The limit of application of the Scherrer equation

Abstract

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.

Synthesis and properties of polyurethane elastomers based on renewable castor oil polyols

“…A narrower half‐breadth at 2 θ = 20° could be observed in diffraction spectrum of PUE‐80. This observation indicates that PUE‐80 has larger average crystallite size than other samples according to Scherrer equation . The slight difference could be explained by the crosslink density and interaction of molecular chains.…”

Effect of the Nano Crystal Size on the X-ray Diffraction Patterns of Biogenic Hydroxyapatite from Human, Bovine, and Porcine Bones

“…Cullity and Stock 38 showed that the Scherrer’s equation is valid only for crystallite sizes up to 200 nm and has close relation to the resolution of the diffractometers. According to Miranda and Sasaki 39 in an X-ray diffraction pattern, there is a multiple scattering, the waves scattered by one atom (or atomic plane) are also scattered by the other atoms (or atomic planes) and those waves are also subsequently scattered by other atoms and so on. The limits of the Scherrer’s equation have been described by Muniz et al .…”

Post-synthetic anion exchange in iron(ii) 1,2,4-triazole based spin crossover materials via mechanochemistry

“…Due to the high potential error in particle size determination via Scherrer analysis, 39 TEM was used to further explore particle size and morphology, as shown in Figure 2. § § An average particle size of 28 ± 19 nm was calculated for 1, based on statistical analysis, with a wide distribution (10 nm to 89 nm).…”