Equilibrium Point Defect Research Articles

Equilibrium of intrinsic and impurity point defects in Ca-doped Sm2Zr2O7

Equilibrium of intrinsic and impurity point defects in Ca-doped Sm2Zr2O7

A solid-state electrochemical device for studying thermodynamic properties of non-stoichiometric oxides: Application to UO2+x

We report attempts at determining the evolution of the oxygen activity in hyper-stoichiometric uranium dioxide for very low values of deviation from stoichiometry, using a solid-state electrochemical device. To this end, solid-state oxidation cycles coupled with oxygen activity measurements are carried out on a dense polycrystalline uranium oxide sample. We thus follow the evolution of the oxygen activity in the material as it oxidises or reduces, for temperatures ranging from 1093 to 1273 K. The data are subsequently analysed using an oxygen point defect model and equilibrium constants, corresponding to the various supposed point defect equilibria, are determined. We show that the model faithfully reproduces the trends observed in the experimental data. A more detailed analysis of the equilibrium constants obtained enables us to identify more precisely the limitations of the experimental method. In particular, we highlight the fact that the presence of residual oxygen in the device prevents us from determining the desired physical quantities for stoichiometry deviations less than 10−3. Ways of circumventing these difficulties which would further allow us to determine point defect diffusion coefficients are outlined.

Oxygen Non-Stoichiometry and Point Defect Equilibria in (La1/6Pr1/6Nd1/6Gd1/6Ba1/6Sr1/6)MnO3- δ

In this work, the A-site of the common SOFC cathode La0.8Sr0.2MnO3-δ (LSM) is modified with additional lanthanide and alkali elements, resulting in the composition (La1/6Pr1/6Nd1/6Gd1/6Ba1/6Sr1/6)MnO3- δ. We show that the amount of oxygen released during reduction measured by thermo-gravimetric analysis is significantly greater for this “high entropy” perovskite oxide (HEPO) in comparison with La2/3Sr1/3MnO3-δ, the latter having the same amount of total acceptor dopant and with a similar average A-site radius. The origins of enhanced reduction will be discussed.

Oxygen stoichiometry and isotope exchange of oxides Ba0.5Sr0.5Co0.8Fe0.2O3−δ doped with Ta, Nb, Mo or W

This study focuses on the oxygen exchange kinetics and the oxygen diffusivity of the Ba0.5Sr0.5Co0.8Fe0.2O3−δ oxides doped with high-charged cations M = Ta, Nb, Mo or W and factors governing the oxygen vacancies mobility and surface exchange activity. The dependence of oxygen content in Nb-doped oxide has been investigated as the function of oxygen pressure and temperature within the ranges of − 4.5 ≤ log(Po2/P0o2) ≤ − 0.7 and 600–900 °C by means of the quasi-equilibrium oxygen release method. Based on «T − Po2 – δ» diagrams the modelling of point defect equilibrium has been performed. The composition and morphology of the surface of all the oxides have been studied by the X-ray photoelectron spectroscopy (XPS) and the scanning electron microscopy (SEM), respectively. The kinetics of interaction of gas phase oxygen with the oxides has been explored by the isotope exchange method with gas phase equilibration (IE-GPE) in the temperature range of 600–800 °C and the oxygen pressure at 6.7 mbar. All the oxides have been divided into two groups with respect to the type of rate-determining step of oxygen surface exchange process, while the strong dependence of oxygen vacancy mobility on dopant concentration has been found. The obtained experimental data and proposed models of point defect equilibrium allowed to reveal the factors governing oxygen diffusion and oxygen surface exchange mechanism in series of oxides.

The N-body interatomic potentials for molecular dynamics simulations of diffusion in C15 Cr[formula omitted]Ta Laves phase

In this work, the interatomic potentials for modeling diffusion in the C15 Cr2Ta Laves phase were constructed within the N-body approach. The potential for Ta–Ta interactions reproduces the lattice parameter, cohesive energy, elastic constants, equation of state, thermal expansion, point defect energies, and phonon dispersion of body-centered cubic Ta in qualitative agreement with density functional theory (DFT) data and almost quantitative agreement with available experimental data in the temperature range of stability of C15 Cr2Ta Laves phase. The potential for Cr–Ta interactions reproduces the elastic constants, point defect properties, equilibrium volumes, and formation enthalpies of Cr–Ta structures in qualitative agreement with DFT data. Also, it reproduces the lattice stability and high-temperature formation enthalpy of C15 Cr2Ta Laves phase in very close agreement with the available experimental data. The calculations of diffusion coefficients with constructed potentials showed that diffusion in C15 Cr2Ta lattice is governed by Cr atoms which cannot move without creation of vacancies. The constructed potentials can be used in further investigations of diffusion processes in Cr–Ta phases at temperatures up to 2000 K, while the obtained results on diffusion coefficients in C15 Cr2Ta Laves phase would be useful in the rational design of Cr–Ta based alloys.

