Welcome to the Electron Scattering and Cross Section Calculator !
This platform is designed to streamline calculations related to electron beam interactions, specifically Knock-on Displacement Cross Sections (σKO) and Ionization Cross Sections (σrBEB). By leveraging well-established theoretical equations, the calculator enables researchers to effortlessly compute essential scattering and energy parameters by simply entering the required inputs.
Key features include:
(McKinley, W. A. & Feshbach, H. The Coulomb scattering of relativistic electrons by nuclei. Phys. Rev. 74, 1759–1763 (1948).)
(Kim, Y.-K., Santos, J. P., & Parente, F. Extension of the binary-encounter-dipole model to relativistic incident electrons. Phys. Rev. A 62, 052710 (2000).)
These calculators are tailored for electron microscopy and e-beam chemistry studies, providing insights into fundamental interactions in nanoscale systems. They are particularly useful for interpreting experimental data, optimizing parameters, and predicting beam-induced phenomena with ease.
By entering key parameters — such as incident electron energy (Ee), atomic number (Z), orbital binding energy (B), and kinetic energy (U) — you can quickly generate results in preferred units (e.g., barn, Ų, nm²). Visualize the data through 2D and 3D interactive plots or download your results for further analysis.
This tool aims to simplify complex theoretical models, making high-precision calculations accessible to researchers in nanoscience, materials engineering, and beyond.
$$\sigma_{KO} = 4\pi\left(\frac{Z e^2}{4 \pi \epsilon_0 2 \gamma m_0 c^2 \beta^2}\right)^2 \left[\left(\frac{E_{\theta}}{E_{threshold}} - 1\right) - \beta^2 \ln\left(\frac{E_{\theta}}{E_{threshold}}\right) + \pi Z \alpha \beta \left(2\left(\sqrt{\frac{E_{\theta}}{E_{threshold}}} - 1\right) - \ln\left(\frac{E_{\theta}}{E_{threshold}}\right)\right)\right]$$
$$ (\text{where, } \gamma = \frac{1}{\sqrt{1 - \beta^2}}, \quad \beta = \sqrt{1 - \left(1 + \frac{E_e}{m_0 c^2} \right)^{-2}} \quad \text{and} \quad E_{\theta} = \frac{E_e \cdot (E_e + 2 m_0 c^2) \cdot (1 - \cos{\theta})}{M c^2}) $$
Emax :
Eθ :
σKO :
$$\sigma_{\text{rBEB}} = \frac{4\pi a_0^2 \alpha^4 N}{2b'(\beta_t^2 + \beta_u^2 + \beta_b^2)} \left\{ \frac{1}{2} \left[ \ln\left(\frac{\beta_t^2}{1-\beta_t^2}\right) - \beta_t^2 - \ln(2b') \right] \left(1 - \frac{1}{t^2}\right) + 1 - \frac{1}{t} - \frac{\ln t}{t+1} \left(\frac{1+2t'}{(1+t'/2)^2}\right) + \frac{b'^2}{(1+t'/2)^2} \frac{t-1}{2} \right\}$$
$$ (\text{where, }t = \frac{E_e}{B}, \quad t' = \frac{E_e}{mc^2}, \quad b' = \frac{B}{mc^2}, \quad u' = \frac{U}{mc^2}, \quad \beta_t^2 = 1 - \frac{1}{(1 + t')^2}, \quad \beta_b^2 = 1 - \frac{1}{(1 + b')^2} \quad \text{and} \quad \beta_u^2 = 1 - \frac{1}{(1 + u')^2})$$
σrBEB :
© 2024–2025 Jongseong Park. Nano Biomedical Engineering (NanoBME), Yonsei University.
Last updated on January, 2025.
For inquiries, contact: pjs939@yonsei.ac.kr