Characterization of Different Shaped Nanocrystallites using X‐ray Diffraction Line Profiles

Abstract

Quantitative information on the X‐ray diffraction line profiles for different shaped nanocrystallites, using nanocrystalline Cu as an example, are obtained by using the Debye scattering equation, which is useful for characterizing nanocrystallite. The apparent lattice parameter obtained from line positions by using the Bragg's law has a larger deviation from the actual value when the crystallite sizes are smaller than about 10nm. When the crystallites are larger than about 6nm, the full width at half maximum (FWHM) ratios of FWHMhkl to FWHM002 are nearly constants which can be used to identify the shape of the crystallites. The Scherrer constant depends not only on the shape of the crystallite but also on the Miller index of the line, the values of the Scherrer constant for different shaped nanocrystallites are given in the present paper.

Fabrication of Maghemite Nanoparticles with High Surface Area

“…With the increase in temperature, the integrated peak intensity of 020 Lp decreases and from >230 °C the integrated peak intensity of 440 Mh increases (Figure 2d). Domain sizes of crystallites were calculated using the Scherrer formula with shape factor = 0.9 [40,41]. The obtained values are 5.6 ± 0.2 nm for (020) Lp and 4.1 ± 0.1 nm for (440) Mh .…”

Anomalous Magnetic Properties of Nanoparticles Arising from Defect Structures: Topotaxial Oxidation of Fe1–xO|Fe3−δO4 Core|Shell Nanocubes to Single-Phase Particles

“…The nanoparticle shape was accounted for by introducing calculated anisotropic constants, k hkl ( k 200 = 0.862 and k 220 = 0.789 for a cubic particle in a cubic crystal system) in the well-known Scherrer equation. This yields d eff = ( k hkl λ)/(2ω cos θ), the effective size of crystal along the normal of the diffraction plane where λ is the wavelength, 2ω is the fwhm of the diffraction peak (in radians), and θ is the Bragg angle . The fwhm of the 220 S and 400 S diffraction lines for NC0 and N120 translates into effective crystal sizes d 400s ≈ 8 nm and d 220s ≈ 6.5 nm and d 400s ≈ 20 nm and d 220s ≈ 9 nm for the core|shell nanocubes NC0 and the single-phase nanocubes NC120, respectively (see Supporting Information).…”

Synthesis and properties of bismuth ferrite multiferroic flowers

“…Mean size of crystallites in the nanoflowers was estimated using the Scherrer's equation [53]: D=Kλ/βcosΘ, where D is the crystallite size (in nm), β is the half-width of the diffraction peak and Θ represents the position of the Bragg peak. The constant K in the Scherrer's equation depends on the morphology of the crystal [54] and here it was assumed that K=0.93 as in the Scherrer report [53]. Mean size of the crystallites in ST and LT samples was assessed to amount to about D=37 nm.…”