Ab initio calculation of thermal expansion with application to understanding Invar behavior in gum metal

A theoretical examination of the thermal expansion behavior of a variety of metals is conducted using a combination of nonlinear elasticity theory and first-principles calculations that is suitable for high throughput computation. Results of this method show good agreement with experimental values. This method is then used to better understand the low thermal expansion behavior of gum metal by comparing the thermal expansion tensor of ${\mathrm{Ti}}_3\mathrm{Nb}$ austenitic ($\beta$) and martensitic (${\alpha }^{\prime \prime }$) gum metal approximants. The thermal expansion coefficient of $\beta$ is found to be in agreement with experimental results for that of annealed gum metal. The thermal expansion tensor of the ${\alpha }^{\prime \prime }$ phase is shown to be highly anisotropic and exhibit negative thermal expansion along ${⟨110⟩}_{\beta }$. It is demonstrated that the thermal expansion of the two-phase system, $\beta +{\alpha }^{\prime \prime }$, can be estimated using the rule of mixing. By applying this averaging scheme and allowing a texturing along $⟨110⟩{\left\{001\right\}}_{\beta }$ in tandem with the growth of the ${\alpha }^{\prime \prime }$ phase, values for the thermal expansion similar to that seen in cold-rolled gum metal are calculated.