Automating first-principles phase diagram calculations

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented

First-principles computation of the vibrational entropy of ordered and disordered Pd3V

Experimental as well as theoretical work indicates that the relative stability of the ordered and the disordered states of a compound may be significantly affected by their difference in vibrational entropy. The origin of this difference is usually attributed to the fact that disordering reduces the number of stiff bonds between different atomic species in favor of soft bonds between identical atomic species. The results of previous theoretical investigations, however, suggest that this simple mechanism is significantly modified as a result of local atomic relaxations. To gain further insight regarding the importance of relaxations, we employ first-principles calculations to investigate the magnitude of the vibrational entropy difference between the ordered and the disordered state of Pd3V. Our investigation reveals that bond stiffness changes due to relaxation entirely mask the large configurational dependence of vibrational entropy provided by bond stiffness differences. Our analysis also suggests a simple technique to estimate vibrational entropy based on the relationship between bond length and bond stiffness

Role of defects and impurities in doping of GaN

We have calculated formation energies and position of the defect levels for all native defects and for a variety of donor and acceptor impurities employing first-principles total-energy calculations. An analysis of the numerical results gives direct insight into defect concentrations and impurity solubility with respect to growth parameters (temperature, chemical potentials) and into the mechanisms limiting the doping levels in GaN. We show how compensation and passivation by native defects or impurities, solubility issues, and incorporation of dopants on other sites influence the acceptor doping levels.Comment: 8 pages, 3 figures, to appear in "The Physics of Semiconductors

Conditions for T2T^2 resistivity from electron-electron scattering

Many complex oxides (including titanates, nickelates and cuprates) show a regime in which resistivity follows a power law in temperature ($\rho\propto T^2$). By analogy to a similar phenomenon observed in some metals at low temperature, this has often been attributed to electron-electron (Baber) scattering. We show that Baber scattering results in a $T^2$ power law only under several crucial assumptions which may not hold for complex oxides. We illustrate this with sodium metal ($\rho_\text{el-el}\propto T^2$) and strontium titanate ($\rho_\text{el-el}\not\propto T^2$). We conclude that an observation of $\rho\propto T^2$ is not sufficient evidence for electron-electron scattering.Comment: 5 pages, 4 figure

Theory of Doping and Defects in III-V Nitrides

Doping problems in GaN and in AlGaN alloys are addressed on the basis of state-of-the-art first-principles calculations. For n-type doping we find that nitrogen vacancies are too high in energy to be incorporated during growth, but silicon and oxygen readily form donors. The properties of oxygen, including DX-center formation, support it as the main cause of unintentional n-type conductivity. For p-type doping we find that the solubility of Mg is the main factor limiting the hole concentration in GaN. We discuss the beneficial effects of hydrogen during acceptor doping. Compensation of acceptors by nitrogen vacancies may occur, becoming increasingly severe as x increases in Al_x Ga_(1-x)N alloys.Comment: 7 pages, 2 figures. Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm