Initial Defect Distribution Research Articles

Chemical abrasion: the mechanics of zircon dissolution

Abstract. Chemical abrasion is a technique that combines thermal annealing and partial dissolution in hydrofluoric acid (HF) to selectively remove radiation-damaged portions of zircon crystals prior to U–Pb isotopic analysis, and it is applied ubiquitously to zircon prior to U–Pb isotope dilution thermal ionization mass spectrometry (ID-TIMS). The mechanics of zircon dissolution in HF and the impact of different leaching conditions on the zircon structure, however, are poorly resolved. We present a microstructural investigation that integrates microscale X-ray computed tomography (µCT), scanning electron microscopy, and Raman spectroscopy to evaluate zircon dissolution in HF. We show that µCT is an effective tool for imaging metamictization and complex dissolution networks in three dimensions. Acid frequently reaches crystal interiors via fractures spatially associated with radiation damage zoning and inclusions to dissolve soluble high-U zones, some inclusions, and material around fractures, leaving behind a more crystalline zircon residue. Other acid paths to crystal cores include the dissolution of surface-reaching inclusions and the percolation of acid across zones with high defect densities. In highly crystalline samples dissolution is crystallographically controlled with dissolution proceeding almost exclusively along the c axis. Increasing the leaching temperature from 180 to 210 ∘C results in deeper etching textures, wider acid paths, more complex internal dissolution networks, and greater volume losses. How a grain dissolves strongly depends on its initial radiation damage content and defect distribution as well as the size and position of inclusions. As such, the effectiveness of any chemical abrasion protocol for ID-TIMS U–Pb geochronology is likely sample-dependent. We also briefly discuss the implications of our findings for deep-time (U-Th)/He thermochronology.

Characterization of Internal Defects and Fiber Distribution of BFRC Based on the Digital Image Processing Technology

Adding basalt fiber into concrete can significantly improve its mechanical properties. In order to explore the influence of basalt fiber content on the uniaxial compressive strength and splitting tensile strength of concrete and the mechanism of fiber action, this paper conducts compressive and splitting tensile tests on three kinds of basalt fiber concrete specimens with different fiber content and obtains the relationship between the macro mechanical properties and the fiber content. At the same time, with the help of CT scanning equipment and digital image processing technology, the microstructure of basalt fiber concrete with three groups of fiber content is reconstructed, and the pore, crack, and fiber distribution are quantitatively described using the calculation and processing function of the Avizo reconstruction software. The results show that when the optimal fiber content is 3 kg/m3, the improvement rates of uniaxial compressive strength and splitting tensile strength are 31.9% and 23.7%, respectively. The network structure formed by fiber in concrete has the best compactness and the least number of pores, with an average sphericity of 0.89 and an average pore volume of 20.26 μm3. Through analysis, it was found that the initial defects of basalt fiber concrete exist in the form of pores, and the addition of basalt fiber will destroy the large pore size of concrete, change the pore size distribution, and increase the average sphericity; The distribution of the fiber in the concrete is a three-dimensional network, and the distribution of the fiber in the initial defect distribution area is parallel to the direction of pore arrangement.

Statistical analysis of defects within concrete under elevated temperatures based on SEM image

Concrete is a multiphase composite material consisting of aggregates, mortar, and initial defects. This work aims to quantitatively study the distribution and evolution of initial defects under elevated temperatures. To minimize the effect of hydration process and thermal and endogenous shrinkage, concrete samples cured in water for 12 months is tested. In order to study the effect of external load on the initial distribution of defects within concrete, concrete samples without pre-loading and pre-applied with 30% of the failure load are selected as research objects. The evolution of defects within the concrete samples are characterized using scanning electron microscopy (SEM). By employing an image processing software, the two-dimensional configurations of defects are extracted from the backscattered images obtained by SEM. Each defect is identified and approximated using an optimal ellipse. Thereafter, the defects are automatically recognized and classified into microcracks and pores by utilizing the image processing software and MATLAB programming. Consequently, the distribution and propagation of microcracks and pores in concrete could be quantitatively and separately analyzed. Statistical analysis of area, perimeter, and fitting ellipse parameters (e.g., major axis, minor axis, coordinates of the center, axis orientation, aspect ratio, and solidity) can provide the distribution of initial defects within concrete. It is demonstrated that the area of microcracks consistently increases with temperature. Log-normal and normal distributions may be suitable for the distribution of aspect ratio and solidity of microcracks, respectively, for both concrete samples with and without pre-applied loading under all elevated temperatures (40, 105, 150, 200, and 250 ℃). However, the distributions of area, coordinates of the center, and axis orientation of microcracks may vary with the initial concrete loading condition and temperature. For the pre-loaded concrete sample, the distribution of parameters does not conform to any type of distributions. Moreover, for the sample without pre-loading, the distributions of area, coordinates of the center, and axis orientation of microcracks exhibit good fitting precisions with log-normal, normal, and normal distributions, respectively at lower temperatures (40–150 ℃); however, such relationships do not apply at higher temperatures (200 and 250 ℃). As reference for identifying the variations in microstructures, 150 ℃ is selected as the threshold temperature. The statistical approach employed in this study can lay the theoretical and experimental bases for determining the microstructure evolution in concrete. It can also be used for identifying the meso-defect and macro-defect and establishing their relationship with concrete properties.

