Defect Equilibria Research Articles

Oxygen nonstoichiometry in LnBaFe2O5+w across Ln = Nd, Sm, Gd

In double-cell perovskites LnBaFe2O5+w, only lanthanoids Ln ​= ​Pr to Gd support wide equilibrium nonstoichiometry w from 0 to >0.5. This study investigates point-defect equilibria behind the variation in w along Ln ​= ​Nd, Sm, Gd by quenching the oxides from flowing gas of controlled oxygen partial pressures and temperatures. The experimental data of w as a function of pO2 and T are least-squares fit via standard enthalpies and entropies of the defect-equilibrium reactions of formation for electronic-defect pair e′ and h• and for anion-Frenkel pair Oi′′ and vO••, and of the Fe2+ oxidation. NdBaFe2O5+w is closest to behaving as a pure undoped oxide at 1000 ​°C, where it has a single plateau in the w versus pO2 plot at the w ​= ​0.5 level. A second plateau, at w ​= ​0, emerges at lower temperatures. The smaller Sm and Gd increase the size difference versus Ba, and their defect equilibria show two plateaus even at 1000 ​°C. The temperature-dependent defect equilibria across this series are therefore approximated by a formal Ln3+ for Ba2+ donor-doping model, and the results are presented in Brouwer diagrams of defect concentrations. The decrease of the anion-Frenkel defect-equilibrium constant KaF due to decreasing ionic size from Nd3+ towards Gd3+ is magnified upon decrease in temperature that feeds the entropy of the anion-Frenkel disorder; at 400 ​°C, Ln ​= ​Nd has KaF ​= ​10−5.4, Sm 10−15.0 and Gd 10−24.3.

The impact of cerium content on oxygen stoichiometry, defect equilibrium, and thermodynamic quantities of Sr1−xCexFeO3−δ

The structure, oxygen non-stoichiometry, and defect equilibrium in perovskite-type Sr1−xCexFeO3−δ (x = 0.05, 0.10, 0.15, 0.20) were studied. X-ray diffraction showed the formation of a cubic structure for all compositions. The electron diffraction detected an incommensurate structure with a modulation wave vector 0.41 a* in compositions with x ≥ 0.10. The phenomenon is assumed to originate from a strong steric disturbance attributed to a large difference in ionic radii of cerium and strontium. The data on the oxygen content acquired in wide ranges of oxygen partial pressure and temperature were used for the modeling of defect equilibrium in oxides. A part of anion vacancies in Sr1−xCexFeO3−δ was found to be inaccessible for oxygen ions. The main factors of cerium substitution impact on the thermodynamic parameters of defect formation reactions in Sr1−xCexFeO3−δ were revealed to be lattice contraction, steric disturbance, and cerium reduction to Ce3+. The concentration of Ce3+ ions in Sr1−xCexFeO3−δ under reducing conditions was found to be substantially greater than that of Fe2+. Interrelations between thermodynamic quantities of oxygen in Sr1−xCexFeO3−δ and thermodynamic parameters of defect formation reactions were considered.

OH point defects in quartz – a review

Abstract. Research results of the past 6 decades on the incorporation of OH point defects in quartz are summarised and evaluated in terms of their application to natural samples and processes, and a link between experimental petrology, natural archives, and model calculations is made. A strong focus is put on recent studies on quartz as a rock-forming mineral, as a geochemical and/or petrological tracer, and as a tool for provenance analysis in sediments and sedimentary rocks. The most relevant defects for natural specimens are generated by coupled substitution involving mono- and trivalent cations, the most prominent being Li+, Al3+, and B3+. OH incorporation is rather a function of the availability of trace metals and water than of pressure and temperature, though temperature indirectly influences the incorporation by the solubility of trace metals in the fluid. Pressure has a negative influence on the formation of OH defects, so the most pure quartzes are probably formed in the deep crust close to the quartz/coesite transition. Natural quartz grains from the Earth's crust have on average 10 wt ppm (weight parts per million) water (5 wt ppm median), but grains with OH defect contents corresponding to up 250 wt ppm water have been discovered in sedimentary archives, matching the concentration of quartz from high-pressure experiments <4 kbar under water-saturated conditions in granitic systems. A rough division into three classes is suggested: (1) grains with pristine igneous and/or hydrothermal origin, (2) mildly thermally annealed grains, and (3) strongly dehydrated grains. While samples derived from the currently exposed Scandinavian Shield are dominated by the third class, considerable contributions of the first two classes are found in the younger rock systems in Central Europe. OH defect contents may be used to estimate mixing ratios for sediments with different sources, provided that a sufficiently large data set exists and that the different sources can be clearly distinguished by their OH inventory. Furthermore, metamorphic overprint leads to a higher degree of equilibration of OH defects between individual grains and may thus be used as a geothermometer. Finally, OH defect retention in quartz allows for estimating timescales of volcanic processes.

