Nonlinear Arrhenius behavior of self-diffusion in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi><mml:mtext>−</mml:mtext><mml:mi>Ti</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Mo</mml:mi></mml:math>

While anomalous diffusion coefficients with non-Arrhenius-like temperature dependence are observed in a number of metals, conclusive comprehensive framework explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory calculate self-diffusion the bcc metals Mo and $\ensuremath{\beta}$-Ti by coupling quasiharmonic transition state large-displacement phonon show that anharmonicity from thermal expansion is major reason for dependence. We modified Debye approach quantify over entire range introduce method relax vacancy structure mechanically unstable crystal such as $\ensuremath{\beta}$-Ti. The effect found be crucial nonlinear, non-Arrhenius ``anomalous'' both systems, showing 60% larger relative nonlinearity parameter than Mo. Our results point prefactor origin self-diffusion. methodology proposed general simple enough applicable other crystals.