Phase stability of Fe from first-principles: atomistic spin dynamics coupled with ab initio molecular dynamics simulations and thermodynamic integration

Abstract

The calculation of free energies from first principles in materials is a formidable task which enables the prediction of phase stability with high accuracy; these calculations are complicated in magnetic materials by the interplay of electronic, magnetic, and vibrational degrees of freedom. In this work, we show the feasibility and accuracy of the calculation of phase stability in magnetic systems with ab initio methods and thermodynamic integration by sampling the magnetic and vibrational phase space with coupled atomistic spin dynamics-ab initio molecular dynamics (ASD-AIMD) simulations [Stockem et al., PRL 121, 125902 (2018)], where energies and interatomic forces are calculated with density functional theory (DFT). We employ the method to calculate the phase stability of Fe at ambient pressure from 800 K up to 1800 K. The Gibbs free energy difference between fcc and bcc Fe at zero pressure as a function of temperature is calculated carrying out thermodynamic integration over temperature on the energies at the DFT level from ASD-AIMD, using a reference free energy difference calculated in the paramagnetic state at temperatures much higher than the magnetic transition temperatures with thermodynamic integration over stress-strain variables with disordered local moment (DLM)-AIMD simulations. We show the importance of the magnetic ordering temperature of bcc Fe on the $\alpha$ to $\gamma$ structural transition temperature, whereas the $\gamma$ to $\delta$ transition is well reproduced independently of the exchange interactions. The Gibbs free energy difference between the two structures is within 5 meV/atom from the CALPHAD estimate, and both transition temperatures are reproduced within 150 K. The present work paves the way to free energy calculations in magnetic materials from first principles with accuracy in the order of 1 meV/atom.

References in corpus (18)

• Ab-initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni
• A method for atomistic spin dynamics simulations: implementation and examples
• Effect of magnetic disorder and strong electron correlations on the thermodynamics of CrN
• General method for atomistic spin-lattice dynamics with first principles accuracy
• Equation of state of paramagnetic CrN from ab initio molecular dynamics
• Anomalous phonon lifetime shortening in paramagnetic CrN caused by magneto-lattice coupling: A combined spin and ab initio molecular dynamics study
• Melting Si: beyond density functional theory
• Computing the Absolute Gibbs Free Energy in Atomistic Simulations: Applications to Defects in Solids
• Electronic correlations determine the phase stability of iron up to the melting temperature
• Constraints on the phase diagram of molybdenum from first-principles free-energy calculations
• Dynamic Simulation of Structural Phase Transitions in Magnetic Iron
• Magnetoelastic coupling in iron
• Superionic-like diffusion in an elemental crystal: bcc Titanium
• Exchange Interactions in Paramagnetic Amorphous and Disordered Crystalline CrN-based Systems
• Thermodynamics of itinerant magnets in a classical spin fluctuation model
• Longitudinal spin fluctuations in bcc and liquid Fe at high temperature and pressure calculated with a supercell approach
• Defects from phonons: Atomic transport by concerted motion in simple crystalline metals
• Longitudinal integration measure in classical spin space and its application to first-principle based simulations of the high temperature magnetism of Fe and Ni