# Lattice Instabilities and Phase Transformations in Fe from Atomistic Simulations

- 263 Downloads

## Abstract

The stability of the body- and face-centered cubic lattices corresponding to the α and γ phases of Fe, respectively, as well as the transformation of one phase to the other were investigated by atomistic simulations. Two interatomic potentials were used: the embedded atom method (EAM) potential of Meyer and Entel and the bond order potential (BOP) developed by Müller et al. The suitability of the potentials for investigating structural transformations in Fe was verified using nonequilibrium free energy calculations and molecular dynamics simulations. The results showed that the EAM potential is capable of describing the bcc → fcc and fcc → bcc transformations whereas no transformation was observed for the computationally more expensive BOP potential with the simulation set up used.

## Keywords

free energy calculations molecular dynamics phase transformations## Notes

### Acknowledgments

R. G. A. Veiga and J. E. Guimarães Silva gratefully acknowledge funding by FAPESP Grant 2014/10294-4. M. G. Di V. Cuppari was awarded a postdoctoral fellowship at Ecole Nationale Superieure de Chimie de Lille within the action CAPES/COFECUB 770/13. The authors would like to acknowledge computing time provided on the Blue Gene/Q supercomputer supported by the Research Computing Support Group (Rice University) and Laboratório de Computação Científica Avançada (Universidade de São Paulo).

