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Although defect clusters are detrimental to electronic and mechanical properties of semiconductor materials, annihilation of such clusters is limited by their lack of thermal mobility due to high migration barriers. Here, we find that small clusters in bulk SiC (a covalent material of importance for both electronic and nuclear applications) can become mobile at room temperature under the influence of electron radiation. So far, direct observation of radiation-induced diffusion of defect clusters in bulk materials has not been demonstrated yet. This finding was made possible by low angle annular dark field (LAADF) scanning transmission electron microscopy (STEM) combined with non-rigid registration technique to remove sample instability, which enables atomic resolution imaging of small migrating defect clusters. We show that the underlying mechanism of this athermal diffusion is ballistic collision between incoming electrons and cluster atoms. Our findings suggest that defect clusters may be mobile under certain irradiation conditions, changing current understanding of cluster annealing process in irradiated covalent materials.

In the Comment by S\"oderlind et al. [Phys. Rev. B 90, 157101 (2014)], the authors argue that (1) density functional theory (DFT), especially with all-electron methods, already models U metal and U-Zr alloy accurately; and (2) $\mathrm{DFT}+U$ results calculated at ${U}_{\mathrm{eff}}=1.24$ for volume, enthalpy, and magnetic moments that they select from our study [Phys. Rev. B 88, 235128 (2013)] suggest adding the Hubbard $U$ potential in $\mathrm{DFT}+U$ reduces accuracy compared to DFT. With respect to argument (1) by S\"oderlind et al., we argue that previously neglected and very recent experimental data suggest that DFT in S\"oderlind's full-potential linear muffin-tin orbital calculations [Phys. Rev. B 66, 085113 (2002)] still models the bulk modulus and elastic constants of \ensuremath{\alpha}U with errors considerably larger than other related elements, e.g., most transition metals. In addition, we demonstrate that the assertion by S\"oderlind et al. that our DFT results are not satisfactory because deficiency exists in our projector augmented wave calculation is unfounded. With respect to argument (2) by S\"oderlind et al., we argue that they have inappropriately focused on just one phase [the bcc phase \ensuremath{\gamma}(U,Zr)], neglecting the other phases which represent the majority of our evidence; made overgeneralizations based on results at only one ${U}_{\mathrm{eff}}$ value of 1.24 eV; and supported their argument with inaccurate assertions that $\mathrm{DFT}+U$ predicts for \ensuremath{\gamma}(U,Zr) an unprecedentedly large positive volume of mixing and an enthalpy of mixing that is inconsistent with the experimental miscibility gap. We therefore hold to our original conclusion that the accuracy of DFT for modeling U and U-Zr has room for improvement and $\mathrm{DFT}+U$ is a good candidate.

We investigate the molecular beam epitaxy (MBE) growth of GaAs1-xBix film using density functional theory with spin-orbit coupling to understand the growth of this film, especially the mechanisms of Bi incorporation. We study the stable adsorption structures and kinetics of the incident molecules (As₂ molecule, Ga atom, Bi atom, and Bi₂ molecule) on the (2 x 1)-Gasub||Bi surface and a proposed q(1 x 1)-Gasub||AsAs surface has a quasi-(1 x 1) As layer above the Ga-terminated GaAs substrate and a randomly oriented As dimer layer on top. We obtain the desorption and diffusion barriers of the adsorbed molecules and also the reaction barriers of three key processes related to Bi evolution, namely, Bi incorporation, As/Bi exchange, and Bi clustering. The results help explain the experimentally observed dependence of Bi incorporation on the As/Ga ratio and growth temperature. Furthermore, we find that As₂ exchange with Bi of the (2 x 1)-Gasub||Bi surface is a key step controlling the kinetics of the Bi incorporation. Finally, we explore two possible methods to enhance the Bi incorporation, namely, replacing the MBE growth mode from codeposition of all fluxes with a sequential deposition of fluxes and applying asymmetric in-plane strain to the substrate.

