Vacuum Window Thickness Calculator

How it works

The maximum stress on a uniformly loaded window is S_max = K·D²·P / (4T²), and to avoid plastic deformation this is held below the apparent elastic limit F_a by a safety factor, S_max = F_a / SF. Solving for T gives the expressions above. The support constant K depends on how the window is held, on the force introduced in clamping, and on how brittle or ductile the material is. Empirically K = 0.75 suits most optical crystals with a clamped perimeter, and a value 50% greater, K = 1.125, when unclamped; the mounting dropdown selects between the two. Clamped puts the maximum stress at the edge of the window, unclamped at its centre.

A safety factor of 4 is described as modest but sufficient for many laboratory applications where operating conditions are reasonably under control; this page defaults to 5. Severe conditions such as thermal shock need special consideration, and may even lead to a decision to use a reduced thickness.

Cautions

• A carefully designed window may still break well below its rated load if the mounting introduces any localised stress.
• Mismatched expansion coefficients generally dictate a resilient material between window and mount.
• Soft gaskets allow flexure at the wall. The clamped constant assumes no flexure, so if the window is seated on a soft gasket or O-ring, use the unclamped figure.
• Thermal outgassing in UHV systems should be approached with caution for crystal windows, as thermal shock may initiate cleavage.
• Published apparent elastic limits are not always reliable. Crystals vary, and cleavage may occur along grain boundaries or according to the particular cut of the ingot. The final design thickness must be a carefully considered decision and may need to be tested empirically.

Source and a note on sapphire

Equations, support constants and elastic limits are from The Design of Pressure Windows, Crystran Ltd, October 2014. Elastic limits used here are the table's SI values. One caveat: that table lists sapphire as “276 MPa = 45000 psi”, but 276 MPa is 40030 psi — the two figures disagree, and every other material in the table is self-consistent. This calculator uses 276 MPa, which matches Crystran's own sapphire datasheet and is the more conservative choice. Crystran's printed worked example for a 25 mm sapphire window at 3800 psi (7.7 mm unclamped, 6.3 mm clamped) was computed from 45000 psi, so it will not reproduce here — you should expect 8.17 mm and 6.67 mm instead. Enter 45000 psi via Custom… if you want to match the printed example. The other five worked examples in that document reproduce exactly.

Atmospheric pressure is taken as 101324 Pa, following the same document; note that 1 bar is 100 kPa exactly and so is slightly less than 1 atm.

Crystran Ltd accept no responsibility for the adoption of these calculations and recommendations, and neither does the author of this page. Verify any safety-critical design independently.

Webpage maintained by Sean Kung at the University of British Columbia.