The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.
The Scherrer equation is a widely used tool to obtain crystallite size from polycrystalline samples. Its limit of applicability has been determined recently, using computer simulations, for a few structures and it was proposed that it is directly dependent on the linear absorption coefficient (μ) and Bragg angle (θ). In this work, a systematic study of the Scherrer limit is presented, where it is shown that it is equal to approximately 11.9% of the extinction length. It is also shown that absorption imposes a maximum value on it and that this maximum is directly proportional to sin θ/μ.
Progress is reported towards the development of a new route to obtain cadmium sulfide (CdS) thin films by using ethylene-diamine-tetra-acetic acid (EDTA) ligand on the chemical bath deposition (CBD) method. Different chemical baths are used to study changes in the structures of the CdS films for different EDTA concentrations. X-ray diffraction (XRD) is used to prove the structural characterization of the samples, and to obtain the grain size with the Scherrer's equation. The pH variations during the growth also affect the structural film quality, and it was verified by using ammonia chloride as an auxiliar-buffer plus Triton-X100.
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