The characterization of native point defects in ZnO is still a question of debate. For example, experimental evidence for ZnO with an excess of Zn is inconclusive as to whether the dominant defects are metal interstitials or oxygen vacancies. This information is essential to understand the behavior of the material and to tailor its numerous technological applications. We use the first-principles pseudopotential method to determine the electronic structure, atomic geometry, and formation energy of native point defects in ZnO. Interstitials, vacancies, and antisites in their relevant charge states are considered and the effects of dopants are also discussed. The results show that both the Zn and O vacancies are the relevant defects in ZnO. We also propose a possible transition mechanism and defect center responsible for the experimentally observed green luminescence.

Structural, thermodynamic, and atomic-transport properties of liquid Ni-Al alloys have been studied by Monte Carlo and molecular-dynamics simulations based upon three different embedded-atom method (EAM) interatomic potentials, namely those due to Foiles and Daw (FD) [J. Mater. Res. 2, 5 (1987)], Voter and Chen (VC) [in Characterization of Defects in Materials, edited by R. W. Siegel et al. MRS Symposia Proceedings. No. 82 (Materials Research Society, Pittsburgh, 1987), p.175] and Ludwig and Gumbsch (LG) [Model. Simul. Mater. Sci. Eng. 3, 533 (1995)]. We present detailed comparisons between calculated results and experimental data for structure factors, atomic volumes, enthalpies of mixing, activities, and viscosities. Calculated partial structure factors are found to be in semiquantitative agreement with published neutron scattering measurements for ${\mathrm{Ni}}_{20}{\mathrm{Al}}_{80}$ alloys, indicating that short-range order in the liquid phase is qualitatively well described. Calculated thermodynamic properties of mixing are found to agree very well with experimental data for Ni compositions greater than 75 atomic %, while for alloys richer in Al the magnitudes of the enthalpies and entropies of mixing are significantly underestimated. The VC and LG potentials give atomic densities and viscosities in good agreement with experiment for Ni-rich compositions, while FD potentials consistently underestimate both properties at all concentrations. The results of this study demonstrate that VC and LG potentials provide a realistic description of the thermodynamic and atomic transport properties for ${\mathrm{Ni}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ liquid alloys with $xg~0.75,$ and point to the limitations of EAM potentials for alloys richer in Al.

We calculate the vibrational density of states (DOS) and corresponding thermodynamic properties of L1{sub 2} ordered and disordered Ni{sub 3}Al in the quasiharmonic approximation using the embedded-atom method. Vibrational and thermodynamic properties, including vibrational entropy differences between ordered and disordered states, are found to be in good agreement with experiment. The DOS of the configurationally disordered alloy resembles a broadened version of the DOS of the L1{sub 2} phase, not a one-atom per cell fcc DOS, and is shifted downward in frequency because the disordered state has a larger volume than the ordered phase. Calculations of the projected DOS indicate that high-frequency modes located predominantly on aluminum atoms broaden the most on disordering. Further, we find that the vibrational entropy difference between the two phases is largely due to the difference in volumes of the phases and their different thermal expansions. {copyright} {ital 1997} {ital The American Physical Society}

Ab initio calculations have been performed on all solid phases of U metal and U-Zr alloy, the basis of a promising metallic fuel for fast nuclear reactors. Based on generalized gradient approximation, both density functional theory (DFT) in its standard form and the so-called DFT plus Hubbard $U$ (DFT+$U$) modification are evaluated. The evolution of calculated energetics, volume, magnetic moments, electronic structure, and $f$-orbital occupation as functions of the effective Hubbard $U$ parameter, ${U}_{\mathrm{eff}}$, is carefully examined at ${U}_{\mathrm{eff}}$ from 0 to 4 eV. DFT is found to overestimate energetics, underestimate volume, downward shift some $f$ bands near Fermi level and overestimate $f$-orbital occupation against existing experimental and/or computational data. The error is \ensuremath{\sim}0.07 eV/atom in terms of enthalpy, which affects phase stability modeling for \ensuremath{\delta}(U,Zr) and \ensuremath{\gamma}(U,Zr). DFT+$U$ at ${U}_{\mathrm{eff}}=1\ensuremath{-}1.5$ eV offers clear improvement on these calculated properties (\ensuremath{\sim}0.05 eV/atom in terms of enthalpy) and in general still neither promotes ordered magnetic moments nor opens unphysical band gaps, which occur at higher ${U}_{\mathrm{eff}}$ values. The empirical ${U}_{\mathrm{eff}}$ values of 1--1.5 eV are close to but smaller than the theoretical estimations of 1.9--2.3 eV that we obtain from the linear response approach. ${U}_{\mathrm{eff}}$ is found to vary only slightly (\ensuremath{\le}0.24 eV) between different phases and at different compositions of U and U-Zr; thus, a single ${U}_{\mathrm{eff}}=1.24$ eV, which is the statistical optimal from energetic fitting, is suggested for both U and U-Zr. Besides correlation, the relativistic effect of spin-orbit coupling (SOC) is also systematically explored. SOC is found to lower energy, increase volume, and split the 5$f$ shell above Fermi level and reduce $f$-orbital occupation. The effect predominates in the unoccupied states and is very small on all these calculated ground state properties (\ensuremath{\sim}0.02 eV/atom in terms of enthalpy).

