Free energy calculation of mechanically unstable but dynamically stabilized bcc titanium

Abstract

The phase diagram of numerous materials of technological importance features high-symmetry high-temperature phases that exhibit phonon instabilities. Leading examples include shape-memory alloys, as well as ferroelectric, refractory, and structural materials. The thermodynamics of these phases have proven challenging to handle by atomistic computational thermodynamic techniques, due to the occurrence of constant anharmonicity-driven hopping between local low-symmetry distortions, while maintaining a high-symmetry time-averaged structure. To compute the free energy in such phases, we propose to explore the system's potential-energy surface by discrete sampling of local minima by means of a lattice gas Monte Carlo approach and by continuous sampling by means of a lattice dynamics approach in the vicinity of each local minimum. Given the proximity of the local minima, it is necessary to carefully partition phase space by using a Voronoi tessellation to constrain the domain of integration of the partition function, in order to avoid double-counting artifacts and enable an accurate harmonic treatment near each local minima. We consider the bcc phase of titanium as a prototypical examples to illustrate our approach.

References in corpus (15)

• The Alloy Theoretic Automated Toolkit: A User Guide
• Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit
• First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3
• The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics
• Lattice dynamics of anharmonic solids from first principles
• Phase transitions in BaTiO${}_3$ from first principles
• Entropy driven stabilization of energetically unstable crystal structures explained from first principles theory
• Lattice anharmonicity and thermal conductivity from compressive sensing of first-principles calculations
• Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic
• Ab initio statistical mechanics of the ferroelectric phase transition in PbTiO3
• Classical potential describes martensitic phase transformations between the $\alpha$, $\beta$ and $\omega$ titanium phases
• Ferroelectric Soft Phonons, Charge Density Wave Instability and Strong Electron-Phonon Coupling in BiS2-Layered Superconductors
• A First-Principles Investigation of Phonon Softenings and Lattice Instabilities in the Shape-Memory System Ni${}_2$MnGa
• A first-principles approach to nonlinear lattice dynamics: Anomalous spectra in PbTe
• A slave mode expansion for obtaining ab-initio interatomic potentials

Cited by in corpus (14)

• Compressive sensing lattice dynamics. I. General formalism
• Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives
• Atomistic modelling of all dislocations and twins in HCP and BCC Ti
• Low energy paths for octahedral tilting in inorganic halide perovskites
• $\text{Ab Initio}$ Study of Antisite Defects in Nb${}_3$Sn: Phase Diagram and Impact on Superconductivity
• Defects from phonons: Atomic transport by concerted motion in simple crystalline metals
• Structurally driven asymmetric miscibility in the phase diagram of W-Ti
• Phonon-assisted diffusion in bcc phase of titanium and zirconium from first-principles
• Vibrational entropy of crystalline solids from covariance of atomic displacements
• Understanding the role of anharmonic phonons in diffusion of bcc metal
• Sampling dependent systematic errors in effective harmonic models
• Machine Learning Potentials for Alloys: A Detailed Workflow to Predict Phase Diagrams and Benchmark Accuracy
• Phase stability in the Hf-N and Zr-N systems
• Efficient first-principles approach to Gibbs free energy with thermal expansion