Anharmonicity changes the solid solubility of an alloy at high temperatures

We have developed 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 anharmonic contribution 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 K 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.Comment: 4 pages, 5 figures, supplementary materia

Elucidating the NuclearQuantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule: A complex paradigmatic system where the making and breaking of H-bonds in a highly anharmonic potential energy surface requires a quantum mechanical treatment not only of the electrons, but also of the nuclei. We combine density-functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates, but between 100 K and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of $2.19 \times 10^{11} \mathrm{s}^{-1}$ at 150 K and $0.63 \times 10^{11} \mathrm{s}^{-1}$ at 100 K, in good agreement with experiment. We also reproduce the puzzling N-H stretching band of porphycene with very good accuracy from thermostatted ring-polymer molecular dynamics simulations. The position and lineshape of this peak, centered at around 2600 cm$^{-1}$ and spanning 750 cm$^{-1}$, stems from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to $cis$-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems