This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

This review discusses how low-energy, valence excitations created by swift electrons can render information on the optical response of structured materials with unmatched spatial resolution. Electron microscopes are capable of focusing electron beams on sub-nanometer spots and probing the target response either by analyzing electron energy losses or by detecting emitted radiation. Theoretical frameworks suited to calculate the probability of energy loss and light emission (cathodoluminescence) are revisited and compared with experimental results. More precisely, a quantum-mechanical description of the interaction between the electrons and the sample is discussed, followed by a powerful classical dielectric approach that can be in practice applied to more complex systems. We assess the conditions under which classical and quantum-mechanical formulations are equivalent. The excitation of collective modes such as plasmons is studied in bulk materials, planar surfaces, and nanoparticles. Light emission induced by the electrons is shown to constitute an excellent probe of plasmons, combining sub-nanometer resolution in the position of the electron beam with nanometer resolution in the emitted wavelength. Both electron energy-loss and cathodoluminescence spectroscopies performed in a scanning mode of operation yield snap shots of plasmon modes in nanostructures with fine spatial detail as compared to other existing imaging techniques, thus providing an ideal tool for nanophotonics studies.

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Optical excitations in electron microscopy

Valence electron-energy loss spectroscopy (VEELS) in a dedicated scanning transmission electron microscope, vacuum ultraviolet spectroscopy and spectroscopic ellipsometry, and ab initio band structure calculations in the local density approximation have been used to determine the optical properties and the electronic structure of SrTiO3 Assignments of the interband transitions in the electronic structure of bulk SrTiO3 have been determined quantitatively by comparison of VEELS spectra with vacuum ultraviolet spectra and with the ab initio calculated densities of states The experimentally determined indirect band gap energy is 325 eV, while the direct band gap energy is 375 eV The conduction bands in SrTiO3 correspond to the bands composed of mainly Ti 3d t2g and eg states, followed at higher energies by the bands of Sr 4d t2g and eg states, and free electron like states dominating at energies above 15 eV The upper valence band (UVB) contains 18 electrons in dominantly O 2p states, hybridized with Ti and Sr states, and has a bandwidth of 5 eV The interband transitions from the UVB to the Ti 3d bands and to the Sr 4d bands give rise to the transitions spanning from the indirect band gap energy of 325 eV up to 15 eV The lower valence band contains 12 electrons in Sr 4p and O 2s states which are separated by 2 eV, while having a bandwidth of 5 eV The interband transitions from the Sr 4p to the Ti 3d and Sr 4d bands give rise to transition energies spanning from 15 to 24 eV Interband transitions from the O 2s band to the conduction bands appear at 26 eV A very narrow band at −33 eV below the top of the valence band is composed of Sr 4s and Ti 3p states and contains eight electrons

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Bulk electronic structure of SrTiO3: Experiment and theory

Bulk properties and electronic structure of SrTiO3, BaTiO3, PbTiO3 perovskites: an ab initio HF/DFT study

Interaction of nanostructured metal overlayers with oxide surfaces

The force-constant matrix and the phonon dispersion curves are calculated for metals (Li, Na, K) by the fully self-consistent direct ab initio supercell approach based on the local-density approximation and on norm-conserving pseudopotentials. Apart from a constant scale factor for each material there is a very good agreement between theoretical and experimental data for the dispersion curves.

Ab initio force-constant method for phonon dispersions in alkali metals.

The local-spin-density approximation and the generalized-gradient approximation (GGA) are used to perform density-functional total-energy calculations at zero temperature for ${\mathrm{Fe}}_{3}\mathrm{Al}$ in the ordered ${D0}_{3}$ and ${L1}_{2}$ structures. Our calculations show that commonly used GGA functionals fail to predict the experimentally stable ${D0}_{3}$ structure as the one with the lower total energy. This qualitative discrepancy with experiment is attributed to an overestimation of the magnetic energy in GGA. The calculations were carried out using the mixed-basis pseudopotential (MBPP) method in the frozen-core approximation and the full-potential linearized-augmented-plane-wave (FLAPW) method, both with and without spin polarization. Although there are small differences in the magnitudes of the magnetic moments and the magnetic energies obtained with MBPP and FLAPW, both methods yield the same qualitative result.

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Density-functional study of Fe3Al: LSDA versus GGA

The influence of the interstitial impurities B, C, N, O, and H on the interfacial cohesion and structure of grain boundaries in body-centered cubic transition metals is investigated by means of the local-density-functional theory (LDFT), using the mixed-basis pseudopotential approach. $\ensuremath{\Sigma}5$ (310) [001] symmetrical tilt grain boundaries (STGB) in Nb and Mo are chosen for this theoretical case study. The analysis of interface energies and geometric translation states, site-projected densities of states and bonding electron densities yields the following systematic trends: B and C form angle-dependent covalentlike bonds with the nearest host-metal neighbors, strengthen the interfacial cohesion by inducing covalent metal-metal bonds across the interface, and favor a mirror-symmetric configuration of the STGB, while N and O as well as H form isotropic polarlike bonds, cause interfacial embrittlement, and break the mirror symmetry of the STGB. The ab initio LDFT results for energetical trends concerning cohesion of boundaries and embrittlement by segregation support the qualitative validity of empirical models of Cottrell and of Rice and Wang for bcc transition metals. In addition, structural trends are derived, which relate the geometrical translation state of the STGB to the type of bonding of the impurity with the host metal at the interface.

Segregated light elements at grain boundaries in niobium and molybdenum

For lithium the absolute concentrations of thermal monovacancies and the self-diffusion constants via vacancies are calculated ab initio using the local-density approximation in combination with the transition-state theory of diffusion. The diffusion data are in good agreement with experimental data for high temperatures.

Christian Elsässer

Papers

Bulk electronic structure of SrTiO3: Experiment and theory

Ab initio force-constant method for phonon dispersions in alkali metals.

Density-functional study of Fe3Al: LSDA versus GGA

Segregated light elements at grain boundaries in niobium and molybdenum

First-Principles Calculations of Absolute Concentrations and Self-Diffusion Constants of Vacancies in Lithium.