E15 · X-ray microanalysis

SEM Microanalysis: EDS & WDS

Scan a synthetic titanium–vanadium specimen. Extract an EDS spectrum from stored pixels, then acquire an independent WDS energy scan of the selected region. Compare raw window brightness with a fit that accounts for titanium, vanadium and continuum.

Active spectrum $\text{—}$

Recorded region spectrum counts $\text{—}$

Fitted vanadium atomic fraction $\text{—}$

Conditional counting standard error $\text{—}$

Selected stored EDS pixels $\text{—}$

Vanadium overvoltage ratio $\text{—}$

Assumed generation depth $\text{—}$

Assumed lateral FWHM $\text{—}$

WDS Bragg angle to crystal plane $\text{—}$

Active acquisition duration $\text{—}$

Experiment target $\text{—}$

Predict · acquire · explain

Is that overlapping peak really vanadium?

Primary electron energy

E_0

10\,\mathrm{keV}

Incident beam current

I

5\,\mathrm{nA}

EDS dwell per scan pixel

\tau

0.05\,\mathrm{s}

EDS response FWHM

130\,\mathrm{eV}

Take-off angle above surface

\alpha

35\,\mathrm{^\circ}

EDS detector solid angle

\Omega

0.1\,\mathrm{sr}

Active spectrum: 0 EDS, 1 WDS

0

WDS response FWHM

20\,\mathrm{eV}

WDS total region exposure per energy step

\tau_W

3\,\mathrm{s}

WDS cursor photon energy

E_X

4.95\,\mathrm{keV}

Region center: specimen horizontal

x_s

-1.8\,\mathrm{\mu m}

Region center: specimen vertical

y_s

1\,\mathrm{\mu m}

Region radius

r_s

0.6\,\mathrm{\mu m}

Target: select the pure titanium region, away from its boundary. Use WDS at 12 eV FWHM or better, overvoltage at least 1.6, more than 1,500 spectrum counts and counting error below 0.03. Confirm the fitted vanadium fraction is below 0.04. A bright overlap window alone cannot confirm vanadium.

Teaching model, not calibrated elemental analysis. Titanium and vanadium line energies and K thresholds use NIST values; line ratios, emission yields, matrix attenuation lengths and detector efficiencies are assumed. Gaussian EDS response is 100–180 eV FWHM; WDS is 8–40 eV and may still overlap. The WDS scan is a separate exposure, with fixed 0.008 sr acceptance and 30% peak reflectivity. Its energy steps count narrow-band photons; EDS channels count pulse energies acquired in parallel. A titanium Kanaya–Okayama range sets an assumed uniform generation depth and Gaussian lateral spreading. Selected-area spectra sum the stored 24-square EDS cube; its pixels are one third of a micrometre wide. Three-component nonnegative least squares gives a conditional atomic-fraction estimate using the known teaching response. Error is a high-count counting approximation, unreliable at a zero-fraction boundary. Each count map has an independent log scale; composition uses fixed linear colors. No ZAF calibration, secondary fluorescence, L lines, pile-up, dead time, damage or full electron transport. The 3D WDS central rays obey first-order Bragg and Rowland geometry; the crystal is drawn as a tangent patch.

Physics tutorial

SEM Microanalysis: EDS & WDS

BackgroundScan a synthetic titanium–vanadium specimen. Extract an EDS spectrum from stored pixels, then acquire an independent WDS energy scan of the selected region. Compare raw window brightness with a fit that accounts for titanium, vanadium and continuum.

Why it mattersTarget: select the pure titanium region, away from its boundary. Use WDS at 12 eV FWHM or better, overvoltage at least 1.6, more than 1,500 spectrum counts and counting error below 0.03. Confirm the fitted vanadium fraction is below 0.04. A bright overlap window alone cannot confirm vanadium.

Start with the essentials

Focus question: Is that overlapping peak really vanadium?
One-sentence intuition: WDS narrows a spectral response; it does not remove the interfering element or correct the matrix. Stored spectra and an explicit response model are needed for interpretation.

Core mathematical model

Overvoltage

U=\frac{E_0}{E_K}

K-shell characteristic emission vanishes at or below the corresponding threshold.

Bragg selection

\lambda=2d\sin\theta_B

First-order reflection; angle is measured to the crystal planes.

Count model

\mu_i=a_{Ti}B_{Ti,i}+a_VB_{V,i}+bB_{c,i}

Fit the recorded spectrum with line and continuum response columns; the fitted fraction is conditional on these assumptions.

Common difficulties

Brightness needs a response model

Typical misconceptionA bright energy window is an element concentration map.

Better mental modelWDS narrows a spectral response; it does not remove the interfering element or correct the matrix. Stored spectra and an explicit response model are needed for interpretation.

Run the experiment

01
Predict the false element
Start on the left-hand pure titanium region. Inspect the overlap-window map and EDS spectrum.
What to observe: The window is bright even though the known region has no vanadium.
02
Acquire a second experiment
Choose the narrow WDS preset. Scan the cursor through the overlapping lines and inspect the moving crystal and counter.
What to observe: A narrow response reveals structure, while fitted titanium still contributes to the apparent vanadium peak. Exposure is per scan step.
03
Challenge the result
Move to the mixed region, widen the WDS response, reduce counts and go below the excitation threshold.
What to observe: Counts, threshold and overlap determine which conclusions are supported. Moving the region reuses the EDS cube but reacquires WDS.