| Abstract: |
| Motivated by the $\beta$--$\omega$ transformation in titanium alloys, we study the total-spreading regime in which two $\omega$ variants can not form a direct interface and must remain separated by the parent $\beta$ phase. Building on the classical multiwell framework and the consistency requirements discussed by Boyer and Lapuerta (2006), we show that the standard model works only in a limited parameter range and may fail under strong chemical driving force. To overcome this limitation, we propose a modified multiwell phase-field model with an additional interfacial-energy term that penalizes mixed $\omega$--$\omega$ states and enforces separation of $\omega$ variants by the $\beta$ phase. At the same time, the model preserves the desired behavior of purely two-phase $\beta$--$\omega$ states. Numerical examples in one spatial dimension show proper separation of four $\omega$ variants by the $\beta$ phase and monotone decay of the total free energy. Two- and three-dimensional simulations further show the formation of thin $\beta$ layers at contacts between variants and the subsequent coarsening of the microstructure. The model provides a natural starting point for future extensions with a more realistic chemical background. |
|