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Updated: Mar 11, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures
Nina Shulumba1,2, Olle Hellman1,3, Zamaan Raza1
1Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.
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.
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