Dynamic range compression in iDPC imaging enables visualisation of light atoms closely surrounded by heavy elements

Abstract text (incl. figure legends and references)

Integrated differential phase contrast (iDPC) imaging in scanning transmission electron microscopy (STEM) was theoretically proposed 45 years ago [1] and has only been experimentally implemented until recent years [2]. This is based on the fact that the shift of the centre of mass (CoM) of a far-field convergent beam electron diffraction (CBED) pattern is linearly related to the projected electric (and magnetic, if exists) field in the specimen. The value of CoM along two orthogonal directions can be approximated by the difference of signals in two opposite quadrant detectors, which leads to the name of DPC. By integrating such signals one can produce the so-called iDPC (or iCoM) image that is linearly proportional to the phase shift of the specimen. This has been used to visualise weak phase objects such as biological tissues [3] as well as light atoms at atomic resolution [4].

Particularly for the latter case, it will become more difficult if there are much heavier (or effectively heavier because of different number of atoms along the column in a unit cell) elements to be detected at the same time (finite dynamic range) and extremely challenging if those heavier elements are more closely adjacent to the light atoms. We simulated iDPC images for a model system with different artificial light filler atoms 140 pm away from neighbouring Sb (Z=51) atoms (Sb : filler = 2 : 1 in a unit cell) in a CoSb3 skutterudite thermoelectric material (Fig 1a). Interestingly, by reducing the outer collection angle below the objective aperture, the peaks of light filler atoms start to become resolvable and higher, while that of Sb atoms is shortened (Fig 1b). This recalls the dynamic range compression in audio signal processing, which reduces the volume of loud sounds and/or amplifies quiet sounds, thus allowing the magnetic tape with limited dynamic range for recording. In fact, this is precisely the reason. We simulated CBED images at the points that are 40 pm upward from the Sb and B atom centre (Fig 2a, c, d), and then calculated the accumulative CoM_y from the difference between North and South quadrants as a function of different collection angles. The results demonstrated that, by reducing the outer collection angle to around 70% of the objective aperture, the CoM_y at the point close to B atoms is boosted while that close to Sb atoms is diminished (Fig 2b, e, f).

Such an electron optical (rather than digital) image dynamic range compression eventually expands the detectable dynamic range and helps resolve light atoms in the extreme cases. This is also experimentally proved and will be shown in the presentation.

References

[1] H. Rose, Ultramicroscopy 2, 251 (1977).

[2] I. Lazić et al., Ultramicroscopy 160, 265 (2016).

[3] X. Li et al., Journal of Structural Biology 214, 107837 (2022).

[4] S. de Graaf et al., Science Advances 6, eaay4312 (2020).

Fig 1. (a) Simulated sample model. CoSb3 skutterudite with different artificial light filler atoms (from H to Cl), 140 pm away from neighbouring Sb atoms (Sb : filler = 2 : 1 in a unit cell). (b) iDPC images as a function of collection angles with line profile along the red arrow.

Fig 2. (a, c, d) Simulated CBED images at the points that are 40 pm upward from the Sb and B atom centre. (b, e, f) Accumulative CoM_y (difference between North and South quadrants) as a function of collection angles.