--- title: "Environmental-cell TEM: Bubbles and Pressure Interactive Lab | Sandbox Physics" description: "How do pressure and beam-driven bubbles change an environmental TEM image? Gas scatters electrons out of the selected image channel and can dim the image." canonical_url: "https://sandboxphysics.com/labs/liquid-cell-tem/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/liquid-cell-tem/" last_modified: "2026-10-27" --- E46 · Environmental electron microscopy # Environmental-cell TEM: Bubbles and Pressure **How do pressure and beam-driven bubbles change an environmental TEM image?** Gas scatters electrons out of the selected image channel and can dim the image. A beam-produced bubble replaces liquid, shortening the liquid path and making that region brighter. Brightness therefore depends on what the electrons pass through. A clearer movie alone cannot establish that a reaction is less disturbed; dose and flow controls are needed. See a beam-driven bubble replace liquid, then switch to gas and measure pressure from transmitted counts. Compare both with the retained liquid-reaction movie. > Interactive simulation: open this page in a web browser to change the parameters and run the model. Model assumptions The bubble branch is a pinned spherical hydrogen bubble in an 80 nm square, flat-window cell at 298.15 K and 100 kPa ambient pressure. Both illuminated area and liquid volume use this same square field. The assigned effective yield is adjustable from zero to 0.01 gas molecules per incident electron. It is not a radiochemical yield for 200 keV electrons in water. Dissolved molecules, bubble molecules, production and removal by liquid renewal are tracked separately. Surface tension is rounded to 0.072 newtons per metre; the dilute Henry coefficient is 0.0000078 mole per cubic metre per pascal, converted to molecules. A predetermined 8 nm heterogeneous nucleus is introduced only when the dissolved inventory can supply its gas and the corresponding equilibrium dissolved inventory. Gas is transferred from solution, not created at nucleation. The bubble uses ideal gas and Laplace pressure, and an assigned interface velocity of 0.0000001 metre per second. Ideal-gas and linear Henry relations are extrapolated to the high internal pressure of a small bubble; nonideality, water vapor, diffusion, coalescence and detailed water chemistry are omitted. These are continuum mean inventories, not individual molecular events. A sphere touching a window or reaching 35 nm radius stops the model before the invalid step; earlier full exposures and any shortened final exposure are retained with their actual durations. Bubble intensity follows the remaining liquid chord, with the same assigned attenuation lengths as the reaction branch. A constant exposure-equivalent radius is fitted from counted spatial profiles using known center, window and liquid thickness; non-detection remains distinct from zero dissolved gas. The 0.25 nm fit grid and deviance cuts are teaching diagnostics, not confidence coverage. The gas branch uses a known uniform pressure from zero to 100 kPa, ideal number density and an assigned selected-channel cross-section of one times ten to the minus twenty square metres. Pressure is inferred from acquired mean counts conditional on known gas path, cross-section and both windows. Negative apparent estimates from noise are retained. Uncertainty is conditional on the count calibration; thickness or cross-section uncertainty is omitted. Each normal run stores 24 finite exposures. The default image is already acquired; presentation motion does not advance physical time. The gas curve is a separate known calibration, with one measured transmission at the applied pressure. Apparatus axial distances are compressed separately from lateral nanometres: the displayed gap is 40 plus 40 times the square root of liquid thickness divided by 1500, or gas thickness divided by 15000. Bubble height uses the same axial factor as its cell, so the displayed ellipsoid represents a sphere under this mapping. Window display thickness is its physical thickness divided by ten. Representative molecules and electron trajectories are schematic; images and fits stay outside the apparatus viewport. The retained reaction-only branch uses the following separate model. The beam passes through two windows and the liquid between them, and the specimen sits on the inner face of the exit window. The effective selected-channel lengths are assumed: 200 nm per window and 350 nm for the liquid. They are not published inelastic mean free paths. Without the beam, the intrinsic conversion rate is 0.1 per second. The beam creates one lumped, dimensionless radiolysis species. It starts at zero, is produced at 0.002 times the electron flux, and is removed at 0.5 per second plus the flow-renewal setting; it raises the conversion rate by 0.12 times its concentration. These are teaching coefficients, not water chemistry or a calibration for a real material. Flow is an effective renewal rate, not a pump's volume flow or a fluid simulation. In this reaction-only branch, gas transport and bubbles are not coupled to the converting patch. Window bowing, pressure mechanics, spatial diffusion, radical networks and quantitative multiple scattering are omitted. Electrons that leave the selected channel are not all absorbed. 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 ## Environmental-cell TEM: Bubbles and Pressure **Background** Two thin windows keep liquid or gas inside a TEM cell. Electrons can scatter out of the selected image channel in that medium. In liquid, the beam can also produce gas: a bubble replaces part of the liquid path and makes that part of the image brighter. The cell and the recorded counts must describe the same path. **Why it matters** In the bubble example, infer the selected radius within 15 percent or 0.5 nm, whichever is larger, from at least four resolved exposures. Keep all 24 exposures complete and collect at least 8 mean counts per pixel. In gas, infer pressure within 10 percent or 2 kPa, with conditional counting uncertainty at most 2 kPa and at least 8 counts per pixel. The retained reaction preset has its separate rate target: 10 percent error, beam hazard at most 8 percent of intrinsic hazard, 20 usable frames, 35 percent intrinsic conversion and an exposure-integrated fit; intrinsic rate times frame interval must be at most 0.2. Start with the essentials - **Focus question**: How do pressure and beam-driven bubbles change an environmental TEM image? - **One-sentence intuition**: A bright region can appear because a bubble has replaced liquid. It need not mean that the specimen became easier to observe without disturbing it. ### Core mathematical model #### Count the gas before creating a nucleus $$ \begin{aligned}\dot N_g&=y_gJ_{\rm on}A\\\dot N_d&=\dot N_g-\nu N_d-\dot N_b\end{aligned} $$ The dissolved inventory supplies the bubble and loses gas through liquid renewal. The predetermined nucleus appears only when that inventory can supply both the seed and its equilibrium dissolved gas. This rule is assigned; it does not calculate a nucleation barrier. #### Bubble inventory and internal pressure $$ \begin{aligned}P_b&=P_{\rm ext}+2\gamma/R\\N_b&=\frac{P_b}{k_BT}\frac{4\pi R^3}{3}\end{aligned} $$ The bubble is a pinned sphere. Its gas follows an ideal equation of state; exchange uses a linear Henry relation. Both are teaching extrapolations at the large internal pressure of a small bubble. The model stops before the sphere touches a window or reaches the lateral bound. #### A bubble shortens the liquid path $$ \begin{aligned}c(r)&=\begin{cases}2\sqrt{R^2-r^2}&r