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 Ti1-xAlxN 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 Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram. ; Funding Agencies|Swedish Foundation for Strategic Research Programs (Stiftelsen for Strategisk Forskning) [SRL10-0026, RMA08-0069]; FUNCASE; Swedish Research Council (Vetenskapsradet) [2012-4401, 621-2011-4426, 2015-04391, 637-2013-7296, 621-2011-4417, 330-2014-6336]; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University (Faculty Grant SFO-Mat-LiU) [2009 00971]; Swedish Governmental Agency for Innovation Systems (Vinnova) through the M-ERA.net project MC2; SECO Tools AB; Marie Sklodowska Curie Actions, Cofund [INCA 600398]; Erasmus Mundus Joint European Doctoral Programme DocMASE; Ministry of Education and Science of the Russian Federation [K2-2016-013]; Deutsche Forschungsgemeinschaft; Federal State Government of Saarland [INST 256/298-1 FUGG]