Bakeout Physics · Part 2 of 3

Module 02: Outgassing & Temperature

Why heat empties a wall: outgassing, molecule by molecule

A vacuum chamber wall is not clean, it is loaded. Water stacked on the surface, hydrogen dissolved inside the steel, traces of oil. Each one is held by a different glue. Temperature is the fastest lever, and its effect is exponential. Drag the slider and watch the wall live.

Wall temperature 20 °C from room temperature to a hot vacuum-furnace regime

Presets

Our fleet

STEP 1The wall, live: read it as strata, top to bottom

Cross-section of a stainless wall, drawn as the four strata a vacuum scientist actually thinks in: physisorbed multilayers on top, then the chemisorbed monolayer, then the Cr₂O₃ oxide skin, then the bulk steel with its dissolved hydrogen. Every particle vibrates about 10¹³ times per second, and every vibration is an escape attempt. Heat acts on the odds: it raises the chance that any one attempt succeeds. Watch the order: the top physisorbed layer peels first, the monolayer only lets go once it is exposed, and the hydrogen has to cross the whole bulk and squeeze past the oxide before it can pair up and leave.

CHAMBER WALL IN CROSS-SECTION · time is compressed, relative rates are real

PHYSISORBED: water multilayers, van der Waals / H-bonds (~0.45 eV) CHEMISORBED: first monolayer, bonded to the oxide (0.9–1.05 eV, this card uses 1.05) hydrocarbon / oil trace (~1.6 eV) Cr₂O₃ passive oxide (~3 nm): the water’s anchor, and a brake on H H dissolved in the bulk (diffusion, ~0.55 eV)

Read the wall from top to bottom. The outer water layers are physisorbed: Post-its stuck on Post-its, each one only weakly held by its neighbours, so the topmost peel off first. The last layer is chemisorbed: duct-taped directly onto the Cr₂O₃ oxide skin, ten times harder to remove. Oil is superglue sitting in the same layer. Hydrogen is dissolved inside the steel and must random-walk to the surface, then squeeze past the oxide, before it can leave as H₂.

The demo refills the reservoirs so the animation keeps running. A real bake empties the surface reservoirs until the next vent.

STEP 2The formula behind the shaking: one exponential rules everything

A molecule sits in an energy well of depth E. It attempts escape ν₀ ≈ 10¹³ times per second, and each attempt succeeds with probability e⁻ᴦ∕ᴿᴩ. Average residence time before escape:

FRENKEL’S LAW · desorption

τ = τ₀ · e^{E / kT} with τ₀ ≈ 10⁻¹³ s

rate per molecule = ν₀ · e^−E/kT

E sits upstairs in an exponential, so doubling E can multiply the residence time by billions. And T sits downstairs, so heating collapses τ just as violently. Residence time here, and hydrogen diffusion below, both follow an exponential in 1/T.

Loaded dice. The molecule rolls 10¹³ dice per second. At room temperature the strongly bound water needs to roll about 10¹⁸ before one wins. At 150 °C the dice get easier by a factor of a hundred thousand, and it wins within seconds.

FICK’S LAW · why hydrogen is different

D = D₀ · e^{−E_diff / kT} hop-by-hop through the lattice

time to drain a depth L ≈ L² / D

Hydrogen is dissolved in the wall, one atom per interstitial site. Its bottleneck is the random walk to the surface, where two atoms recombine into H₂ and leave. Same exponential in T, but the reservoir is the whole thickness of the steel. That is why the final pressure of a well-baked UHV system is dominated by H₂, with CO and CH₄ as the main remaining traces.

H in stainless, right now

time to drain a 1 mm depth

Water, loose stack

E = 0.45 eV · Post-it

residence time now

Water, bound layer

E = 1.05 eV · duct tape

residence time now

Hydrocarbon trace

E = 1.6 eV · superglue

residence time now

Real surfaces carry a distribution of binding energies, where this model uses three sharp values. These are representative points, chosen to show the regimes. The exponential logic is exact.

STEP 3The Arrhenius map: every bake decision on one chart

Residence time (or drain time for H₂) against wall temperature, log scale. The horizontal bands are human time: a second, an hour, a day, a month, a year. A species is “gone within your bake” once its curve dives below your bake duration. With the fleet toggle on, the grey zone marks everything beyond our 150 °C ceiling. It stays on the chart for reference. The gold line is our 48 h bake. The vertical line tracks the slider. Hover the chart to explore.

Hover to read each species at any temperature.

STEP 450 °C vs 150 °C vs 250 °C: three different jobs

Same wall, same physics, but the exponential means each temperature targets a different species. The numbers below are computed live from the formulas above. The active card follows the slider.

Warm-up / dry-out

50 °C

Loose water:
Bound water:
Hydrocarbon:
H₂ (1 mm):

Speeds up the loose water a little and leaves the bound monolayer in place. This is a dry-out.

The standard accelerator bake

150 °C

Loose water:
Bound water:
Hydrocarbon:
H₂ (1 mm):

The water killer. Bound-water residence collapses from days to seconds, so a 48 h bake drains the whole reservoir. Hydrocarbons and bulk H₂ are still mostly out of reach.

Deep clean

250 °C

Loose water:
Bound water:
Hydrocarbon:
H₂ (1 mm):

Water left long ago. Now the hydrocarbons let go, and hydrogen diffusion finally wakes up, days instead of decades. Push to 400–950 °C in a vacuum furnace and you permanently deplete the H₂ stock itself.

WHAT THE RGA SEES BEFORE AND AFTER · the fingerprint of a good bake

Unbaked chamber: mass 18 towers over everything, water is 90-plus percent of the gas load. After a proper 150 °C bake the water reservoir is empty and the spectrum flips: mass 2 dominates, fed forever by slow diffusion from the bulk. A hydrogen-dominated spectrum is the signature that the bake worked.

This module derived why heat works. Why We Bake applies it: the operational card set of race, sim, recipes, and the wall running forward under a real bake.

Sources · 3

[A] P.A. Redhead, Recommended practices for measuring and reporting outgassing data, JVST A 20, 1667 (2002).
[A] P. Chiggiato, Outgassing properties of vacuum materials for particle accelerators, CERN Accelerator School : Vacuum for Particle Accelerators, Glumslov 2017, arXiv:2006.07124.
[A] M.R. Louthan & R.G. Derrick, Hydrogen transport in austenitic stainless steel, Corrosion Science 15, 565 (1975).

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