## References

- 1.M.S. Daw, S.M. Foiles, and M.I. Baskes, The Embedded-Atom Method: A Review of Theory and Applications,
*Mater. Sci. Rep.*, 1993,**9**(7–8), p 251-310CrossRefGoogle Scholar - 2.D.G. Pettifor,
*Bonding and Structure of Molecules and Solids*, Oxford University Press, Oxford, 1995Google Scholar - 3.T.B. Massalski and D.E. Laughlin, The Surprising Role of Magnetism on the Phase Stability of Fe (Ferro),
*Calphad*, 2009,**33**(1), p 3-7CrossRefGoogle Scholar - 4.H. Hasegawa and D.G. Pettifor, Microscopic Theory of the Temperature-Pressure Phase Diagram of Iron,
*Phys. Rev. Lett.*, 1983,**50**(2), p 130-133ADSCrossRefGoogle Scholar - 5.R. Meyer and P. Entel, Martensite Austenite Transition Phonon Dispersion Curves Fe1-xNix Studied by Molecular Dynamics Simulations,
*Phys. Rev. B*, 1998,**57**(9), p 5140-5147ADSCrossRefGoogle Scholar - 6.M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun, and M. Asta, Development of New Interatomic Potentials Appropriate for Crystalline and Liquid Iron,
*Philos. Mag.*, 2003,**83**(35), p 3977-3994ADSCrossRefGoogle Scholar - 7.S.L. Dudarev and P.M. Derlet, A ‘Magnetic’ Interatomic Potential for Molecular Dynamics Simulations,
*J. Phys.: Condens. Matter*, 2005,**17**(44), p 7097ADSGoogle Scholar - 8.P.M. Derlet and S.L. Dudarev, Million-Atom Molecular Dynamics Simulations of Magnetic Iron,
*Prog. Mater Sci.*, 2007,**52**(2–3), p 299-318CrossRefGoogle Scholar - 9.S. Chiesa, P.M. Derlet, S.L. Dudarev and H. van Swygenhoven, Optimization of the Magnetic Potential for alpha-Fe,
*J. Phys. Condens. Matter*, 2011,**23**(20), art. 206001Google Scholar - 10.R. Drautz and D.G. Pettifor, Valence-Dependent Analytic Bond-Order Potential for Transition Metals,
*Phys. Rev. B*, 2006,**74**(17), art. 174117Google Scholar - 11.R. Drautz and D.G. Pettifor, Valence-Dependent Analytic Bond-Order Potential for Magnetic Transition Metals,
*Phys. Rev. B*, 2011,**84**(21), art. 214114Google Scholar - 12.M. Müller, P. Erhart and K. Albe, Analytic Bond-Order Potential for bcc and fcc Iron—Comparison with Established Embedded-Atom Method Potentials,
*J. Phys. Condens. Matter*, 2007,**19**(32), art. 326220Google Scholar - 13.S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics,
*J. Comput. Phys.*, 1995,**117**(1), p 1-19ADSCrossRefzbMATHGoogle Scholar - 14.S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods,
*J. Chem. Phys.*, 1984,**81**(1), p 511-519ADSCrossRefGoogle Scholar - 15.W. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions,
*Phys. Rev. A*, 1985,**31**(3), p 1695-1697ADSCrossRefGoogle Scholar - 16.M. Parrinello and A. Rahman, Crystal Structure and Pair Potentials: A Molecular-Dynamics Study,
*Phys. Rev. Lett.*, 1980,**45**(14), p 1196-1199ADSCrossRefGoogle Scholar - 17.M. Parrinello and A. Rahman, Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method,
*J. Appl. Phys.*, 1981,**52**(12), p 7182-7190ADSCrossRefGoogle Scholar - 18.C. Engin and H.M. Urbassek, Molecular-Dynamics Investigation of the fcc-bcc Phase Transformation in Fe,
*Comput. Mater. Sci.*, 2008,**41**, p 297-304CrossRefGoogle Scholar - 19.R. Freitas, M. Asta, and M. de Koning, Nonequilibrium Free-Energy Calculation of Solids using LAMMPS,
*Comput. Mater. Sci.*, 2016,**112**, p 333-341CrossRefGoogle Scholar - 20.R. Meyer and P. Entel, Lattice Dynamics of Martensitic Transformations Examined by Atomistic Simulations,
*J. Phys. IV*, 1997,**7**(C5), p C5-29-C5-34Google Scholar - 21.M. Shimono, H. Onodera, and T. Suzuki, FCC-BCC Phase Transition in Iron Under a Periodic Boundary Condition,
*Mater. Trans., JIM*, 1999,**40**(11), p 1306-1313CrossRefGoogle Scholar - 22.C. Bos, J. Sietsma, and B.J. Thijsse, Molecular Dynamics Simulation of Interface Dynamics during the fcc-bcc Transformation of a Martensitic Nature,
*Phys. Rev. B*, 2006,**73**(10), art. 104117Google Scholar - 23.H. Song and J.J. Hoyt, A Molecular Dynamics Simulation Study of the Velocities, Mobility and Activation Energy of an Austenite-Ferrite Interface in Pure Fe,
*Acta Mater.*, 2012,**60**, p 4328-4335CrossRefGoogle Scholar - 24.H. Song and J.J. Hoyt, An Atomistic Simulation Study of the Migration of an Austenite-Ferrite Interface in Pure Fe,
*Acta Mater.*, 2013,**61**, p 1189-1196CrossRefGoogle Scholar - 25.H. Song and J.J. Hoyt, A Molecular Dynamics Study of Heterogeneous Nucleation at Grain Boundaries during Solid-State Phase Transformations,
*Comput. Mater. Sci.*, 2016,**117**, p 151-163CrossRefGoogle Scholar - 26.H. Song and J.J. Hoyt, Barrier-Free Nucleation at Grain-Boundary Triple Junctions During Solid-State Phase Transformations,
*Phys. Rev. Lett.*, 2016,**117**(23), art. 238001Google Scholar - 27.M. Watanabe and W. Reinhardt, Direct Dynamical Calculation of Entropy and Free Energy by Adiabatic Switching,
*Phys. Rev. Lett.*, 1990,**65**(26), p 3301-3304ADSCrossRefGoogle Scholar - 28.M. de Koning and A. Antonelli, Einstein Crystal as a Reference System in Free Energy Estimation Using Adiabatic Switching,
*Phys. Rev. E*, 1996,**53**(1), p 465-474ADSCrossRefGoogle Scholar - 29.M. de Koning and A. Antonelli, Adiabatic Switching Applied to Realistic Crystalline Solids: Vacancy-Formation Free Energy in Copper,
*Phys. Rev. B*, 1997,**55**(2), p 735-744ADSCrossRefGoogle Scholar - 30.D. Frenkel and A.J.C. Ladd, New Monte Carlo Method to Compute the Free Energy of Arbitrary Solids. Application to the fcc and hcp Phases of Hard Spheres,
*J. Chem. Phys.*, 1984,**81**(7), p 3188-3193ADSCrossRefGoogle Scholar - 31.D. Frenkel and B. Smit,
*Understanding Molecular Simulation: from Algorithms to Applications*, Academic Press, Cambridge, 2002zbMATHGoogle Scholar - 32.J. Li, AtomEye: An Efficient Atomistic Configuration Viewer,
*Model. Simul. Mater. Sci. Eng.*, 2003,**11**(2), p 173-177ADSCrossRefGoogle Scholar