A New Maintenance Optimization Model Based on Three-Stage Time Delay for Series Intelligent System with Intermediate Buffer

For the maintenance problem of intelligent series system with buffer stock, a preventive maintenance model based on the threestage time delay theory is proposed. Firstly, the intelligent series system is decomposed into n − 1 virtual series systems by using approximate decomposition method. The impact factor is introduced to establish the failure rate and maintenance rate model of each virtual machine. Secondly, a preventive maintenance model based on the three-stage time delay theory is proposed for each virtual series system. The machine state from normal operation to failure stage is divided into three steps: initial defect, serious defect, and fault, and different distribution functions are defined in different stages to simulate the degradation process of the machine. Based on the three-stage time delay theory, the machine cost ratio model was established by taking the machine monitoring time and buffer stock as decision variables and the minimum unit time cost rate as objective function. Finally, the rationality and validity of the model are verified by an example analysis, which provides a basis for the maintenance of the intelligent series system.

Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation.

The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called “Y-Junctions”, form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the Drosophila compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores as well as the spatial distribution of Y-junctions across entire retinae. We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals. In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery. In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion. Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries. In contrast to paradigmatic models of fate specification in mostly motionless cell packings, this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.

Simulations of high-velocity impacts on metal in preparation for the Psyche mission

In 2026, the NASA Discovery mission Psyche will orbit the asteroid (16) Psyche, the largest known metal-rich asteroid in the main belt. To estimate relative ages of the surface, identify re-surfacing events and better constrain Psyche's history, impact craters will be counted and characterized. No spacecraft has ever visited a metal-rich small body; therefore, laboratory-scale impact experiments and numerical simulations will play an important role in the interpretation of the mission's data. However, the planetary applications of high-velocity impacts have so far mostly been studied for silicate targets. Limited attention has been drawn to planetary objects predominantly made of metal, and more laboratory experiments and numerical calibrations are needed. As part of this effort, we present a suite of numerical simulations using an adaptative smoothed particles hydrodynamics numerical code (ASPH) reproducing a high-velocity impact experiment conducted on a steel target. This work primarily focuses on the influence of the chosen equation of state and initial distribution of flaws in the material on the estimated crater dimensions, damage and temperature. We find that changing the EOS and initial flaw distribution affects the crater dimensions, though for a vast majority of cases the dimensions remain within 20% of the experimental values. The target is in most cases only locally weakened but not fully damaged, independently from the EOS chosen. Finally, temperatures at the impact point and around the forming crater can reach values above the melting point of iron at <100 GPa, which is in agreement with experimental observations. These results allow us to speculate on the differences expected between the surfaces of visited silicate-rich asteroids and that of the metal-rich target of the Psyche mission.

Analysis of the Basal Plane Dislocation Density and Thermomechanical Stress during 100 mm PVT Growth of 4H-SiC.

Basal plane dislocations (BPDs) in 4H silicon carbide (SiC) crystals grown using the physical vapor transport (PVT) method are diminishing the performance of SiC-based power electronic devices such as pn-junction diodes or MOSFETs. Therefore, understanding the generation and movement of BPDs is crucial to grow SiC suitable for device manufacturing. In this paper, the impact of the cooldown step in PVT-growth on the defect distribution is investigated utilizing two similar SiC seeds and identical growth parameters except for a cooldown duration of 40 h and 70 h, respectively. The two resulting crystals were cut into wafers, which were characterized by birefringence imaging and KOH etching. The initial defect distribution of the seed wafer was characterized by synchrotron white beam X-ray topography (SWXRT) mapping. It was found that the BPD density increases with a prolonged cooldown time. Furthermore, small angle grain boundaries based on threading edge dislocation (TED) arrays, which are normally only inherited by the seed, were also generated in the case of the crystal cooled down in 70 h. The role of temperature gradients inside the crystal during growth and post-growth concerning the generation of shear stress is discussed and supported by numerical calculations.