The high-pressure behavior of magnetite has been widely debated in the literature. Experimental measurements have found conflicting high-pressure transitions: a charge reordering in magnetite from inverse-spinel to normal-spinel [Pasternak et al., J. Phys. Chem. Solids 65, 1531 (2004); Rozenberg et al., Phys. Rev. B 75, 020102 (2007)], iron high-spin to intermediate-spin transition in magnetite [Ding et al., Phys. Rev. Lett. 100, 045508 (2008)], electron delocalization in magnetite [Baudelet et al., Phys. Rev. B 82, 140412 (2010); Glazyrin et al., Am. Mineral. 97, 128 (2012)], and a structural phase transition from magnetite to $h$-Fe${}_{3}$O${}_{4}$ [Dubrovinsky et al., J. Phys.: Condens. Matter 15, 7697 (2003); Fei et al., Am. Mineral. 84, 203 (1999); Haavik et al., Am. Mineral. 85, 514 (2000)]. We present ab initio calculations of iron's spin state in magnetite and $h$-Fe${}_{3}$O${}_{4}$, which help resolve the high-pressure debate. The results of the calculations find that iron remains high spin in both magnetite and $h$-Fe${}_{3}$O${}_{4}$; intermediate-spin iron is not stable. In addition, magnetite remains inverse-spinel but undergoes a phase transition to $h$-Fe${}_{3}$O${}_{4}$ near 10 GPa. Magnetite has a complex magnetic ordering, multiple valence states (Fe${}^{2+}$ and Fe${}^{3+}$), charge ordering, and different local Fe site environments, all of which were accounted for in the calculations. The lack of intermediate-spin iron in magnetite helps resolve the spin state of iron in perovskite, the major mineral in the lower mantle. In both magnetite and perovskite, x-ray emission spectroscopy (XES) measurements in the literature show a drop in satellite peak intensity by approximately half, which is interpreted as intermediate-spin iron. In both minerals, calculations give no indication of intermediate-spin iron and predict high-spin iron to be stable for defect-free crystals. The results question the interpretation of a nonzero drop in XES satellite peak intensities as intermediate-spin iron.

Using a rate theory model for a generic one-component material, we investigated interactions between grain size and recombination kinetics of radiation-induced defects. Specifically, by varying parametrically nondimensional kinetic barriers for defect diffusion and recombination, we determined the effect of these parameters on the shape of the dose to amorphization versus temperature curves. We found that whether grain refinement to the nanometer regime improves or deteriorates radiation resistance of a material depends on the barriers to defect migration and recombination, as well as on the temperature for the intended use of the material. We show that the effects of recombination barriers and of grain refinement can be coupled to each other to produce a phenomenon of interstitial starvation. In interstitial starvation, a significant number of interstitials annihilate at the grain boundary, leaving behind unrecombined vacancies, which in turn amorphize the material. The same rate theory model with material-specific parameters was used to predict the grain-size dependence of the critical amorphization temperature in SiC. Parameters for the SiC model were taken from ab initio calculations. We find that the fine-grained SiC has a lower radiation resistance when compared to the polycrystalline SiC due to the presence of high-energy barrier for recombination of carbon Frenkel pairs and due to the interstitial starvation phenomenon. � 2012 American Physical Society.

