Nanocrystals: Breaking limitations of data analysis

Abstract

Abstract. A series of "virtual powder diffraction experiments" was made on models of small single crystals and nanocrystals with the core-shell structure. The results of those experiments were elaborated with application of standard methods of data analysis routinely used for reciprocal and real space analyses of polycrystalline materials. It is shown that the assumption of a uniform crystal structure of nano-materials is not justified and, therefore, application of routine procedures of collection and elaboration of diffraction data may lead to misinterpretation of the experiments and to incorrect conclusions about their structure. Tentative ways of using powder diffraction data to learn about the structure of nanocrystals with different atomic architecture of the core and of the surface of the grains are discussed. A need for elaboration of a model of the atomic structure of an individual nanograin with a non-uniform structure is discussed. An alternative approach to diffraction studies of nanocrystals by presenting the "footprints" of materials under study in the form of plots showing distribution of the experimental apparent lattice parameters as a function of diffraction vector Q, or bond length distribution as a function of r-distances derived from PDF function is suggested.

Core–Shell Lead–Free Piezoelectric Ceramics: Current Status and Advanced Characterization of the Bi1/2Na1/2TiO3–SrTiO3 System

“…Table is only valid for micrometer‐sized systems, where Rietveld refinement is applicable. For nanosized particles the Rietveld formalism cannot be used and coherently diffracted waves ( I = ∣ A core + A shell ∣ 2 ) can be treated directly using the Debye formula . The reader is referred to Ref.…”

“…For nanosized particles the Rietveld formalism cannot be used and coherently diffracted waves (I = |A core + A shell | 2 ) can be treated directly using the Debye formula. 145 The reader is referred to Ref. [146] for a general treatment of X-ray diffraction from nanoparticles.…”

Total scattering atomic pair distribution function: new methodology for nanostructure determination

“…[6,7,33,34] On the other hand, as small nanoparticles show a nonuniform structure, additional extensions to the modelling of nanoparticle structure may be needed to accommodate core/shell structure model. [35,36] This was noted recently on in a study by Palosz et al [36] where they reported the limitations and the perspectives of diffraction studies of the atomic structure of nanoparticles.…”

Lattice parameters and site occupancy factors of magnetite–maghemite core–shell nanoparticles. A critical study

“…values are not available; Gorski & Scherer, 2010;Gotic et al, 2009) is attributed to Fe 3 O 4 NPs. While at the microscale such small variations might be neglected, at the nanoscale they become highly important since they act as possible indicators of surface effects (Palosz et al, 2003(Palosz et al, , 2010Qi & Wang, 2005), as also disclosed by our Debye function analysis (DFA) model on iron oxide NPs. Diehm et al (2012) have recently reviewed this topic and found that, in a nearly systematic manner, small metal oxide NPs tend to slightly expand (typically, but not exclusively, in the 0.1-0.4% range) because of negative surface stress (within the frame of the capillary pressure model).…”