Element Model Of Diffusion Research Articles

Using Lunar Granulites to Constrain Re‐Equilibration Timescales of Contact Thermal Metamorphism on the Moon

AbstractRocks of the lunar granulite suite are the product of high‐temperature metamorphism within the Moon's crust. However, to date, their formation conditions have few constraints. Here, we combine Ti‐in‐pyroxene element diffusion modeling and two‐pyroxene thermometry with thermal modeling of the lunar crust in order to assess potential heat sources that could generate granulite metamorphism within the lunar highland crust. For the samples investigated in this study, the pyroxene crystals experienced peak metamorphic temperatures between ∼1,027 and 1,091°C over timescales ranging from ∼153 years to ∼15.1 Kyrs. To best satisfy these temperature and timescale constraints, hot (∼2,300°C) impact melt sheets with thickness ranging from 350 m to 3.35 km—equating to impact crater diameters between ∼60 and 280 km—have the potential to heat the underlying anorthositic crust. Deep (>20 km) igneous bodies, such as the large (>10 km thick) sills observed by the GRAIL mission near the base of the lunar crust, also have the potential to generate the required peak metamorphic temperatures; however, the thermal equilibration timescales in this scenario are modeled to be much larger (>100 Kyrs) than was witnessed by the granulites investigated. Our modeling highlights that while lunar granulites are only a minor component within the Apollo and meteorite collection, they are likely an important and ubiquitous lithology within the lunar highland crust.

The Effect of the Variation of Input Parameters on the Onset of Corrosion of the Bridge Deck Exposed to Chlorides Considering Selected Reinforcement Protection

The contribution focuses on the effect of selected input parameters on probabilistic estimation of chloride induced reinforced concrete bridge deck corrosion initiation. The reinforced concrete bridge deck with steel protected by epoxy-coating is considered. A finite element diffusion model in conjunction with a probabilistic method using Monte Carlo technique is used to address the inherited randomness of input variables. Presented parametric study shows the sensitivity of estimation of the corrosion initiation likelihood on variation of input parameters.

Understanding and modelling the diffusion process of low molecular weight substances in polyethylene pipes

Peroxides are widely used as crosslinkers in polyethylene (PE) drinking water pipes. Cross-linked polyethylene (PEX) has better mechanical properties than PE, but peroxide decomposition by-products can migrate from PEX water pipes into the drinking water unless sufficient preventive actions are undertaken. This work systematically examines the migration of tert-Butyl methyl ether (MTBE), a dominating crosslinking by-product from PEX water pipes, into tap water by utilizing both experimental techniques and finite element (FEM) diffusion modeling. The effects of pipe geometry, tap water temperature (23–80 °C), boundary conditions (air or water interface) and degasing (at 180 °C) were considered. The MTBE diffusivity increased strongly with increasing temperature and it was concluded that a desired water quality can be achieved with proper degasing of the PEX pipes. As the FEM simulations were in excellent agreement with the experimental results, the model can accurately predict the MTBE concentration as a function of time, water temperature and PEX pipe geometry, and enable the pipe manufacturers to aid in ensuring desirable drinking water quality.

Research on the theoretical model of the rake face wear of carbide cutting tool

Elements in the carbide tool and workpiece material will diffuse during the cutting process, thus affecting tool life. To address the problem of diffusion wear on the rake face of the carbide tool, a cutting test scheme was proposed to analyze the heat and force conditions of element diffusion. A static clamping diffusion experiment of the tool and workpiece material was conducted to obtain diffusion data on the tool-chip element. Based on the analysis of element diffusion in the contact area of the tool-chip during the cutting process, the theoretical model of element diffusion in the tool was established using the Gaussian solution of Fick’s second law to determine the threshold value of the element concentration when the tool was damaged. The hardness of the tool surface was also measured and analyzed. The results showed that the wear depth of the rake face can be predicted using the established element diffusion model, whose results are consistent with the experimental findings. The element concentration on the crescent surface at the tool rake face remained constant under different cutting time, while the loss of W was more obvious. The experiments of the diffusion couple verified that element diffusion causes a decrease in the hardness of the tool surface, and tool hardness increases with greater distance from the bonding surface, which eventually reaches the hardness of the tool substrate. The research results lay a theoretical foundation for investigating the failure process of carbide cutting tools and predicting their service life.

Element diffusion model with variable coefficient in bimetallic bonding process

The bimetallic bonding mechanisms including macroscopic deformation, microstructure evolution and element diffusion were investigated by using bimetallic hot compression tests of X65/316L. An element concentration diffusion model with a variable coefficient was proposed to determine the element concentration in the metallurgical bonding transition zone (MBTZ). Diffusion distance, strain, deformation temperature and holding time were taken into account in the model. A finite element model of the clad pipes hot extrusion process to investigate the element diffusion behavior in the MBTZ was developed by the proposed diffusion model. The concentration predicted by the proposed model have a good agreement with the experimental results and the proposed model is more accurate than the reference model.

