Computing Shapes of Nanocrystals from X-ray Diffraction Data

Abstract

An elegant mathematical technique has been developed and tested for computing the shapes of nanocrystals from X-ray diffraction (XRD) data. The method is specially suited to the shape analysis of crystallites in nanopowder specimens. Unlike visualization techniques such as transmission electron microscopy (TEM), it can find the full 3-D crystallite shape even in the presence of agglomeration. The technique has been validated using XRD and TEM data on the systems CeO 2 , Ge, ZnO, Zr 56 C 44 , In 2 O 3 , MnFe 2 O 4 , and iron(II-III) hydroxysulfate. This will aid in the shape-selective synthesis and design of materials. Other merits of the method and some extensions are also discussed.

Simulated XRD profiles of carbon nanotubes (CNTs): An efficient algorithm and a recurrence relation for characterising CNTs

“…and D.S. ), in related work, have advanced a mathematical algorithm to compute the 3-D shapes of nano-crystals [5]. In the present paper, we report further progress in the same direction.…”

“…4. Peak intensities vs. Tube length for (5,5) CNT. The length is normalized using the unit cell length of the CNT.…”

“…(a) Simulated XRD for SWCNT of type(5,5). Normalized intensity is plotted against the scattering parameter (Å −1 ).…”

Effect of the size and structure factors on the magnetic susceptibility of nanoparticles of cadmium sulfide

“…The nanoparticle size in the hkl directions in which A hkl differs from unity was found from the formula D hkl = . Finally, similarly to the method for construct ing particles that was described in [20], we drew seg ments of length D hkl /2 from the conditional particle center (with allowance for the hexagonal symmetry) in the forward and backward hkl directions, connected their ends, and thus obtained an image of a particle of certain shape. This construction allowed us to deter mine the size and shape of wurtzite particles before and after the susceptibility jump at T cr .…”

Defect-free and Defective Surfaces of the Pyrochlore Oxide La2Zr2O7: A Theoretical Study

“…The lower and upper bounds to the ratio of 's for the most stable, defect-free surface terminations can be obtained and compared to experimental results obtained by the analysis [15] of published XRD patterns [4,5] (Figure 5). Specifically, for a given XRD pattern, a set of crystal thicknesses 's can be obtained, one for each indexed (hkl) peak following the algorithm of Reference [15]. A given is perpendicular to the plane (hkl) and is a direct measure of the crystal growth velocity in that direction.…”