E33 · X-ray microanalysis

STEM-EDS: Nanochemical Maps

Scan a thin synthetic foil with a vanadium-rich nanodomain. Store a photon-energy spectrum at every probe position. Extract region spectra and line profiles from the acquired cube, then compare raw windows with a response-corrected composition estimate.

Recorded region spectrum counts $\text{—}$

Fitted vanadium atomic fraction $\text{—}$

Conditional counting standard error $\text{—}$

Selected stored pixels $\text{—}$

Assumed effective FWHM $\text{—}$

Horizontal drift during full raster $\text{—}$

Raster acquisition duration $\text{—}$

Incident electron areal dose $\text{—}$

Composition response assumption $\text{—}$

Experiment target $\text{—}$

Predict · acquire · explain

Does a sharper electron probe guarantee a sharper chemical map?

Specified foil thickness

t

80\,\mathrm{nm}

Incident beam current

I

100\,\mathrm{pA}

Dwell per scan pixel

\tau

0.05\,\mathrm{s}

X-ray detector solid angle

\Omega

0.4\,\mathrm{sr}

Take-off angle above foil

\alpha

20\,\mathrm{^\circ}

EDS response FWHM

130\,\mathrm{eV}

Incident probe FWHM

1\,\mathrm{nm}

Sample drift along horizontal axis

v_d

0\,\mathrm{\frac{nm}{s}}

Absorption response: 0 off, 1 on

0

Stored region center: horizontal

x_s

0\,\mathrm{nm}

Stored region center: vertical

y_s

0\,\mathrm{nm}

Stored region radius

r_s

6\,\mathrm{nm}

Target: isolate the nanodomain interior with an absorption-corrected fit. Keep thickness at or below 60 nm, probe FWHM at or below 2 nm and total drift at or below 1 nm. Obtain more than 2,000 region counts, error below 0.04 and a fitted vanadium fraction within 0.05 of 0.55.

Fixed 200 keV thin-foil teaching model, not calibrated atomic-column analysis. The 60 nm square field has 2.5 nm pixels and a specified cylindrical nanodomain. NIST titanium/vanadium line energies are used with assumed relative yields, fixed matrix attenuation lengths and Gaussian EDS response. Emission scales linearly with foil thickness; a uniform-depth escape integral models self-absorption toward a top-side collector. Gaussian spreading increases with thickness; its coefficient is an invented teaching value, not a multiple-scattering calculation. Constant sample drift is applied at raster pixel times, excluding flyback. Correction uses the supplied thickness and known response; it cannot undo spatial mixing or recover an unknown thickness. Nonnegative spectral fits use stored counts, with a conditional high-count error estimate that omits model uncertainty and zero-fraction boundary effects. Count colors are independently logarithmic; fitted composition uses a fixed linear scale and masks pixels below 30 counts. Specimen thickness is enlarged in 3D. No dynamical channeling, calibrated cross sections, shadowing, fluorescence, damage, dead time or pile-up. Dose is incident electrons per pixel area, not a damage prediction.

Physics tutorial

STEM-EDS: Nanochemical Maps

BackgroundScan a thin synthetic foil with a vanadium-rich nanodomain. Store a photon-energy spectrum at every probe position. Extract region spectra and line profiles from the acquired cube, then compare raw windows with a response-corrected composition estimate.

Why it mattersTarget: isolate the nanodomain interior with an absorption-corrected fit. Keep thickness at or below 60 nm, probe FWHM at or below 2 nm and total drift at or below 1 nm. Obtain more than 2,000 region counts, error below 0.04 and a fitted vanadium fraction within 0.05 of 0.55.

Start with the essentials

Focus question: Does a sharper electron probe guarantee a sharper chemical map?
One-sentence intuition: A chemical map combines probe spreading, spectral overlap, self-absorption and counting precision. Reprocessing stored counts changes interpretation, but does not acquire more photons or reverse spatial mixing.

Core mathematical model

Uniform-depth escape

A=\frac{1-e^{-u}}{u},\qquad u=\frac{t}{\ell\sin\alpha}

Depth-average Beer–Lambert survival toward a collector above the flat foil.

Conditional composition

\widehat c_V=\frac{a_V}{a_{Ti}+a_V}

Response columns may include the supplied absorption correction. This does not invert probe spreading.

Incident dose

D=\frac{I\,\tau}{e\,A_{pixel}}

Incident electrons per scan-pixel area; dose does not quantify damage in this Lab.

Common difficulties

Brightness needs a response model

Typical misconceptionA bright energy window is an element concentration map.

Better mental modelA chemical map combines probe spreading, spectral overlap, self-absorption and counting precision. Reprocessing stored counts changes interpretation, but does not acquire more photons or reverse spatial mixing.

Run the experiment

01
Predict a blurred boundary
Compare the thin and thick presets without changing the nanodomain reference.
What to observe: More thickness creates more photons but broadens the count-derived boundary.
02
Reuse the measurement
Toggle absorption correction and move the selected region.
What to observe: The recorded cube is unchanged. Spectra and composition estimates are recomputed from the same pixels.
03
Separate error sources
Try low counts, a broad probe and drift. Check the target in a thin, stationary foil.
What to observe: A small counting error cannot certify a spatially mixed or drifted measurement.