Using a combination of random configuration sampling, molecular dynamics simulated annealing with empirical potential, and ensuing structural refinement by first-principles density functional calculations, we perform an extensive ground-state search for the most stable configurations of small carbon interstitial clusters in SiC. Our search reveals a ``magic'' cluster number of three atoms, where the formation energy per interstitial shows a distinct minimum. A carbon tri-interstitial cluster with trigonal ${C}_{3v}$ symmetry is discovered, in which all carbon atoms are fourfold coordinated. In addition to its special thermodynamic stability, its localized vibrational modes are also in a very good agreement with the experimental photoluminescence spectra of the D${}_{\mathrm{II}}$ center in both 3C- and 4H-SiC. The D${}_{\mathrm{II}}$ center is one of the most persistent defects in SiC, and we propose that the discovered carbon tri-interstitial is responsible for this center.

The thermodynamics of Bi incorporation into bulk and epitaxial GaAs was studied using density functional theory (DFT) and anharmonic elasticity calculations. The equilibrium concentration of Bi was determined as a function of epitaxial strain state, temperature, and growth conditions. For a bulk, unstrained system, Bi in GaAs under typical growth conditions (Ga-rich and Bi-metal-rich at 400 \ifmmode^\circ\else\textdegree\fi{}C) has a dilute heat of solution of 572 meV/Bi and a solubility of $x=5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ in GaAs${}_{1\ensuremath{-}x}$Bi${}_{x}$. However, epitaxial strain can greatly enhance this solubility, and under the same conditions an epitaxial film of GaAs${}_{1\ensuremath{-}x}$Bi${}_{x}$ with 5$%$ in-plane tensile strain is predicted to have a Bi solubility of $x=7.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, representing approximately a hundred times increase in solubility over the unstrained bulk case. Despite these potentially large increases in solubility, the equilibrium solubility is still very low compared to values that have been achieved experimentally through nonequilibrium growth. These values of solubility are also sensitive to the choice of the Bi reference state. If the primary route for phase separation is the formation of GaBi within the same structure, rather than Bi metal, GaBi would serve as the source/sink for Bi. If GaBi is used as the Bi reference state, the epitaxial formation energy on a bulk unstrained GaAs substrate is reduced dramatically to 144 meV/Bi, yielding a Bi solubility of $x=0.083$ in GaAs${}_{1\ensuremath{-}x}$Bi${}_{x}$. These calculations suggest that Bi solubility could be greatly enhanced if Bi metal formation is inhibited and the system is forced to remain constrained to the GaAs${}_{1\ensuremath{-}x}$Bi${}_{x}$ structure. Although GaBi is not a naturally stable compound, it could potentially be stabilized through a combination of kinetic limitations and alloying.

Recent experimental observations indicate that bulk Sc${}_{2}$O${}_{3}$ (\ensuremath{\sim}200 nm thick), an insulator at room temperature and pressure, must act as a good electronic conductor during thermionic cathode operation, leading to the observed high emitted current densities and overall superior emission properties over conventional thermionic emitters which do not contain Sc${}_{2}$O${}_{3}$. Here, we employ ab initio methods using both semilocal and hybrid functionals to calculate the intrinsic defect energetics of Sc and O vacancies and interstitials and their effects on the electronic properties of Sc${}_{2}$O${}_{3}$ in an effort to explain the good conduction of Sc${}_{2}$O${}_{3}$ observed in experiment. The defect energetics were used in an equilibrium defect model to calculate the concentrations of defects and their compensating electron and hole concentrations at equilibrium. Overall, our results indicate that the conductivity of Sc${}_{2}$O${}_{3}$ solely due to the presence of intrinsic defects in the cathode operating environment is unlikely to be high enough to maintain the magnitude of emitted current densities obtained from experiment, and that the presence of impurities is necessary to raise the conductivity of Sc${}_{2}$O${}_{3}$ to a high enough value to explain the current densities observed in experiment. The necessary minimum impurity concentration to impart sufficient electronic conduction is very small (approximately 7.5 \ifmmode\times\else\texttimes\fi{} 10${}^{\ensuremath{-}3}$ ppm) and is probably present in all experiments.

