Size Strain Analysis

Most Rietveld software can perform size-strain analysis, even though this may require some manual calculations based on the software output. Some powder diffraction peak profiling programs also provide simple options for size-strain analysis. Table 17.19 gives a miscellaneous non-comprehensive list of programs. 

ARITVE Modelling the Silica Glass Structure by the Rietveld Method. A. Le Bail, J. Non Cryst. Solids, 1995, 183, 39 42, and Reverse Monte Carlo and Rietveld Modelling of the NaPbM2F9 (M = Fe, V) Fluoride Glass Structures, A. Le Bail, J. Non Cryst. Solids, 2000, 271, 249 259 

BGMN BGMN a new fundamental parameters based Rietveld program for laboratory X ray sources, its use in quantitative analysis and structure investigations, J. Bergmann, P. Friedel and R. Kleeberg, Int. Union Crystallogr., Commission Powder Dijfr. Newsletter 1998, No. 20, pp. 5 8 

EXTRACT EXTRACT A Fortran Program for the Extraction of Integrated Intensities from a Powder Pattern, Ch. Baerlocher, (1990) Institut fur Kristallographie, ETH, Zurich, Switzerland 

Fullprof FULLPROF. A Program for Rietveld Refinement and Pattern Matching Analysis, J. Rodriguez Carvajal, Abstracts of the Satellite Meeting on Powder Diffraction of the XV Congress of lUCr, (1990) Toulouse, France, p. 127 

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An interesting discussion about reliability of size/strain analysis methods can be found in Ref. [29] where the results on peak shape analysis of a round-robin sample are reported and commented. 

Table 17.19 Available size-strain analysis software.

LHPM a Computer Program for Rietveld Analysis of X ray and Neutron Powder Diffraction Patterns, R. J. Hill, and C. J. Howard (1986) AAEC Report No. Ml 12 and QPDA A User Friendly, Interactive Program for Quantitative Phase and Crystal Size/Strain Analysis of Powder Diffraction Data, I. C. Madsen and R. J. Hill, Powder Diffr., 1990, 5, 195 199 A Rietveld analysis program RIETAN 98 and its applications to zeolites, F. Izumi and T. Ikeda, Mater. Sci. Forum, 2000, 321-324, 198 203 and F. Izumi, Development and Applications of the Pioneering Technology of Structure Refinement from Powder Diffraction Data, J. Ceram. Soc. Jpn., 2003, 111, 617 623... 

C. Suryanarayanaand M. G. Norton, X-Ray Diffraction, A. Practical Approach , Plemnn Press, New York, 1998, An excellent elementary introduction to powdermethods with worked examples and exercises that allow the reader to work through determination of unit cell dimensions, crystalhte size, strain and quantitative phase analysis. Highly recommended for the novice. 

The successful testing of DDM method for structure refinement purposes allows us to predict its applicability in other fields of powder diffraction, such as the analysis of microstructure and quantitative phase analysis (QPA). Trial runs of DDM for the XRD data supplied by the International Union of Crystallography Commission on Powder Diffraction for the Size-Strain and QPA round-robins gave encouraging results. Respective examples are included in the DDM program package. In particular, the biases in the phase contents determined by DDM refinement for the QPA round-robin samples from the weighted amounts were less than 1 wt.%. 

Simultaneous Crystallite Size, Strain and Structure Analysis from X ray Powder Diffraction Patterns, S. A. Howard and R. L. Snyder, NYS College of Ceramics Technical Publication, New York State College of Ceramics, Alfred University, Alfred, NY 14802, USA... 

N.C., STEPHENS P.W., TOBY B.H., Size-strain line-broadening analysis of the ceria round-robin sample ,/. Appl. Cryst, vol. 37, p. 911-924,2004. 

Chi antenna size" strains were identified. A biochemical and molecular analysis of these new transformants is now being undertaken. 

DNA insertional mutagenesis library Proceed with the genetic, molecular and biochemical analysis of the two additional (recently isolated) putative "truncated Chi antenna size" strains that have been isolated. 

A series of copolymers of D,L-lactide and CL were synthesized by ROP using zinc lactate as a catalyst and carrying out the reaction at 145""C for 8 days. The characterization of PCL and its copolymers with lactides is often done by size exclusion chromatography, DSC, NMR, and stress-strain analysis. Kister et al. used vibrational spectroscopy, particularly Raman spectroscopy, for determination of morphology, conformation, configuration, and composition of the copolymers [49]. Raman spectroscopy thus appeared to be a suitable method for the identification of P(DLA-co-CL) samples directly from solid samples without any special preparation. 

This plastic deformation is localised around the crack tip and is present in all stressed engineering materials at normal temperatures. The shape and size of this plastic zone can be calculated using Westergaards analysis. The plastic zone has a characteristic butterfly shape (Fig. 8.83). There are two sizes of plastic zone. One is associated with plane stress conditions, e.g. thin sections of materials, and the other with plane strain conditions in thick sections-this zone is smaller than found under plane stress. 

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

The peak profile analysis techniques allow separating the intrinsic and extrinsic causes producing peak broadening and shift. Accurate peak profile analysis requires the instrumental broadening well characterized and, in general, significantly smaller than the one due to sample defects (size and strain). New high quality X-ray sources and... 

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