Giant and Controllable Photoplasticity and Photoelasticity in Compound Semiconductors.

We show that the wide-band gap compound semiconductors ZnO, ZnS, and CdS feature large photoplastic and photoelastic effects that are mediated by point defects. We measure the mechanical properties of ceramics and single crystals using nanoindentation, and we find that elasticity and plasticity vary strongly with moderate illumination. For instance, the elastic stiffness of ZnO can increase by greater than 40% due to blue illumination of intensity 1.4 mW/cm^{2}. Above-band-gap illumination (e.g., uv light) has the strongest effect, and the relative effect of subband gap illumination varies between samples-a clear sign of defect-mediated processes. We show giant optomechanical effects can be tuned by materials processing, and that processing dependence can be understood within a framework of point defect equilibrium. The photoplastic effect can be understood by a long-established theory of charged dislocation motion. The photoelastic effect requires a new theoretical framework which we present using density functional theory to study the effect of point defect ionization on local lattice structure and elastic tensors. Our results update the longstanding but lesser-studied field of semiconductor optomechanics, and suggest interesting applications.

An extended computational approach for point-defect equilibria in semiconductor materials

Concentrations of intrinsic and extrinsic point defects in crystalline materials with a bandgap are typically calculated in a constant-μ approach from defect formation energies based on density functional theory. In this work, calculations of thermal and charge equilibria among point defects are extended to a constant-N approach. The two approaches for point-defect equilibria are comparatively demonstrated in the application to Mg2Si doped with Li, Na, and Ag, which is a lightweight and environmentally friendly thermoelectric candidate material. Our results reveal the systematic behavior of defect and carrier concentrations. The dopant atoms form interstitial defects at similar concentrations to substitutional defects at the Mg sites, resulting in significantly reduced free-carrier concentrations compared to the expected values. The developed procedures could be utilized to find an optimal avenue for achieving higher carrier concentrations, e.g., with regard to annealing temperature and the concentration of dopant atoms, in various semiconductors and insulators.

Possible ferromagnetism or antiferromagnetism in defective AlN via strain engineering: Hybrid versus GGA calculations

Extensive calculations with hybrid and GGA functionals of the electronic and magnetic properties in cubic AlN for the charged Al and N vacancies are carried out to study the formation energies, the defect equilibrium the induced localized magnetism, the type and range of the magnetic interactions and the possible realization of the magnetic percolation via epitaxial strain engineering during the coherent growth of AlN films. Our calculations are based on the plane wave pseudo-potential spin polarized density functional theory. Our calculations with hybrid and GGA show that only Al vacancies can induce localized magnetic moments. Point defect equilibrium calculation shows that among all the charged Al vacancies, the charge-neutral is the stablest moment carrying state. Study of the collective magnetism between vacancy pairs using the Heisenberg model shows that these defects couple ferromagnetically for the first and third FCC distances and antiferromagnetically for the fourth distance. Thermodynamic considerations show that we cannot achieve magnetic percolation at equilibrium conditions since the minimal vacancy concentration needed for wall to wall percolation is many order of magnitude higher that the equilibrium calculated concentration. Nevertheless, our work shows that we can drastically enhance the vacancy concentration during the coherent growth of AlN films via a tensile epitaxial strain.

Defect chemistry and oxygen nonstoichiometry of CeBaFe2O5.5

While lanthanoids Ln ​= ​Gd to Pr form Ba–Ln ordered double-cell iron perovskites with a wide equilibrium nonstoichiometry from LnBaFe2O5 to over O5.5, the Ce variant of this study no longer forms the CeBaFe2O5 composition. Point-defect equilibria behind oxygen nonstoichiometry of the CeIIIBaFeIII2O5.5 that forms are studied by quenching from flowing gas of controlled oxygen partial pressures pO2 and temperatures. Their thermodynamic parameters are evaluated on the defect model of pure undoped CeIIIBaFeIII2O5.5 with an electronic-defect pair e′ and h•, anion-Frenkel pair Oi′′ and vO••, and redox behavior at equilibrium with oxygen in the reaction atmospheres to fit the experimentally determined nonstoichiometry.

