Behavior Of Point Defects Research Articles

Interphase Defects, Structures, and Phase Stability

Interface is defined as a common boundary of two spaces or phases. In solid-state materials, this usually means a two-dimensional defect that separates two regions of otherwise perfect bulk, and sometimes it goes to three dimensional, e.g., in the case of diffuse interface or disconnections. In general, the different bulk regions surrounding the interface can be different materials or crystal phases, so these interface boundaries can be called interphase boundaries. Solid-state materials with abundant internal interfaces may possess unusual physical properties or functionalities. This promising opportunity motivates many research studies, both experimental and theoretical in nature, geared toward incorporating knowledge of atomic-level structure and properties of interfaces into mechanistically informed interface design of materials. The unusual physical properties caused by interfaces include, for example, extraordinary radiation damage resistance and mechanical behaviors. The physical basis behind these extraordinary performances of materials is due to the fact that the interfaces can interact with point defects and dislocations in a strong manner. Understanding of the detailed mechanisms, including thermodynamic and kinetic factors at atomistic levels, is thus very important. The characterization of interface structures is a foundation step in the understanding. Additionally, how the stability of phases maybe affected by external driving forces is also of high importance because it is desired to keep the phases stable so the performance of materials maybe sustainable. Five articles are included in this issue representing some of the recent research efforts in understanding interphase defects, structures, and phase stabilities in different perspectives. The first article by X.M. Bai and B.P. Uberuaga gives a review of atomistic simulation works that examined the influence of grain boundaries, which are of the homophase interface boundary type, on the defects production during collision cascades. Collision cascade is a set of atomic collision events induced by energetic particles in material when the material is under irradiated conditions. Radiation damage is of great concern for materials in nuclear energy applications and is connected directly to the defect production in collision cascade processes. Atomistic simulation studies demonstrated that grain boundaries absorb more interstitials than vacancies during collision cascades. The absorbed interstitials can also spontaneously emit from interfaces to annihilate vacancies in the nearby bulk. The grain boundaries also disrupt the channeling effect in collision cascades, thus reducing cascade sizes. As a result, the number of defects produced is also lowered. Several different materials including face-centered cubic (fcc) Ag, Ni, Cu, bodycentered cubic (bcc) Fe, UO2, TiO2, and SiC were examined. And it was noted that the influences of grain boundaries are also sensitive to the type of materials. These atomistic simulation results provide an improved understanding of how interfaces may influence radiation damage evolution in materials. The second article by K. Kolluri et al. focuses on a research summary of the behavior of vacancies and interstitials at heterophase fcc-bcc semicoherent interfaces. Experimentally, nanolayered fcc-bcc composites such as Cu-Nb exhibit significantly enhanced radiation-damage tolerance as compared to monolithic metals. Knowledge of defects behavior at interfaces is essential for the understanding of such effects as well as other material properties such as creep and swelling. Using atomic-scale simulations, it is found that the formation, migration, and clustering of interfacial vacancies and interstitials at Cu-Nb KS interfaces is determined by the structure of these interfaces, which can be described with ordered arrays of misfit dislocations. In addition, the migration of defects at the interfaces is through a mechanism that depends on interfacial misfit dislocation properties and can be described using dislocation mechanics. To systematically test the effect of bonding and lattice parameter on point defect behavior, potentials were ‘‘tuned’’ by changing either the dilute of heats of mixing between Cu and Nb or the Xiang-Yang (Ben) Liu is the guest editor for the Chemistry and Physics of Materials Committee of the TMS Structural Materials Division, and coordinated the topic Interphase Defects, Structures, and Phase Stability in this issue. JOM, Vol. 65, No. 3, 2013

Behavior of Vacancies and Interstitials at Semicoherent Interfaces

Using atomistic simulations on a model semicoherent interface, we show that the formation, migration, and clustering of vacancies and interstitials at semicoherent interfaces depend on the structure of the misfit dislocation network of the interface. Interfacial point defects trap at misfit dislocation intersections and migrate from one intersection to another along misfit dislocations by a multistage process. Interfacial point defect clusters are thermodynamically less stable than individual defects and the largest cluster size depends on the spacing between misfit dislocation intersections. Our results show that the behavior of interfacial point defects is intimately connected to interface structure.

