E45 · In-situ electron microscopy

In-situ TEM: Measure a Thermal Rate

Heat a thin foil on a MEMS chip. Tune illumination, exposure cadence and drift; extract conversion from stored frames and compare the fitted apparent rate with the unilluminated thermal 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 $\text{—}$

Experiment target $\text{—}$

Predict · acquire · fit · explain

Is the beam watching the transformation, or helping it happen?

Assumed uniform foil temperature

T

650\,\mathrm{K}

Incident electron flux

J

400\,\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

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

Follow known drift: 1 on

a

0

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 the heating branch of in-situ TEM. The assumed first-order material has a 0.8 eV activation barrier and a rate of 0.1 per second at 650 K. Beam conversion adds 0.0002 square nanometres per electron times accumulated dose. The 30 nm foil has an assumed effective selected-channel length of 300 nm. Blanking turns the beam off between exposures while thermal conversion continues. No electrical bias, mechanical loading, nucleation, grain growth or calibrated real-material kinetics are claimed. 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

In-situ TEM: Measure a Thermal Rate

BackgroundHeat a thin foil on a MEMS chip. Tune illumination, exposure cadence and drift; extract conversion from stored frames and compare the fitted apparent rate with the unilluminated thermal 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: Is the beam watching the transformation, or helping it happen?
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

Thermal and beam hazards

\begin{aligned}k_T&=k_*e^{-\frac{E_a}{k_B}(1/T-1/T_*)}\\H(t)&=k_Tt+\sigma D(t)\end{aligned}

A prescribed first-order conversion law; no nucleation or material-specific claim.

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.

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. Choose a temperature the cadence can resolve.
What to observe: Check the target against both count and perturbation limits.