Evaluation of the Performance of Published Point Defect Parameter Sets in Cone and Body Phase of a 300 mm Czochralski Silicon Crystal

Prediction and adjustment of point defect (vacancies and self-interstitials) distribution in silicon crystals is of utmost importance for microelectronic applications. The simulation of growth processes is widely applied for process development and quite a few different sets of point defect parameters have been proposed. In this paper the transient temperature, thermal stress and point defect distributions are simulated for 300 mm Czochralski growth of the whole crystal including cone and cylindrical growth phases. Simulations with 12 different published point defect parameter sets are compared to the experimentally measured interstitial–vacancy boundary. The results are evaluated for standard and adjusted parameter sets and generally the best agreement in the whole crystal is found for models considering the effect of thermal stress on the equilibrium point defect concentration.

Synthesis and equilibrium oxygen nonstoichiometry of PrBaFe2O5+w

A double-cell perovskite PrBaFe2O5+w is synthesized and its equilibrium nonstoichiometry investigated after quenching from flowing gas of varied oxygen partial pressures and temperatures. Whereas w ​= ​0 is reached at 856 ​°C in wet H2 of pH2O ​= ​0.02 ​bar yielding pO2 ​= ​4×10−21 ​bar, w ​= ​0.75 obtains at 400 ​°C in O2. Below ~1000 ​°C, compositions with w ​≥ ​0.5 order into a Cmmm superstructure that fully converts back upon heating to 1020 ​°C. PrBaFe2O5 of all equivalent Fe2.5+ sites orders into Fe2+ and Fe3+ upon cooling through a first-order transition at 204 ​K, with a 2 ​K hysteresis, as investigated by powder X-ray diffraction and differential scanning calorimetry. The valence-mixed and charge-ordered structures are refined from synchrotron X-ray powder diffraction patterns. The nonstoichiometry w is expressed as a function of T and pO2 of the flowing gas in a formal donor-dopant defect model via least-squares fit of thermodynamic parameters for point-defect equilibria in the solid.

Enforcing local equilibrium of point defects near sinks in object kinetic Monte Carlo simulations

A model for the emission of point defects by point defect sinks is proposed for object kinetic Monte Carlo simulations. Local equilibrium of point defects in the vicinity of sinks is ensured by construction, even if elastic interactions are taken into account for the diffusion of point defects. The emission of vacancies by dislocation segments is treated in detail and validated numerically. The model is then used to simulate the annealing of a vacancy Frank loop in a system containing surfaces. Results are in overall good agreement with analytical formulas, which are based on the approximation of instantaneous equilibration of the vacancy field during the loop evolution process. For small loops the shrinkage is so rapid that this quasi-static approximation is no more valid.

Особенности спектров люминесценции ZnSе · О с привлечением теории антипересекающихся зон

Investigations are presented in the light of the band anticrossing theory (ВАС) of the influence on the emission spectra of the structural features self-activated zinc selenide and crystals with activators. The disunity of numerous literature data makes it difficult to understand this question. Theory-ВAС requires taking into account the influence of isoelectronic admixture of oxygen, which is invariably present in the ZnSе lattice, on the zone structure. Improvement of methods for calcu-lating the equilibrium of intrinsic point defects (STD) intendes use of these data in the analysis of the optical properties of АIIВVI, in particular zinc selenide.The aim of thе work was to re-veal the features and nature of individual luminescence bands that are widely used to obtain information on the quality of crystals.For this, the spectra of photo, cathode, pulsed lumines-cence, excitation, and stimulated emission of ZnSе are investigated in a single context with the use of these features. Stable states of crystals with stacking faults were revealed upon introduc-tion of activators or background copper impurity. The data are of interest for the diagnostics of crystals that are useful for creating lasers.

