E15 · X-ray microanalysis

SEM Microanalysis: EDS & WDS

Do X-ray counts at the vanadium energy prove that a sample contains vanadium? Not by themselves. A titanium line sits almost on top of the main vanadium line, so titanium alone puts counts there. WDS has much sharper energy resolution and helps, but the titanium contribution is still there. Fit titanium, vanadium and the background together with a known detector response, then see whether any vanadium is left.

Scan a simulated titanium–vanadium specimen and pull an EDS spectrum from the stored pixels of any region. Then record a separate WDS energy scan of that region, and compare how bright the raw energy window looks with a fit that includes titanium, vanadium and the continuum background.

Recorded region spectrum counts $\text{—}$

Fitted vanadium atomic fraction $\text{—}$

Conditional counting standard error $\text{—}$

Assumed lateral FWHM $\text{—}$

More measurements and target

Active spectrum $\text{—}$

Selected stored EDS pixels $\text{—}$

Vanadium overvoltage ratio $\text{—}$

Assumed generation depth $\text{—}$

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

Active acquisition duration $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

More examples

Primary electron energy

E_0

10\,\mathrm{keV}

EDS dwell per scan pixel

\tau

0.05\,\mathrm{s}

EDS response FWHM

130\,\mathrm{eV}

Active spectrum: 0 EDS, 1 WDS

0

Advanced settings

Incident beam current

I

5\,\mathrm{nA}

Take-off angle above surface

\alpha

35\,\mathrm{^\circ}

EDS detector solid angle

\Omega

0.1\,\mathrm{sr}

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}

Learning goal and model limits

Make a prediction, then test it

Do X-ray counts at the vanadium energy prove that a sample contains vanadium?

Target: select the pure titanium region, away from its boundary. Use a WDS width of 12 eV FWHM or better and an overvoltage of at least 1.6, and record more than 1,500 spectrum counts with a counting error below 0.03. Then check that the fitted vanadium fraction is below 0.04. A bright overlap window on its own cannot confirm vanadium.

Model assumptions

This is a teaching model, not a calibrated elemental analysis. Line energies and K thresholds for titanium and vanadium come from NIST; line ratios, emission yields, matrix attenuation lengths and detector efficiencies are assumed. The EDS response is Gaussian with a FWHM of 100–180 eV. The WDS response is 8–40 eV wide, so lines can still overlap. The WDS scan is a separate exposure with a fixed 0.008 sr acceptance and 30% peak reflectivity. At each energy step it counts photons in a narrow band, while EDS records the energy of every pulse in all channels at once. The Kanaya–Okayama electron range in titanium sets an assumed uniform generation depth and a Gaussian sideways spread. The stored EDS cube is a 24-by-24 grid of spectra with pixels one third of a micrometre wide, and a selected-area spectrum adds up the pixels in the selection. Below the vanadium K threshold, the composition cannot be determined even when titanium lines are recorded; a gray pixel in the map can also mean the ratio cannot be identified. A three-component nonnegative least-squares fit estimates the atomic fraction, and that estimate holds only for the known teaching response. The quoted error is a counting estimate for high counts and is unreliable when a fraction sits at zero. Each count map has its own logarithmic color scale; the composition map uses a fixed linear scale. The model leaves out ZAF calibration, secondary fluorescence, L lines, pile-up, dead time, beam damage and full electron transport. In the 3D view and the side projection, the central WDS ray follows first-order Bragg reflection and Rowland-circle geometry; the crystal is drawn as a flat patch tangent to the circle.

Physics tutorial

SEM Microanalysis: EDS & WDS

BackgroundIn an X-ray spectrum, a titanium line sits close enough to a vanadium line that the two overlap. This Lab scans a simulated titanium–vanadium specimen, stores an EDS spectrum at every pixel and records a separate WDS energy scan of the region you select.

Why it mattersYour task is to select the pure titanium region, away from its boundary. Use a WDS width of 12 eV FWHM or better, an overvoltage of at least 1.6, more than 1,500 spectrum counts and a counting error below 0.03. Then check that the fitted vanadium fraction is below 0.04. A bright overlap window on its own cannot confirm vanadium.

Start with the essentials

Focus question: Do X-ray counts at the vanadium energy prove that a sample contains vanadium?
One-sentence intuition: Narrower WDS peaks do not remove the interfering element or correct for the matrix, so you still need the stored spectra and an explicit response model to read them.

Core mathematical model

Overvoltage

U=\frac{E_0}{E_K}

This is the beam energy divided by the K-shell threshold. At or below the threshold, the element emits no K-shell characteristic X-rays.

Bragg condition for the analyzing crystal

\lambda=2d\sin\theta_B

The crystal reflects the wavelength that matches its plane spacing in first order. The angle is measured from the crystal planes.

Expected counts in each channel

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

The expected counts are a sum of titanium, vanadium and continuum responses. Fitting the recorded spectrum gives their amplitudes, and the fitted fraction holds only if these assumed responses are right.

Common difficulties

Window brightness needs a response model

Typical misconceptionIf the energy window is bright, that element must be there in high concentration.

Better mental modelA window map counts every photon in an energy band, whichever element emitted it. WDS narrows the response but does not remove the interfering element or correct for the matrix, so reading the brightness takes the stored spectra and an explicit response model.

Run the experiment

01
Spot the false vanadium
Start on the pure titanium region on the left. Look at the overlap-window map and the EDS spectrum.
What to observe: The window lights up even though this region is known to contain no vanadium.
02
Record a WDS scan
Choose the narrow WDS preset. Move the cursor across the overlapping lines and watch the crystal and counter move.
What to observe: The narrow response shows more of the line structure, but the fit shows that titanium still contributes to what looks like a vanadium peak. The exposure time applies to each scan step.
03
Test the conclusion
Move to the mixed region, widen the WDS response, lower the counts and drop the beam energy below the excitation threshold.
What to observe: What you can conclude depends on the counts, the excitation threshold and the overlap. Moving the region reuses the stored EDS cube but records a new WDS scan.

SEM Microanalysis: EDS & WDS

SEM Microanalysis: EDS & WDS

Core mathematical model

Overvoltage

Bragg condition for the analyzing crystal

Expected counts in each channel

Common difficulties

Window brightness needs a response model

Run the experiment

Spot the false vanadium

Record a WDS scan

Test the conclusion

Related experiments and articles

X-rays: discovery, characteristic radiation and precision spectra