title: Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures.
abstract: We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti_{1-x}Al_{x}N alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti_{1-x}Al_{x}N alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti_{0.5}Al_{0.5}N alloys agree with the calculated phase diagram.
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.|Functional Materials, Saarland University, Campus D3 3, D-66123 Saarbrücken, Germany.
authors.forename: Nina
authors.initials: N
authors.lastname: Shulumba
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.|Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Olle
authors.initials: O
authors.lastname: Hellman
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.
authors.forename: Zamaan
authors.initials: Z
authors.lastname: Raza
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.|Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany.
authors.forename: Björn
authors.initials: B
authors.lastname: Alling
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.|Functional Materials, Saarland University, Campus D3 3, D-66123 Saarbrücken, Germany.
authors.forename: Jenifer
authors.initials: J
authors.lastname: Barrirero
authors.affiliation: Functional Materials, Saarland University, Campus D3 3, D-66123 Saarbrücken, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Mücklich
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.|Materials Modeling and Development Laboratory, NUST "MISIS," 119049 Moscow, Russia.
authors.forename: Igor A
authors.initials: IA
authors.lastname: Abrikosov
authors.affiliation: Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.
authors.forename: Magnus
authors.initials: M
authors.lastname: Odén