Discrete
STEM
/
EDX
tomography for quantitative 3D reconstructions of chemical nanostructures
Authors: Robin Eric , Lopez‐Haro Miguel , Mollard Nicolas , Rueda‐Fonseca Pamela , Orru Marta , Bellet‐Amalric Edith , Genuist Yann , Andre Regis , Artioli Alberto , Tatarenko Serge , Ferrand David , Cibert Joel , Hajraoui Khalil El , Hertog Martien Den , Cremel Thibault , Kheng Kuntheak , Guetaz Laure 
Published: December 2016

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):

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):

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.