Arrhenius behavior is the default assumption for thermally activated processes: plot the logarithm of the rate against inverse temperature, get a straight line, extract a single activation energy. Grain growth in polycrystalline materials was supposed to follow this pattern — grains coarsen at a rate exponentially sensitive to temperature, with one characteristic energy barrier governing the process.

In strontium titanate, it does not. Grain growth shows non-Arrhenius behavior: the curve bends. The activation energy appears to change with temperature. A new model explains why. The growth rate depends on both temperature-dependent factors (boundary mobility, diffusion rates) and temperature-independent factors (grain size, geometry). These interact multiplicatively. At low temperatures, grain growth is abnormal — a few grains grow rapidly at the expense of their neighbors — and the coupling between temperature-dependent and temperature-independent factors produces non-Arrhenius kinetics. At high temperatures, the system transitions to normal grain growth where Arrhenius behavior returns.

The structural insight is about what “having an activation energy” requires. A single activation energy exists when one barrier dominates. When multiple factors contribute — some scaling with temperature, some not — the apparent activation energy is a compound quantity that changes depending on where you measure it. The process does not have a definitive characteristic temperature because no single barrier defines it. The non-Arrhenius behavior is not a correction to the simple picture; it is the natural outcome of a process governed by interacting variables on different thermal dependencies.

This matters for any system where the rate-limiting step changes with conditions. The Arrhenius plot assumes the mechanism stays constant. When it doesn’t — when the mix of driving forces shifts with temperature — the plot curves, and the curvature is the information.

(arXiv:2603.18552)