Electrochemical determination of SrFe12O19 impurity in perovskite ferrites

A strong negative effect of SrFe12O19 impurity presence in perovskite-type ferrites on the results of the coulometric titration has been revealed. A multistage decomposition of this impurity during reductive titration causes distortion of oxygen content isotherms and makes the obtained data inapplicable for the defect equilibrium analysis. Even a small amount of SrFe12O19 undetected by X-ray diffraction has been shown to affect data considerably. In this study, a method has been developed to determine the amount of impurity and recover the oxygen content data in perovskite-type ferrites from measurements of these ferrites contaminated with SrFe12O19. The method has been verified on the perovskite-type NdxSr1−xFe0.8Mo0.2O3−δ (x = 0, 0.1, 0.2), the latter two compositions of which have been found to be contaminated with ~0.9 and 1.8 wt% of SrFe12O19, respectively, whereas 5.8 wt% of hexaferrite has been intentionally admixed to the x = 0 composition. The recovered data have been used for thermodynamic modeling of the defect equilibrium in NdxSr1−xFe0.8Mo0.2O3−δ. Good agreement of all obtained thermodynamic parameters with the published results for similar compositions and their monotonous change with neodymium content confirms the correct functionality of the method.

Spinney: Post-processing of first-principles calculations of point defects in semiconductors with Python

Understanding and predicting the thermodynamic properties of point defects in semiconductors and insulators would greatly aid in the design of novel materials and allow tuning the properties of existing ones. As a matter of fact, first-principles calculations based on density functional theory (DFT) and the supercell approach have become a standard tool for the study of point defects in solids. However, in the dilute limit, of most interest for the design of novel semiconductor materials, the “raw“ DFT calculations require an extensive post-processing. Spinney is an open-source Python package developed with the aim of processing first-principles calculations to obtain several quantities of interest, such as the chemical potential limits that assure the thermodynamic stability of the defect-laden system, defect charge transition levels, defect formation energies, including electrostatic corrections for finite-size effects, and defect and carrier concentrations. In this paper we demonstrate the capabilities of the Spinney code using c-BN, GaN:Mg, TiO2 and ZnO as examples. Program summaryProgram Title:SpinneyCPC Library link to program files:https://doi.org/10.17632/2xp4ddwmgx.1Developer’s repository link:https://gitlab.com/Marrigoni/spinneyCode Ocean capsule:https://codeocean.com/capsule/4970623Licensing provisions: MITProgramming language: Python 3External libraries: NumPy [1], SciPy [2], Pandas [3], Matplotlib [4], ASE [5]Nature of problem: Post-processing of first-principles calculations in order to obtain important properties of defect laden systems in the dilute-limit: chemical potential values ensuring thermodynamic stability, thermodynamic charge transition levels, defect formation energies and corrections thereof using state-of-the-art corrections schemes for electrostatic finite-size effects, equilibrium defect and carriers concentrations.Solution method: Flexible low-level interface for allowing the post-processing of the raw fist-principles data provided by any computer code. High-level interface for parsing and post-processing the first-principles data produced by the popular computer codes VASP and WIEN2k.Additional comments including restrictions and unusual features: An extensive documentation is available at: https://spinney.readthedocs.io

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.

