Thermal expansion coefficients (CTE).

Why this matters

Thermal stack-up arithmetic.

• A 12″ aluminum part swings 0.016″ over a 100°F change.

  12 in × 13.1 ppm/°F × 100°F = 0.0157″. Multiply that by the number of dissimilar-metal interfaces in your assembly and you can see why aerospace optical-bench designs lean hard on Invar.

• Dissimilar metals: subtract the CTEs.

  A bushing pressed in an aluminum housing using a titanium pin — Δ CTE = 23.6 − 8.6 = 15 ppm/°C. Over a 60°C swing on a 25 mm bushing: 25 × 15 × 60 / 1,000,000 = 0.023 mm of differential. Either accept it, design clearance for it, or pick same-CTE materials.

• Cryogenic CTE is not the room-temp value.

  Most metals contract more slowly per degree at very low temperatures. For 4 K and 77 K dimensional analysis (cryostat hardware, superconducting magnets), use cryogenic-specific contraction data — it’s not a linear extrapolation from 20 °C values.

• Plastics expand 3–4× more than metals.

  Delrin (POM) at 110 ppm/°C will move >0.001″ per inch per 10 °C. For tight-tolerance plastic features, design with thermal expansion explicitly in the calculation — and consider PEEK (47 ppm/°C) for tighter applications.

• Match the CTE for sensitive optical/sensor work.

  Mounting an Invar-grade structure to an aluminum baseplate creates massive thermal stresses. For optical benches, sensor mounts, and dimensional-stability hardware, match CTE within ~3 ppm or accept the consequences.