Ali A. Husain

Ali A. Husain

ألا بذكر الله تطمئن القلوب

Electron Inelastic Mean Free Path

1 minute read

Published:

Unlike x-ray and neutron scattering, electron scattering in a solid is often so strong that the first Born approximation is not enough to describe the distribution of scattered electrons. To understand when higher order (or multiple) scattering occurs, it is useful to have an estimate for the inelastic mean free path (IMFP) for the probe electron. Estimates for the IMFP based on material parameters is therefore a useful metric when performing Electron Energy Loss Spectroscopy (EELS). Indeed, many formulas for estimating the IMFP have been studied in the literature and are nicely compiled in Electron Energy-Loss Spectroscopy in the Electron Microscope by R. Egerton.

Below is a simple calculator based on the Matlab code of R. Egerton to estimate the electron IMFP. To do this calculation, one inputs the chemical formula of the material of interest (written with spaces between elements), beam convergence angle α, detector acceptance angle β, the unit cell volume, and the number of formula units of the compound in a single unit cell. Alternatively, there is the option to directly input the mass density instead of the unit cell volume and formula units per cell to perform this calculation. Note that the full convergence and acceptance angles should be inputted, not the semiangles.

Input FormulaParsed Formula

La1.85Sr0.15CuO4

Convergence AngleAcceptance Angle
mrad mrad
Unit Cell VolumeMass Density
Å3 g/cm3
Formula Units Per Cell

You May Also Enjoy

Chemical Molar and Mass Fractions

1 minute read

Published:

It is common when growing single crystals to use compounds which contain an element of interest, rather than using the pure element on its own. For example, copper in the form of CuO is often used instead of pure elemental copper, and fluorine is often used in the form of FeF2 rather than dangerous fluorine gas. When using compounds rather than elements, it is useful to know the relative mass fraction of each element to calculate the mixing ratios needed to grow a particular crystal.

Core Electron Transition Energies

1 minute read

Published:

It is useful when performing resonant x-ray scattering, x-ray absorption spectroscopy, or other core-level spectroscopies, to have a quick reference for the element-dependent electron binding energies in solids. These binding energies describe how deep the core electron levels are with respect to the Fermi level (or vacuum, top of valence band, etc.). Because chemical bonding in solids only involves valence electrons, the core levels of atoms in a solid are mostly unchanged compared to that of a free atom in space. Thus, the core level binding energies form a fingerprint uniquely identifying an element.

Useful Calculator for the Diffraction Kinematics of Relativistic Electrons

1 minute read

Published:

When dealing with electron diffraction within an electron microscope, it is often useful to have a quick converter to convert between the beam energy, angles, and reciprocal lattice units (r.l.u.). Below is a simple calculator that converts between electron beam energies, angles, and momentum transfer. For added benefit, there is also a lattice parameter option to present the momentum transfer in reciprocal lattice units where $1\textrm{ r.l.u.} = 2\pi/a$ and $a$ is the lattice parameter.