集束イオンビームによるゲルマニウム表面ナノセル構造の作製

Characteristic cellular structure is formed on the ion implanted surface of GaSb, InSb and Ge, by the self-organizational behavior of point defects induced by ion irradiation. In this work, fabrication of the nano-cell structure is performed for Ge. Formation process of the cellular structure in Ge is somewhat different from those in GaSb and InSb. In Ge, the irradiated layer is amorphized prior to the cell formation while its amorphization occurs after the cell formation in GaSb and InSb. Two kinds of nano-cell fabrication were performed and the nano-cell developments in both fabrications were compared. One is initially to form the ordered void lattice and to develop it to the cell lattice. In the other method, initially the surface layer of Ge wafer was amorphized by ordinary ion irradiation and then, nano-cell structure was formed on it by the same process. These processes were performed using 30 keV Ga+ in a focused ion beam apparatus at room temperature. The results showed that secondary void formation was remarkable in the initially amorphized Ge. Probably the high mobility of the vacancy-type defects in amorphous Ge might have accelerated the formation of secondary voids between the initial voids.

Theoretical study of the impact of stress on the behavior of intrinsic point defects in large-diameter defect-free Si crystals

For the development of the crystal pulling process for 450mm-diameter defect-free Si crystals, it is important to evaluate the impact of thermal stress on intrinsic point defect behavior during crystal growth. In this study, we evaluated the impact of thermal stress between −30MPa (tensile) and 30MPa (compressive), which covers the complete range of stress levels that can be expected in mass production for 450mm-diameter crystals, on the so-called Voronkov criterion. This criterion predicts the dominant point defect based on a critical pulling speed over axial temperature gradient ratio. The internal pressure dependencies of both the formation and the migration enthalpies of intrinsic point defects were obtained with a density functional theory study, and it was found that assuming internal stress only, the thermal stress shifts the growing Si crystal towards more vacancy-rich under compressive and towards more self-interstitial-rich under tensile stresses. Also Si crystals containing interstitial clusters and heavily doped crystals were studied to evaluate the effect of thermal and dopant-related stresses on the intrinsic point defect formation and diffusivity. It was concluded that the experimentally observed increase in the number of interstitial clusters and the increase in the concentration of self-interstitials in heavily doped Si cannot be explained by the thermal and/or dopant-related stresses.

Fractionalization of interstitials in curved colloidal crystals

Understanding the effect of curvature and topological frustration in crystals yields insights into the fragility of the ordered state. For instance, a one-dimensional crystal of identical charged particles can accommodate an extra particle (interstitial) if all the particle positions are readjusted, yet in a planar hexagonal crystal interstitials remain trapped between lattice sites and diffuse by hopping. Using optical tweezers operated independently of three-dimensional imaging, we inserted interstitials in a lattice of similar colloidal particles sitting on flat or curved oil/glycerol interfaces, and imaged the ensuing dynamics. We find that, unlike in flat space, the curved crystals self-heal through a collective particle rearrangement that redistributes the increased density associated with the interstitial. This process can be interpreted in terms of the out-of-equilibrium interaction of topological defects with each other and with the underlying curvature. Our observations suggest the existence of particle fractionalization on curved surface crystals.

2 MeV e‐irradiation UHVEM study on the impact of O and Ge doping on {113}‐defect formation in Si

AbstractFirst results are presented of a study on the impact of O and Ge doping on {113}‐defect formation in Si using in situ 2 MeV e‐irradiation in a high voltage electron microscope. Comparison with undoped Si, reveals a suppression of {113}‐defect formation due to O and Ge. The observations are discussed in the frame of a theoretical model assuming quasi‐chemical reactions to describe the intrinsic point defect behaviour during irradiation as a function of irradiation temperature and specimen thickness. It is shown that for irradiations at high temperatures, intrinsic point defect diffusivity values derived from crystal growth and metal diffusion experiments can be used to explain the observations semi‐quantitatively.

Ab initio analysis of a vacancy and a self‐interstitial near single crystal silicon surfaces: Implications for intrinsic point defect incorporation during crystal growth from a melt

AbstractThe microscopic model of the Si (001) crystal surface was investigated by first principles calculations to clarify the behavior of intrinsic point defects near crystal surfaces. A c(4 × 2) structure model was used to describe the crystal surface in contact with vacuum. The calculations show lower formation energy near the surface and the existence of formation energy differences between the surface and the bulk for both types of intrinsic point defects. The tetrahedral (T)‐site and the dumbbell (DB)‐site, in which a Si atom is captured from the surface and forms a self‐interstitial, are found as stable sites near the third atomic layer. The T‐site has a barrier of 0.48 eV, whereas the DB‐site has no barrier for the interstitial to penetrate into the crystal from the vacuum. Si atoms in a melt can migrate and reach at the third layer during crystal growth when bulk diffusion coefficient is used. Therefore, the melt/solid interface is always a source of intrinsic point defects.