Система локализованных экситонов на кислородных комплексах в CdS

Intense CdS luminescence in the blue and green spectral regions is widely used in all areas of optoelectronics. In this spectrum band are working on lasers CdS. This paper presents the results of a study of the exciton region of the CdS spectrum based on the theory of anti-intersecting bands (bands anticrossing theory - BAC) with the involvement of broader initial data for the analysis of optical properties. Depending on the growth conditions of CdS, the presence and change in the oxygen concentration, as well as the equilibrium of intrinsic point defects, which determines the change in the composition of the crystals. The concept of the nonuniform distribution of isoelectronic centers in the bulk of CdS due to their predominant segregation on compensating stacking faults is introduced. Cathodoluminescence (CL) spectra were studied using various recording methods, excitation intensity and temperature, as well as pulsed CL at high excitation intensities. In a scanning electron microscope from local registration and a high excitation density, the emission of the edge luminescence components of CdS was detected at 300 K To analyze the optical data, we used the capabilities of the method for constructing band models based on the BAC theory, which. collects extensive and multilateral information about specific samples. A model of a CdS O multizone with stacking faults is presented, which determines the spectrum of edge emission. An explanation of the nature of the green edge emission of cadmium sulfide as excitons localized on oxygen-containing complexes in SF layers has been obtained for the first time. It was found that the system of levels of localized excitons at stacking faults does not change either with temperature up to 300 K, or with a change in the oxygen solubility in the crystal to the limiting one. It is shown that the presence of isoelectronic oxygen centers appear itself in the electro-physical properties of crystals. Recommendations are given for the diagnostics of crystals suitable for the creation of luminescent systems or lasers that are stable in operation.

(Invited) Electro-Chemo-Mechanical Equilibrium of Point Defects at Interfaces

Formation and migration of point defects underlie nearly all materials for energy transformation, such as electrodes and solid electrolytes for lithium-ion batteries and solid oxide fuel cells. The distribution of point defects such as lithium and oxygen vacancies reflect electro-chemo-mechanical equilibria. In this talk, I will present a general theory framework for understanding how mechanical contribution plays a key role in determining the space-charge effect at interfaces.

Topological properties after light ion irradiation on Weyl semimetal niobium phosphide from first principles

A member of the nonmagnetic Weyl semimetal family, niobium phosphide (NbP), is a new low-energy dissipative material due to the properties of its nontrivial energy band structure and topologically protected nodes. This paper mainly focus on the changes of the topological properties of the crystal NbP after H and He ions irradiation, a novel research view. In order to demonstrate the formation process of doping defects, we use TD-DFT to simulate the whole path of H ion passing the bulk NbP, while both the total energy change for system and the radial drag force as a function of the projectile position are investigated. The energy band structures and density of states for the equilibrium point defect have been analyzed by means of the DFT method based on the CASTEP package. A strikingly phenomenon discovered is that diverse kinds of defects are able to modify the symmetrically protected Weyl points to some extent. Specifically, when H or He as an interstitial particle in the crystal NbP, the degenerate bands are uncoupled; meanwhile, the Fermi levels are shifted upward 0.12 eV and 0.18 eV, respectively. In contrast to the defect structures formed by P, the defects caused by Nb present the greater destructive power to the Weyl points. By contrast, the calculations of formation energy have demonstrated that H substitute for Nb is the most easily formed defect structure, and the defect with interstitial H atom is most stable structure within the scope of this research.

Equilibrium point defect and charge carrier concentrations in a material determined through calculation of the self-consistent Fermi energy

A concise procedure to determine the self-consistent Fermi energy and defect and carrier concentrations in an extended crystalline system is presented. It is assumed that the formation enthalpies of a set of variously charged point defects in thermodynamic equilibrium are known, as well as the density of electronic states in the defect-free system. By applying the constraint of overall charge neutrality, the self-consistent Fermi energy is determined using an iterative searching routine. The procedure is incorporated within a Fortran code ‘SC-FERMI’: the input consists of the defect formation energies, density of sites where they can form, and the degeneracy of each charge state; the material band gap; and the calculated density of states of the pristine system. The output is the self-consistent Fermi energy, the total concentrations of each defect as well as the concentration of its individual charge states, and the free carrier concentrations. Furthermore, the procedure facilitates fixing the concentration of one or more defects and determining the resulting self-consistent Fermi energy and concentrations of other defects (performed using the related code ‘FROZEN-SC-FERMI’), thus modelling ‘frozen-in’ defects which may form by kinetic, rather than thermodynamic, processes. One can fix the total concentration or the concentration of a particular charge state; it is also possible to introduce new defects with a fixed concentration, but here the charge state must be specified. The background theory is discussed in some detail, and the operation of the program is demonstrated by some examples. Program summaryProgram Title:SC-FERMIProgram Files doi:http://dx.doi.org/10.17632/dh3hjdf4fc.1Licensing provisions: MIT licenseProgramming language:FORTRAN 90Nature of problem: To determine the self-consistent Fermi energy and equilibrium defect and carrier concentrations given a set of point defect formation energies in a crystalline system, assuming the constraint of charge neutrality.Solution method: The concentrations of each defect in each charge state are calculated, as are the free carrier concentrations. These concentrations are functions of the Fermi energy. The code, using an iterative search algorithm, determines the Fermi energy that satisfies the charge neutrality constraint (the self-consistent Fermi energy). The defect and carrier concentrations at that Fermi energy are then reported, as well as the Fermi energy itself.Restrictions: Thermodynamic equilibrium is assumed. The defect formation enthalpies and electronic density of states of the pristine system must be known.Additional comments: The concentrations of defects can be fixed to a particular value, thus modelling ‘frozen-in’ defects formed by e.g. kinetic processes. This procedure is facilitated by the related program, FROZEN-SC-FERMI, which is identical to SC-FERMI apart from the additional defect concentration fixing routine.

