determination, 3) preparation of a |F (hkl) | set, 4) determination of approximate atomic coordinates, 5) structure refinement. Each of the above steps is described especially for the organic compounds.