E45 · In-situ electron microscopy

In-situ TEM: Stimulus or Beam?

In an in-situ TEM experiment, is the beam observing the response or helping drive it? It can be doing both. Electrons can change a thermal reaction, push a charged object or soften a loaded specimen. More counts make the motion easier to measure, but do not establish its cause. Compare controlled runs at different doses; fitting and drift correction cannot remove a response the beam itself created.

Apply electrical bias, mechanical load or heat. Track markers or conversion in recorded count images, then test whether the inferred material response is changed by the imaging beam.

Count-derived response $\text{—}$

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

Beam perturbation audit $\text{—}$

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

More measurements and target

Inferred coefficient, modulus or thermal rate $\text{—}$

Fitted response time $\text{—}$

Known beam-off response $\text{—}$

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

Selected exposure midpoint $\text{—}$

Exposure duration $\text{—}$

Total incident areal dose $\text{—}$

Usable sampled frames $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Stimulus: 0 heat · 1 bias · 2 load

h

1

Applied potential difference

V

1.5\,\mathrm{V}

Applied uniaxial stress

\sigma

100\,\mathrm{\mathrm{MPa}}

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}}

Blank beam between exposures: 1 on

b

0

Advanced settings

Counting noise: 1 on

n_P

1

Exposure fraction of each interval

d

0.5

Horizontal specimen drift

v_d

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

Correct drift: 1 on

a

0

Exposure-integrated fit: 1 on

m

1

Selected stored frame · zero-based

n

12

Learning goal and model limits

Drive, record, then infer

In an in-situ TEM experiment, is the beam observing the response or helping drive it?

Drag the gold holder handle to change bias or load. Target: parameter error at most 15 percent, beam perturbation at most 8 percent, at least 20 resolved frames and 8 counts per pixel; use the exposure-integrated fit. The thermal branch keeps its separate rate target, explained below.

Model assumptions

The bias branch is an overdamped, singly charged tethered marker in a uniform field across a 200 nm electrode gap, with stiffness 0.00012 newtons per metre and a 2 s relaxation time. Its assigned beam force is 0.0000000000000003 newtons per unit areal flux. The load branch is a Kelvin–Voigt specimen with 1 GPa initial modulus and fixed 2 GPa-second viscosity; its assigned modulus falls as one divided by one plus 0.00005 times the dose. These are teaching parameters, not a calibrated material. Two Gaussian absorption markers have a calibrated 3.5 nm image width and 0.7 contrast. Their positions come from Poisson profile fits to the acquired counts; the bias branch uses a stationary marker to estimate common drift, while the load branch uses their separation. The response fit uses the exposure timing and counted positions, without the driving force, true positions or beam history. Material inference additionally requires the applied voltage or stress and the stated calibrations. A fitted constant time scale is an apparent parameter when the beam changes the dynamics. Unresolved profiles remain unavailable. Above 20 percent strain, or when a contact enters the 80 nm field, the calibration is declared invalid. The membrane fills the field; its absorption is held fixed under strain, neglecting thickness and density changes. Fringing fields, inertia, plasticity, fracture, charging dynamics and realistic beam-damage chemistry are omitted. The beam-off reference and perturbation audit use known inputs, independently of the measured fit. Lateral distances map to nanometres; axial apparatus spacing and lens paths are schematic. The thermal branch models in-situ TEM heating. The material converts by an assumed first-order law with a 0.8 eV activation barrier and a rate of 0.1 per second at 650 K. The beam drives extra conversion: it adds 0.0002 square nanometres per electron, times the accumulated dose, to the hazard. The 30 nm foil has an assumed effective selected-channel length of 300 nm. With blanking on, the beam is off between exposures while thermal conversion carries on. Nucleation, grain growth and calibrated kinetics of a real material are not modeled. The beam is fixed at 200 keV and travels along positive z, with x to the right and y up. The 80 nm square field has 64 by 64 pixels at 1.25 nm pitch, and each run stores 24 exposures. The selected-channel intensity is an assumed linear mix of two unresolved states with 0.45 contrast; it is not atomic phase contrast and does not identify a material. The converting patch has a uniform 14 nm radius and a 4 nm cosine edge. Each image sums 16 midpoint samples across the exposure, including the horizontal drift during that time. The detector records 80 percent of electrons, using fixed, independent random seeds: counts follow Poisson statistics below 40 expected counts and a normal approximation above. The display uses a fixed linear scale from zero to one of the incident level; it clips colors only, never counts. Conversion fractions come from a 6 nm core region, using known flat-field transmission and contrast calibrations. Following the known drift moves the sampling region with the reference motion; it does not estimate registration from the images. A frame whose field misses part of the region is marked unavailable. The rate fit sees only the counted fractions and the exposure timing, never the known specimen or the intrinsic rate. Noise can push fractions outside zero to one, and they stay in the fit. The fit finds one constant apparent rate between zero and five per second, so it cannot tell what caused the conversion. Changing the selected frame, the sampling alignment or the fit method reuses the stored counts. On-screen motion runs separately from acquisition time. Lens paths, thickness and magnification are schematic. There is no wave optics, diffraction, absorption spectroscopy, temperature gradient or damage calculation.

