# Linearity of thermal expansion of metals?

I am having to do a path length correction for a metal tube (stainless steel 316, 16ppm/C) from 0-100 degC. I need to correct to within approximately 1 ppm. How much do typical engineering metals deviate from linearity over this temperature range?

• My usual path of finding these things out is: step 1) check the matweb page on the material in question (matweb is great). If not there, proceed to step two. Step 2) use the manufacturer links on the matweb page to check the technical specs the manufacturers have (Only once have I ever found that the manufacturers didn't have the data). If still not there, go to step 3. Step 3) Choose a reasonably similar alternate material and go back to step 1. If there are no reasonably similar materials, go to step 4. Step 4) Cry. – Jim Jan 30 '15 at 15:59
• Thanks - never come across matweb before. I'm mainly electronics and s/w, but have a physics background and am doing some physics R&D – user56903 Jan 30 '15 at 16:47

They cite the empirically deduced thermal expansion of austenitic stainless steel to be: $$\frac{\Delta l}{l} = 10^{-6}(16 + 4.76\times10^{-3}T - 1.243\times10^{-6}T^2)\cdot(T-20)$$ with $T$ having units of degC.