Sample broadening crystallite size

It is noted that for CZ samples, the crystallite sizes decreased from 12.5 to -10.9 nm as the calcination temperature was increased from 900 to 1000 °C. This may be due to the occurrence of the phase separation for CZ samples during calcinations within the temperature range of 900-1000 °C, which led to the broadening of XRD diffraction peak The crystallite growth rate of ACZ sample was slower than that of CZ sample (Figure 3). This reveals that the doped Al ions via coprecipitation route could suppress the crystallite growth of Ceo.5Zfo.5O2 effectively. 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

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. 

There are two major problems associated with the x-ray method. The first problem is encountered during sample preparation. At this step, preferred orientation of the particles must be minimized [1], Reduction of particle size is one of the most effective ways of minimizing preferred orientation, and this is usually achieved by grinding the sample. Grinding, however, can also disorder the crystal lattice. Moreover, decreased particle size can cause a broadening of x-ray lines, which in mm affects the values of /c and /a. The relationship between the crystallite size, t, and its x-ray line breadth, /3, (assuming no lattice strain) is given by the Scherrer equation [2] ... 

Preferred orientation of the particles must be minimized. One of the most effective ways to achieve this is to reduce the particle size by grinding the sample [1], As already discussed in Section III.A, however, grinding can disorder the crystal lattice. Grinding can also induce other undesirable transitions, such as polymorphic transformations [59]. In order to obtain reproducible intensities, there is an optimum crystallite size. The crystallites have to be sufficiently small so that the diffracted intensities are reproducible. Careful studies have been carried out to determine the desired crystallite size of quartz, but no such studies have been reported for pharmaceutical solids [60]. Care should be taken to ensure that the crystallites are not very small, since decreased particle size can cause a broadening of x-ray lines. This effect, discussed earlier (Eq. 9), usually becomes apparent when the particle size is below 0.1 jum. 

Peak widths. The lineshapes and linewidths of peaks in a powder XRD pattern depend on the crystallinity of the sample, as well as features of the instrumentation and the data collection procedure. In particular, peaks in the powder XRD pattern may be broadened as a consequence of small crystallite size. If the powder XRD patterns of two samples with the same crystal structure have significantly different linewidths, the visual appearance may differ substantially, especially in regions of significant peak overlap. 

In Equation 4.1, the factor fiF(0) is included, which is the peak profile function, that describes particle size broadening and other sources of peak broadening. The XRD method can be used as well for the measurement of the crystallite size of powders by applying the Scherrer-Williamson-Hall methodology [4,35], In this methodology, the FWHM of a diffraction peak, p, is affected by two types of defects, that is, the dislocations, which are related to the stress of the sample, and the grain size. It is possible to write [35]... 

In order to study the growth of particles with temperature, anatase powder (preheated to 150°C) was heated for a period of 3 h at 400, 600, 800 and 1000°C. Marked increase in particle size was noticed in the 600-1000°C region, as indicated by the photo-micrographs. The specific surface area (B.E.T.) of anatase heated at 400°C was 55 m2/g and decreased markedly for samples heated to higher temperatures. The crystallite size normal to the (101) and (110) reflecting planes of anatase and rutile samples was calculated by measuring the X-ray diffraction line-widths of the samples heated at 200, 400, 600, 800 and 1000°C for 3 h. The Scherrer equation corrected for instrumental line-broadening by Warren s equation was employed for the calculation.16 The line-width of the sample heated at 1000°C was taken as the reference. The crystallite size increases rapidly after 600°C (fig. lb). The transformation of pure anatase also starts only above 600°C. 

In utilizing the Scherrer equation, care must be exercised to properly account for instrumental factors which contribute to the measured peak width at half maximum. This "intrinsic" width must be subtracted from the measured width to yield a value representative of the sample broadening. When the experimental conditions have been properly accounted for, reasonably accurate values for the average crystallite size can be determined. Peak shapes and widths, however, can also provide other information about the catalyst materials being studied. For example, combinations of broad and sharp peaks or asymmetric peak shapes in a pattern can be manifestations of structural disorder, morphology, compositional variations, or impurities. 

In addition, diffraction line breadth contains information on lattice strain, lattice defects, and thermal vibrations of the crystal structure. The chief problem to determine crystallite size from line breadth is the determination of /3(20) from the diffraction profile, because broadening can also be caused by the instrument. To correct for the instrumental broadening on the pattern of the sample, it is convenient to run a standard peak from a sample in which the crystallite size is large enough to eliminate all crystallite size broadening. By use of a convolu-... 

It should be remembered that the accuracy with which the crystallite size may be determined decreases with increasing crystallite size. The limit is about 2000 A with careful and accurate measurement of the peak profile, the FWHM and the instrumental broadening. Furthermore, the result is an average over all the crystallite sizes, as the method does not provide the distribution of sizes in the sample. ... 

If the strain field is not homogeneous on the length scale of the crystallite size or smaller, according to Equation (9), different parts of the material diffract at slightly different angles, thus producing a broadened profile. Profile width and shape will evidently depend on the strain distribution across the sample. Considering the root mean square strain (or microstrain), Equation... 

This assumes that the two broadening effects are simply additive, and a plot of 3 X cos 0 versus sin 0 will yield Es and dy from the slope and intercept, respectively. The assumption of linear additivity of the broadening effects assumes that both have a Lorentzian shape (Cauchy approximation). The three other cases, Gauss-Gauss, Gauss-Cauchy and Cauchy-Gauss, have each been considered (see for example Ref. [175]). It is usually found that Es increases with decreasing crystallite size. One common problem with XRD measurements of particle size is that they may provide a false impression of the sample if there is amorphous material present that will not diffract [176]. 

The widths of the peaks in the pattern give an indication of the crystalline quality of the sample. They are dependent upon the intrinsic instrumental peak width, the crystallite size (or more precisely, the size of the diffracting domains), and the amount of stress or strain in the material. As the domains of coherent scattering decrease below ca 1000 A, the peaks will broaden noticeably. If the crystallites are very thin plates, the reflections from planes perpendicular to the short dimension may be broader than those from planes in other... 

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