Equilibrium distribution of point defects in Fe-Y-O as a typical representative of nanocluster-strengthened alloys

The statistical mechanic approach [1, 2] has been used to estimate the equilibrium defect distribution in a multiphase system by minimizing its free energy using microstructural characteristics and a finite set of defects obtained by first-principles calculations. Recently the approach was extended to take in consideration defects at the interface of the precipitate and matrix [3]. Herein we apply the developed approach to the investigation of the stability of bcc Fe containing yttria, Y2O3, nanoclusters as a prototype of nanostructured ferritic alloys. It has been obtained that (100)Fe-O interface is unstable with respect to vacancies production. In a contrast to (100)Fe-O interface, the so called Klim interface is stable, i.e. local vacancy concentration at this interface at 600 K is below 10−12. It has been demonstrated that due to large defect formation energies the ODS particles are extremely stable and the main defect corresponds to Fe atoms substitute Y in Y2O3 precipitate. Moreover, under thermodynamic equilibrium condition, the preexist vacancies in bulk Fe do not accumulate oxygen atom. The later observation not necessarily forbid the existence of a large amount of preexisting Fe vacancy - oxygen atom clusters at the initial stages of alloy formation far from equilibrium.

Pushing the Study of Point Defects in Thin Film Ferrites to Low Temperatures Using In Situ Ellipsometry

AbstractUnveiling point defects concentration in transition metal oxide thin films is essential to understand and eventually control their functional properties, employed in an increasing number of applications and devices. Despite this unquestionable interest, there is a lack of available experimental techniques able to estimate the defect chemistry and equilibrium constants in such oxides at intermediate‐to‐low temperatures. In this study, the defect chemistry of a relevant material such as La1−xSrxFeO3−δ (LSF) with (x = 0.2, 0.4 and 0.5 (LSF20, LSF40 and LSF50 respectively) is obtained by using a novel in situ spectroscopic ellipsometry approach applied to thin films. Through this technique, the concentration of holes in LSF is correlated to measured optical properties and its evolution with temperature and oxygen partial pressure is determined. In this way, a systematic description of defect chemistry in LSF thin films in the temperature range from 350 °C to 500 °C is obtained for the first time, which represents a step forward in the understanding of LSF20, LSF40 and LSF50 for emerging low temperature applications.

Impact of oxygen content on preferred localization of p- and n-type carriers in La0.5Sr0.5Fe1-xMnxO3-δ.

The oxygen content in La0.5Sr0.5Fe1-xMnxO3-δ, measured by coulometric titration in a wide range of oxygen partial pressure at various temperatures, was used for defect chemistry analysis. The obtained data were well approximated by a model assuming defect formation in La0.5Sr0.5Fe1-xMnxO3-δvia Fe3+ and Mn3+ oxidation reactions and charge disproportionation on Fe3+ and Mn3+ ions. The partial molar enthalpy and entropy of oxygen in La0.5Sr0.5Fe1-xMnxO3-δ obtained by statistical thermodynamic calculations were found to be in satisfactory agreement with those obtained using the Gibbs-Helmholtz equations, thus further confirming the adequacy of the model. The impact of manganese substitution on defect equilibrium in La0.5Sr0.5Fe1-xMnxO3-δ was shown to be attributed to a lower enthalpy of Mn3+ oxidation reaction (vs. for the oxidation of Fe3+) and the charge disproportionation reaction on Mn3+ (vs. for that on Fe3+). The former makes Mn4+ ions more resistant to reduction than Fe4+. The latter favors the presence of Mn2+, Mn3+, and Mn4+ ions in oxides in comparable concentrations. The distribution of charge carriers over iron and manganese ions was determined as a function of oxygen content in La0.5Sr0.5Fe1-xMnxO3-δ.

Design strategies for ceria nanomaterials: untangling key mechanistic concepts.

