We report here on the quantitative 3D reconstruction of core-shell nanostructures by STEM/EDX using two X-ray maps acquired at two different tilt angles perpendicular to each other (Rueda et al., 2016; fig. 1). The method is based on the modelling of the NW cross-section using a series of imbricated ellipses whose dimensions are defined by their major and minor diameters (fig. 2). The number of ellipse depends on the number of chemical phases which are identified from the concentration profiles. The position and orientation of each ellipse are determined by the coordinates of their respective centers and the overall tilt of the nanowire, respectively. More sophisticated models, using hexagons or rectangles instead of ellipses, have been developed in order to take into account the crystal structure of nanowires exhibiting facetted sidewalls. These models are based on the elliptical model, by constructing the tangents to an ellipse, and hence, are defined by the same parameters, which is useful when comparing models. Considering a system of a number of K ellipses with ξ_k,j the local concentration of element j for the k^th ellipse (k=1 for the largest ellipse), then the average concentration C_i,j of element j for the i^th pixel along the x-axis must satisfy the following equations (equations 1):

                                                       C_i,jt_1,i = ξ_K,jt_K,i  for K=1

                                                       C_i,jt_1,i = Σ^K_k=2 ξ_k-1,j(t_k-1,i – t_k,i) + ξ_K,jt_K,i  for K≥2

With t_1,i and t_k,i, the local thickness at pixel i of the first and k^th ellipse, respectively. The local thickness of the first ellipse (= the total thickness of the cross-section) and the average concentration C_i,j of element j present along the beam axis is determined using the zeta-factor method (Watanabe and Williams, 2006):

                                                        t_1,i = Σ^m_j=1I_i,jζ_jA_i,j/I_bρ                (equation 2)

                                                        C_i,j = I_i,jζ_jA_i,j/Σ^m_j=1I_i,jζ_jA_i,j                  (equation 3)

With: m the total number of element, I_b the beam current; ρ the sample density; ζ_j the zeta-factor of element j determined using reference samples of known composition and thickness (Lopez-Haro et al., 2014); I_i,j and A_i,j the net X-ray intensity and the absorption correction term for element j at pixel i, respectively. The absorption correction term is estimated from a simple model that takes into account the direction of the X-ray emission relative to the position of the detectors, knowing the thickness, density, and mass absorption coefficient of the material through which the radiation travels (Rueda et al., 2016).

The method for reconstructing the cross-section can be divided into three steps: 1) the appropriate cross-sectional model is selected by comparing the thickness profile calculated from equation [2] with the thickness profile simulated for elliptical, hexagonal, and rectangular cross-sections (figure 3); 2) the number of ellipses is determined, and their dimensions are evaluated, from the concentration profiles; 3) the local concentrations ξ_k,j are determined and the dimensions of the ellipses are adjusted by minimizing the compositional differences between profiles calculated from equation [3] and simulated by equation [1].

This method was applied for reconstructing core-shell nanostructures on (Mg, Mn, Cd, Zn)(Te,Se) and (Al, Cu)Ge nanowires and (Pt, Co) nanoparticles. Advantages and limitations of the method will be presented and discussed at the conference.

Figures:

Quantitative 3D reconstruction of a CdTe insertion in a ZnTe nanowire based on the modelling of the cross-section using the zeta-factor method for reconstructing the local thickness and composition.

a) Modelling of a core-shell nanowire of elliptical cross-section simulated with five imbricated ellipses; b) and c) hexagonal and rectangular cross-sections simulated by constructing the tangents to the ellipse.

Thickness profile of the ZnTe nanowire shown in fig. 1 calculated from equation [2] (dots) and corresponding profiles (solid black curves) simulated for elliptical, hexagonal, and rectangular cross-sections. Normalized HAADF profiles are plotted with a red curve. The rectangular cross-section best fit the data.

« Back to The 16th European Microscopy Congress 2016

EMC Abstracts - https://emc-proceedings.com/abstract/discrete-stemedx-tomography-for-quantitative-3d-reconstructions-of-chemical-nanostructures/