E46 · In-situ electron microscopy

Liquid-cell TEM: Observing or Driving?

Send electrons through two sealed windows and a flowing liquid layer. Balance transmitted counts against beam-driven chemistry, then fit the same stored image sequence without substituting a noiseless reference.

Count-derived apparent rate $\text{—}$

Known unilluminated rate $\text{—}$

Rate error against known input $\text{—}$

Beam to intrinsic hazard ratio $\text{—}$

Mean counts per sampled pixel $\text{—}$

Model selected-channel transmission $\text{—}$

Selected exposure midpoint $\text{—}$

Exposure duration $\text{—}$

Total incident areal dose $\text{—}$

Usable sampled frames $\text{—}$

Assumed radiolysis species · dimensionless $\text{—}$

Experiment target $\text{—}$

Predict · acquire · fit · explain

Can a clearer liquid-cell movie give a less faithful reaction rate?

Liquid path length

L

300\,\mathrm{nm}

Thickness of each window

w

50\,\mathrm{nm}

Effective liquid renewal rate

\nu

0\,\mathrm{s^{-1}}

Incident electron flux

J

500\,\mathrm{\frac{e^{-}}{nm^2\,s}}

Exposure cadence

f

2\,\mathrm{s^{-1}}

Exposure fraction of each interval

d

0.5

Blank beam between exposures: 1 on

b

0

Horizontal specimen drift

v_d

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

Follow known drift: 1 on

a

1

Exposure-integrated fit: 1 on

m

1

Selected stored frame · zero-based

n

12

Target: fit the unilluminated rate within 10 percent, with beam hazard at most 8 percent of intrinsic hazard, at least 8 mean counts per sampled pixel, 20 usable frames, at least 35 percent intrinsic conversion, and an exposure-integrated fit. Keep intrinsic rate times frame interval at most 0.2.

This Lab implements a liquid cell, not a gas cell. Two windows and the liquid share the same beam path; specimen is on the inner exit-window face. Assumed effective selected-channel lengths are 200 nm per window and 350 nm for liquid, not published inelastic mean free paths. Baseline intrinsic conversion is 0.1 per second. A dimensionless lumped radiolysis species starts at zero, is generated at 0.002 times electron flux, and is removed at 0.5 per second plus the flow-renewal setting; it adds 0.12 times concentration to the conversion rate. These are teaching coefficients, not water chemistry or a real-material calibration. Flow is an effective renewal rate, not a volumetric pump rate or fluid solver. No bubbles, window bowing, pressure mechanics, spatial diffusion, radical network, gas chemistry or quantitative multiple scattering. Rejected-channel electrons are not all absorbed. Fixed 200 keV beam, 80 nm square field, 64 by 64 pixels at 1.25 nm pitch and 24 stored exposures. Beam travels along positive z; x right, y up. Selected-channel intensity is an assumed linear mixture of two unresolved states with 0.45 contrast, not atomic phase contrast or material identification. A 14 nm uniform-radius patch has a 4 nm cosine edge. Each image integrates 16 midpoint samples over the exposure, including horizontal drift. Counts use 80 percent efficiency and fixed independent seeds; Poisson below 40 expected counts and normal approximation above. Fixed linear zero-to-one incident-normalized display clips only colors, never counts. A 6 nm core region extracts fractions using known flat-field transmission and contrast calibrations. Following the known drift is reference-assisted sampling, not image-estimated registration; missing field coverage is marked unavailable. The rate fit receives counted fractions and exposure metadata, never the known specimen or intrinsic rate. Noise can give fractions outside zero to one; these remain in the fit. It fits a single constant apparent rate over zero to five per second, which cannot identify the physical cause. Frame selection, sampling alignment and fit method reuse the stored counts. Presentation motion is separate from acquisition time. Lens paths, thickness and magnification are schematic; no wave optics, diffraction, absorption spectroscopy, temperature gradients or damage solver.

Physics tutorial

Liquid-cell TEM: Observing or Driving?

BackgroundSend electrons through two sealed windows and a flowing liquid layer. Balance transmitted counts against beam-driven chemistry, then fit the same stored image sequence without substituting a noiseless reference.

Why it mattersTarget: fit the unilluminated rate within 10 percent, with beam hazard at most 8 percent of intrinsic hazard, at least 8 mean counts per sampled pixel, 20 usable frames, at least 35 percent intrinsic conversion, and an exposure-integrated fit. Keep intrinsic rate times frame interval at most 0.2.

Start with the essentials

Focus question: Can a clearer liquid-cell movie give a less faithful reaction rate?
One-sentence intuition: More counts can reduce random error while increasing physical perturbation. Exposure-aware fitting and following a known drift improve measurement, but neither can remove a beam-driven reaction.

Core mathematical model

Radiolysis and renewal

\begin{aligned}\dot c&=\alpha J_{\rm on}-(\beta+\nu)c\\\dot H&=k_0+\gamma c\end{aligned}

A dimensionless lumped species; this does not solve water chemistry.

Counted conversion

\begin{aligned}\widehat u&=\frac{1-\overline N/N_{\rm flat}}{C}\\N_{\rm flat}&=\eta Jp^2\Delta t\,\mathcal T\end{aligned}

Known flat-field and contrast calibrations; counts are not replaced by an ideal image.

Exposure-aware rate fit

\begin{aligned}\overline u(k)&=1-e^{-kt_0}\frac{1-e^{-k\Delta t}}{k\Delta t}\\u(t)&=1-e^{-H(t)}\end{aligned}

Fit a constant apparent rate to integrated exposures. A good fit does not prove a thermal cause.

Selected-channel attenuation

\mathcal T=\exp\!\left(-\frac{L}{\Lambda_l}-\frac{2w}{\Lambda_w}\right)

Effective assumed lengths represent leaving the selected image channel, not pure absorption.

Common difficulties

Separate measured rate from known input

Typical misconceptionThe fitted curve reveals the unilluminated process by itself.

Better mental modelThe fit uses stored counts; intrinsic and beam hazards are separate known model diagnostics. Real experiments need independent dose controls and calibration.

Run the experiment

01
Predict the cause
Compare the bright-movie preset with low dose. Observe counts, fitted rate and the declared cause audit.
What to observe: Precision and fidelity are separate quantities.
02
Inspect stored data
Move the selected frame; switch known-drift sampling and the fit method.
What to observe: Processing settings reuse exactly the same acquisition.
03
Reach the target
Balance illumination, cadence and exposure. Reduce cell thickness and renew liquid.
What to observe: Check the target against both count and perturbation limits.