Physics tutorial

In-situ TEM: Stimulus or Beam?

BackgroundA TEM can film a specimen while a holder heats it, applies bias or pulls it. The imaging beam also acts on the specimen. Start with bias: two dark markers let you measure displacement while removing their shared drift. Then compare the same measurement at a higher dose.

Why it mattersFor bias and load, recover the response coefficient or modulus within 15 percent of the known input, with beam perturbation at most 8 percent. Use the exposure-integrated fit, at least 20 resolved frames and 8 mean counts per pixel. In the thermal preset, the separate target remains a rate within 10 percent, at least 35 percent intrinsic conversion and an intrinsic rate times frame interval at most 0.2.

Start with the essentials

Focus question: In an in-situ TEM experiment, is the beam observing the response or helping drive it?
One-sentence intuition: A beam can make a response easier to measure and change that response at the same time.

Core mathematical model

Bias displaces a tethered marker

\begin{aligned}\gamma\dot x+kx&=qV/g+F_b(t)\\x_{\infty,0}/V&=q/(gk)\end{aligned}

The field is uniform between electrodes. Stiffness, charge and gap are known inputs. The beam contributes an assigned force during illumination; it is not inferred from the displacement alone.

Load stretches a viscoelastic specimen

\begin{aligned}\eta\dot\varepsilon+E(D)\varepsilon&=\sigma\\E(D)&=E_0/(1+\alpha D)\\\widehat\varepsilon&=(\widehat x_R-\widehat x_L)/L_0-1\end{aligned}

The spring and dashpot act in parallel. The specimen has a fixed viscosity and an assigned dose-dependent modulus. Marker separation removes common translation. The model is limited to strains no larger than 20 percent.

Fit the recorded exposure, not its midpoint

\overline r=A\left[1-e^{-t_0/\tau}\frac{\tau}{\Delta t}\left(1-e^{-\Delta t/\tau}\right)\right]

Marker positions are fitted from counted profiles with a known point-spread width and flat-field level. Their displacement or strain is fitted to this exposure mean. The inferred voltage coefficient or modulus also uses the applied drive. A changing modulus makes this a constant-parameter approximation.

Thermal and beam contributions to the hazard

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

The conversion follows a prescribed first-order law. It does not model nucleation or describe a specific material.

Conversion measured from counts

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

The flat-field level and the contrast are known calibrations, and the fraction is computed from the recorded counts themselves.

Fitting a rate to finite exposures

\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}

Each frame averages the conversion over its exposure, and the fit matches one constant apparent rate to those averages. A good fit does not prove that heat caused the change.

Common difficulties

A good fit does not identify the cause

Typical misconceptionIf the curve fits the frames, its coefficient is the material property without the beam.

Better mental modelThe fit sees the recorded response. The beam-off reference and perturbation audit are separate calculations from known inputs. They are available in this teaching model; a real experiment needs dose controls and independent calibration. The electrical and softening laws here illustrate the ambiguity and do not represent a calibrated material.

Run the experiment

01
Bias and count-derived drift correction
Drag the gold handle or change the voltage. Switch drift correction off in the advanced controls, then inspect the same stored sequence.
What to observe: The stationary marker estimates translation from the image. Correcting it leaves the moving marker’s displacement; changing processing settings does not acquire new counts.
02
Distinguish load from beam softening
Compare Load with The beam softens the specimen. Look at the counted marker separation and the inferred modulus.
What to observe: The brighter sequence has more counts and more strain. Attributing all that strain to the applied stress underestimates the initial modulus.
03
Test each limit
Choose Too few electrons to track, then Heat. In the thermal branch, adjust temperature, flux and cadence and inspect the count-derived rate.
What to observe: Unresolved marker profiles cannot give a material coefficient. The thermal branch instead measures conversion, with its own drift calibration and target.