Calculation of x-ray spectra for nanocrystalline materials

The calculation of two-theta x-ray diffraction profiles for multimillion atom computer generated nanocrystalline (nc) $\mathrm{Ni}$ systems is presented. Peak profile analysis is performed using a standard Williamson-Hall analysis. The derived mean grain size and root-mean-square inhomogeneous strain quantities are compared to similar quantities obtained by direct structural investigation and visualization of the nc atomic configurations. Debye-Waller factors are also calculated from the theoretical x-ray spectra and compare well with those derived from the phonon properties of the nc system.

Figure 1

(Color online) Calculated XRD spectra for $\mathrm{Ni}12$ and $\mathrm{Ni}5$ nc systems.

Figure 2

(Color online) A Williamson-Hall plot of the $\mathrm{Ni}5$ and $\mathrm{Ni}12$ samples in terms of the scattering magnitude $s=\sin \theta ∕\lambda$.

Figure 3

(Color online) (a) and (c) are cross sections of the $\mathrm{Ni}5$ and $\mathrm{Ni}12$ nc samples with atoms colored (shaded) according to their local crystallinity. (b) and (d) are the same cross sections with the atoms colored (shaded) according to their local hydrostatic pressure. Here red (light gray) represents atoms with greater than $2\mathrm{GPa}$ and blue (dark gray) less than $-2\mathrm{GPa}$ hydrostatic pressure; see color (grayscale) bar.

Figure 4

(Color online) Local pressure distribution of the grain interiors of the $\mathrm{Ni}5$ and $\mathrm{Ni}12$ samples.

Figure 5

(Color online) XRD spectra for thermally averaged and instantaneous configurations for (a) $\mathrm{Ni}5$ and (b) $\mathrm{Ni}12$.

Figure 6

(Color online) (a) The VDOS for fcc $\mathrm{Ni}$ and $\mathrm{nc}\text{−}\mathrm{Ni}$ as a function of grain size. (b) The partial nc VDOSs for PFCC, GFCC, and GB atoms.

Figure 7

(Color online) A general high angle grain boundary with atoms represented by (a) local crystallinity, (b) local hydrostatic pressure, and (c) position disorder.

Figure 8

(Color online) A Williamson-Hall plot of electrodeposited nc $\mathrm{Ni}$ (Ref. 16) and inert gas condensed nc $\mathrm{Cu}$ (Ref. 35), along with the simulated XRD data of the $\mathrm{Ni}5$ and $\mathrm{Ni}12$ samples.