Literature

2025

Operando Heating and Cooling Electrochemical 4D-STEM Probing Nanoscale Dynamics at Solid−Liquid Interfaces.: Uses ML-assisted 4D-STEM (−40 to 95 °C) and electrochemical liquid-cell scanning TEM (EC-STEM) to explore temperature- and potential-dependent heterogeneous growth of Cu nanostructures. Promising work can be done on catalyst activation and degradation mechanisms, and battery fatigue in extreme conditions.

Review papers

Pychography

Book

Advanced Computing in Electron Microscopy

Algorithms

Challenges in EM

Light elements have weak electrostatic potential, resulting in limited contrast in BF or DF TEM.

Challenges in 4D-STEM

The multislice method can be used to model thick samples.
Defocusing can reduce electron damage to specimens.
Improved open-source computational frameworks (Python, NumPy) and hardware (GPU) have enhanced accessibility.
Improved detector recording speed enables capturing diffraction patterns more efficiently.

Terms and glossray

iDPC: Integrated Differential Phase Contrast, local electric and magnetic fields by determining the graident of phase shift.
ptychography: A computational imaging technique, first introduce by Hoppe in 1969 [1].
EFETM: Energy-Filtered TEM
tcBF-STEM: Tilt-Corrected Bright-Field STEM
EMPAD: Electron Microscope Pixel Array Detector
SSB: single-side band.
ICOM: Iterative Constrained Optimization Method

Phase retrival

DPC

Assumes a small shift. \(\psi_{exit}(x,y) \approx \psi_{in}(x,y)[1 + i \sigma V(x,y)].\) The graident is computed as \(\nabla \psi(x,y) \propto \vec r_{CoM}(x,y)\). For thick and strongly scattering samples, DPC becomes nonlinear.

What is “moment”? It is a distribution of a weighted average of a variable (position, intensity, etc.) raised to some power with the equation of \(M_n = \int x^n f(x) dx\). \(n=0\) means total intensity, \(n=1\), mean or center of mass, \(n=2\), variance (spread).

In each (x, y) position in real space, you have a 2D diffraction pattern, which is itself a 2D image (for example, 1,000 by 1,000 pixels). For each pixel in this diffraction pattern, there is an associated intensity value. To analyze the data, you compute the weighted average of the diffraction positions (1 million of them) for each (x, y) position. Here is the mathematical formula:

Imagine that all the diffraction intensity is concentrated on the right half of the bright-field disk. In that case, the “center of mass” of the diffraction pattern will shift toward the right, for that particular probe position (x,y). In other words, phase has been shifted to the right, electric field towards the left.

\[\mathbf{r}_{\text{CoM}}(x, y) = \frac{ \sum I(x, y, k_x, k_y)\,(k_x, k_y) }{ \sum I(x, y, k_x, k_y) }\]

Now, the phase graident is

FAQs in Electron Microscopy

How would you define MOFs, perovskites, zeolites, mordenite (MOR)? Why are they of interest? What makes MOFs sensitive to electrons?: TBA
What is a numerical aperture?: TBA
How does 4D-STEM detector work?: TBA
How are the electrons generated?: TBA
How do you determine orientaiton mapping?: TBA
Why do you want to find the orientation?: TBA
What is strain mapping?: TBA
How is abberation corrected in EM?: TBA
Why do you want to find the strains?: TBA
Why do we tilt the speciemen with greater thickness?: TBA
What is the general process of ptychography in EM?: TBA
What’s the relationship between convergence angle and Bragg disks in diffraction patterns?: Greater convergence angle results in larger Bragg disks. With a greater angle of incidence, electrons scatter at larger angles.
What’s the difference between “in situ” and “operando”?: In situ means dynamic observation, while operando refers to observation under actual operating conditions. In situ is a broader term.
What are the convergence angles?: Cryogenic conditions: 0.5–0.01 mrad, HRSTEM: 10–30 mrad, 4D-STEM strain mapping: 1–4 mrad.
Why do samples drift?: During cooling and heating, the distances between atoms can change, causing drift.
What’s convergence angle?: The angle formed between rays from the C2 condenser lens and the focused beam onto the sample plane.
What is ETEM mode?: ETEM stands for Environmental Transmission Electron Microscopy. It enables studying samples under controlled environments with gases or vapors, and at varying temperatures.
How is ETEM different from traditional TEM?: TEM requires a vacuum, but ETEM maintains high vacuum in the electron column while providing a controlled amount of gas around the sample.
What is a condenser lens?: A lens that controls the intensity, size, and convergence of the incoming electron beam.
What’s the focal point?: The point where the incoming rays converge after passing through the lens. The focal length is the shortest distance between the lens and the focal point.
What are probe step sizes in 4D-STEM?: 5–40 nm [1]
How is the “real” image displayed?: Each specimen point is mapped to a unique point in the image plane. The incident beam hits the specimen, and each point produces scattered electrons at different angles (wavevectors). The objective lens bends electrons from each specimen point to a single direction. Differences in thickness, composition, and crystal orientation affect the scattering, resulting in image contrast.
Why do we also have a diffraction pattern from the objective lens?: Closer to the objective lens, another plane can be observed. Electrons that left the specimen at the same angle are bent similarly by the magnetic field, showing a map of scattered angles. See this helpful diagram.
What is axial symmetry?: The system looks the same when rotated around its axis. Imagine a cylinder.
Why use a monochromator?: It is an optical device that only allows electrons with a narrow energy range to be transmitted. It only works on the source beam.
Why do we want to filter transmitted electrons?: To improve image contrast and resolution.
How do we filter transmitted electrons?: Apertures block high-angle scattered electrons. Alternatively, a magnetic field separates electrons based on energy loss; higher-energy electrons are bent less. A slit can select electrons with specific energy loss.
Why is the eucentric point important?: The eucentric point allows tilting or rotating the specimen without losing the area of interest from the field of view. The tilt axis lies in the specimen plane and is perpendicular to the optical axis. See this helpful video.

History

Dates from Dr. Yougi Liao’s Practical Electron Microscopy and Database (2006) book

TBA - 4D-STEM

1897 – J. J. Thomson discovers the electron.
1924 – Louis de Broglie determines the wave-like behavior of electrons.
1931 – Knoll & Ruska build the first electron microscope.
1939 – von Borries & Ruska build a practical EM with 10 nm resolution.
1986 – Nobel Prize in Physics awarded for the design of the first electron microscope to Ruska. Nobel lecture.
2017 – Nobel Prize in Chemistry awarded for cryo-electron microscopy, developed by Jacques Dubochet, Joachim Frank, and Richard Henderson.

[1]

W. Hoppe. Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen. Acta Crystallographica Section A, 25(4):495–501, Jul 1969. URL: https://doi.org/10.1107/S0567739469001045, doi:10.1107/S0567739469001045.