We present an ab initio temperature–pressure phase diagram of elemental thorium up to 250 GPa and 12 000 K based on the Gibbs free energies of the $\mathrm{fcc}, \mathrm{bct}$, and $\mathrm{bcc}$ phases. Static-lattice cold curves, vibrational free energies, and electronic free-energy contributions were calculated using density functional theory. Phonons were calculated within the quasiharmonic approximation for the $\mathrm{fcc}$ and $\mathrm{bct}$ phases. Mechanical stability analysis shows that the $\mathrm{fcc}$ phase develops an elastic instability above $\sim 80\mathrm{GPa}$, whereupon the $\mathrm{bct}$ phase becomes the stable compressed phase. In contrast, harmonic $\mathrm{bcc}$ phonons exhibit imaginary frequency modes across the explored volume range at $T=0$, precluding a purely quasiharmonic treatment. We therefore perform finite-temperature molecular dynamics and extract second-order temperature-dependent force constants using the temperature-dependent effective potential (TDEP) method, obtaining dynamically stable $\mathrm{bcc}$ phonons and corresponding vibrational free energies. We also perform Z-method simulations to obtain the melt curves of the fcc, bct, and bcc phases. Combining these contributions, we calculate the Gibbs free energy and determine the $\mathrm{fcc}–\mathrm{bct}–\mathrm{bcc}$ phase boundaries and the topology of the thorium phase diagram, including the high-temperature stabilization of $\mathrm{bcc}$.

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• Equations of state
• Phase diagrams
• Thermodynamics
• Actinides
• Density functional calculations