Crystallite sizes

The crystallite size can be obtained from the wide-angle X-ray scattering (WAXS) pattern of a silk fiber. Radial integration along the equator and meridian on the WAXS gives the radial peak width on the (200), (120), and (002) reflections. According to Scherrer s formula [85], the crystal size is 

6 and X = 1.5418A. The equatorial data can be deconvoluted into three crystalline 

It was found that the crystaUites become slightly smaller or the crystalline order 

The effect of reeling speed on the crystallite size can be explained by the 

The study of the silk secretion of Bombyx mori and Nephila clavipes when the silk 

Average crystallite sizes can be estimated from peak widths (e.g., see [22]) using the Scherrer equation  

A treatment of the analysis of line-shapes to extract particle size, shape and strain information is discussed in detail in Chapter 13. Here we present an overview. 

The slope k of that line leads to an apparent mean size according to  

This Et has the same signification as the defined below from the Fourier analysis. In both cases, the true mean size is the product of the apparent dimension by the Scherrer constant relative to the variance, K . Tournarie and Wilson have tabulated K for different crystallite shapes as a function of the Miller indices hkl. 

Finally, Bertaut imagined the homogeneous domains of coherent diffraction as constituted by columns of elementary cells juxtaposed orthogonally to the diffracting planes, and he defined a size distribution P(n) as the numerical fraction of columns of length n cells. From that size distribution function, the size-only Fourier coefficients can be defined  

Fourier coefficients. Note that it is preferred here to use summations instead of integrals, since the problem is discontinuous (number of cells). To the harmonic number n is associated a distance M, expressed in angstroms, in the direction orthogonal to the diffracting planes  

People often use the x-ray diffraction (XRD) technique to estimate the crystal size based on the crystallite facets. For Pt, the prominent crystalline surfaces are the (111), (200), and (220) and (311), respectively. Based on the broadening of the x-ray diffraction peaks, the crystallite sizes are calculated according to the Debye-Scherrer equation. 

For spherical catalyst particles, the surface area per unit mass can be calculated. If the radius of the particle is r and the density of the metal is d, then the volume (v), the surface area (s), and the mass (m) of each particle are, respectively. 

Unit Mass Surface Areas of Different-Sized Ft Particles 

Particle Diameter (nm) Surface Area (cm g ) Surface Area (m g ) 

Pt unit mass surface area versus particle diameter. 

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Crystallite Size. From the width of the peaks the computer can determine the size of the crystaUites in the sample. The smaller the crystaUite size, the broader are the diffraction peaks. This kind of analysis is important for determining particulate size of certain materials (eg, sUica) where a range of crystaUite size may be a health hazard if inhaled into the lungs. 

Portiand cement clinker structures (18,19) vary considerably with composition, particle size of raw materials, and burning conditions, resulting in variations of clinker porosity, crystallite sizes and forms, and aggregations of crystallites. Alite sizes range up to about 80 p.m or even larger, most being 15—40 )J.m. 

PAN fibers develop a structure with little point-to-point relationship between atoms in neighboring basal planes. This structure is labeled the turbostratic configuration and is characterized by interplanar spacing values greater than 0.344 nm. The crystallite size in the direction normal to the basal planes, or stack height (L, ), in turbostratic graphite is typically less than 5 nm. 

Substance Saturation strain 10 (pressure) Crystallite size... 

In a comparison of shock-modified powder to powder subjected to other intense deformation, data on shock-modified TiC was compared to a well annealed TiC powder wet milled for many hours to similar values of residual strain. As depicted in Fig. 7.4 the anisotropies observed in residual strain and crystallite size in the two cases are quite different. The shock-modified powders show less anisotropy in strain and more anisotropy in crystallite size... 

Fig. 7.3. Crystallite size determined from x-ray diffraction line broadening studies show substantial shock-induced reductions. The chemical reactivity of such powders would be expected to be greatly enhanced [86M02].

Fig. 7.4. Residual strain and crystallite size are compared for TiC powders subjected to wet milling and shock modification. Significant differences are observed in the anisotropies of both features (after Morosin and co-workers [86M02]).

Table 7.3. Shock-modified powders Crystallite size, strain, and static magnetization data on hematite (after Williamson et al. [86W03]).

The barium ferrite was found to have an increase in magnetic anisotropy, as in the nickel ferrite, but its overall effect on magnetization was less because of greater magnetocrystalline anisotropy. The shock modification caused reduced crystallite size and local damage that resulted in increased microwave absorption. 

Fig. 7.12. The monoclinic to tetragonal conversion of shock-modified zirconia was studied with DTA by Hammetter and co-workers. The conversion temperature was found to be strongly changed and dependent on shock-modification conditions. The higher-pressure behavior was found to be strongly correlated with reduction in crystallite size [84H01],...

Similarly to the previously considered case of the first-order transitions, the above picture applies to a specific situation in which the sample exhibits just one type of crystallites, all of the same size, and where we neglect the effects of energetical heterogeneity that are bound to be present at the crystallite boundaries. In real samples one expects to find a distribution of the crystallite sizes, and hence more complex behavior. 

Table 4 Degree of Crystallinity and Average Crystallite Size of Differently Drawn PET Fibers...

Draw ratio Degree of crystallinity Lattice disorder coefficient (k) Average crystallite size perpendicular to the crystallographic plane (hkl) Dhki (nm) ... 

The low electrical conductivity of PET fibers depends essentially on their chemical constituency, but also to the same extent on the fiber s fine structure. In one study [58], an attempt was made to elucidate the influence of some basic fine structure parameters on the electrical resistivity of PET fibers. The influence of crystallinity (jc) the average lateral crystallite size (A), the mean long period (L), and the overall orientation function (fo) have been considered. The results obtained are presented in the form of plots in Figs. 9-12. 

Figure 15 Electrostatic charge of PET fiber versus average crystallite size perpendicular to the chain direction.

Coke materials are generally made by heat-treatment of petroleum pitch or coal-tar pitch in an N2 atmosphere. Coke made from petroleum is called "petroleum coke" and that from coal is called "pitch coke". These materials have the closest-packed hexagonal structures. The crystallinity of coke materials is not so high as that of graphite. The crystallite size of coke along the c-axis (Lc) is small (about 10-20 A) and the interlayer distance (d value about 3.38-3.80 A) is large. 

For a fixed filling ratio, the degree of crystallinity and mean crystallite size are somewhat higher in PFCM than in mechanical mixtures of similar composition and similar matrix characteristics [299, 300]. 

Figure 2. Variation of crystallite size with calcination temperature...

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