What dictates coefficient of thermal expansion in alloys?

Factual Questions
1

In alloys of metallic elements, what determines what the coefficient of thermal expansion will be? Is it roughly a volumetric mean of the constituents, or is it strongly nonlinear with mix ratio, or something else?

In particular, is it expedient to think of CTE as essentially the same as the main element, in alloys that have a strong preponderance of one element? Or can minor constituents cause major differences (like they can in strength for example)?

I understand the Lennard-Jones potential and how its asymmetry causes CTE, but that’s not useful here without knowing the distribution of these potential functions. I’m interested in a practical or empirical statement about alloys, not a fundamental mechanistic principle.

Thanks!

2

From wikipedia “A detailed explanation of Invar’s anomalously low CTE has proven elusive for physicists.” Invar

Most alloys have CTE similar (<+/-10%) than the predominant metal. But some like Invar do not.

Here’s a reference of common metal and alloys CTE http://psec.uchicago.edu/thermal_coefficients/cte_metals_05517-90143.pdf

3

Would it depend on the phases present? If there’s phase A at 0-30%, B at 30-60% and C at 60-100%, I’d expect there to be some jump in the CTEs.

4

Invar is an interesting case. After posting I found a graph of CTE as a function of Ni:Fe ratio, and its behavior is bizarre and peaky, certainly not a linear interpolation of the two constituent CTEs. Such a graph appears at the top of the Wikipedia article on invar, which is liked by am77494. So, Invar is a counterexample to my simple guess.

But perhaps a rare counterexample. Apparently Invar is weird this way.

AaronX, you raise an interesting point – I didn’t think of that, but it seems reasonable.