Line profile analysis

Fig. 4.29. EDXS line-profile analysis across the interfacial region of a C-fiber reinforced SiC composite and corresponding TEM bright-field image.

When applied to the XRD patterns of Fig. 4.5, average diameters of 4.2 and 2.5 nm are found for the catalysts with 2.4 and 1.1 wt% Pd, respectively. X-ray line broadening provides a quick but not always reliable estimate of the particle size. Better procedures to determine particle sizes from X-ray diffraction are based on line-profile analysis with Fourier transform methods. 

A line profile analysis of the saturated acetylide surface reveals the buckled nature of the overlayer with a periodicity of seven protrusions or 14 lattice units along the < 110 > axis. The nominal 14 units actually match 13 lattice units therefore to accommodate seven protrusions on 13 lattice units with equal spacing would result in surface buckling (Figure 5.13). The distance between two terminal silver atoms is 5.37 A, which is 2% shorter than that in silver acetylide based on the assumption of covalent radii. 

Profound line profile analysis is possible if a set of reflections is observed, i.e., peaks from several crystallographic orders indexed by (h) are accessible. With respect to a principal reflection found at the position, V(, the positions of the higher orders are... 

Both for isotropic and anisotropic scattering patterns line profile analysis can be performed. If a curve from an anisotropic pattern is analyzed, the results are limited... 

Application. In practice, three or more peak orders must be observed. The shape of the lines should be Gaussian or Lorentzian. On these premises it is promising to carry out line profile analysis. Corresponding graphical separation methods are readily derived from the breadth relations that have just been discussed, after that the breadths B ( (x)) and B (Hdq,) (s)) of a polycrystalline ensemble have been related to structure and substituted in Eq. (8.29) or Eq. (8.30). For the size term the structure relation is... 

Better procedures for determining particle sizes from X-ray diffraction are based on line profile analysis with Fourier transform methods. The average size is obtained from the first derivative of the cosine coefficients and the distribution of particle sizes from the second derivative. When used in this way, XRD offers a fundamental advantage over electron microscopy, because it samples a much larger portion of the catalyst. The reader is referred to publications by Cohen and coworkers for more details and examples [4,10,11],... 

Another contribution to variations of intrinsic activity is the different number of defects and amount of disorder in the metallic Cu phase. This disorder can manifest itself in the form of lattice strain detectable, for example, by line profile analysis of X-ray diffraction (XRD) peaks [73], 63Cu nuclear magnetic resonance lines [74], or as an increased disorder parameter (Debye-Waller factor) derived from extended X-ray absorption fine structure spectroscopy [75], Strained copper has been shown theoretically [76] and experimentally [77] to have different adsorptive properties compared to unstrained surfaces. Strain (i.e. local variation in the lattice parameter) is known to shift the center of the d-band and alter the interactions of metal surface and absorbate [78]. The origin of strain and defects in Cu/ZnO is probably related to the crystallization of kinetically trapped nonideal Cu in close interfacial contact to the oxide during catalyst activation at mild conditions. A correlation of the concentration of planar defects in the Cu particles with the catalytic activity in methanol synthesis was observed in a series of industrial Cu/Zn0/Al203 catalysts by Kasatkin et al. [57]. Planar defects like stacking faults and twin boundaries can also be observed by HRTEM and are marked with arrows in Figure 5.3.8C [58],... 

Jf-Ray Methods. - A -ray line-broadening is often used to estimate the mean size of supported metal crystallites and introductory accounts of the technique in relation to catalyst examination are available. Recently, more detailed information is being extracted, e.g., the distribution of crystallite size, the presence of strain, and an indication of crystallite shape. The crystallite size distribution obtained from X-ray line-profile analysis can be complicated by spurious oscillations. A method for the smoothing of crystallite size distribution by use of a least-squares procedure with a stabilization scheme has been described (with references to other methods). One such correction procedure was appUed to obtain crystallite size distributions in... 

INDIVIDUAL PEAK FITTING AND LINE PROFILE ANALYSIS... 

The view about line profile analysis given in this chapter is pessimistic, it is the consequence of the complexity of the Bragg peak shapes as they occur from poorly-crystallized material. More optimistic is the future of the main whole powder pattern fitting applications (decomposition or Rietveld methods) that have moved beyond the initial stages, enabling structure determinations (almost routinely) and refinements (routinely) of moderately complex structures to even complex crystal structures such as proteins (sometimes). 

Two important fields of interest in powder diffraction research today are ab initio structure determination from powder diffraction data (SDPD) and line profile analysis (LPA). 

The analysis of line profiles in Powder Diffraction patterns is a topic nearly as old as diffraction itself However, despite the long time that has passed since the pioneering studies of Scherrer (1918), and the rich literature and textbooks produced over many decades, line profile analysis is still a subject of active research. ... 

BOU 01b] BOULLE A., LEGRAND C., GUINEBRETIERE R., MERCURIO J.P., DAUGER A., Application of X-ray diffraction line profile analysis to the study of planar faults in layered Bi - containing perovskites , J. Appl. Cryst., vol. 34, p. 699-703,2001. 

DEL 82] DELHEZ R., DE KEIJSER T.H., MITTEMEIJER E.J., Determination of crystallite size and lattice distorsions through x-ray diffraction line profile analysis , Fresenius Z Anal. Chem., vol. 312, p. 1-16, 1982. 

SCA 02] SCARDI P., LEONI M., Line profile analysis pattern modeling versus profile fitting , J. Appl. Cryst, vol. 39, p. 24-31, 2006. 

SUT 95] SUTTA P., JACKLIAK Q., TVAROZEK V., NOVOTNY I., X-ray diffraction line profile analysis of ZnO thin films deposited on Al-Si02-si substrates . Science and technology of electroceramic thin films, Kluwer Academic Publishing, p. 327-334,1995. 

UNG 99] UNGAR T., The dislocation based model of strain broadening in x-ray line profile analysis , in SNYDER R.L., FIALA J., BUNGE H.J. (eds.). Defect and microstructure analysis by diffraction, lUCr Monographs on crystallography, no. 10, Oxford University Press, p. 264-317,1999. 

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