Enhanced native acceptor-related blue emission of ZnO thin films annealed in an oxygen ambient

The thermodynamic behaviors of charged point defects in unintentionally-doped ZnO thin films were investigated. The as-grown sample displayed two different types of blue-emission bands: one at ∼2.95 eV from native-donor zinc interstitial (Zn i ) and the other at ∼3.17 eV from native-acceptor zinc vacancies (V Zn ). In the samples annealed at oxygen ambience, V Zn -related emission was dramatically enhanced, and Zn i -related emission was drastically reduced. The behavior was observed to become more apparent when the annealing temperature was increased. The results can be explained by both the increased generation probability and the lowered formation enthalpy of V Zn in an oxygen-rich environment, particularly at higher temperatures.

Intrinsic point defects and grown-in microdefects in silicon crystals—comment on: “Intrinsic point defect behaviour in silicon crystals during growth from the melt: A model derived from experimental results”, T. Abe, T. Takahashi, Journal of Crystal Growth 334 (2011) 16

Intrinsic point defects and grown-in microdefects in silicon crystals—comment on: “Intrinsic point defect behaviour in silicon crystals during growth from the melt: A model derived from experimental results”, T. Abe, T. Takahashi, Journal of Crystal Growth 334 (2011) 16

A study on density functional theory of the effect of pressure on the formation and migration enthalpies of intrinsic point defects in growing single crystal Si

In 1982, Voronkov presented a model describing point defect behavior during the growth of single crystal Si from a melt and derived an expression to predict if the crystal was vacancy- or self-interstitial-rich. Recently, Vanhellemont claimed that one should take into account the impact of compressive stress introduced by the thermal gradient at the melt/solid interface by considering the hydrostatic pressure dependence of the formation enthalpy of the intrinsic point defects. To evaluate the impact of thermal stress more correctly, the pressure dependence of both the formation enthalpy (Hf) and the migration enthalpy (Hm) of the intrinsic point defects should be taken into account. Furthermore, growing single crystal Si is not under hydrostatic pressure but almost free of external pressure (generally in Ar gas under reduced pressure). In the present paper, the dependence of Hf and Hm on the pressure P, or in other words, the pressure dependence of the formation energy (Ef) and the relaxation volume (vf), is quantified by density functional theory calculations. Although a large number of ab initio calculations of the properties of intrinsic point defects have been published during the last years, calculations for Si crystals under pressure are rather scarce. For vacancies V, the reported pressure dependences of HfV are inconsistent. In the present study, by using 216-atom supercells with a sufficient cut-off energy and mesh of k-points, the neutral I and V are found to have nearly constant formation energies EfI and EfV for pressures up to 1 GPa. For the relaxation volume, vfI is almost constant while vfV decreases linearly with increasing pressure P. In case of the hydrostatic pressure Ph, the calculated formation enthalpy HfI and migration enthalpy HmI at the [110] dumbbell site are given by HfI = 3.425 − 0.057 × Ph (eV) and HmI = 0.981 − 0.039 × Ph (eV), respectively, with Ph given in GPa. The calculated HfV and HmV dependencies on Ph given by HfV = 3.543 − 0.021 × Ph2 − 0.019 × Ph (eV) and HmV = 0.249 + 0.018 × Ph2 − 0.037 × Ph (eV), respectively. These results indicate that, when assuming that the pre-factors in the Arrhenius equation are not influenced, hydrostatic pressure up to 1 GPa leads to a slight increase of the thermal equilibrium concentration and diffusion of vacancies but this increase is much smaller than that of self-interstitials. The thermal stress in growing Si crystal is compressive, and thus the point defects are under internal pressure. Taking into account the differences in the enthalpies of point defects between hydrostatic pressure and internal pressure, Si crystal shifts to being V-rich with an increase in thermal stress during crystal growth.

Ab initio study of vacancy and self-interstitial properties near single crystal silicon surfaces