Numerical Simulation of Stress Distribution of AZ31B Magnesium Alloy/LY12 Aluminum Alloy Diffusion Welded Joint

The finite element model of diffusion bonding was established based on the analysis software of ANSYS, and the stress distribution characteristics of AZ31B/LY12 vacuum diffusion welded joint using Cu foil as the intermediate layer were analyzed. The effects of three factors, the welding temperature, the thickness of the intermediate layer Cu foil and the welding pressure, on the stress distribution of the AZ31B/Cu/LY12 joint were studied. The simulation results show that, when diffusion bonding of AZ31B and LY12 with intermediate layer Cu, the stress located on the center area of joint distribution is uniform, while the edge stress value is larger; welding parts along the axial stress distribution does not change significantly, while the maximum axial stress increases slightly when the temperature increases from 520 to 540 °C; when the thickness of intermediate layer Cu foil changes from 50 to 100 μm, the maximum shear stress value increases, while the position of that has no significant change; The stress distribution does not change, while the region of high stress increases when the welding pressure changes from 1 to 3 MPa.

Tracing the thermal evolution of the Corsican lower crust during Tethyan rifting

AbstractContinental rifting requires thinning the continental lithosphere from ~120 km to <20 km by a series of processes which each impart a characteristic thermal signature to the extending lithosphere. Here high‐resolution thermochronology is used to trace the synrift thermal evolution within a lower crustal section of an upper plate hyperextended margin sampled in Corsica. Novel zircon, rutile, and apatite 206Pb/238U depth profiling coupled with garnet trace element diffusion modeling provide compelling evidence for rift‐related crustal reheating. A Jurassic thermal pulse is recorded in the footwall of the Belli Piani Shear Zone (BPSZ), where 200–180 Ma zircon 206Pb/238U overgrowth ages on Permian core populations and the preservation of stranded diffusion profiles in resorbed garnets implies the dominant footwall fabric formed as a result of high‐temperature (T ~ 800°C) ductile thinning of the lower crust. Conductive reheating of middle crustal rocks in the immediate BPSZ hanging wall, demonstrated by Jurassic apatite 206Pb/238U ages, was likely achieved by synkinematic juxtaposition against the hot footwall and wholesale conductive steepening of geothermal gradients. Subsequent rapid cooling from 180 to 160 Ma, coeval with extensional unroofing of the footwall, underscores the importance of extreme ductile thinning during crustal hyperextension. The results of this study suggest that early lithospheric‐scale depth‐dependent thinning follows an early phase of diffuse rifting and tectonic subsidence and triggers crustal reheating during early hyperextension. Continued extension results in rapid exhumation and cooling of the lower crust, extreme crustal attenuation, and mantle exhumation followed by relaxation to a steady state thermal field coeval with the start of seafloor spreading.

Element diffusion model of bimetallic hot deformation in metallurgical bonding process

The effect of process parameters on the diffusion behavior of different elements in the metallurgical bonding process of bimetallic hot deformation is investigated. The diffusion distance of different elements increases with the effective strain, deformation and holding temperatures, deformation and holding times. On the other hand, it decreases with the increase of effective strain rate. In addition, an element diffusion model considering the influences of different processing parameters on element diffusion behavior is proposed to predict element concentration values near the metallurgical bonding interface. The proposed element diffusion model is based on the Fick's second law for unidirectional flow under non-steady state condition and is applied to the finite element simulation to investigate the diffusion behavior of different elements in metallurgical bonding process. The study shows that the modified model can predict the concentration profile and diffusion distance in the transition zone with a higher accuracy compared with the reference element diffusion model without considering the effects of effective strain and strain rate.

Study on the adhering failure mechanism of cemented carbide inserts and element diffusion model during the heavy-duty cutting of water chamber head

In view of the serious adhering failure of cemented carbide inserts during the heavy-duty cutting of water chamber head, the adhering failure mechanism of inserts and the element diffusion model of the adhering process were investigated. First, based on cutting simulations, the cutting force was found to be as high as 45.2 kN while the maximum cutting temperature was 930 °C. Under the combined action of mechanical and thermal loads, element diffusion occurred between insert and workpiece and formed an adhering layer, resulting in the adhering failure of inserts. After that, the element diffusion dynamics equation of the adhering process was proposed according to Fick’s law. Based on the semi-infinite long-bar diffusion model and its initial conditions and boundary conditions, the dynamics equation was solved, with the element diffusion concentration model obtained. In the end, the experimental scheme of element diffusion was put forward, and the element diffusion between the cemented carbide insert and workpiece at elevated temperatures was experimentally investigated. The diffusion distance of Co in 508III steel was measured as 8 μm. The element diffusion concentration within the diffusion distance was compared with the value predicted by the model, with the effectiveness of the element diffusion model validated. The concentration distribution of diffusing elements in the diffusion cross section was characterized through experiments and compared with the theoretical concentration distribution. The research results can provide a basis for the in-depth study of the formation mechanism of insert-chip adhering layers and their influence on the cutting performance and service life of inserts.

