E61 · Photoelectron spectroscopy

APXPS: Gas, Reaction & Operando States

Record a reacting surface through a gas layer. Shorten the sample–aperture gap, separate a gas-phase peak and fit the acquired counts. Compare a synthetic matched vacuum control and see how a long exposure averages a changing chemical state.

Fitted exposure-averaged oxidized fraction $\text{—}$

Measured solid area / matched vacuum area $\text{—}$

Fitted solid and gas peak areas · counts $\text{—}$

Instrument Gaussian-equivalent FWHM $\text{—}$

Recorded operando counts $\text{—}$

Known exposure-averaged fraction $\text{—}$

Known reaction start / end fractions $\text{—}$

Known gas transport survival $\text{—}$

Assumed gas mean free path $\text{—}$

Oxidized-line analyzer kinetic energy $\text{—}$

Count-scaled fit residual $\text{—}$

Experiment target $\text{—}$

Pressure changes chemistry and transmission

Fit a curved continuumReprocess stored counts with a quadratic instead of linear background.Include the gas-phase lineSeparate a known gas template from the two solid chemical states.Chamber gas pressure

p

10\,\mathrm{mbar}

Sample–aperture distance

d

1.5\,\mathrm{mm}

Sample and gas temperature

T

400\,\mathrm{K}

Reaction age at scan start

t_0

4\,\mathrm{s}

Photon energy

h\nu

1500\,\mathrm{eV}

Pass energy

E_p

100\,\mathrm{eV}

Entrance and exit slit width

s

1.2\,\mathrm{mm}

Scan-integrated exposure per acquisition

\tau

1\,\mathrm{s}

Predict a fading peak before changing pressure. Fit the curved continuum and gas line. At nonzero pressure, keep gas survival between 25% and 90%, resolution below 0.6 eV and fitted solid area above 3000 counts. Recover the interval-averaged state within 3 percentage points and survival within 8 points, after at least 2 seconds of reaction. Then compare a long exposure.

A synthetic material has reduced, oxidized and gas-phase lines at 100, 103.2 and 105.5 eV. Line widths, equal solid sensitivities, reaction rates, gas cross section, continuum and flux are teaching assumptions. Gas survival uses an ideal uniform-gas exponential with ideal-gas number density and an energy-dependent assumed cross section; no local pressure depletion or gas-flow solver. The fixed 0.2 mm aperture has a gap of at least twice its diameter; collection follows an assumed inverse-square gap law. Differential pumping stages are schematic, without calculated pump pressures. Competing first-order reaction rates start from 5% oxidized; each spectrum integrates the exact state average over the selected interval. The matched vacuum spectrum is an independently sampled synthetic control with that average state artificially frozen, identical geometry and no gas. It is not a real evacuation trajectory. Nonnegative peak areas and a linear or quadratic continuum are fitted from stored counts; a residual or signal failure leaves the state unresolved. Photon flux and cross-section changes are assumed, without realistic gas chemistry, catalysis, liquid interfaces, charging or elastic scattering. Presentation time does not advance reaction time or exposure. Counts use Poisson noise below 40 expected counts and rounded Gaussian noise above. Analyzer width is Gaussian-equivalent at 150 mm radius and 2-degree entrance half-angle. Apparatus lengths are magnified; detector color uses logarithmic display gain.

Start with the essentials

Focus question: Does the peak fade—or does the surface change?
One-sentence intuition: Use fitted areas from a stored spectrum, identify the gas contribution and compare a matched synthetic control. The fitted state represents the exposure interval, not an instantaneous frame.

Core mathematical model

Gas number density

n_g=\frac{p}{k_B T}

Pressure is converted from mbar to pascals, distance from mm to metres. Sample and gas share the selected temperature in this uniform-gas teaching model.

Unscattered gas survival

\mathcal{T}_g=\exp(-n_g\sigma_g d)

The assumed cross section depends on kinetic energy. A shorter gap reduces loss. Scattering redistributes electrons into omitted loss channels; survival is not total electron conservation.

Two competing reaction rates

\frac{df}{dt}=k_{\mathrm{ox}}(1-f)-k_{\mathrm{red}}f

Invented activated oxidation and reduction rates preserve a fraction between zero and one. They illustrate an operando trajectory without identifying a real catalyst.

Exact interval average

\overline{f}=\frac{1}{\tau}\int_{t_0}^{t_0+\tau} f(t)\,dt

The acquired spectrum integrates the state over the whole exposure. More counts can accompany worse temporal localization. Animation does not advance this physical interval.

Recorded solid and gas templates

D_i\simeq A_rP_{ri}+A_oP_{oi}+A_gP_{gi}+B_i

Two equal-sensitivity solid states and a gas line have nonnegative fitted areas. The smooth continuum is linear or quadratic. Missing a line can leave a large residual.

Count-derived state and transmission

\widehat f=\frac{A_o}{A_r+A_o},\qquad\widehat{\mathcal{T}}_g=\frac{A_r+A_o}{A_{r,\mathrm{vac}}+A_{o,\mathrm{vac}}}

The synthetic vacuum control freezes the exposure-averaged state and uses matching optics and an independent count draw. Actual pumping could change chemistry, so a real vacuum comparison requires further justification.

Common difficulties

Pressure is not one atmosphere here

Typical misconceptionAmbient-pressure spectroscopy means every pressure setting is atmospheric.

Better mental modelThis Lab explores near-ambient conditions up to 20 mbar. The name describes a family of instruments, not a promise of atmospheric operation.

A frozen control is synthetic

Typical misconceptionThe matched vacuum spectrum predicts what happens when the real sample is evacuated.

Better mental modelThe control deliberately holds chemistry fixed to isolate gas loss. Real evacuation has its own trajectory.

An exposure is an interval

Typical misconceptionA long spectrum measures the state at its ending time.

Better mental modelCounts integrate changing populations. The known kinetics curve is a separate reference, not a reconstruction from one spectrum.

Run the experiment

01
Predict a pressure increase
Start with Vacuum control, then use Recover the working state. Compare solid areas, gas area and fitted state.
What to observe: Pressure both promotes the assumed oxidation and removes outgoing solid electrons.
02
Shorten the lossy path
Use Gas blocks the solid, shorten the gap and lower pressure until a fitted solid state becomes usable.
What to observe: Low count or residual failures suppress the result; a smooth-looking fit is insufficient.
03
Separate background and gas
Toggle the curved continuum and gas template while keeping all acquisition settings fixed.
What to observe: Stored counts stay fixed. Processing choices change fitted areas and residuals.
04
Trade counts for time localization
Complete the target, then use Long exposure averages change. Compare start, end and average states.
What to observe: The fit follows the interval average, which can differ strongly from the final state.