The morphologies of ceria nanocrystals play an essential role in determining their redox and catalytic performances in many applications, yet the effects of synthesis variables on the formation of ceria nanoparticles of different morphologies and their related growth mechanisms have not been systematised. The design of these morphologies is underpinned by a range of fundamental parameters, including crystallography, optical mineralogy, the stabilities of exposed crystallographic planes, CeO2-x stoichiometry, phase equilibria, thermodynamics, defect equilibria, and the crystal growth mechanisms. These features are formalised and the key analytical methods used for analysing defects, particularly the critical oxygen vacancies, are surveyed, with the aim of providing a source of design parameters for the synthesis of nanocrystals, specifically CeO2-x. However, the most important aspect in the design of CeO2-x nanocrystals is an understanding of the roles of the main variables used for synthesis. While there is a substantial body of data on CeO2-x morphologies fabricated using low cerium concentrations ([Ce]) under different experimental conditions, the present work fully maps the effects of the relevant variables on the resultant CeO2-x morphologies in terms of the commonly used raw materials [Ce] (and [NO3-] in Ce(NO3)3·6H2O) as feedstock, [NaOH] as precipitating agent, temperature, and time (as well as the complementary vapour pressure). Through the combination of consideration of the published literature and the generation of key experimental data to fill in the gaps, a complete mechanistic description of the development of the main CeO2-x morphologies is illustrated. Further, the mechanisms of the conversion of nanochains into the two variants of nanorods, square and hexagonal, have been elucidated through crystallographic reasoning. Other key conclusions for the crystal growth process are the critical roles of (1) the formation of Ce(OH)4 crystallite nanochains as the precursors of nanorods and (2) the disassembly of the nanorods into Ce(OH)4 crystallites and NO3--assisted reassembly into nanocubes (and nanospheres) as an unrecognised intermediate stage of crystal growth.

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.

Defect chemistry and charge transport in LaSr3Fe3−xMoxO10−δ

Molybdenum containing solid solution LaSr3Fe3−xMoxO10−δ with triple-layer Ruddlesden-Popper structure is considered a promising mixed conducting material for high-temperature electrochemical applications. Oxygen content and electrical conductivity in the compositions with x=0.1 and 0.2 were measured in the range of oxygen partial pressure from 10−20 to 0.5 atm at temperatures 750-950°C. Experimental data were employed for the simulation of defect equilibrium and charge transfer in oxides. The defect distribution over two B-sublattices and four anion sublattices was determined depending on oxygen partial pressure and temperature. The main transport pathways of electrons, holes, and oxygen ions were found to be spatially separated in these oxides between B1, B2, and O4 sublattices, respectively. An increase in the molybdenum content was found to result in higher electron and oxygen ion conductivity. The enhancement of electron conductivity is explained by partial molybdenum reduction and involvement of Mo5+ ions in electron transport. As for ion conductivity, its improvement is suggested to be attributed to oxygen mobility increase due to a decrease in a fraction of tetrahedrally coordinated iron ions in the B1 sublattice and respective vacancy disordering in the O4 sublattice.

Defect-Accommodating Intermediates Yield Selective Low-Temperature Synthesis of YMnO3 Polymorphs.

In the synthesis of complex oxides, solid-state metathesis provides low-temperature reactions where product selectivity can be achieved through simple changes in precursor composition. The influence of precursor structure, however, is less understood in solid-state synthesis. Here we present the ternary metathesis reaction (LiMnO2 + YOCl → YMnO3 + LiCl) to target two yttrium manganese oxide products, hexagonal and orthorhombic YMnO3, when starting from three different LiMnO2 precursors. Using temperature-dependent synchrotron X-ray and neutron diffraction, we identify the relevant intermediates and temperature regimes of reactions along the pathway to YMnO3. Manganese-containing intermediates undergo a charge disproportionation into a reduced Mn(II,III) tetragonal spinel and oxidized Mn(III,IV) cubic spinel, which lead to hexagonal and orthorhombic YMnO3, respectively. Density functional theory calculations confirm that the presence of Mn(IV) caused by a small concentration of cation vacancies (∼2.2%) in YMnO3 stabilizes the orthorhombic polymorph over the hexagonal. Reactions over the course of 2 weeks yield o-YMnO3 as the majority product at temperatures below 600 °C, which supports an equilibration of cation defects over time. Controlling the composition and structure of these defect-accommodating intermediates provides new strategies for selective synthesis of complex oxides at low temperatures.

