Diffraction line profiles of spherical hollow nanocrystals

Emiliano Burresi,Leander Tapfer

doi:10.1177/1847980419832386

Abstract

An analytical expression of diffraction line profiles of spherical hollow nanocrystals (NCs) is derived. The particular features of the profile lines, enhanced peak tail intensity, are analyzed and discussed as a function of the NC size parameters (outer and inner radius, shell thickness). The explicit formula for the integral breadth, the Fourier particle size, and the Scherrer constants are also obtained and discussed in detail. The diffraction line profiles of hollow CdS NCs of zincblende and wurtzite crystallographic structure are calculated and compared with Debye scattering profiles. The diffraction profiles of both approaches exhibit an enhanced peak tail intensity that can be considered as a fingerprint of the hollow NC structure.

Highlights

Hollow NCs are attracting an increased scientific and technological interest due to their intriguing optical, electronic, electro- and photochemical, and catalytic properties that may find use in potential applications in diverse fields such as nanoscale encapsulation and drug delivery, photocatalysis and plasmon photonics, energy storage, and nanoreactors
Different synthesis approaches for the fabrication of nanoscale hollow structures are reported: Kirkendall cavitation process,[1,2,3] template-free hydrothermal method,[4] templateengaged replacement reactions,[5] galvanic replacement reaction by combining colloidal synthesis and solid state chemistry,[6] aminothermal synthesis,[7] and solvothermal method.[8]
In the following, we report the analytical expressions for the Scherrer constants obtained by the procedure described in[15] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 4 pðR3 À r3Þ

Summary

Introduction

Hollow NCs are attracting an increased scientific and technological interest due to their intriguing optical, electronic, electro- and photochemical, and catalytic properties that may find use in potential applications in diverse fields such as nanoscale encapsulation and drug delivery, photocatalysis and plasmon photonics, energy storage (anode material in Li-ion batteries), and nanoreactors. Scherrer constants of spherical hollow NCs. The “true” size p, definepdffiffiffiaffiffis the cube root of the mean crystallite volume (p 1⁄4 3 V0), is related to the apparent size through Scherrer’s equation; p 1⁄4 Kb Á eb or p 1⁄4 Kk Á ek for the integral breadth or Fourier apparent size, respectively. In order to calculate the Debye diffraction pattern (equation (14)), unrelaxed spherical CdS clusters with zb and w phase were built (Figure 6)[24]; a first cutoff radius R from the center of the crystal defines the external size whereas a second cutoff radius r corresponds to the internal radius of the hollow cluster. Peak is well pronounced and is notably evident if compared with the diffraction line profile of full NCs (Figure 9(b)) calculated with both approaches by taking r 1⁄4 0 nm

Conclusions

Á 46ðR2 À r2Þ2 þ 4tr2ðt À

À ln RÀr Rþr ðA20Þ