Reaction–diffusion modelling for microphysiometry on cellular specimens

Using modeling and simulation, we quantify the influence of spatiotemporal dynamics on the accuracy of data obtained from sensors placed in microscaled reaction volumes. The model refers to cellular reaction (i.e. proton extrusion and oxygen consumption) in complex, buffering solutions. Whole cells or viable tissues cultured in such devices are monitored in real time with integrated sensors for pH and dissolved oxygen. A 3D finite element model of diffusion and metabolic reaction was set up. With respect to pH, the effect of buffering species on proton diffusion is analysed in detail. To account for the delayed time response of real sensors, the sensor impulse response time was implemented by linear convolution. A validation of the model has been achieved by an electrochemical approach. The model reveals significant deviations of measured pH and O2, and values of these parameters actually occurring at different sites of the cell culture volume. It is applicable to any setting of (bio-) sensors involving reaction and diffusion of dissolved gases and particularly H(+) ions in buffered solutions.

The dynamics of Kerguelen Plateau magma evolution: New insights from major element, trace element and Sr isotope microanalysis of plagioclase hosted in Elan Bank basalts

The Kerguelen Plateau and Broken Ridge in the southern Indian Ocean together represent one of the most voluminous large igneous provinces (LIPs) ever emplaced on Earth. A scientific objective of Ocean Drilling Program (ODP) Leg 183 was to constrain the post-melting magma evolution of Kerguelen Plateau magmas. In an effort to better understand this evolution, isotopic and trace element analysis of individual plagioclase crystals hosted within two Kerguelen Plateau basalts recovered from Elan Bank were undertaken. Previous whole-rock studies established that the two host basalts investigated in this study are samples of crustally contaminated (lower group) and relatively uncontaminated (upper group) basalt. Plagioclase phenocrysts from the uncontaminated basalt are dominantly normal zoned and exhibit a 87Sr/ 86Sr I range of 0.704845–0.704985, which overlaps uncontaminated group whole-rock values previously reported. Plagioclase crystals from the contaminated basalt are dominantly reverse zoned and exhibit a 87Sr/ 86Sr I range of 0.705510–0.705735, which all lie within contaminated group whole-rock values previously reported. There are no systematic within crystal core to rim variations in 87Sr/ 86Sr I from either group, with the exception that contaminated group crystal rims have overall less radiogenic 87Sr/ 86Sr I than other zones. These observations indicate that crustal assimilation occurred before the formation of Unit 10 plagioclase phenocrysts, which is supported by parent magma trace element abundance data inverted using carefully calculated partition coefficients. Trace element diffusion modeling indicates that the upper group basalt (Unit 4) experienced a more vigorous eruptive flux than the lower group basalt (Unit 10). We suggest that plagioclase phenocrysts in both the upper and lower group basalts originated from the shallowest section of what was likely a complex magma chamber system. We contend that the magmatic system contained regions of extensive plagioclase-dominated crystal mush. Crustal assimilation was not a significant ongoing process in this portion of the Elan Bank magmatic system. Both basalts exhibit compelling evidence for remobilization and partial resorption of crystalline debris (e.g., reverse zoned crystals, glomerocrysts). We suggest Unit 4 and 10 magmas ascended different sections of the Elan Bank magma system, where the Unit 10 magmas ascended a section of the magma system that penetrated a stranded fragment of continental crust.

Oxygen isotope evidence for short-lived high-temperature fluid flow in the lower oceanic crust at fast-spreading ridges

Millimeter-scale amphibole veins in the lower oceanic crust record fracture-controlled fluid flow at high-temperatures but the importance of this fluid flow for the thermal and chemical evolution of the lower oceanic crust is unclear. In the section of lower oceanic crust recovered at Hess Deep from ODP Hole 894G, which formed at the fast-spreading East Pacific Rise, these veins are randomly distributed with an average spacing of ∼ 1 m. We unravel the history of fluid flow through one of these veins by combining in situ O-isotope analyses of wall-rock plagioclase with major element analyses, geothermometry and diffusion modeling. Thermometry indicates vein sealing by amphibole at ∼ 720 °C over a narrow temperature interval (± 20 °C). In situ O-isotope analyses by ion microprobe, with a precision of < 0.5‰, reveal zoning of O-isotopes in plagioclase adjacent to the vein. The zoning profiles can be reproduced using a diffusion model if the duration of O-isotope exchange was ≤ 100 yr. A similar interval of fluid–rock exchange is suggested by modeling potassium depletion in plagioclase adjacent to the vein. If representative of fracture controlled fluid flow in the lower oceanic crust the limited duration of fluid flow, and its occurrence over a narrow temperature interval, suggest that high-temperature fluid flow in this porosity network does not transport significant heat.