Defect chemistry and oxygen non-stoichiometry in SrFe0.2Co0.4Mo0.4O3-δ ceramic oxide for solid oxide fuel cells

SrFe0.2Co0.4Mo0.4O3-δ (SFCM) is a ceramic oxide that has the potential to replace conventional Ni-based cermet anodes and is appropriate for use in solid oxide fuel cells operating at low temperatures (below 650 °C). SFCM was shown to be phase stable with n-type conductivity above 43 S/cm under reducing conditions and reversibly creates secondary phases under oxidizing conditions with p-type conductivity around 4 S/cm at 600 °C. SFCM begins desorbing oxygen and creating vacancies under nitrogen at 350 °C and continues to do so above 800°C. Under oxidizing conditions, SFCM remains near stoichiometric, with oxygen non-stoichiometry changes below δ = 0.003. Once exposed to reducing conditions, SFCM can obtain a non-stoichiometry up to δ = 0.176 due to the reduction of the three multivalent B-site cations resulting in a low enthalpy of formation for oxygen vacancies at 109 kJ mol − 1. This data is used to propose a low pO2 defect equilibrium model and diagram to explain the oxygen vacancy generation behavior under reducing conditions across temperatures.

Nonequilibrium kinetics of excess defect generation and dynamic scaling in the Ising spin chain under slow cooling.

We investigate the relaxation dynamics of a one-dimensional Ising chain via Glauber kinetic Monte Carlo simulations, when the system is cooled slowly from infinite temperature to zero temperature with different cooling protocols. The main quantity of interest is the excess defect density that represents the total defect density minus the equilibrium defect density at varying temperatures. We find that, for three classes of cooling protocols, the time dependence of the excess defect density for various cooling speed shows a dynamic scaling behavior that largely encompasses the Kibble-Zurek mechanism as well as Krapivsky's calculation of the final defect density at zero temperature. We also find distinct features in the behavior of the dynamic scaling when the temperature approaches in a power-law fashion to zero temperature and the excess defect density reaches a peak at finite temperature, where the scaling of the excess defect density at its peak and that at zero temperature exhibits different asymptotic behavior due to different logarithmic corrections. This characteristic behavior can be attributed to the exponential divergence of the relaxation time near zero temperature. While the qualitative theoretical predictions by Krapivsky on the asymptotic exponents are confirmed, the asymptotic predictions for amplitudes overestimate by up to 40% the simulation results.

(Invited) Potentiometric Measurements of Defect Equilibrium of Nonstoichiometric Oxides Under Mechanical Load

Nonstoichiometric compounds are widely used for solid state electrochemical devices such as lithium ion batteries and solid oxide fuel cells. Their functions arise from point defects of which the equilibrium concentration varies with temperature, pressure, and chemical potential of the constituent elements in the surrounding environment. In an actual device, materials are used in combination with other compounds among which internal stress appears due to the mismatch of the thermal or chemical strain. The mechanical load, or stress tensor, applied to the solid may also affect the local defect equilibrium. In thermodynamic considerations by Johnson and Schmalzried [1], the modification of the defect equilibrium by the mechanical load was correlated by the chemical strain or the volume change upon variation of defect concentration.In our previous reports [2,3], we proposed a potentiometric method to monitor the shift of oxygen defect equilibrium of a mixed conducting oxides placed under mechanical load. The measurements were done using a small ball of stabilized zirconia (YSZ) which was used for a potentiometric oxygen sensor as well as for a pushing jig to apply compressive stress on the sample at the measurement point. As a mixed conducting oxide, (La,Sr)(Co,Fe)O3 was chosen and the measurements were done using a universal mechanical testing machine. The emf was monitored over the YSZ ball between the sample and a reference electrode which was placed on the free surface of the ball. The results were as expected, i.e. a negative voltage appeared on the sample side on the instance of applying load, and it gradually approached back to zero. On removing the load, a positive voltage appeared, and it decayed to zero with time. The observed phenomena were explained as follows: On application of the load, the local composition tends to shift to a new equilibrium under the load. However, it does not occur instantly since it accompanies mass transport. Instead, the sample behaves first as a closed system and the local chemical potential varies, which was monitored by the YSZ ball. Equilibration with the gas phase proceeds gradually via chemical diffusion of oxygen in the sample. The maximum voltage in the negative and positive directions showed good agreement with those estimated from the local stress and the chemical expansion coefficient for vacancy formation reaction. The similar measurements were made with (La,Sr)CoO3, (La,Sr)FeO3, and (La,Sr)MnO3, and the similar results were obtained when oxygen nonstoichiometry variation is large enough compared to the thermal fluctuation.Recently, the similar measurements were made by monitoring a voltage across a mixed conducting oxide itself on pressing its surface with an alumina ball. Gadlinia doped ceria, GDC, was used as the sample, and the surface was pushed with a small alumina ball coated with platinum paste. Reference Pt electrode was placed on the GDC sample at the place far from the applied load. The voltage across GDC was monitored using the Pt coat on alumina ball and Pt electrode on GDC. Under reducing atmosphere, the negative shift of potential followed by a gradual decay was observed. The maximum voltage was as expected if the transference number that is less than unity was taken into consideration. Under oxidizing atmosphere, a quick appearance of positive voltage was observed upon loading. It was similar to that observed with YSZ ball when it was pushed against Pt foil. The oxygen dissolved or adsorbed on Pt or at the interface could be the source of the response. With GDC, a persistent voltage was also observed in some cases, of which the reason is not clear yet.The similar approach as GDC was explored to a Ba(Ce,Y)O3 based proton conducting oxides. In this case, not only proton but also electron hole and oxide ion vacancy may contribute to the transport and thus the appearance of EMF. The results observed so far was the negative voltage on loading under oxidizing atmospheres, and negative voltage under reducing atmospheres. Rather large persistent volrage was also detected. Details of the results and the explanation will be discussed.