Study of Interfacial Interactions in Physically Transient Soft Layered Structures: A Step toward Understanding Interfacial Bonding and Failure in Soft Degradable Structures

Soft multilayer structures have broad applications in transient electronics. Strain‐mismatch‐induced fracture is key in achieving physical transiency. Here, swelling‐mismatch‐induced fragmentation of physically transient electrodes is studied. The fragment size of the electrode layer as a function of initial defect distribution is investigated. The average fragment size is predicted and verified by a combination of experimental and FEM analysis. It is found that only large defects initiate fragmentation; this concept can be used to control disintegration of physically transient electronics by means of materials and design, and can be extended to study transiency of soft multilayer structures.

Influence of free surfaces on microstructure evolution of radiation damage in Fe from molecular dynamics and object kinetic Monte Carlo calculations

The influence of surfaces on the evolution of damage of irradiated Fe is studied using object kinetic Monte Carlo with input from molecular dynamics simulations and ab initio calculations. Two effects are analysed: the influence of traps and the initial distribution of damage in the cascade. These simulations show that for a trap concentration of around 100 appm, there are no significant differences between defect concentrations in bulk and thin films. However, the initial distribution of defects plays an important role not only on total defect concentration but also on defect type, for the model used in this study.Damage produced by a 100 keV Fe ion impinging a Fe thin film. Blue (dark) spheres are self‐interstitials, red (light) spheres are vacancies.

Kinetics of defect accumulation and duality of the weller curve in gigacycle fatigue of metals

We propose a model describing the kinetics of accumulation of defects under cyclic loading in metals. Analysis of experimental data on the initial defect distribution and of the role of the free surface of the sample in straining makes it possible to explain the features of generation of fatigue cracks in the bulk, which is typical of the gigacycle fatigue regime at a low stress level. The duality of the Weller curve in the gigacycle fatigue regime is attributed to the emergence of a fine-grain region in the form of a dissipative peaking structure in the defect ensemble.

Probability density functions: From porosities to fatigue lifetime

This paper proposes a novel method to establish and identify a probability density function characterizing the fatigue lifetime. The method is initiated with a quantitative analysis of the microstructure of the material, which provides the initial probability distribution of defects. After identifying a given probability density function of defects, one can transport it into a lifetime probability density function using a growth law involving a measure of the loading over a cycle. Several parameters of the growth law are finally estimated from a given set of fatigue experiments on specimens and several techniques are discussed. The method is applied on real defect observations and lifetime data. The estimated lifetimes using the novel technique is of similar quality with standard estimation providing the probability density function of lifetime as an additional output. This output can be used directly as an input in a stress–strength interference method.

Towards a methodology for the practical applications of the EIFS (Equivalent Initial Flaw Size) concept

This work intends to introduce a probabilistic approach for the crack propagation analysis. It presents a methodology that is based on the distribution of the initial flaw size a0. Departing from fatigue test results for specific structural components, an estimation of the initial flaw distribution is obtained, and from this distribution it becomes possible to establish the appropriate initial flaw size for crack propagation analysis for the chosen statistical distribution, such as Weibull or Log-normal. The methodology allows to apply different values of a0 for different components or structural details, reflecting the quality of the manufacturing process for the item evaluated. Two examples of practical applications of the EIFS concept are presented, corresponding to lugs and shear joints usually used for aerospace applications.

Experimental investigation of axial impact buckling response of pseudo-elastic NiTi cylindrical shells

The axial dynamic buckling responses of pseudo-elastic NiTi alloy cylindrical shells were investigated experimentally for various length/diameter ratios and end constraint conditions by using a modified single pulse SHPB apparatus. The results show that under single pulse axial loading it will first appear the axisymmetrical buckling waviness and then transit into non-axisymmetric buckling mode. This multiple buckling mode and mode transition behavior is possibly due to the wave effect under dynamic loading. The non-axisymmetric buckling patterns are significantly related to the length/diameter ratio and end constraint condition. The initial defect distribution will affect even dominate the non-axisymmetric buckling pattern. It was observed that multiple phase transition hinges (THs) formed in the specimen, which can increase the energy absorption efficiency. The critical buckling threshold and the energy absorption efficiency under impact loading are much greater than that under quasi-static loading. The THs and the dynamic buckling folds are recoverable for NiTi specimens due to the thermo-elastic austenite–martensite phase transition, which differs substantially from the behavior of the conventional elastic–plastic shells.

