Spectral bounds for the Hellmann potential

The method of potential envelopes is used to analyse the bound state spectrum of the Schroedinger Hamiltonian H=-\Delta+V(r), where the Hellmann potential is given by V(r) = -A/r + Be^{-Cr}/r, A and C are positive, and B can be positive or negative. We established simple formulas yielding upper and lower bounds for all the energy eigenvalues.Comment: 9 pages, 2 figures, typos correcte

Extension of the Wu-Jing equation of state (EOS) for highly porous materials: thermoelectron based theoretical model

A thermodynamic equation of state (EOS) for thermoelectrons is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS and the Wu-Jing (W-J) model, an extended Hugoniot EOS model is developed which can predict the compression behavior of highly porous materials. Theoretical relationships for the shock temperature, bulk sound velocity, and the isentrope are developed. This method has the advantage of being able to model the behavior of porous metals over the full range of applicability of pressure and porosity, whereas methods proposed in the past have been limited in their applicability.Comment: 18 pages, 1 figure, appeared at J. Appl. Phys. 92, 5924 (2002

Ab initio modeling of oxygen impurity atom incorporation into uranium mononitride surface and subsurface vacancies

The incorporation of oxygen atoms has been simulated into either nitrogen or uranium vacancy at the UN(001) surface, sub-surface or central layers. For calculations on the corresponding slab models both the relativistic pseudopotentials and the method of projector augmented-waves (PAW) as implemented in the VASP computer code have been used. The energies of O atom incorporation and solution within the defective UN surface have been calculated and discussed. For different configurations of oxygen ions at vacancies within the UN(001) slab, the calculated density of states and electronic charge re-distribution was analyzed. Considerable energetic preference of O atom incorporation into the N-vacancy as compared to U-vacancy indicates that the observed oxidation of UN is determined mainly by the interaction of oxygen atoms with the surface and sub-surface N vacancies resulting in their capture by the vacancies and formation of O-U bonds with the nearest uranium atoms. Keywords: Density functional calculations, uranium mononitride, surface, defects, N and U vacancie

Use of site symmetry in supercell models of defective crystals: Polarons in CeO2

The authors thank R. Merkle and G. W. Watson for stimulating discussions. E. K. also acknowledges partial financial support from the Russian Science Foundation for the study of charged defects under the project 14-43-00052. A. C. also acknowledges financial support from the University of Latvia Foundation (Arnis Riekstins's "MikroTik" donation). E. K. and D. G. express their gratitude to the High Performance Computer Centre in Stuttgart (HLRS, project DEFTD 12939) for the provided computer facilities whereas R. A. E. thanks the St. Petersburg State University Computer Center for assistance in high-performance calculations.In supercell calculations of defective crystals, it is common to place a point defect or vacancy in the atomic position with the highest possible point symmetry. Then, the initial atomic structure is often arbitrary distorted before its optimization, which searches for the total energy minimum. In this paper, we suggest an alternative approach to the application of supercell models and show that it is necessary to preliminarily analyze the site symmetry of the split Wyckoff positions of the perfect crystal supercell atoms (which will be substituted or removed in defective crystals) and then perform supercell calculations with point defects for different possible site symmetries, to find the energetically most favorable defect configuration, which does not necessarily correspond to the highest site symmetry. Using CeO2 as an example, it is demonstrated that this use of the site symmetry of the removed oxygen atoms in the supercells with vacancies allows us to obtain all the possible atomic and magnetic polaron configurations, and predict which vacancy positions correspond to the lowest formation energies associated with small polarons. We give a simple symmetry based explanation for the existence of controversies in the literature on the nature of the oxygen vacancies in CeO2. In particular, the experimentally observed small polaron formation could arise for oxygen vacancies with the lowest Cs site symmetry, which exist in 3 x 3 x 3 and larger supercells. The results of first principles calculations using a linear combination of atomic orbitals and hybrid exchange-correlation functionals are compared with those from previous studies, obtained using a widely used DFT+U approach.Russian Science Foundation 14-43-00052; Saint Petersburg State University; University of Latvia Foundation (Arnis Riekstins's "MikroTik" donation); Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Ab initio calculations of pure and Co+2-doped MgF2 crystals