Using ab initio calculations, we have identified stable group-V dopant-vacancy complexes complexes in ZnO consisting of interstitial dopants surrounded by three V${}_{\mathrm{Zn}}$ (${D}_{I}$-3V${}_{\mathrm{Zn}}$ with $D=\mathrm{P}$, As, or Sb). In contradiction with previous reports, our calculations show that the acceptor level of group-V dopant--vacancy complexes is too deep to be the shallow acceptor level identified experimentally as contributing to $p$-type conductivity in ZnO. The interstitial-vacancy complexes we have identified can be generalized to other compositions, dopants, and structures.

Ab initio methods are used to predict the diffusion coefficient of As dopants in ZnO as a function of Fermi level. Contributions to As diffusion from interstitial, simple substitutional, and cluster diffusion are considered. Formation and migration energies for Zn vacancies (V${}_{\mathrm{Zn}}$), As substituting on Zn lattice sites (As${}_{\mathrm{Zn}}$), complexes of As with up to two Zn vacancies (As${}_{\mathrm{Zn}}$-1V${}_{\mathrm{Zn}}$ and As${}_{\mathrm{Zn}}$-2V${}_{\mathrm{Zn}}$), and interstitial Zn and As (Zn${}_{\mathrm{I},\mathrm{oct}}$ and As${}_{\mathrm{I},\mathrm{oct}}$) are calculated using GGA $+$ $U$ and hybrid Hartree-Fock density-functional theory calculations. As${}_{\mathrm{Zn}}$ is the dominant As-containing donor and As${}_{\mathrm{Zn}}$-2V${}_{\mathrm{Zn}}$ is the dominant As-containing acceptor. At low Fermi levels, As is mostly immobile, while at high Fermi levels, As${}_{\mathrm{Zn}}$-2V${}_{\mathrm{Zn}}$ is mobile with a migration energy of 1.6 eV.

Ag defects in $\ensuremath{\Sigma}3$ grain boundary of SiC were analyzed to test the hypothesis that Ag release from tristructural isotropic (TRISO) fuel particles can occur through grain boundary diffusion. Although $\ensuremath{\Sigma}3$ grain boundaries cannot provide a connected path through the crystal, they are studied here to provide guidance for overall trends in grain boundary vs bulk Ag transport. Formation energies of Ag defects are found to be 2--4 eV lower in the grain boundaries than in the bulk, indicating a strong tendency for Ag to segregate to the grain boundaries. Diffusion of Ag along $\ensuremath{\Sigma}3$ was found to be dramatically faster than through the bulk. At ${1600}^{\ensuremath{\circ}}$C, which is a temperature relevant for TRISO accident conditions, Ag diffusion coefficients are predicted to be $3.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ m${}^{2}$/s and $3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}29}$ m${}^{2}$/s in the $\ensuremath{\Sigma}3$ grain boundary and bulk, respectively. While at this temperature $\ensuremath{\Sigma}3$ diffusion is still two orders of magnitude slower than diffusion estimated from integral release measurements, the values are close enough to suggest that grain boundary diffusion is a plausible mechanism for release of Ag from intact SiC coatings. The remaining discrepancies in the diffusion coefficients could be possibly bridged by considering high-energy grain boundaries, which are expected to have diffusivity faster than $\ensuremath{\Sigma}3$ and which provide a connected percolating path through polycrystalline SiC.

Knowledge of Fe composition in lower-mantle minerals (primarily perovskite and ferropericlase) is essential to a complete understanding of the Earth’s interior. Fe cation diffusion potentially controls many aspects of the distribution of Fe in the Earth’s lower mantle, including mixing of chemical heterogeneities, element partitioning, and the extent of core-mantle communications. Fe in ferropericlase has been shown to undergo a spin transition starting at about 40 GPa and exists in a mixture of high-spin and low-spin states over a wide range of pressures. Present experimental data on Fe transport in ferropericlase is limited to pressures below 35 GPa and provides little information on the pressure dependence of the activation volume and none on the impact of the spin transition on diffusion. Therefore, known experimental data on Fe diffusion cannot be reliably extrapolated to predict diffusion throughout the lower mantle. Here, first-principles and statistical modeling are combined to predict diffusion of Fe in ferropericlase over the entire lower mantle, including the effects of the Fe spin transition. A thorough statistical thermodynamic treatment is given to fully incorporate the coexistence of high- and low-spin Fe in the model of overall Fe diffusion in the lower mantle. Pure low-spin Fe diffuses approximately 10 4 times slower than high-spin Fe in ferropericlase but Fe diffusion of the mixed-spin state is only about 10 times slower than that of high-spin Fe. The predicted Fe diffusivities demonstrate that ferropericlase is unlikely to be rate limiting in transporting Fe in deep earth since much slower Fe diffusion in perovskite is predicted.

