# Clarifying the Ti-V Phase Diagram Using First-Principles Calculations and Bayesian Learning

arXiv: https://arxiv.org/abs/2506.17719 · HTML: https://mlsanity.com/paper/2506.17719/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 21 Jun 2025.

## Builds on (most cited first, 6 of 6)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [Accurate melting point prediction through autonomous physics-informed learning](https://mlsanity.com/paper/2306.13345/) (2023)
- [Bayesian inference of composition-dependent phase diagrams](https://mlsanity.com/paper/2309.01271/) (2023)

## Abstract (arXiv)

Conflicting experiments disagree on whether the titanium-vanadium (Ti-V) binary alloy exhibits a body-centred cubic (BCC) miscibility gap or remains completely soluble. A leading hypothesis attributes the miscibility gap to oxygen contamination during alloy preparation. To resolve this disagreement, we use an ab initio + machine-learning workflow that couples an actively-trained Moment Tensor Potential with Bayesian inference of free energy surface. This workflow enables construction of the Ti-V phase diagram across the full composition range with systematically reduced statistical and finite-size errors. The resulting diagram reproduces all experimental features, demonstrating the robustness of our approach, and clearly favors the variant with a BCC miscibility gap terminating at T = 980 K and c = 0.67. Because our simulations model a perfectly oxygen-free Ti-V system, the observed gap cannot originate from impurity effects, in contrast to recent CALPHAD reassessments.