Dependence of Sizes and Shapes of Crystallites in Zinc Oxide Powder on Annealing Temperature

Kojdecki, Marek Andrzej; Mielcarek, W.

doi:10.4028/www.scientific.net/msf.321-324.1040

Cited by 11 publications

(30 citation statements)

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“…with the relative accuracy within 0.001 (Kojdecki & Mielcarek, 2000;Kojdecki, 2004); moreover the FWHM of each profile (5), originating from the strain distribution, is proportional to tan # 0 . Equations (12) and (13) illustrate the influence of the size anisotropy (in the case of a prismatic crystallite) or isotropy (in the case of a spherical crystallite) on a pure line profile.…”

Section: X-ray Diffraction Pattern From Model Polycrystalline Materialsmentioning

confidence: 98%

“…A similar model was proposed implicitly by Wilson (1962Wilson ( , 1963Wilson ( , 1970 but without a good method for finding microstructure characteristics. Kojdecki (1991) proposed a new model, together with a stable method for determining microstructure characteristics; a version of this approach, recently improved and updated, has made it possible to achieve convincing results (Kojdecki & Mielcarek, 2000, 2001Kojdecki, 2001Kojdecki, , 2004. Researchers active in the field of the diffraction analysis of the microstructure of materials generally accept crystallite shape, crystallite size distribution and crystalline lattice strain distribution as the principal microstructural characteristics of polycrystalline materials.…”

Section: Model Of Polycrystalline Materials 21 Statistical Model Of mentioning

confidence: 99%

“…when both the line profiles, g from a standard sample (instrumental) and h from an investigated sample (experimental), are known; s is the reciprocal-lattice vector length, s ' 4 À1 # À # 0;hkl À Á cos # 0;hkl , is the X-ray wavelength and is a sufficiently large number (Wilson, 1963). In the vicinity of the Bragg angle, the pure X-ray diffraction line profile f (for the hkl reflection) from a crystal like that described above, with a volume-weighted crystallite size distribution v, and a second-order crystalline lattice strain distribution r, may be interpreted (up to an approximately constant multiplier) as (Wilson, 1963;Kojdecki, 1991Kojdecki, , 2004Kojdecki & Mielcarek, 2000;, under the assumption that the structure factor is constant for all crystallites. For assumed crystallite shape and fixed n, the function É hkl ðn; sÞ ¼ n À3 È hkl ðn; sÞ describes the pure diffraction line (hkl reflection) from a single crystallite (scattering X-rays coherently) with a perfect lattice and with a size characterized by the number n (taken with weight n À3 ); N must be sufficiently large [so that vðnÞ ¼ 0 for n > N].…”

Section: X-ray Diffraction Pattern From Model Polycrystalline Materialsmentioning

confidence: 99%

“…is the interplanar distance for the ðhkl Þ planes (Kojdecki, 1991(Kojdecki, , 2004Kojdecki & Mielcarek, 2000).…”

Section: X-ray Diffraction Pattern From Model Polycrystalline Materialsmentioning

confidence: 99%

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Crystalline microstructure of sepiolite influenced by grinding

et al. 2005

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The crystalline microstructure of ground sepiolite has been investigated. A reference sample of sepiolite and products of its comminution by dry grinding were studied through X-ray diffraction pattern analysis, specific surface measurements by nitrogen adsorption and complementary analysis of field emission scanning electron microscope images. A statistical model of polycrystals was applied to describe and determine the crystalline microstructure of the studied specimens. The model parameters characterizing the microstructure were prevalent crystallite shape, volume-weighted crystallite size distribution and second-order crystalline lattice strain distribution, and they were determined for each sample by modelling a selected part of the X-ray diffraction pattern and fitting the simulated pattern to a measured one. A strict correlation of microstructure parameters with grinding time and with specific surface magnitudes was observed. A parallelepiped with edge-length ratios almost independent of grinding time (for longer times) was found to be the predominant crystallite shape. The crystallite size distributions were found to be close to logarithmic normal ones, with the mean values decreasing with increasing grinding time and the standard-deviation-to-mean-value ratios approximately constant. The second-order crystalline lattice strain distributions were found to be close to some simple function with the mean value equal to zero, the mean deviation increasing with increasing grinding time and the standard-to-mean-deviation ratios approximately constant. It was demonstrated that the specific surface can be calculated on the basis of the microstructure characteristics. Some details of the relation between crystallites and crystalline grains were explained by comparing the results of analyses via X-ray diffraction and scanning electron microscopy.

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Section: X-ray Diffraction Pattern From Model Polycrystalline Materialsmentioning

confidence: 98%

Section: Model Of Polycrystalline Materials 21 Statistical Model Of mentioning

confidence: 99%

Section: X-ray Diffraction Pattern From Model Polycrystalline Materialsmentioning

confidence: 99%

“…is the interplanar distance for the ðhkl Þ planes (Kojdecki, 1991(Kojdecki, , 2004Kojdecki & Mielcarek, 2000).…”

Section: X-ray Diffraction Pattern From Model Polycrystalline Materialsmentioning

confidence: 99%

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Crystalline microstructure of sepiolite influenced by grinding

et al. 2005

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“…A similar model was proposed implicitly by Wilson (1962Wilson ( , 1963Wilson ( , 1970 but without a good method for finding the microstructure characteristics. Kojdecki (1991) proposed a new model together with a stable method for determining the microstructure characteristics; a version of this approach, recently improved and updated, has made it possible to achieve convincing results (Kojdecki & Mielcarek, 2000, 2001Kojdecki et al, , 2005Kojdecki, 2004). A similar approach, although distinct in many details, was developed and recently summarized by .…”

Section: Model Of Polycrystalline Materials 21 Statistical Model Of mentioning

confidence: 99%

Microstructural evolution of mullites produced from single-phase gels

Kojdecki

Sola

Serrano³

et al. 2007

J Appl Cryst

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The crystalline microstructure of mullites obtained by heating monophasic gels has been investigated. Gels with alumina to silica molar ratio of 3:2 (as in secondary mullite) and 2:1 (as in primary mullite) were prepared by gelling mixtures of aluminium nitrate and tetraethylorthosilicate. Phase transformations were induced by heating the gel precursors, with different final treatment temperatures between 1173 and 1873 K. The mullites formed as a result of thermal treatment were studied by means of X‐ray diffraction, scanning electron microscopy and transmission electron microscopy. The crystalline structure (unit‐cell parameters) and microstructure were determined from X‐ray diffraction patterns. The formation of mullites of homogeneous chemical composition and with unit‐cell parameters depending almost linearly on the treatment temperature was found. Their compositions, expressed as alumina to silica molar ratio, were determined from the unit‐cell parameters and were in the range of those characterizing primary and secondary mullites. Mullites processed at lower temperatures were accompanied by small amounts of vitreous phase. The crystalline microstructure of the obtained mullites was interpreted by means of a mathematical model of polycrystalline material, involving prevalent crystallite shape, volume‐weighted crystallite size distribution and second‐order crystalline lattice strain distribution as model parameters. The model parameters were determined for each sample by modelling its X‐ray diffraction pattern and fitting it to a measured pattern. Bimodality of the size distribution was observed and explained as a consequence of two crystallite nucleation and growth processes, which started from small alumina‐rich and alumina‐poor domains, spontaneously formed in a precursor gel at early stages of heating. Images produced by scanning and transmission electron microscopy agreed well with the characteristics obtained from the analysis of the X‐ray diffraction patterns.

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