(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.

Block copolymer directed self-assembly defect modes induced by localized errors in chemoepitaxial guiding underlayers: A molecular simulation study

Block copolymer (BCP) directed self-assembly (DSA) has been presented as a potential economically attractive enhancement to extend the capabilities of optical lithography for semiconductor manufacturing. One concern in DSA is the level of defectivity that can be achieved in such a process. Although entropic effects will always lead to some degree of defectivity, highly ordered structures with a low theoretical equilibrium defect density can be produced by guiding the ordering and placement of the BCP domains using a patterned underlayer. Recent experimental studies have shown that while DSA processes can significantly reduce the observed defect density, defectivity levels are generally still higher than allowable for high-volume manufacturing and higher than what would be anticipated from free energy estimates of the observed defect modes. In particular, bridge defects are one of the most commonly observed defect modes in experimental DSA studies. A number of hypotheses have been proposed to explain the origins of these defects. One hypothesis is that so-called affinity defects present in the underlayer can spawn bridge defects in the overlying BCP film. The goal of the work reported here was to investigate the extent to which bridge defects can be generated or further reinforced in lamellae-forming block copolymer films due to affinity defects in the underlayer pattern. Coarse-grained molecular dynamics simulations were used to simulate the chemoepitaxial DSA of monodisperse block copolymer films atop underlayers with varying affinity defect sizes. Affinity defects were simulated by creating circular regions of a single polymer block type (which is the opposite block type of that used to pattern the underlayer guiding stripes) in the nominally neutral background region of the underlayer. These affinity defects were positioned in regions of the underlayer where they were the incorrect type to match the overlying block copolymer pattern. It was observed that the presence of an affinity defect in the neutral region of the underlayer caused the energetically preferential polymer block to wet the affinity defect, thus creating the nucleus of what could potentially become a bridge defect—even when the affinity defects were very small. As the radius of the underlayer affinity defect (RoD) increased, the amount of block copolymer of incorrect type (with respect to a perfectly assembled copolymer pattern) that assembled above the affinity defect increased; but, in general, the thickness of the wetting layer in contact with the affinity defect was only roughly one polymer chain thick. These data suggest that an affinity defect in the underlayer alone is unlikely to be noticeably enhanced by significant bridge defect formation in a monodisperse block copolymer film.

Quasi-chemical analysis of point defect structure іn Mn-doped CdTe single crystals

Electrical properties of CdTe single crystals, doped by Mn (1 × 1017–1 × 1019 at/cm3), were studied in the wide temperature range using high-temperature Hall effect measurements.To explain the obtained electrical properties the numerical simulation of the structure of both native and foreign point defect densities in the crystals was applied. Between the possibilities of whether predominantly Mn-single donors only or combined with Mn-containing associates occurrence in the crystals the second possibility was confirmed.High-temperature electrical measurements were explained in the framework of the Kröger's theory of quasi-chemical reactions between point defects in solids. It was done by investigating the series of differently Mn-doped CdTe single crystals. In the 1 × 1017–1 × 1019 at/cm3 Mn concentration range the measured free electron densities at high-temperature defect equilibrium were almost identical indicating clear donor activity of the dopant.