DEFECT FORMATION MECHANISMS OF ZINC SELENIDE LAYERS DOPED BY ISOVALENT IMPURITIES OF THE II GROUP

The paper discusses the mechanisms of defect formation in melt zinc selenide crystals doped with isovalent impurities of the second group of the Periodic Table. An analytical calculation of the concentrations of equilibrium point defects was carried out by the method of quasichemical reactions using the concepts of electronegativity and effective charge. It has been established that the dominant defects in the doped material are singly charged vacancies of zinc V'Zn and selenium V·Se, as well as singly charged interstitial selenium Se'i. It is shown that the increase in doping temperature Ta from 373 to 1237 K causes se increase of acceptor centers number (V'Zn and Se'i) and decrease of concentration of donor ounces V·Se however, the conductivity of doped substrates at 300 K remains a hole in the whole range of change Ta. At Ta = 373 K the estimated concentration of free holes is ~1019 cm-3 and satisfactorily consistent with the value p determined from the temperature dependence of the layer resistance ZnSe:Ca.

Interstitial-mediated dislocation climb and the weakening of particle-reinforced alloys under irradiation

Dislocations can climb out of their glide plane by absorbing (or emitting) point defects (vacancies and self-interstitial atoms (SIAs)). In contrast with conservative glide motion, climb relies on the point defects' thermal diffusion and hence operates on much longer timescales, leading to some forms of creep. Whilst equilibrium point defect concentrations allow dislocations to climb to relieve non-glide stresses, point defect supersaturations also lead to osmotic forces, driving dislocation motion even in the absence of external stresses. Self-interstitial atoms typically have significantly higher formation energies than vacancies, so their contribution to climb is usually ignored. However, under irradiation conditions, both types of defect are athermally created in equal numbers. In this letter, we use simple thermodynamic arguments to show that the contribution of interstitials cannot be neglected in irradiated materials, and that the osmotic force they induce on dislocations is many orders of magnitude larger than that caused by vacancies. This explains why the prismatic dislocation loops observed by {\it in situ} transmission electron microscope irradiations are more often of interstitial rather than vacancy character. Using discrete dislocation dynamics simulations, we investigate the effect on dislocation-obstacle interactions, and find reductions in the depinning time of many orders of magnitude. This has important consequences for the strength of particle-reinforced alloys under irradiation.

Calculation of point defect concentration in Cu2ZnSnS4: Insights into the high-temperature equilibrium and quenching

Herein, we study the native point defect equilibrium in Cu2ZnSnS4 (CZTS) by applying a statistical thermodynamic model. The stable chemical-potential space (SCPS) of CZTS at an elevated temperature was estimated directly, on the basis of deviations from stoichiometry calculated for the different combinations of chemical potential of the components. We show that the SCPS is narrow due to high concentration of VCu−−ZnCu+ complex which is dominant over other complexes and isolated defects. The CZTS was found to have p-type conductivity for both stoichiometric and Cu-poor/Zn-rich composition. It is established that the reason for this is that the majority of donor-like ZnCu+ antisites are involved in the formation of VCu−−ZnCu+ complex making CuZn− dominant and providing p-type conductivity even for Cu-poor/Zn-rich composition. However, our calculation reveals that the hole concentration is almost insensitive to the variation of the chemical composition within the composition region of the single-phase CZTS due to nearly constant concentration of dominant charged defects. The calculations for the full equilibrium and quenching indicate that hole concentration is strongly dependent on the annealing temperature and decreases substantially after the drastic cooling. This means that the precise control of annealing temperature and post-annealing cooling rate are critical for tuning the electrical properties of CZTS.