Electron Microprobe Laboratory
Earth & Environmental Sciences
Rensselaer Polytechnic Institute
The Electron Microprobe method
A general explanation
Jonathan D. Price
The electron microprobe is an analytical tool. It can determine the composition of small regions of many materials. How do electrons provide compositional information about a sample? Below is a brief outline of the electron microprobe analysis.
Identifying atoms by fluorescence

To obtain composition, we need a measurable characteristic for each element: a "fingerprint" that tells us what atoms are present.

Positively charged protons in the nucleus attract negatively charged particles, known as electrons. While electron movement is complicated, they occupy specific energy levels as a function of their position. These energy levels may be diagramed as series concentric circles.

Atoms emit photons (fluoresce) if their electrons move to an energy level closer to the nucleus. Movement may be induced when electron is hit by photon or another electron.

The energy of the photon is equivalent to the change in energy of the electron (to higher energy site EH from the lower energy site EL )

Ephoton = EH - EL

The it is also equivalent to a the product of Plank's constant (h = 6.626 x 10-34 m2 kg/s) and the frequency (f) of the photon.

Ephoton = EH - EL = h f

Which is equivalent to the product of Plank's constant with the speed of light (c = 3 x 108 m/s) divided by the wavelength (lambda) of the photon.

Ephoton = EH - EL = h f = h c / lambda


Electron structure is element specific. No two elements are the same. In other words, every Ephoton is the result of a specific jump in a specific element.
Heavier atoms (those with more protons) have many energy levels. Barium (Ba) is a good example of a relatively heavy element (56 protons). Below is a an energy map for this element. Of import to our discussion are those electron jumps to the innermost and second innermost levels.

The scale on the left is the energy in electron volts (eV). Each line represents a discrete energy level that may host up to two electrons. For example K is 37,440 eV (or 37.44 keV). Three other levels are listed below.

LI, LII, LII are the light, intermediate, and dark blue lines on the map, respectively. These are sublevels in what is known as the L shell.
Since Ephoton = EH - EL = h f = h c / lambda, we can determine the wavelength (lambda) of the photon produced by the movement of an electron from LII to K. We need only to rearrage Ephoton = h c / lambda to lambda = h c / Ephoton .

3.9 x 1011 m is a very small wavelength that corresponds to a part of the electromagnetic spectrum known as x-ray radiation. If we want to measure the amount of fluoresced radiation from this jump, we need a tool that can quantify x-rays.
In short, electron movement in atoms produces x-rays with specific wavelengths (characteristic x-rays). It is a "fingerprint" for a specific element. Next we learn how we can generate and focus electrons to excite small volumes of material to produce x-rays).

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