$\text{La}B{\text{O}}_{3}$ ($B=\text{Mn}$, Fe, Co, and Ni) perovskites form a family of materials of significant interest for cathodes of solid oxide fuel cells (SOFCs). In this paper ab initio methods are used to study both bulk and surface properties of relevance for SOFCs, including vacancy formation and oxygen binding energies. A thermodynamic approach and the density functional theory plus $U$ method are combined to obtain energies relevant for SOFC conditions ($T\ensuremath{\approx}800\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$, $P{\text{O}}_{2}\ensuremath{\approx}0.2\text{ }\text{atm}$). The impact of varying ${U}_{\text{eff}}$ $({U}_{\text{eff}}=U\ensuremath{-}J)$ on energy and electronic structure is explored in detail and it is shown that optimal ${U}_{\text{eff}}$ values yield significantly better agreement with experimental energies than ${U}_{\text{eff}}=0$ (which corresponds to the standard generalized gradient approximation). $\text{La}B{\text{O}}_{3}$ oxygen vacancy formation energies are predicted to be in the order $\text{Fe}g\text{Mn}g\text{Co}g\text{Ni}$ (where the largest implies most difficult to form a vacancy). It is shown that (001) $B{\text{O}}_{2}$ terminated surfaces have 1--2 eV lower vacancy formation energies and therefore far higher vacancy concentrations than the bulk. The stable surface species at low temperature are predicted to be the superoxide $\text{O}_{2}{}^{\ensuremath{-}}$ for $B=\text{Mn}$, Fe, Co and a peroxide $\text{O}_{2}{}^{2\ensuremath{-}}$ with a surface oxygen for $B=\text{Ni}$. Entropy effects are predicted to stabilize the monomer oxygen surface state for all $B$ cations at higher temperatures. Overall oxygen coverage of the (001) $B{\text{O}}_{2}$ surface is predicted to be quite low at SOFC operating conditions. These results will aid in understanding the oxygen reduction reaction on perovskite SOFC cathodes.

First principles computations have been used to study Li mobility in the orthorhombic ${\text{Li}}_{2}{\text{NiO}}_{2}$ structure with the $Immm$ space group $({\text{I-Li}}_{2}{\text{NiO}}_{2})$. Understanding Li mobility in ${\text{I-Li}}_{2}{\text{NiO}}_{2}$ structure other than the conventional layered structure helps extend our understanding of Li transport in different oxide structures. Our results indicate that ${\text{I-Li}}_{2}{\text{NiO}}_{2}$ is a reasonably good lithium ionic conductor with two-dimensional diffusion when the structure is maintained upon lithiation or delithaion. It is predicted that in the orthorhombic cell the activation barriers along the $b$ axis and diagonal direction between $a$ and $b$ axes are fairly low, ensuring the facile lithium diffusion along those directions, while migration along the $a$ axis is unlikely given the very high activation barrier $(\ensuremath{\sim}2\text{ }\text{eV})$.

We investigate Li diffusion in the favorable intercalation compound ${\text{Li}}_{x}{\text{TiS}}_{2}$ as a function of Li concentration, $x$, from first principles. We find that Li ions hop between neighboring octahedral interstitial sites of the ${\text{TiS}}_{2}$ host by passing through an adjacent tetrahedral site. The migration barriers for these hops are significantly reduced when the end points belong to a divacancy. We use a cluster expansion within kinetic Monte Carlo simulations to describe the configuration dependence of the migration barriers and predict a diffusion coefficient that varies by several orders of magnitude with Li concentration, exhibiting a maximum close to $x=0.5$. The kinetic Monte Carlo simulations predict that diffusion is mediated predominantly by divacancies. We also find that the migration barriers depend strongly on the $c$-lattice parameter, which decreases as Li ions are removed from ${\text{Li}}_{x}{\text{TiS}}_{2}$.