Performance Evaluation of Concrete Bridge Deck Affected by Chloride Ingress

Modeling is presented for the effect of cracks on chloride ingress into bridge decks with epoxy-coated reinforcing steel. A finite element diffusion model is used in conjunction with a Monte Carlo probabilistic method to address the inherited randomness of input variables. Field data from New York and Pennsylvania bridge decks under service are used to derive the distributions of diffusion coefficients and concrete cover depths under common specifications and construction practices for bridges in the northeastern United States.

Magma evolution and ascent at volcanic arcs: constraining petrogenetic processes through rates and chronologies

Large 226Ra excesses in a number of mafic arc magmas, and geophysical observations of earthquake hypocenters locations, indicate that mafic melts can get transferred from source to surface within days to ∼1 kyr. Decreasing 226Ra– 230Th disequilibria with increasing SiO 2 in co-magmatic suites of individual arc volcanoes suggest that magma differentiation often occurs on timescales of a few thousand years in closed systems, or less in open systems. However, the rapid decrease of global 238U– 230Th disequilibria with increasing SiO 2 within basaltic andesite compositions suggests that rapid closed system differentiation does not typically produce more evolved compositions from mafic parental magmas with large 238U excesses. In the case of rapid magmatic evolution, open system processes are frequently involved in the production of andesites and dacites, and the data imply that the open system component is close to 238U– 230Th secular equilibrium. MELTS modeling of magma evolution at Santorini in the Aegean arc provides corroborating evidence from an individual well-studied arc volcano, that closed system fractional crystallization fails to produce the more evolved compositions, and increasing 87Sr/ 86Sr ratios with increasing SiO 2 from andesites to rhyolites suggests assimilation of old crust is involved. These observations can be conceptualized through thermal modeling of basaltic sill injections into the lower and upper crust. Melt production in deep crustal hot zones provides an explanation for low 238U– 230Th disequilibria of the evolved magmatic component, as significant accumulation of evolved melts through partial re-melting of previously intruded basalts requires >100 kyr incubation time at typical magmatic flux rates. Thermal modeling also provides a framework for understanding assimilation of old upper crustal rocks in more mature magmatic systems. Further insights into magmatic evolution can be gained from dating of minerals from mafic, intermediate and felsic arc magmas. (a) Many U–Th mineral isochrons in mafic arc magmas yield ages significantly older than those obtained from Ra–Th mineral isochrons from the same samples. A crystal size distribution case study from Soufrière, St. Vincent, indicates that this may result from the abundance of cumulate xenocrysts within more mafic arc magmas. (b) The majority of U–Th mineral isochrons in intermediate arc magmas yield ages within error of eruption age, indicating that other dating techniques that may be more suitable for deciphering the shorter timescales yielded by these compositions. In a case study of crystals of remobilized andesites from the Soufrière Hills volcano, Montserrat, intra-crystalline trace element diffusion modeling yields crystallization timescales of the order of 10–1000 years. Varying temperature-time histories of individual crystals can be interpreted to reflect multi-stage magma ascent and the development of ephemeral subvolcanic magma reservoirs. (c) U–Th mineral isochrons from felsic arc magmas yield very variable ages from >200 ka to shortly prior to eruption. A case study from the Taupo Volcanic Zone has shown that both remobilization of previous intrusives and melting of old country rock are occurring, giving rise to a this range in ages. Both intermediate and felsic magmas therefore can be shown to have multi-stage ascent histories. Future work will have to address the reasons for the apparent inter-volcano variability in time-averaged subvolcanic magma volumes within the arc crust. These include differences in magma supply rate; thickness, composition and thermal structure of the crust; and magma composition and volatile content, which may vary between different tectonic settings.

Materials Problems Affecting Reliability and Yield of Wire Bonding in VLSI Devices

AbstractMaterials problems have always been a significant cause of wire bond failures in microelectronics. However, modern VLSI materials, processing, and packaging methods combined often result in new or masked versions of old failure mechanisms. This paper describes the classical Au-Al intermetallic compound problem as described by a new two-dimensional finite element diffusion model and demonstrates that diffusion in poor welds is more rapid than in bulk couples. Failures resulting from modern bonding material couples (e.g., Cu-Au, Al-Ag, etc.) can result in bond failures superficially resembling Au-Al type failures. Failures resulting from bonds made to contaminated gold electroplated films are described, and a new failure model resulting from hydrogen in these films is shown.