The microscopic model of the Si(001) crystal surface was investigated by first principles calculations to clarify the behavior of intrinsic point defects during crystal growth and thermal annealing. A c(4 × 2) structure model was used to describe the crystal surface in contact with vacuum. The calculations show that a vacancy in the first or second atomic layer has about a 2.0 eV lower formation energy than deeper inside the bulk and that there is a diffusion barrier to penetrate into the deeper crystal region. Furthermore, a vacancy in the first or second atomic layer is stabilized by the fact that Si atoms with dangling bonds attract each other due to ionic and/or covalent bonding. There is, however, no barrier for the diffusion of a vacancy from the first layer to the second one. The tetrahedral (T)-site and dumbbell (DB)-site, in which a Si atom is captured from the surface and forms a self-interstitial, are found as stable sites near the third atomic layer. The T-site has a barrier of 0.48 eV, whereas the DB-site has no barrier for the interstitial to penetrate into the crystal from the vacuum. Self-interstitials in both the T- and DB-sites in the third atomic layer have a 1.7 to 2.8 eV lower formation energy than deeper in the bulk and there is a diffusion barrier to penetrate into the deeper crystal region; 32 sites were found as stable sub-surface vacancy positions, whereas only 8 sites were found as stable self-interstitial positions. Using these results, a mechanism for the elimination of crystal-originated pits by thermal annealing is proposed. It is shown that the microscopic model is consistent with and allows to fine-tune existing macroscopic models that are used to calculate the intrinsic point defects behavior during crystal growth from a melt.

Positron annihilation in titanium alloys modified by proton irradiation

Measurements of angular distribution annihilation photons (ADAP) were applied to investigate the behavior of point defects in the annealed, plastically deformed and the irradiated titanium alloys. It is shown that irradiation by protons with E=30 MeV is accompanied by formation of vacancy clusters in titanium alloys. The presence of the deformation defects and alloying elements in the initial structure of the material leads to considerable changes in radiation damage spectra. It is determined that the role of the initial defects in the radiation damage of titanium alloys caused by a proton irradiation becomes apparent not only in the deceleration of the swelling process, but also in the evolution, transformation and the redistribution of the initial defects. These findings confirm once again a necessity of taking into account the presence of impurity atoms and preliminarily created structural damages in an irradiated material.

First-principles study on oxidation effects in uranium oxides and high-pressure high-temperature behavior of point defects in uranium dioxide

Formation Gibbs free energy of point defects and oxygen clusters in uranium dioxide at high-pressure high-temperature conditions are calculated from first principles, using the LSDA+U approach for the electronic structure and the Debye model for the lattice vibrations. The phonon contribution on Frenkel pairs is found to be notable, whereas it is negligible for the Schottky defect. Hydrostatic compression changes the formation energies drastically, making defect concentrations depend more sensitively on pressure. Calculations show that, if no oxygen clusters are considered, uranium vacancy becomes predominant in overstoichiometric UO2 with the aid of the contribution from lattice vibrations, while compression favors oxygen defects and suppresses uranium vacancy greatly. At ambient pressure, however, the experimental observation of predominant oxygen defects in this regime can be reproduced only in a form of cuboctahedral clusters, underlining the importance of defect clustering in UO2+x. Making use of the point defect model, an equation of state for non-stoichiometric oxides is established, which is then applied to describe the shock Hugoniot of UO2+x. Furthermore, the oxidization and compression behavior of uranium monoxide, triuranium octoxide, uranium trioxide, and a series of defective UO2 at zero Kelvin are investigated. The evolution of mechanical properties and electronic structures with an increase of the oxidation degree are analyzed, revealing the transition of the groundstate of uranium oxides from metallic to Mott insulator and then to charge-transfer insulator due to the interplay of strongly correlated effects of 5f orbitals and the shift of electrons from uranium to oxygen atoms.

Intrinsic point defect behavior in silicon crystals during growth from the melt: A model derived from experimental results

During the growth of float-zoning (FZ) and Czochralski (CZ) Si crystals, the temperature distributions from the growth interface were measured using a two-color infrared thermometer for the FZ crystal surfaces and three thermocouples within the CZ bulk crystals. The results showed that the thermal gradient is a decreasing function of the growth rate, which forms the basis of this work. In a comparison of the shape variations in the growth interfaces observed in both FZ and CZ crystals of three different diameters, all of the results were in agreement with the above premise. In consideration of Stefan's condition the premise above is discussed. One of the most important observations is that the region of increasing thermal gradient extends not only to the region grown before but also to the region afterward by stopping the pulling in FZ crystals or lowering the growth rate in CZ crystals. This phenomenon is termed the “BA (before and after) effect”. The growing CZ crystals are detached from the melt and rapidly cooled so that the point defects are frozen. Using the anomalous oxygen precipitation (AOP) phenomenon obtained by the above detaching, which demonstrates the existence of vacancies in the crystal, we found that the growth interface is always filled with vacancies. By increasing the thermal gradient, which can be controlled by lowering the growth rate, the vacancy (AOP) region is reduced, due to the generation of a silicon interstitial-rich region. The ratio of vacancies from the growth interface and silicon interstitials generated by the thermal gradient ultimately determines the nature of the bulk silicon crystal grown from the melt, i.e., with voids, defect-free or with dislocation loops.

Nano-cell fabrication on InSb utilizing point defects behavior induced by focused ion beam

In ion irradiated GaSb, InSb and Ge, the induced point defects form voids and these voids develop to the cells by further irradiation. The nano-fabrication technique utilizing this behavior is performed on (100) InSb by focused Ga + ion beam (FIB). Fabrication of nano-cell lattices with cell an interval of 30–300 nm are tried varying the acceleration voltage and the ion dose at room temperature, and the plan views and the cross-sectional views of the nano-cell structures are observed by scanning electron microscopy (SEM). The possible ranges of the cell interval, the cell diameter and the cell height are obtained from the results.

Recovery behavior of point defects after low-dose neutron irradiation of sintered SiC by thermal diffusivity and swelling measurements

Effects of neutron irradiation on physical property change of two kinds of sintered α-SiC ceramics were examined through the post-irradiation recovery experiments. Changes of macroscopic length and thermal diffusivity due to post-irradiation isothermal annealing up to 6h between room temperature and 1400°C were measured. Results of both measurements indicated almost same recovery tendency for each specimen. The SiC specimen containing Al2O3 showed large change in the activation energy of both recoveries at ∼950°C and 1200°C, and these of the SiC specimen containing B4C showed large change at ∼800°C, 950°C and 1200°C. Activation energies of macroscopic length recovery for both specimens from irradiation temperature to the lower temperature boundary were 0.1–0.2eV and those of the second temperature range were 0.8–0.9eV, respectively. These values indicated that the recovery of these properties is proceeded by the recombination of Frenkel pairs of both C and Si at various configurations.

Modeling of Defects Generation in 300 mm Silicon Monocrystals during Czochralski Growth

Defect generation was usually predicted by using the V/G (where V is growth rate and G is axial temperature gradient at the interface of melt/solid) theory, but it was hard to get appropriate critical V/G value and the value could not show the distribution of grown-in defects. Otherwise, direct defect simulation is a very useful method of interpreting initial point defect behavior and micro void generation. In this research, the direct defect simulation was preformed with variable process parameters and optimized by comparing with experiment results. With optimized direct defect analysis, the critical V/G value was modified as 0.00155 cm2 min-1 K-1. The critical pulling rate range was defined as that has low residual point defect concentration in silicon crystal, thus a high-quality wafer can be obtained at the critical pulling rate. The initial point defect distribution and the critical pulling rate range were analyzed by using direct defect model. Additionally, the generation of micro void density was also calculated with variable pulling rates and compared with experiment results. In this research, the initial point defect incorporation and the tendency of micro void generation were well explained by using direct defect model.

Point-defect study from low-temperature photoluminescence of CdGa2Se4 layers through the postannealing in various ambient

The CdGa2Se4 layers were grown by the hot-wall epitaxy method. From the absorption measurement, the band-gap variation in CdGa2Se4 was well interpreted using Varshni’s equation. After the postannealing in various ambient, the behavior of point defects in CdGa2Se4 was investigated by measuring photoluminescence (PL). Point defects originating from VCd, VSe, Cdint, and/or Seint were classified as donor or acceptor types. Thus, the Ga in CdGa2Se4 did not form native defects because the Ga existed in the form of stable bonds in CdGa2Se4. Based on these PL results, we schemed out a band diagram of the recombination process in CdGa2Se4.

Electronic-Excitation-Induced Processing in GaSb Compound Nanoparticles

Temperature dependence of electronic-excitation-induced structural changes in nanoparticles has been studied by in situ transmission electron microscopy. When GaSb nanoparticles kept at 340 K were excited by 25 keV electrons, the compound transforms to the porous compound or the two-phase structure consisting of an antimony core and a gallium shell with increasing the total electron dose. On the other hand, in GaSb nanoparticles kept at 293 K the structure remains the original compound phase. It is suggested that such temperature dependence of the structural changes may arise from synergetic behaviors of point defects introduced athermally by the excitation and thermal mobility.

Diffusion and coalescence of vacancies and interstitials in graphite: A first-principles study

The study of dynamics of point defects in graphite is crucial for understanding the evolution of defect-induced ferromagnetism in 12C + irradiated graphite. In this work, we perform first-principles calculations to explore the diffusion and coalescence of vacancies and interstitials in graphite. Different kinds of point defects, such as monovacancy, divacancy, ‘bridge’ and ‘spiro’ interstitials are considered using non-interacting and interacting models. The energetics, the diffusion paths, and the migration energies of these defects and the energy barriers for the reaction between these defects are predicted. The annealing behaviors of point defects and related ferromagnetism found in 12C + irradiated graphite are discussed.