Nematic-Smectic Transition under Confinement in Liquid Crystalline Colloidal Shells

We carry out the first study of smectic liquid crystalline colloidal shells and investigate how their complex internal structure depends on the director configuration in the nematic phase, preceding the smectic phase on cooling. Differences in the free energy cost of director bend and splay give an initial skewed distribution of topological defects in the nematic phase. In the smectic phase, the topological and geometrical constraints of the spherical shell imposed on the developing 1D quasi-long-range order create a conflict that triggers a series of buckling instabilities. Two different characteristic defect patterns arise, one driven by the curvature of the shell, the other by the strong nonuniformities in the director field in the vicinity of the topological defects.

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.

Doping of germanium by phosphorus implantation: Prediction of diffused profiles with simulation

Wafers made of germanium epitaxied on silicon were implanted at various doses and energies and were then annealed at temperatures ranging from 515 to 600 °C and process times ranging from 10 to 60 s. The corresponding SIMS profiles were used as targets for the optimization of the parameters of a diffusion model. Although diffusion in germanium is often believed to be mediated by vacancies, physical considerations on the damaging of the substrate led us to consider an interstitially mediated diffusion mechanism. The amorphization caused by the implantation was taken into account to set the initial distribution of point defects. Our predictions of the diffused phosphorus profiles were obtained using a pair-model with various charge states including solubility limit and outdiffusion. This modelling allowed us to accurately fit with the same set of parameters more than 15 experimental profiles, even the box-shaped ones that occur at higher thermal budget.

Thermodynamics of mono- and di-vacancies in barium titanate

The thermodynamic and kinetic properties of mono- and di-vacancy defects in cubic (para-electric) barium titanate BaTiO3 are studied by means of density-functional theory calculations. It is determined which vacancy types prevail for given thermodynamic boundary conditions. The calculations confirm the established picture that vacancies occur in their nominal charge states almost over the entire band gap. For the dominating range of the band gap the di-vacancy binding energies are constant and negative. The system, therefore, strives to achieve a state in which, under metal-rich (oxygen-rich) conditions, all metal (oxygen) vacancies are bound in di-vacancy clusters. The migration barriers are calculated for mono-vacancies in different charge states. As oxygen vacancies are found to readily migrate at typical growth temperatures, di-vacancies can be formed at ease. The key results of the present study with respect to the thermodynamic behavior of mono- and di-vacancies influence the initial defect distribution in the ferroelectric phases and therefore the conditions for aging.

An interacting micro-crack damage model for failure of brittle materials under compression

A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.

Fatigue Modeling for Elastic Materials With Statistically Distributed Defects

Abstract The paper is devoted to formulation and analysis of a new model of structural fatigue that is a direct extension of the model of contact fatigue developed by Kudish (2000, STLE Tribol. Trans., 43, pp. 711–721). The model is different from other published models of structural fatigue (Collins, J. A., 1993, Failure of Materials and Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley, New York) in a number of aspects such as statistical approach to material defects, stress analysis, etc. The model is based on fracture mechanics and fatigue crack propagation. The model takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model considers the kinetics of crack distribution by taking into account the fact that the crack distribution varies with the number of applied loading cycles due to crack growth. A qualitative and quantitative parametric analysis of the model is performed. Some analytical formulas for fatigue life as a function of the initial defect distribution, material fatigue resistance, and stress state are obtained. Examples of application of the model to predicting fatigue of beam bending and torsion and contact fatigue for tapered bearings is presented.

Vers un modèle probabiliste pour la formation de réseaux de fissures dans les roches lors de l’injection de CO2

Injection of CO 2 into geologic formations is being practiced today to decrease the greenhouse gas effect, but it is not yet possible to predict with confidence storage volume, formation integrity and long term reliability. Potential CO 2 leakage towards the surface is associated with the cracking state of caprocks through the permeability-fracturing state relationship. A probabilistic method based on the initial distribution of defects is proposed to describe different aspects of the formation of crack networks in rocks under CO 2 injection conditions. Propagation of single cracks is discussed by studying the stress intensity factor variation and the possibility of crack network formation is shown. The interaction between cracks is modelled by considering obscuration zones corresponding to shielding effects created by each crack.