We report on a significant failure of the local density approximation (LDA) and the generalized gradient approximation (GGA) to reproduce the phase stability and thermodynamics of mixed-valence ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ compounds. Experimentally, ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ compositions $(0l~xl~1)$ are known to be unstable and phase separate into ${\mathrm{LiFePO}}_{4}$ and ${\mathrm{FePO}}_{4}.$ However, first-principles calculations with LDA/GGA yield energetically favorable intermediate compounds and hence no phase separation. This qualitative failure of LDA/GGA seems to have its origin in the LDA/GGA self-interaction which delocalizes charge over the mixed-valence Fe ions, and is corrected by explicitly considering correlation effects in this material. This is demonstrated with LDA+U calculations which correctly predict phase separation in ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ for $U\ensuremath{-}J\ensuremath{\gtrsim}3.5\mathrm{eV}.$ The origin of the destabilization of intermediate compounds is identified as electron localization and charge ordering at different iron sites. Introduction of correlation also yields more accurate electrochemical reaction energies between ${\mathrm{FePO}}_{4}/{\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ and $\mathrm{Li}/{\mathrm{Li}}^{+}$ electrodes.

First-principles electronic structure methods have been used to calculate the ground state, transition temperature, and thermodynamic properties of magnetic excitations in spinel MnO2. The magnetic interactions are mapped onto a Heisenberg model whose exchange interactions are fitted to results of first-principles calculations of different spin configurations. The thermodynamics are calculated using Monte Carlo methods. The Heisenberg model gives an extremely accurate representation of the true first-principles magnetic energies. We find a critical temperature and Weiss constant significantly larger than experimental results and believe the error to come from the local spin density approximation. We predict a new magnetic ground state different from that proposed previously, but consistent with experimental data.

A detailed analysis of the formation energies for alkali, earth-alkali, and transition-metal hydrides is presented. The hydriding energies are computed for various crystal structures using density functional theory. The early transition metals are found to have a strong tendency for hydride formation which decreases as one goes to the right in the transition-metal series. A detailed analysis of the changes in band structure and electron density upon hydride formation has allowed us to understand the hydriding energy on the basis of three contributions. The first is the energy to convert the crystal structure of the metal to the structure formed by the metal ions in the hydride (fcc in most cases). In particular, for metals with a strong bcc preference such as V and Cr, this significantly lowers the driving force for hydride formation. A second contribution, which for some materials is dominant, is the loss of cohesive energy when the metal structure is expanded to form the hydride. This expansion lowers the cohesive energy of the metal and is a significant impediment to form stable hydrides for the middle to late transition metals, as they have high cohesive energies. The final contribution to the hydride formation energy is the chemical bonding between the hydrogen and metal in which it is inserted. This is the only contribution that is negative and hence favorable to hydride formation.

Fundamental aspects of the cooperative Jahn-Teller effect are investigated using density functional theory in the generalized gradient approximation. ${\mathrm{LiNiO}}_{2},$ ${\mathrm{LiMnO}}_{2},$ and ${\mathrm{LiCuO}}_{2}$ are chosen as candidate materials as they possess small, intermediate, and large cooperative Jahn-Teller distortions, respectively. The cooperative distortion is decomposed into the symmetrized-strain modes and $k=0$ optical phonons, revealing that only the ${E}_{g}$ and ${A}_{1g}$ strain modes and ${E}_{g}$ and ${A}_{1g}$ $k=0$ optical-phonon modes participate in the cooperative distortion. The first-principles results are then used to find values for the cooperative Jahn-Teller stabilization energy and the electron-strain and electron-phonon coupling. It is found that the dominant source of anisotropy arises from the third-order elastic contributions, rather than second-order vibronic contributions. Additionally, the importance of higher-order elastic coupling between the ${E}_{g}$ and ${A}_{1g}$ modes is identified, which effectively causes expansion of ${A}_{1g}$-type modes and allows for a larger ${E}_{g}$ distortion. Finally, the strain anisotropy induced by the antiferromagnetically ordered states is shown to cause a significant difference in the cooperative Jahn-Teller stabilization energy for the different orientations of the cooperative distortion.