This research was partly supported by the Kazakhstan Science Project № AP05134367«Synthesis of nanocrystals in track templates of SiO2/Si for sensory, nano- and optoelectronic applications», as well as by Latvian Research Council project lzp-2018/1-0214. Calculations were performed on Super Cluster (LASC) in the Institute of Solid State Physics (ISSP) of the University of Latvia. Authors are indebted to S. Piskunov for stimulating discussions.Ab initio calculations of the atomic, electronic and vibrational structure of a pure and Co+2 doped MgF2 crystals were performed and discussed. We demonstrate that Co+2 (3d7) ions substituting for Mg is in the high spin state. In particular, the role of exact non-local exchange is emphasized for a proper reproduction of not only the band gap but also other MgF2 bulk properties. It allows us for reliable estimate of the dopant energy levels position in the band gap, and its comparison with the experimental data. Thus, the present ab initio calculations and experiment data demonstrate that the Co+2 ground state level lies at ≈2 eV above the valence band top.Kazakhstan Science Project № AP05134367; Latvian Council of Science project lzp-2018/1-0214; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Identity of electrons and ionization equilibrium

It is perhaps appropriate that, in a year marking the 90th anniversary of Meghnad Saha seminal paper (1920), new developments should call fresh attention to the problem of ionization equilibrium in gases. Ionization equilibrium is considered in the simplest "physical" model for an electronic subsystem of matter in a rarefied state, consisting of one localized electronic state in each nucleus and delocalized electronic states considered as free ones. It is shown that, despite the qualitative agreement, there is a significant quantitative difference from the results of applying the Saha formula to the degree of ionization. This is caused by the fact that the Saha formula corresponds to the "chemical" model of matter.Comment: 9 pages, 2 figure

Quantum oscillations of nitrogen atoms in uranium nitride

The vibrational excitations of crystalline solids corresponding to acoustic or optic one phonon modes appear as sharp features in measurements such as neutron spectroscopy. In contrast, many-phonon excitations generally produce a complicated, weak, and featureless response. Here we present time-of-flight neutron scattering measurements for the binary solid uranium nitride (UN), showing well-defined, equally-spaced, high energy vibrational modes in addition to the usual phonons. The spectrum is that of a single atom, isotropic quantum harmonic oscillator and characterizes independent motions of light nitrogen atoms, each found in an octahedral cage of heavy uranium atoms. This is an unexpected and beautiful experimental realization of one of the fundamental, exactly-solvable problems in quantum mechanics. There are also practical implications, as the oscillator modes must be accounted for in the design of generation IV nuclear reactors that plan to use UN as a fuel.Comment: 25 pages, 10 figures, submitted to Nature Communications, supplementary information adde

Field- and irradiation-induced phenomena in memristive nanomaterials

The breakthrough in electronics and information technology is anticipated by the development of emerging memory and logic devices, artificial neural networks and brain-inspired systems on the basis of memristive nano-materials represented, in a particular case, by a simple 'metal-insulator-metal' (MIM) thin-film structure. The present article is focused on the comparative analysis of MIM devices based on oxides with dominating ionic (ZrOx, HfOx) and covalent (SiOx, GeOx) bonding of various composition and geometry deposited by magnetron sputtering. The studied memristive devices demonstrate reproducible change in their resistance (resistive switching - RS) originated from the formation and rupture of conductive pathways (filaments) in oxide films due to the electric-field-driven migration of oxygen vacancies and/or mobile oxygen ions. It is shown that, for both ionic and covalent oxides under study, the RS behaviour depends only weakly on the oxide film composition and thickness, device geometry (down to a device size of about 20x20 mu m(2)). The devices under study are found to be tolerant to ion irradiation that reproduces the effect of extreme fluences of high-energy protons and fast neutrons. This common behaviour of RS is explained by the localized nature of the redox processes in a nanoscale switching oxide volume. Adaptive (synaptic) change of resistive states of memristive devices is demonstrated under the action of single or repeated electrical pulses, as well as in a simple model of coupled (synchronized) neuron-like generators. It is concluded that the noise-induced phenomena cannot be neglected in the consideration of a memristive device as a nonlinear system. The dynamic response of a memristive device to periodic signals of complex waveform can be predicted and tailored from the viewpoint of stochastic resonance concept. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei