First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

First principles phase diagram calculations were performed for the wurtzite-structure quasibinary systems AlN–GaN, GaN–InN, and AlN–InN. Cluster expansion Hamiltonians that excluded, and included, excess vibrational contributions to the free energy, Fvib, were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, (XC,TC), for AlN–GaN, GaN–InN, and AlN–InN equal to (0.50, 305 K), (0.50, 1850 K), and (0.50, 2830 K) without Fvib, and (0.40, 247 K), (0.50, 1620 K), and (0.50, 2600 K) with Fvib, respectively. In spite of the very different ionic radii of Al, Ga, and In, the GaN–InN and AlN–GaN diagrams are predicted to be approximately symmetric

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First-principles calculation of phase equilibrium of V-Nb, V-Ta, and Nb-Ta alloys

In this paper, we report the calculated phase diagrams of V-Nb, V-Ta, and Nb-Ta alloys computed by combining the total energies of 40–50 configurations for each system (obtained using density functional theory) with the cluster expansion and Monte Carlo techniques. For V-Nb alloys, the phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature T_c=1250 K. Including the constituent strain to the cluster expansion Hamiltonian does not alter the consolute temperature significantly, although it appears to influence the solubility of V- and Nb-rich alloys. The phonon contribution to the free energy lowers T_c to 950 K (about 25%). Our calculations thus predicts an appreciable miscibility gap for V-Nb alloys. For bcc V-Ta alloy, this calculation predicts a miscibility gap with T_c=1100 K. For this alloy, both the constituent strain and phonon contributions are found to be significant. The constituent strain increases the miscibility gap while the phonon entropy counteracts the effect of the constituent strain. In V-Ta alloys, an ordering transition occurs at 1583 K from bcc solid solution phase to the V_(2)Ta Laves phase due to the dominant chemical interaction associated with the relatively large electronegativity difference. Since the current cluster expansion ignores the V_(2)Ta phase, the associated chemical interaction appears to manifest in making the solid solution phase remain stable down to 1100 K. For the size-matched Nb-Ta alloys, our calculation predicts complete miscibility in agreement with experiment

First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

We report first-principles phase diagram calculations for the binary systems HfC–TiC, TiC–ZrC, and HfC–ZrC. Formation energies for superstructures of various bulk compositions were computed with a plane-wave pseudopotential method. They in turn were used as a basis for fitting cluster expansion Hamiltonians, both with and without approximations for excess vibrational free energies. Significant miscibility gaps are predicted for the systems TiC–ZrC and HfC–TiC, with consolute temperatures in excess of 2000 K. The HfC–ZrC system is predicted to be completely miscibile down to 185 K. Reductions in consolute temperature due to excess vibrational free energy are estimated to be ~7%, ~20%, and ~0%, for HfC–TiC, TiC–ZrC, and HfC–ZrC, respectively. Predicted miscibility gaps are symmetric for HfC–ZrC, almost symmetric for HfC–TiC and asymmetric for TiC–ZrC

Method for locating low-energy solutions within DFT+U

The widely employed DFT+U formalism is known to give rise to many self-consistent yet energetically distinct solutions in correlated systems, which can be highly problematic for reliably predicting the thermodynamic and physical properties of such materials. Here we study this phenomenon in the bulk materials UO_2, CoO, and NiO, and in a CeO_2 surface. We show that the following factors affect which self-consistent solution a DFT+U calculation reaches: (i) the magnitude of U; (ii) initial correlated orbital occupations; (iii) lattice geometry; (iv) whether lattice symmetry is enforced on the charge density; and (v) even electronic mixing parameters. These various solutions may differ in total energy by hundreds of meV per atom, so identifying or approximating the ground state is critical in the DFT+U scheme. We propose an efficient U-ramping method for locating low-energy solutions, which we validate in a range of test cases. We also suggest that this method may be applicable to hybrid functional calculations

Structural and electronic properties of SrZrO3 and Sr(Ti,Zr) O3 alloys

Using hybrid density functional calculations, we study the electronic and structural properties of SrZrO3 and ordered Sr(Ti,Zr)O3 alloys. Calculations were performed for the ground-state orthorhombic (Pnma) and high-temperature cubic (Pm3m) phases of SrZrO3. The variation of the lattice parameters and band gaps with Ti addition was studied using ordered SrTixZr1-xO3 structures with x=0, 0.25, 0.5, 0.75, and 1. As Ti is added to SrZrO3, the lattice parameter is reduced and closely follows Vegard's law. On the other hand, the band gap shows a large bowing and is highly sensitive to the Ti distribution. For x=0.5, we find that arranging the Ti and Zr atoms into a 1×1SrZrO3/SrTiO3 superlattice along the [001] direction leads to interesting properties, including a highly dispersive single band at the conduction-band minimum (CBM), which is absent in both parent compounds, and a band gap close to that of pure SrTiO3. These features are explained by the splitting of the lowest three conduction-band states due to the reduced symmetry of the superlattice, lowering the band originating from the in-plane Ti 3dxy orbitals. The lifting of the t2g orbital degeneracy around the CBM suppresses scattering due to electron-phonon interactions. Our results demonstrate how short-period SrZrO3/SrTiO3 superlattices could be exploited to engineer the band structure and improve carrier mobility compared to bulk SrTiO3

First-principles theory of the luminescence lineshape for the triplet transition in diamond NV centre

In this work we present theoretical calculations and analysis of the vibronic structure of the spin-triplet optical transition in diamond nitrogen-vacancy centres. The electronic structure of the defect is described using accurate first-principles methods based on hybrid functionals. We devise a computational methodology to determine the coupling between electrons and phonons during an optical transition in the dilute limit. As a result, our approach yields a smooth spectral function of electron-phonon coupling and includes both quasi-localized and bulk phonons on equal footings. The luminescence lineshape is determined via the generating function approach. We obtain a highly accurate description of the luminescence band, including all key parameters such as the Huang-Rhys factor, the Debye-Waller factor, and the frequency of the dominant phonon mode. More importantly, our work provides insight into the vibrational structure of nitrogen vacancy centres, in particular the role of local modes and vibrational resonances. In particular, we find that the pronounced mode at 65 meV is a vibrational resonance, and we quantify localization properties of this mode. These excellent results for the benchmark diamond nitrogen-vacancy centre provide confidence that the procedure can be applied to other defects, including alternative systems that are being considered for applications in quantum information processing