Invar, a nickle-iron alloy, was commercially highly relevant for accuracy of mechanical watch balance springs in the 19th century. Investigations of that presumably lead to the 1920 Nobel in physics.
The article claims to produce the first equation to model this effect accurately, together with an experimental technique to validate the main components. This would support in-silico material exploration, esp. predictions for high temperatures that induce expansion.
But because this demonstrates phase shifts in how electrons interact, the significance could be broader that just the use of constant-size invar (iron/nickel alloy).
Paper excerpts:
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Here we use a thermodynamic Maxwell relation to explicitly separate the contributions to thermal expansion from phonons and spins. [...] These two contributions were measured by nuclear resonant X-ray scattering on Invar under pressure. We find that a competition with phonons is necessary to complete the explanation of the near-zero thermal expansion of Invar.
An advantage to [our] equation is that the two main components of thermal expansion—phonon and magnetic—can be experimentally obtained by nuclear resonant X-ray scattering
Excellent agreement between experiment and theory is found. There is a remarkable spin–lattice coupling, and a precise cancellation of the phonon and spin contributions that causes the anomalously low thermal expansion in Invar near ambient conditions of T and P. Furthermore, the transition to a more typical thermal expansion at higher pressures is shown to arise from the magnetic transition to the paramagnetic state that quenches the negative contribution from the spin system. Finally, the electronic contribution is found to have only a small effect on thermal expansion.